BEGIN:VCALENDAR
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BEGIN:VEVENT
SUMMARY:David F. Anderson (University of Wisconsin\, Madison (USA))
DTSTART:20201112T160000Z
DTEND:20201112T163000Z
DTSTAMP:20260421T094423Z
UID:MoRN/1
DESCRIPTION:Title: Rea
ction network implementations of neural networks\nby David F. Anderson
(University of Wisconsin\, Madison (USA)) as part of Seminar on the Mathe
matics of Reaction Networks\n\n\nAbstract\nI will give an overview of my r
ecent paper with Badal Joshi and Abhishek Deshpande\, which is entitled "O
n reaction network implementations of neural networks." In particular\, I
will show how reaction networks can be constructed that "implement" a giv
en neural network. I will also detail our theoretical results\, which pro
ve that the ODEs associated with certain reaction network implementations
of neural networks have desirable properties including (i) existence of un
ique positive fixed points that are smooth in the parameters of the model
(necessary for gradient descent)\, and (ii) fast convergence to the fixed
point regardless of initial condition (necessary for efficient implementat
ion). I'll start the talk with a brief primer on neural networks\, but wi
ll assume familiarity with reaction networks.\n
LOCATION:https://researchseminars.org/talk/MoRN/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Beatriz Pascual Escudero (Universidad Carlos III (Spain))
DTSTART:20201203T160000Z
DTEND:20201203T163000Z
DTSTAMP:20260421T094423Z
UID:MoRN/2
DESCRIPTION:Title: Nec
essary conditions for ACR in Reaction Networks\nby Beatriz Pascual Esc
udero (Universidad Carlos III (Spain)) as part of Seminar on the Mathemati
cs of Reaction Networks\n\n\nAbstract\nA biological system has absolute co
ncentration robustness (ACR) for some molecular species if the concentrati
on of this species does not vary among the different steady states that th
e network admits. In particular\, this concentration is independent of the
initial conditions. This interesting feature confers the system a highly
desirable property in order to adapt to environmental conditions\, which m
akes it useful\, for instance\, in synthetic biology. While some classes o
f networks with ACR have been described (Shinar and Feinberg 2010\; Karp e
t al. 2012)\, as well as some techniques to check a network for ACR (Pére
z Millán 2011\; Kuwahara et al. 2017)\, finding networks with this proper
ty is a difficult task in general.\n\nMotivated by this problem\, we studi
ed local and global notions of robustness on the set of (real positive) so
lutions of a system of polynomial equations\, and in particular on the set
of steady states of a reaction network. Algebraic geometry allowed us to
provide a practical test on necessary conditions for ACR. Properties of re
al and complex algebraic varieties are necessary for the results\, while t
he test ends up being a linear algebra computation.\n
LOCATION:https://researchseminars.org/talk/MoRN/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Casian Pantea (West Virginia University (USA))
DTSTART:20201203T163000Z
DTEND:20201203T170000Z
DTSTAMP:20260421T094423Z
UID:MoRN/3
DESCRIPTION:Title: Inh
eritance of Hopf bifurcations in reaction networks\nby Casian Pantea (
West Virginia University (USA)) as part of Seminar on the Mathematics of R
eaction Networks\n\n\nAbstract\nInspired by recent work on multistationari
ty\, we consider the question: "when can we conclude that a network admits
Hopf bifurcations if one of its subnetworks has them?” In particular\,
we analyze a number of operations on reaction networks (like adding certai
n reactions\, or adding inflows/outflows) that may preserve Hopf bifurcat
ions as we build up the network . This is joint work with C.Conradi\, A. D
ickenstein\, and M. Mincheva.\n
LOCATION:https://researchseminars.org/talk/MoRN/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lea Popovic (Concordia University)
DTSTART:20201112T163000Z
DTEND:20201112T170000Z
DTSTAMP:20260421T094423Z
UID:MoRN/4
DESCRIPTION:Title: A s
patially heterogeneous stochastic model for chemical reaction networks
\nby Lea Popovic (Concordia University) as part of Seminar on the Mathemat
ics of Reaction Networks\n\n\nAbstract\nI will present a measure-valued fr
amework for stochastic modelling of chemical reaction networks with spatia
l heterogeneity. Reactions rates at a spatial location are proportional to
the mass of different species present locally\, and to a location specifi
c chemical rate that is allowed to be a function of the local or global ma
ss of different species. The benefit of the framework is in rigorous appro
ximation limits that exploit multi-scale aspects of the system. When the m
ass of all species scales the same way\, we get classical deterministic li
mit described by PDEs. When the mass of some species in the scaling limit
is discrete while the mass of the others is continuous\, we obtain a new t
ype of spatial random evolution process in which discrete mass evolves sto
chastically and the continuous mass evolves according to PDEs between cons
ecutive jump times of the discrete part. Some useful properties of the lim
iting process are inherited from the pre-limiting sequence\, and could be
used in devising simulation algorithms.\n\nThis is joint work with Amandin
e Veber (Paris V\, Polytechnique-Saclay)\n
LOCATION:https://researchseminars.org/talk/MoRN/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nida Obatake (Texas A&M (USA))
DTSTART:20201210T160000Z
DTEND:20201210T163000Z
DTSTAMP:20260421T094423Z
UID:MoRN/5
DESCRIPTION:Title: Mix
ed volume of reaction networks\nby Nida Obatake (Texas A&M (USA)) as p
art of Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nAn i
mportant invariant of a chemical reaction network is its maximum number of
positive steady states. This number\, however\, is in general difficult t
o compute. We introduce an upper bound on this number— namely\, a networ
k’s mixed volume — that is easy to compute. We show that\, for certain
biological signaling networks\, the mixed volume does not greatly exceed
the maximum number of positive steady states. We investigate this overcoun
t and also compute the mixed volumes of small networks (those with only a
few species or reactions). Joint work with Anne Shiu\, Dilruba Sofia\, Ang
elica Torres\, and Xiaoxian Tang.\n
LOCATION:https://researchseminars.org/talk/MoRN/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ankit Gupta (ETHZ (Switzerland))
DTSTART:20201210T163000Z
DTEND:20201210T170000Z
DTSTAMP:20260421T094423Z
UID:MoRN/6
DESCRIPTION:Title: Fre
quency Spectra and the Color of Cellular Noise\nby Ankit Gupta (ETHZ (
Switzerland)) as part of Seminar on the Mathematics of Reaction Networks\n
\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/MoRN/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Polly Yu (University of Wisconsin\, Madison)
DTSTART:20210114T160000Z
DTEND:20210114T163000Z
DTSTAMP:20260421T094423Z
UID:MoRN/7
DESCRIPTION:Title: Dyn
amically Equivalent Mass-Action Systems: A Survey of Recent Results\nb
y Polly Yu (University of Wisconsin\, Madison) as part of Seminar on the M
athematics of Reaction Networks\n\n\nAbstract\nUnder mass-action kinetics\
, each reaction network uniquely gives rise to a system of ODEs. However\,
the converse is not true\; for a given system of ODEs known to come from
a mass-action systems\, there are many reaction networks that serve as a c
andidate. In this talk\, I will introduce the notion of dynamical equivale
nce\, emphasize a convenient way of thinking about it\, and survey some re
cent results on dynamical equivalence to complex-balanced or detailed-bala
nced systems.\n
LOCATION:https://researchseminars.org/talk/MoRN/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chuang Xu (Technical University of Munich)
DTSTART:20210225T160000Z
DTEND:20210225T163000Z
DTSTAMP:20260421T094423Z
UID:MoRN/8
DESCRIPTION:Title: Dyn
amics of one dimensional stochastic reaction networks\nby Chuang Xu (T
echnical University of Munich) as part of Seminar on the Mathematics of Re
action Networks\n\n\nAbstract\nIn this talk\, I will present recent result
s on criteria for dynamics as well as identity and recursive formula of li
mit distributions of one-dimensional mass-action stochastic reaction netw
orks (SRNs). I will also mention applications of these criteria to weakly
reversible SRNs\, and SRNs with transition of dynamics induced by volume s
cales. Finally\, I will list some related topics on bifurcation as well as
tails and approximation of stationary distributions of SRNs . This talk i
s based on joint works with Mads Christian Hansen and Carsten Wiuf.\n
LOCATION:https://researchseminars.org/talk/MoRN/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jinsu Kim (UC Irvine)
DTSTART:20210128T160000Z
DTEND:20210128T163000Z
DTSTAMP:20260421T094423Z
UID:MoRN/9
DESCRIPTION:Title: Ide
ntifiability of Stochastically Modelled Reaction Networks\nby Jinsu Ki
m (UC Irvine) as part of Seminar on the Mathematics of Reaction Networks\n
\n\nAbstract\nWhen an underlying reaction network is given for a biochemic
al system\, the system dynamics can be modeled with various mathematical f
rameworks such as continuous-time Markov processes. In this manuscript\, t
he identifiability of the underlying network structure with a given stocha
stic system dynamics is studied. It is shown that some data types related
to the associated stochastic dynamics can uniquely identify the underlying
network structure as well as the system parameters. The accuracy of the p
resented network inference is investigated when given dynamical data is ob
tained via stochastic simulations.\n
LOCATION:https://researchseminars.org/talk/MoRN/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elisa Tonello (Freie Universität\, Berlin)
DTSTART:20210211T160000Z
DTEND:20210211T163000Z
DTSTAMP:20260421T094423Z
UID:MoRN/11
DESCRIPTION:Title: Bo
olean interaction networks: some classical results and recent trends\n
by Elisa Tonello (Freie Universität\, Berlin) as part of Seminar on the M
athematics of Reaction Networks\n\n\nAbstract\nBoolean interaction network
s are one of the tools in the arsenal of\nmodellers investigating biologic
al systems. They aim to capture\nqualitative behaviours\, and can be usefu
l especially in absence of\ndetailed kinetic information. I will start by
giving an overview of the\nmain graph structures associated to Boolean net
works. I will then\nsummarise some of the results that connect structure t
o dynamics\, and\ntouch on some current trends and directions of research.
\n
LOCATION:https://researchseminars.org/talk/MoRN/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Angelyn Lao (De La Salle University Manila)
DTSTART:20210211T163000Z
DTEND:20210211T170000Z
DTSTAMP:20260421T094423Z
UID:MoRN/12
DESCRIPTION:Title: Ch
emical reaction network decompositions and realizations of S-systems\n
by Angelyn Lao (De La Salle University Manila) as part of Seminar on the M
athematics of Reaction Networks\n\n\nAbstract\nWe present novel decomposit
ion classes of chemical reaction networks (CRNs) derived from S-system kin
etics. Based on the network decomposition theory initiated by Feinberg in
1987\, we introduce the concept of incidence independent decompositions an
d develop the theory of $\\mathscr{C}$- and $\\mathscr{C}^*$- decompositio
ns which partition the set of complexes and the set of nonzero complexes r
espectively\, including their structure theorems in terms of linkage class
es. Analogous to Feinberg's independent decomposition\, we demonstrate the
important relationship between sets of complex balance equilibria for an
incidence independent decomposition of weakly reversible subnetworks for a
ny kinetics. We show that the $\\mathscr{C}^*$-decompositions are also in
cidence independent. We also introduce in this paper a new realization for
an S-system that is analyzed using a newly defined class of species cover
able CRNs. This led to the extension of the deficiency formula and charact
erization of fundamental decompositions of species decomposable reaction n
etworks.\n
LOCATION:https://researchseminars.org/talk/MoRN/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Justin Eilertsen (University of Michigan)
DTSTART:20210114T163000Z
DTEND:20210114T170000Z
DTSTAMP:20260421T094423Z
UID:MoRN/13
DESCRIPTION:Title: Th
e current state of quasi-steady-state approximations: manifolds\, time sca
les\, singularities\, and stochastic fluctuations\nby Justin Eilertsen
(University of Michigan) as part of Seminar on the Mathematics of Reactio
n Networks\n\n\nAbstract\nOver the past decade\, mathematicians have made
considerable progress concerning the theory and\napplicability of quasi-st
eady-state (QSS) approximations in chemical kinetics. The application of F
enichel theory has revealed that QSS reduction in chemical kinetics is far
richer than previously thought\, even in low-dimensional systems that do
not exhibit oscillatory behavior. In this talk\, I will discuss recent dis
coveries that have emerged in the \nfield of mathematical enzyme kinetics\
, including methodologies for obtaining perturbation parameters\, singular
points\, dynamic bifurcations and scaling laws. If time permits\, I will
also discuss the applicability of QSS reductions in stochastic environment
s\, and comment on some open problems in both deterministic and stochastic
enzyme kinetics.\n
LOCATION:https://researchseminars.org/talk/MoRN/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Curiel (University of Hawaii at Manoa)
DTSTART:20210128T163000Z
DTEND:20210128T170000Z
DTSTAMP:20260421T094423Z
UID:MoRN/14
DESCRIPTION:Title: Wh
en do two networks have the same steady-state ideal?\nby Mark Curiel (
University of Hawaii at Manoa) as part of Seminar on the Mathematics of Re
action Networks\n\n\nAbstract\nUnder the assumption of mass action kinetic
s\, the associated dynamical system of a reaction network is polynomial. W
e consider the ideals generated by these polynomials\, which are called st
eady-state ideals. Steady-state ideals appear in multiple contexts within
the chemical reaction network literature\, however they have yet to be sys
tematically studied. To begin such a study\, we ask and partially answer t
he following question: when do two reaction networks give rise to the same
steady-state ideal? In particular\, our main results describe three opera
tions on the reaction graph that preserve the steady-state ideal. Furtherm
ore\, since the motivation for this work is the classification of steady-s
tate ideals\, monomials play a primary role. To this end\, combinatorial
conditions are given to identify monomials in a steady-state ideal\, and w
e give a sufficient condition for a steady-state ideal to be monomial.\n
LOCATION:https://researchseminars.org/talk/MoRN/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linard Hoessly (University of Copenhagen)
DTSTART:20210325T160000Z
DTEND:20210325T163000Z
DTSTAMP:20260421T094423Z
UID:MoRN/15
DESCRIPTION:Title: On
an algebraic approach to product-form stationary distributions of some re
action networks\nby Linard Hoessly (University of Copenhagen) as part
of Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nExact re
sults for product-form stationary distributions of Markov chains are of in
terest in different fields. In stochastic reaction networks (CRNs)\, stati
onary distributions are mostly known in special cases where they are of pr
oduct-form. However\, there is no full characterization of the classes of
networks whose stationary distributions have product-form. We develop an a
lgebraic approach to product-form stationary distributions in the framewor
k of CRNs. Under certain hypotheses on linearity and decomposition of the
state space for conservative ergodic CRNs\, this gives sufficient and nece
ssary algebraic conditions for product-form stationary distributions. Corr
espondingly we obtain a semialgebraic subset of the parameter space that c
aptures rates where\, under the corresponding hypotheses\, CRNs have produ
ct-form. We employ the developed theory to CRNs and some models of statist
ical mechanics\, besides sketching the pertinence in other models from app
lied probability.\n
LOCATION:https://researchseminars.org/talk/MoRN/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Müller (University of Vienna)
DTSTART:20210311T163000Z
DTEND:20210311T170000Z
DTSTAMP:20260421T094423Z
UID:MoRN/16
DESCRIPTION:Title: De
tailed balance = complex balance + cycle balance\nby Stefan Müller (U
niversity of Vienna) as part of Seminar on the Mathematics of Reaction Net
works\n\n\nAbstract\nWe further clarify the relation between detailed-bala
nced and complex-balanced equilibria\nof reversible chemical reaction netw
orks.\nOur results hold for arbitrary kinetics and also for boundary equil
ibria.\n\nDetailed balance\, complex balance\, ''formal balance''\, and th
e new notion of ''cycle balance''\nare all defined in terms of the underly
ing graph.\nThis fact allows elementary graph-theoretic (non-algebraic) pr
oofs of \na previous result (detailed balance = complex balance + formal b
alance)\, \nour main result (detailed balance = complex balance + cycle ba
lance)\,\nand a corresponding result in the setting of continuous-time Mar
kov chains.\n\nJoint work with Badal Joshi.\n
LOCATION:https://researchseminars.org/talk/MoRN/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Balazs Boros (University of Vienna)
DTSTART:20210225T163000Z
DTEND:20210225T170000Z
DTSTAMP:20260421T094423Z
UID:MoRN/17
DESCRIPTION:Title: Dy
namics of planar deficiency-one mass-action systems\nby Balazs Boros (
University of Vienna) as part of Seminar on the Mathematics of Reaction Ne
tworks\n\n\nAbstract\nFor a deficiency-zero mass-action system with a sing
le linkage class\, whenever there exists a positive equilibrium\, it is gl
obally asymptotically stable. In this talk we discuss what other qualitati
ve behaviors could arise when the deficiency is one. We restrict our atten
tion to the planar case. Joint work with Josef Hofbauer.\n
LOCATION:https://researchseminars.org/talk/MoRN/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tung Nguyen (University of Wisconsin-Madison)
DTSTART:20210311T160000Z
DTEND:20210311T163000Z
DTSTAMP:20260421T094423Z
UID:MoRN/18
DESCRIPTION:Title: Pr
evalence of deficiency zero for random reaction networks\nby Tung Nguy
en (University of Wisconsin-Madison) as part of Seminar on the Mathematics
of Reaction Networks\n\n\nAbstract\nIn the study of reaction networks\, t
here is usually a strong connection between the network structure and the
qualitative behavior of the dynamical system. Certain network structures s
uch as deficiency zero ensure many desirable behaviors of the dynamical sy
stems including existence and stability of equilibrium.\n\nIn this talk\,
I will attempt to address a natural question: how prevalent these structur
es (in particular deficiency zero) are among random reaction networks. To
answer this question\, it is important to have a framework to generate ran
dom reaction networks. I will present two such frameworks: an Erdos-Renyi
framework\, and a stochastic block model framework-which is essentially a
more generalized version of Erdos-Renyi. Next\, I will examine the scaling
limit (as the number of species goes to infinity) of the probability that
a random reaction network has deficiency zero.\n
LOCATION:https://researchseminars.org/talk/MoRN/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alan Rendall (Johannes Gutenberg University Mainz)
DTSTART:20210408T153000Z
DTEND:20210408T160000Z
DTSTAMP:20260421T094423Z
UID:MoRN/19
DESCRIPTION:Title: Us
ing Bogdanov-Takens bifurcations to study existence and stability of perio
dic solutions\nby Alan Rendall (Johannes Gutenberg University Mainz) a
s part of Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nH
opf bifurcations are a favourite way to prove the existence of periodic\ns
olutions of a dynamical system. The aim of this talk is to describe a vari
ant\nof this procedure using the less familiar concept of a Bogdanov-Taken
s\nbifurcation. Surprisingly\, the latter procedure has the advantage that
\nalthough the bifurcation itself is more complicated the conditions which
need\nto be checked to determine the stability of the periodic solutions
produced are\nmore straightforward. I will give a general discussion of th
ese matters\,\nillustrating them by the example of a model for the kinase
Lck. This is\nbased on work with Lisa Kreusser\, where we studied the occu
rrence of\ninteresting dynamical features\, such as multistability\, perio
dic solutions and\nhomoclinic loops\, in models for enzymes subject to aut
ophosphorylation. I will\nalso discuss how features of this type can be li
fted from smaller to larger\nreaction networks.\n
LOCATION:https://researchseminars.org/talk/MoRN/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaoxian Tang (Beihang University)
DTSTART:20210422T150000Z
DTEND:20210422T150000Z
DTSTAMP:20260421T094423Z
UID:MoRN/20
DESCRIPTION:Title: Mu
ltistability of One-Dimensional Reaction Networks\nby Xiaoxian Tang (B
eihang University) as part of Seminar on the Mathematics of Reaction Netwo
rks\n\n\nAbstract\nWe report our recent progress on multistability of reac
tion networks. For the networks with one-dimensional stoichiometric subspa
ce\, we have the following results.\n (1) If the maximum number of positiv
e steady states is an even number N\, then the maximum number of stable po
sitive steady states\n is N/2.\n (2) If the maximum number of positive ste
ady states is an odd number N\, then we provide a condition on the network
such that the maximum number of stable positive steady states is (N-1)/2
if this condition is satisfied\, and this maximum number is (N+1)/2 otherw
ise.\n
LOCATION:https://researchseminars.org/talk/MoRN/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hyukpyo Hong (KAIST)
DTSTART:20210513T150000Z
DTEND:20210513T153000Z
DTSTAMP:20260421T094423Z
UID:MoRN/21
DESCRIPTION:Title: De
rivation of stationary distributions of stochastic chemical reaction netwo
rks via network translation\nby Hyukpyo Hong (KAIST) as part of Semina
r on the Mathematics of Reaction Networks\n\n\nAbstract\nLong-term behavio
rs of biochemical reaction networks are described by steady states in dete
rministic models and stationary distributions in stochastic models. Unlike
deterministic steady states\, stationary distributions capturing inherent
fluctuations of reactions are extremely difficult to derive analytically
due to the curse of dimensionality. In this talk\, we introduce a new meth
od to derive stationary distributions from deterministic steady states by
transforming reaction networks to have a special dynamic property based on
chemical reaction network theory. Specifically\, we merge nodes and edges
to make a steady state complex balanced\, i.e.\, the in- and out-flows of
each node are equal\, and then we derive a stationary distribution from t
he complex balanced steady state. Furthermore\, we provide a user-friendly
computational package\, called CASTANET\, that transforms BRNs and then a
nalytically derives their stationary distributions.\n
LOCATION:https://researchseminars.org/talk/MoRN/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amirhosein Sadeghimanesh (Coventry University)
DTSTART:20210422T153000Z
DTEND:20210422T160000Z
DTSTAMP:20260421T094423Z
UID:MoRN/22
DESCRIPTION:Title: St
udying dynamical behavior of the three connected populations with Allee ef
fect using algebraic tools\nby Amirhosein Sadeghimanesh (Coventry Univ
ersity) as part of Seminar on the Mathematics of Reaction Networks\n\n\nAb
stract\nWe consider three connected populations with the strong Allee effe
ct\, and give a complete classification of the steady state structure of t
he system with respect to the Allee threshold and the dispersal rate. One
may expect that by increasing the dispersal rate between the patches\, the
system would become more well-mixed hence simpler. However\, we show that
it is not always the case\, and the number of steady states may (temporar
ily) increase by increasing the dispersal rate. Besides sequences of pitch
fork and saddle-node bifurcations\, we find triple-transcritical bifurcati
ons and also a sun-ray shaped bifurcation where twelve steady states meet
at a single point then disappear. The major tool of our investigations is
a novel algorithm that decomposes the parameter space with respect to the
number of steady states using cylindrical algebraic decomposition with res
pect to the discriminant variety of the polynomial system. This is a joint
work with Gergely Röst.\n
LOCATION:https://researchseminars.org/talk/MoRN/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolette Meshkat (Santa Clara University)
DTSTART:20210408T150000Z
DTEND:20210408T150000Z
DTSTAMP:20260421T094423Z
UID:MoRN/23
DESCRIPTION:Title: Ab
solute concentration robustness in networks with many conservation laws\nby Nicolette Meshkat (Santa Clara University) as part of Seminar on the
Mathematics of Reaction Networks\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/MoRN/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carsten Wiuf (University of Copenhagen)
DTSTART:20210520T150000Z
DTEND:20210520T153000Z
DTSTAMP:20260421T094423Z
UID:MoRN/24
DESCRIPTION:Title: On
the sum of two reactions\nby Carsten Wiuf (University of Copenhagen)
as part of Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\n
It is standard in (bio)chemistry to represent a series of reactions by a s
ingle reaction\, often called a complex reaction in contrast to an element
ary reaction. For example\, photosynthesis $6\\ \\text{CO}_2+6\\ \\text{H}
_2\\text{O}\\ \\to \\ \\text{C}_6\\text{H}_{12}\\text{O}_6+6\\ \\text{O}_2
$ is such complex reaction. We introduce a mathematical operation that cor
responds to summing two chemical reactions. Specifically\, we define an as
sociative and non-communicative operation on the product space $\n_0^n\\ti
mes \n_0^n$ (representing the reactant and the product of a chemical react
ion\, respectively). The operation models the overall effect of two reacti
ons happening in succesion\, one after the other. We study the algebraic p
roperties of the operation and apply the results to stochastic reaction ne
tworks\, in particular to reachability of states\, and to reduction of rea
ction networks.\n
LOCATION:https://researchseminars.org/talk/MoRN/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mercedes Perez Millan (Universidad de Buenos Aires)
DTSTART:20210520T153000Z
DTEND:20210520T160000Z
DTSTAMP:20260421T094423Z
UID:MoRN/25
DESCRIPTION:Title: Ci
rcuits of multistationarity in structured enzymatic networks\nby Merce
des Perez Millan (Universidad de Buenos Aires) as part of Seminar on the M
athematics of Reaction Networks\n\n\nAbstract\nIn this work we focus on mi
nimal sets of intermediate species\nand their location in the network to a
llow for multistationarity in the\ncorresponding mass-action chemical reac
tion system. This question has also\nbeen studied in Feliu and Wiuf (2013)
and also in Sadeghimanesh and Feliu\n(2019) using degree theory technique
s. Our results simplify the analysis\nfor chemical reaction systems with c
ertain structure\, called "linearly\nbinomial networks" [Dickenstein\, P.M
.\, Shiu\, Tang (2019)]. We apply our\nresults on several signaling networ
ks. We also refer to the problem of\nlifting of multistationarity\, and we
give easy combinatorial conditions\nfor MESSI networks [P.M.\, Dickenste
in (2018)] to be linearly binomial.\nThis is joint work with Alicia Dicken
stein\, Magalí Giaroli and Rick\nRischter.\n
LOCATION:https://researchseminars.org/talk/MoRN/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicola Vassena (FU Berlin)
DTSTART:20210513T153000Z
DTEND:20210513T160000Z
DTSTAMP:20260421T094423Z
UID:MoRN/26
DESCRIPTION:Title: Si
gn-sensitivity of metabolic networks: which structures determine the sign
of the responses\nby Nicola Vassena (FU Berlin) as part of Seminar on
the Mathematics of Reaction Networks\n\n\nAbstract\nPerturbations are ubiq
uitous in metabolism. A central tool to understand\ntheir effect is sensit
ivity analysis\, which investigates how the network\nresponds to external
perturbations. In this talk we follow a structural\napproach\, only based
on the network stoichiometry and not requiring any\nquantitative knowledge
of the reaction rates. We consider perturbations of\nreaction rates\, at
equilibrium\, and we investigate the responses of the\nreaction fluxes. We
focus in particular on the sign of such responses\,\ni.e. whether a respo
nse is positive\, negative or whether its sign depends\non the reaction ra
tes parameters. We identify and describe certain kernel\nvectors of the st
oichiometric matrix\, which are the main players in the\nsign description.
\n
LOCATION:https://researchseminars.org/talk/MoRN/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nidhi Kaihnsa (Brown University)
DTSTART:20211028T153000Z
DTEND:20211028T160000Z
DTSTAMP:20260421T094423Z
UID:MoRN/27
DESCRIPTION:Title: Co
operativity and Absolute Interaction\nby Nidhi Kaihnsa (Brown Universi
ty) as part of Seminar on the Mathematics of Reaction Networks\n\n\nAbstra
ct\nThis is based on a joint work with Yue Ren\, Mohab Safey El Din\, and
Johannes Martini. We consider a measure of cooperativity based on the min
imal absolute interaction required to generate an observed titration behav
ior. We describe the corresponding algebraic optimization problem and show
how it can be solved using the nonlinear algebra tool \\texttt{SCIP}.\nMo
reover\, we compute the minimal absolute interactions for various binding
polynomials that describe the oxygen binding of various hemoglobins under
different conditions.\n
LOCATION:https://researchseminars.org/talk/MoRN/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tang Quoc Bao (Karl-Franzens-University of Graz)
DTSTART:20210923T153000Z
DTEND:20210923T160000Z
DTSTAMP:20260421T094423Z
UID:MoRN/28
DESCRIPTION:Title: Co
nvergence to equilibrium for chemical reaction-diffusion systems\nby T
ang Quoc Bao (Karl-Franzens-University of Graz) as part of Seminar on the
Mathematics of Reaction Networks\n\n\nAbstract\nThis talk presents the qua
ntitative large time behaviour of reaction-diffusion systems modelling com
plex balanced chemical reaction networks. The convergence to equilibrium i
s investigated by using the so-called entropy method\, which is robust eno
ugh to apply to renormalised solutions. When the system possesses no bound
ary equilibria\, the solution is shown to converge exponentially to equili
brium with a semi-explicit rate. For certain systems with boundary equilib
ria\, we investigate the competition between attraction of the positive eq
uilibrium and hypothetical convergence towards the boundary to show the do
minance of the former.\n\nThis talk is based on joint works with Laurent D
esvillettes and Klemens Fellner.\n
LOCATION:https://researchseminars.org/talk/MoRN/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Badal Joshi (California State University San Marcos)
DTSTART:20210916T153000Z
DTEND:20210916T160000Z
DTSTAMP:20260421T094423Z
UID:MoRN/29
DESCRIPTION:Title: Dy
namic Absolute Concentration Robustness\nby Badal Joshi (California St
ate University San Marcos) as part of Seminar on the Mathematics of Reacti
on Networks\n\n\nAbstract\nOutput or functional robustness in biochemical
systems has been experimentally observed in the IDHKP-IDH glyoxylate bypas
s regulation system and the EnvZ/OmpR system in E. coli. To model output r
obustness\, we define the notion of dynamic absolute concentration robustn
ess (dynamic ACR) in systems of ODEs. A species in a biochemical reaction
network has dynamic ACR if its concentration converges to the same positiv
e value irrespective of overall initial conditions. Dynamic ACR builds on
the notion of static ACR wherein the concentration of a species has the sa
me value in any positive steady state. We will define stronger and weaker
forms of both static and dynamic ACR along with various naturally occurri
ng domains/basins for each. We will give a complete classification of smal
l networks\, using both algebraic and topological characterization\, by th
eir static ACR\, strong static ACR\, dynamic ACR\, and weak dynamic ACR pr
operties.\n
LOCATION:https://researchseminars.org/talk/MoRN/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne Shiu (Texas A&M University)
DTSTART:20210916T150000Z
DTEND:20210916T153000Z
DTSTAMP:20260421T094423Z
UID:MoRN/30
DESCRIPTION:Title: Ab
solute concentration robustness and multistationarity\nby Anne Shiu (T
exas A&M University) as part of Seminar on the Mathematics of Reaction Net
works\n\n\nAbstract\nA reaction system exhibits “absolute concentration
robustness” (ACR) in some species if the positive steady-state value of
that species does not depend on initial conditions. We present results cha
racterizing ACR for small networks\, specifically\, those with only a few
species or reactions - or with low-dimensional stoichiometric subspace. W
e also investigate the relationship between ACR and multistationarity (tha
t is\, the capacity of a network to admit multiple positive steady states)
. Finally\, we highlight several open problems on these topics.\n
LOCATION:https://researchseminars.org/talk/MoRN/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hye-Won Kang (University of Maryland)
DTSTART:20210923T150000Z
DTEND:20210923T153000Z
DTSTAMP:20260421T094423Z
UID:MoRN/31
DESCRIPTION:Title: St
ochastic Modeling of Reaction-Diffusion Processes in Biology\nby Hye-W
on Kang (University of Maryland) as part of Seminar on the Mathematics of
Reaction Networks\n\n\nAbstract\nInherent fluctuations may play an importa
nt role in biochemical and biophysical systems when the system involves so
me species with low copy numbers. This talk will present the recent work o
n the stochastic modeling of reaction-diffusion processes in glucose metab
olism. In this talk\, I will introduce a compartment-based model for a sim
ple glycolytic pathway using a continuous-time Markov jump process\, which
describes system features at different scales of interest. Then\, we will
see how the multiscale approximate method reduces the model complexity. W
e will briefly discuss how the compartment size in the spatial domain can
affect the spatial patterns of the system.\n
LOCATION:https://researchseminars.org/talk/MoRN/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giulia Giordano (University of Trento)
DTSTART:20211118T163000Z
DTEND:20211118T170000Z
DTSTAMP:20260421T094423Z
UID:MoRN/32
DESCRIPTION:Title: Lo
oking at biochemical reaction networks through the lens of the BDC-decompo
sition\nby Giulia Giordano (University of Trento) as part of Seminar o
n the Mathematics of Reaction Networks\n\n\nAbstract\nSome properties and
emerging behaviours of a biochemical reaction network are exclusively due
to its structure (i.e.\, its stoichiometry along with qualitative assumpti
ons) and are independent of parameter values\, which are often uncertain\,
unknown or time-varying. Structural analysis is aimed at assessing proper
ties that hold for a whole family of systems\, characterised by a given st
ructure\, regardless of parameter values and precise functional expression
s. We propose the BDC-decomposition as a tool for both a local and a globa
l representation of a nonlinear system with an underlying network structur
e. We show how the BDC-decomposition can help us structurally assess impor
tant properties\, including stability\, stabilisability and the sign of st
eady-state input-output influences in complex interconnected uncertain sys
tems\, with a special focus on biochemical reaction networks.\n\nGiulia Gi
ordano is currently an Assistant Professor at the University of Trento\, I
taly. She received the B.Sc. and M.Sc. degrees in electrical engineering a
nd the Ph.D. degree in systems and control theory from the University of U
dine\, Italy\, in 2010\, 2012\, and 2016\, respectively. She visited the C
alifornia Institute of Technology\, Pasadena (CA)\, USA\, in 2012\, and th
e University of Stuttgart\, Germany\, in 2015. She was a Research Fellow a
t Lund University\, Sweden\, from 2016 to 2017\, and an Assistant Professo
r at the Delft University of Technology\, The Netherlands\, from 2017 to 2
019. She was recognised with the Outstanding Reviewer Letter from the IEEE
Transactions on Automatic Control in 2016 and from the Annals of Internal
Medicine in 2020. She received the EECI Ph.D. Award 2016\, the NAHS Best
Paper Prize 2017\, and the SIAM Activity Group on Control and Systems Theo
ry Prize 2021. Her main research interests include the analysis and the co
ntrol of dynamical networks\, with applications especially to biology and
epidemiology.\n
LOCATION:https://researchseminars.org/talk/MoRN/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:***
DTSTART:20211014T150000Z
DTEND:20211014T160000Z
DTSTAMP:20260421T094423Z
UID:MoRN/33
DESCRIPTION:Title: **
* Networking event (closed to registered participants) ***\nby *** as
part of Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nDea
r colleagues\,\n\nThank you very much for participating in the ‘Mathemat
ics of Reaction Networks’ seminar series! We will resume the series in S
eptember\, and information on the exact dates will appear on https://resea
rchseminars.org/seminar/MoRN as usual.\n\nWe are very happy that so many o
f you attended the talks and engaged in inspiring discussions afterwards!
To our surprise\, we also noticed many new names/faces among the attendees
. We are excited about this\, and we would like to provide an opportunity
to get to know each other better.\n\nWe would like to host a ‘networking
event’ in October (tentatively on October 14)\, at the same time as the
regular seminars. The idea is that all interested people may briefly intr
oduce themselves or give a short presentation (indicating their base insti
tution\, research interests and background\, and optionally showing some r
esults or advertising open research positions). The presentations will tak
e place either in one or several rooms\, and interaction will be encourage
d.\n\nAs soon as we know how many people are interested\, we will send out
further details. So\, please let us know if you would like to participate
by sending an email by August 30.\n\nHave a nice Summer!\n\nDaniele\, Eli
senda\, and Stefan (organizers of MoRN)\n\nThis is a closed event announce
d through the mailing list. Only people that registered earlier can join.\
n
LOCATION:https://researchseminars.org/talk/MoRN/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alicia Dickenstein (University of Buenos Aires)
DTSTART:20220519T153000Z
DTEND:20220519T160000Z
DTSTAMP:20260421T094423Z
UID:MoRN/35
DESCRIPTION:Title: Be
yond Boolean Networks\nby Alicia Dickenstein (University of Buenos Air
es) as part of Seminar on the Mathematics of Reaction Networks\n\n\nAbstra
ct\nI will report on work in progress with Juliana García Galofre\, Merce
des Pérez Millán and Reinhard Laubenbacher\, which is an invitation to m
odel biological networks with any (fixed) finite number of states for ever
y node\; in particular\, to predict the qualitative behavior of gene regul
atory networks. To model the dynamics\, we represent each transition funct
ion via operations used in multivalued logic\, which are intuitive and clo
se to biological interpretations. We generalize several good properties of
Boolean networks and we give an algorithm for computing the steady states
of the system that in many instances has a complexity that does not essen
tially increase with the number of states.\n
LOCATION:https://researchseminars.org/talk/MoRN/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gheorghe Craciun (University of Wisconsin\, Madison)
DTSTART:20220127T160000Z
DTEND:20220127T163000Z
DTSTAMP:20260421T094423Z
UID:MoRN/36
DESCRIPTION:Title: Re
action networks\, global stability\, and toric differential inclusions
\nby Gheorghe Craciun (University of Wisconsin\, Madison) as part of Semin
ar on the Mathematics of Reaction Networks\n\n\nAbstract\nKey properties o
f reaction network models (such as polynomial dynamical systems given by m
ass-action kinetics) are closely related to fundamental results about glob
al stability in classical thermodynamics. For example\, the Global Attract
or Conjecture can be regarded as a finite dimensional version of Boltzmann
’s H-theorem. We will discuss some of these connections\, and we will fo
cus especially on introducing toric differential inclusions as a tool for
proving the Global Attractor Conjecture.\n
LOCATION:https://researchseminars.org/talk/MoRN/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Germán Enciso (University of California\, Irvine)
DTSTART:20211209T163000Z
DTEND:20211209T170000Z
DTSTAMP:20260421T094423Z
UID:MoRN/37
DESCRIPTION:Title: St
ochastic Modeling of Nucleosome Dynamics and Gene Expression\nby Germ
án Enciso (University of California\, Irvine) as part of Seminar on the M
athematics of Reaction Networks\n\n\nAbstract\nDNA is tightly packaged aro
und histone proteins in order to increase its density inside cells\, and a
potential mechanism for DNA expression regulation is to control DNA-histo
ne interactions. In this talk I will present recent models of this behavio
r\, including a novel ultrasensitive\, noncooperative mechanism for DNA pa
ckaging\, as well as a collaboration to study time-dependent NFkB inputs i
n inflammatory signaling.\n
LOCATION:https://researchseminars.org/talk/MoRN/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claudio del Sole (Università bocconi di Milano)
DTSTART:20211028T150000Z
DTEND:20211028T153000Z
DTSTAMP:20260421T094423Z
UID:MoRN/38
DESCRIPTION:Title: Sc
aling limits of stochastic models with Fast Absorption and Slow Escape
\nby Claudio del Sole (Università bocconi di Milano) as part of Seminar o
n the Mathematics of Reaction Networks\n\n\nAbstract\nAutocatalytic reacti
on systems often exhibit a peculiar switching behaviour\, due to random fl
uctuations and discreteness in the number of molecules\, which produces th
e phenomenon of discreteness-induced transitions. The 2-dimensional versio
n of a model proposed by Togashi and Kaneko (2001) is a prominent example
of such patten. We analyze this model within a multiscale framework\, in w
hich fast autocatalytic cascades are triggered by much slower inflow and o
utflow reactions. Under suitable assumptions\, we study the limit behaviou
r of the rescaled stochastic process\, and prove weak convergence to a nat
urally arising piecewise-deterministic Markov process on the Skorohod spac
e equipped with Jakubowsky S-topology. Building upon this model\, we discu
ss extensions of such procedure to a larger family of autocatalytic reacti
on systems\, in which a fast subsystem is rapidly absorbed into a set of a
bsorbing states\, occasionally giving rise to abrupt state switches of pos
sibly random size.\n
LOCATION:https://researchseminars.org/talk/MoRN/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Agazzi (Duke University)
DTSTART:20211209T160000Z
DTEND:20211209T163000Z
DTSTAMP:20260421T094423Z
UID:MoRN/39
DESCRIPTION:Title: La
rge Deviations for Degenerate Markov Jump Processes\nby Andrea Agazzi
(Duke University) as part of Seminar on the Mathematics of Reaction Networ
ks\n\n\nAbstract\nThe dynamics of a network of chemical reactions under th
e laws of mass action kinetics are typically modeled as a system of couple
d ordinary differential equations. This macroscopic model can be recovered
\, under the appropriate scaling\, as the functional law of large numbers
for a family of jump Markov processes capturing the discrete nature of the
underlying\, microscopic dynamical model. The large deviations behavior o
f these models has been recently investigated under relatively strong assu
mptions on the existence of reactions with rates bounded away from 0\, all
owing to guarantee the nondegeneracy of the Markov process being investiga
ted. We show that these assumptions\, which are violated by many models of
interest\, can be significantly relaxed\, establishing large deviations p
rinciples for a large class of degenerate jump Markov processes.\n
LOCATION:https://researchseminars.org/talk/MoRN/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Ovchinnikov (City University of New York)
DTSTART:20211118T160000Z
DTEND:20211118T163000Z
DTSTAMP:20260421T094423Z
UID:MoRN/40
DESCRIPTION:Title: St
ructural parameter identifiability of ODE models\nby Alexey Ovchinniko
v (City University of New York) as part of Seminar on the Mathematics of R
eaction Networks\n\n\nAbstract\nStructural parameter identifiability analy
sis is one of the key steps of the analysis of an ODE system that depends
on parameters. This problem is to decide whether the parameters of the sys
tem can be determined by a given subset of the variables of the system. We
will discuss recent algorithms addressing this problem as well as related
remaining challenges.\n\nBio: Alexey Ovchinnikov received the Diploma in
Mathematics and Applied Mathematics from Moscow State University\, Russia\
, in 2004\, and the M.S. and Ph.D. degrees in Mathematics from North Carol
ina State University\, Raleigh\, NC\, USA\, in 2005 and 2007\, respectivel
y\, and a Candidate of Physical and Mathematical Sciences degree from Mosc
ow State University\, Russia\, in 2008. He is a Professor at the Departmen
t of Mathematics of Queens College\, City University of New York (CUNY)\,
USA\, and a Doctoral Faculty of the Ph.D. Programs in Mathematics and in C
omputer Science at the CUNY Graduate Center. Prior to joining CUNY\, he wa
s a Research Assistant Professor at the Department of Mathematics\, Statis
tics and Computer Science\, University of Illinois at Chicago\, USA (2007
–2009). His research interests are in symbolic and symbolic-numeric comp
utation for differential and difference equations and their applications t
o problems in the sciences. He is an editorial board member of Advances in
Applied Mathematics and of Journal of Symbolic Computation. He was the re
cipient of a 2010 National Science Foundation (NSF) CAREER Award and of a
2013 Alfred P. Sloan Foundation – CUNY Junior Faculty Research Award in
Science and Engineering.\n
LOCATION:https://researchseminars.org/talk/MoRN/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastian Walcher (RWTH Aachen)
DTSTART:20220210T163000Z
DTEND:20220210T170000Z
DTSTAMP:20260421T094423Z
UID:MoRN/41
DESCRIPTION:Title: Mi
chaelis-Menten - The quest for small parameters\nby Sebastian Walcher
(RWTH Aachen) as part of Seminar on the Mathematics of Reaction Networks\n
\n\nAbstract\nThere is a vast amount of literature on the classical Michae
lis-Menten reaction network for an enzyme-catalyzed reaction\, with a focu
s on reduction of dimension. The publications make evident that there exis
t different communities interested in this matter. The difference is manif
est both in the type of questions asked and in the type of arguments found
acceptable. From a mathematical perspective\, the standard reductions can
be traced back to singular perturbation theory\, as first noted in the se
minal paper by Heineken\, Tsuchiya and Aris. Thus one obtains convergence
results as some "small parameter" approaches zero. But from a practitioner
's perspective\, there remains a quest for stronger\, quantitative results
to be used in applications\, and there is a variety of "small parameters"
to be found in the literature. The talk aims at bridging (or at least nar
rowing) the gap between the communities from the mathematics side.\n
LOCATION:https://researchseminars.org/talk/MoRN/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hamid Rahkooy (Max Planck Institute for Informatics\, Saarbrücken
)
DTSTART:20220210T160000Z
DTEND:20220210T163000Z
DTSTAMP:20260421T094423Z
UID:MoRN/42
DESCRIPTION:Title: Co
mputations On Toricity/Binomiality of Chemical Reaction Networks\nby H
amid Rahkooy (Max Planck Institute for Informatics\, Saarbrücken) as part
of Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nChemica
l Reaction Networks (CRN) with Toric steady state\nvarities (or binomial s
teady state ideals) are of high interest. In\nthis talk\, we summarizy sev
eral theoretical as well as computational\nresults on toricity/binomiality
of CRNs. We\nintroduce the geometric\nconcept of shifted toricity (in con
trast to algebraic binomiality) and\npresent experimental and theoretical
results for detecting (shifted)\ntoricity. We present a polynomial time al
gorithm for detecting\nbinomiality of reversible CRNs. Finally\, if time a
llows\, we discuss\nsome experiments on parametric toricity/binomiality us
ing quantifier\nelimination and comprehensive Gr\\"obner systems.\n
LOCATION:https://researchseminars.org/talk/MoRN/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wasiur Khuda Bukhsh (University of Nottingham)
DTSTART:20220127T163000Z
DTEND:20220127T170000Z
DTSTAMP:20260421T094423Z
UID:MoRN/43
DESCRIPTION:Title: In
corporating age and delay into models for biophysical systems\nby Wasi
ur Khuda Bukhsh (University of Nottingham) as part of Seminar on the Mathe
matics of Reaction Networks\n\n\nAbstract\nIn many biological systems\, ch
emical reactions or changes in a physical state are assumed to occur insta
ntaneously. For describing the dynamics of those systems\, Markov models t
hat require exponentially distributed inter-event times have been used wid
ely. However\, some biophysical processes such as gene transcription and t
ranslation are known to have a significant gap between the initiation and
the completion of the processes\, which renders the usual assumption of ex
ponential distribution untenable. In this talk\, we consider relaxing this
assumption by incorporating age-dependent random time delays (distributed
according to a given probability distribution) into the system dynamics.
We do so by constructing a measure-valued Markov process on a more abstrac
t state space\, which allows us to keep track of the 'ages' of molecules p
articipating in a chemical reaction. We study the large-volume limit of su
ch age-structured systems. We show that\, when appropriately scaled\, the
stochastic system can be approximated by a system of partial differential
equations (PDEs) in the large-volume limit\, as opposed to ordinary differ
ential equations (ODEs) in the classical theory. We show how the limiting
PDE system can be used for the purpose of further model reductions and for
devising efficient simulation algorithms. To describe the ideas\, we will
use a simple transcription process as a running example.\n
LOCATION:https://researchseminars.org/talk/MoRN/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abhishek Deshpande (International Institute of Information Technol
ogy\, Hyderabad)
DTSTART:20220224T163000Z
DTEND:20220224T170000Z
DTSTAMP:20260421T094423Z
UID:MoRN/44
DESCRIPTION:Title: Au
tocatalytic recombination networks\nby Abhishek Deshpande (Internation
al Institute of Information Technology\, Hyderabad) as part of Seminar on
the Mathematics of Reaction Networks\n\n\nAbstract\nAutocatalytic systems
are ubiquitous in the ‘‘origin of life" models. In this talk\, we will
study the dynamics of the relative populations in autocatalytic recombina
tion networks\, and show that it can be analyzed using autonomous polynomi
al dynamical systems. In addition\, we will use results from reaction netw
ork theory to prove permanence of several families of autocatalytic recomb
ination networks.\n
LOCATION:https://researchseminars.org/talk/MoRN/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lea Sta (University of Leeds)
DTSTART:20220224T160000Z
DTEND:20220224T163000Z
DTSTAMP:20260421T094423Z
UID:MoRN/45
DESCRIPTION:Title: Ma
thematical modelling of a receptor-ligand system\nby Lea Sta (Universi
ty of Leeds) as part of Seminar on the Mathematics of Reaction Networks\n\
n\nAbstract\nEffector T cells rely on IL-7 signalling for their survival.
The IL-7 receptor (IL-7R)\, composed of the common gamma chain and the spe
cific alpha chain\, is also associated with the kinase JAK3 which triggers
its signalling pathway. Recent single-cell analysis showed a seemingly pa
radoxical observation: increased availability of gamma chains reduces the
IL-7 response. We describe two IL-7R mathematical models that provides an
explanation for this inhibitory activity and shows that a balance between
the IL-7R subunits is crucial for optimal signaling. Use of the Groebner b
asis provides analytical expressions for the maximum IL-7 response (or amp
litude) and for the half maximal effective concentration (EC50) of our mod
els. The results obtained inspired the study of a more general family of s
equential models of receptor with extrinsic kinase.\n
LOCATION:https://researchseminars.org/talk/MoRN/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeremy Gunawardena (Harvard Medical School\, Department of Systems
Biology)
DTSTART:20220519T150000Z
DTEND:20220519T153000Z
DTSTAMP:20260421T094423Z
UID:MoRN/46
DESCRIPTION:Title: Pa
rameter geography\nby Jeremy Gunawardena (Harvard Medical School\, Dep
artment of Systems Biology) as part of Seminar on the Mathematics of React
ion Networks\n\n\nAbstract\nI will discuss some puzzling findings from our
analysis of parametric regions for bistability in multisite\nmodification
systems (Nam et al\, PLoS Comput Biol 16:e1007573 2020)\, which remain un
explained\nand poorly understood. The findings suggest that parametric reg
ions can have macroscopic shape\nproperties\, such as volume\, that seem t
o behave reasonably as conserved quantities are changed but this is not ma
tched at the level of individual parameter points\, which can exhibit surp
risingly complicated behaviours.\n
LOCATION:https://researchseminars.org/talk/MoRN/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Greg Rempala (Ohio State University)
DTSTART:20220310T160000Z
DTEND:20220310T163000Z
DTSTAMP:20260421T094423Z
UID:MoRN/47
DESCRIPTION:Title: Ap
proximating bio-chemical dynamics using survival models\nby Greg Rempa
la (Ohio State University) as part of Seminar on the Mathematics of Reacti
on Networks\n\n\nAbstract\nIn a stochastic chemical network one can often
use the notion of a reaction hazard in order to provide a simple statistic
al model for the system evolution. This approach is especially helpful if
we want to consistently follow the fate of a single molecule of some sp
ecial species through its different transformations\, as is the case\, for
instance\, for a single individual in the classical model of a stochastic
epidemic network. I will provide a short overview of the survival approac
h and give some examples extracted from a much broader recent work comple
ted jointly with Daniele Cappelletti.\n
LOCATION:https://researchseminars.org/talk/MoRN/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Irene Otero Muras (Institute for Integrative Systems Biology)
DTSTART:20220428T150000Z
DTEND:20220428T153000Z
DTSTAMP:20260421T094423Z
UID:MoRN/48
DESCRIPTION:Title: De
tection of bistability in biochemical reaction networks: from mass action
to arbitrary kinetics\, and from deterministic to stochastic regimes\n
by Irene Otero Muras (Institute for Integrative Systems Biology) as part o
f Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nIn this t
alk\, I will describe the mathematical conditions and algorithms that we h
ave developed over the last decade (together with Antonio A. Alonso) for t
he detection of multistationarity and bistability in biochemical reaction
networks: from a condition for multistationarity for biochemical reaction
networks with mass action kinetics\, to the most recent developments in bi
stability detection for networks of arbitrary kinetics. Our approach relie
s on concepts from Chemical Reaction Network Theory\, Bifurcation Theory a
nd Nonlinear Optimization. I will explain the relevance of bistability in
the context of cell decision making\, and how cell decisions and bistabili
ty are affected in the presence of molecular noise.\n\nMoreover\, I will i
llustrate the specific biological problems that we have solved in the cont
ext of systems and synthetic biology using tools for efficient bistability
detection (like elucidating mechanisms responsible for differential signa
lling\, or designing programmable genetic biosensors in bacteria).\n
LOCATION:https://researchseminars.org/talk/MoRN/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Johnston (Lawrence Technological University)
DTSTART:20220310T163000Z
DTEND:20220310T170000Z
DTSTAMP:20260421T094423Z
UID:MoRN/49
DESCRIPTION:Title: An
alyzing Steady States of Mass Action Systems through Network Splitting
\nby Matthew Johnston (Lawrence Technological University) as part of Semin
ar on the Mathematics of Reaction Networks\n\n\nAbstract\nThe process of n
etwork translation corresponds a mass action system to a generalized mass
action system with equivalent dynamics. Recent research has shown that\, w
hen the generalized chemical reaction network underlying the second networ
k has desirable structure\, such as weak reversibility and low deficiency\
, then we may use the network to establish properties of the steady state
set and to explicitly construct a steady state parametrization. In this ta
lk\, I will extend this theory by introducing the method of "splitting" ne
tworks. In a split network\, we allow the original network to be partition
ed into subnetworks\, called "slices"\, while imposing that the union of t
he subnetworks preserves the stoichiometry of the original network. I show
that this process expands the scope of mass action systems whose steady s
tates can be characterized by the method of network translation.\n
LOCATION:https://researchseminars.org/talk/MoRN/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Massimiliano Esposito (University of Luxembourg)
DTSTART:20220324T163000Z
DTEND:20220324T170000Z
DTSTAMP:20260421T094423Z
UID:MoRN/50
DESCRIPTION:Title: Fr
ee energy transduction in chemical reaction networks from enzymes to metab
olism\nby Massimiliano Esposito (University of Luxembourg) as part of
Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nI will rigo
rously define energy transduction in open chemical reaction networks (CRNs
). The method is based on the stoichiometric matrix and the chemostatted s
pecies to identify the fundamental set of thermodynamic forces and fluxes
contributing to the CRN dissipation at steady state. Transduction arises w
hen some fluxes flow against their force thus creating negative contributi
ons to the dissipation. This is possible because other fluxes power transd
uction by being aligned with their force and ensuring the overall positivi
ty of the dissipation. Transduction is an emergent phenomenon arising at t
he network level because fluxes of elementary reactions are always aligned
with their force. I will apply our method to study the efficiency of meta
bolic pathways in central metabolism. Our method generalizes to arbitrary
(nonlinear) CRNs the work by Terrell L. Hill on free energy transduction i
n pseudo first order (linear) CRNs.\n
LOCATION:https://researchseminars.org/talk/MoRN/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enrico Bibbona (Politecnico di Torino)
DTSTART:20220324T160000Z
DTEND:20220324T163000Z
DTSTAMP:20260421T094423Z
UID:MoRN/51
DESCRIPTION:Title: Ba
yesian inference of RNA life-cycle kinetic rates from sequencing data with
multiple latent clustering\nby Enrico Bibbona (Politecnico di Torino)
as part of Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\
nWe here propose a hierarchical Bayesian model to infer RNA synthesis\, pr
ocessing\, and degradation rates from sequencing data\, based on an ordina
ry differential equation system that models the RNA life cycle.\nWe parame
trize the latent kinetic rates\, that rule the system\, with a novel funct
ional form\, and estimate their parameters through 6 Dirichlet process mix
ture models. Owing to the complexity of this approach\, we are able to sim
ultaneously perform inference\, clustering and model selection. We apply o
ur method to investigate transcriptional and post-transcriptional response
s of murine fibroblasts to the activation of proto-oncogene Myc. Our appro
ach uncovers simultaneous regulations of the rates\, which had not previou
sly been observed in this biological system.\n
LOCATION:https://researchseminars.org/talk/MoRN/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hugo Dourado (Heinrich-Heine-Universität Düsseldorf)
DTSTART:20220428T153000Z
DTEND:20220428T160000Z
DTSTAMP:20260421T094423Z
UID:MoRN/52
DESCRIPTION:Title: Op
timality principles of cellular resource allocation: enzyme/substrate rela
tionship and growth laws\nby Hugo Dourado (Heinrich-Heine-Universität
Düsseldorf) as part of Seminar on the Mathematics of Reaction Networks\n
\n\nAbstract\nMuch recent progress has been made to understand the impact
of proteome allocation on bacterial growth\; much less is known about the
relationship between the abundances of the enzymes and their substrates\,
which jointly determine metabolic fluxes. Here\, we suggest an optimal rel
ationship between the concentrations of enzymes and their substrates as a
consequence of the optimal biomass allocation: for a cellular reaction ne
twork composed of effectively irreversible reactions\, maximal reaction fl
ux is achieved when the dry mass allocated to each substrate is equal to t
he dry mass of the unsaturated (or “free”) enzymes waiting to consume
it. Calculations based on this optimality principle successfully predict t
he quantitative relationship between the observed enzyme and metabolite ab
undances in E. coli\, parameterized only by dissociation constants ($K_m$)
. This optimal relationship is also shown to explain the emergence of line
ar “growth laws” of proteome allocation under carbon limitation\; thes
e can be seen as approximations to the optimal enzyme/substrate relationsh
ip\, including the existence of aparent protein “offsets” at zero grow
th. The apparent offsets relate directly to the levels of substrate satura
tion of catalytic proteins\, explaining also how the “under-utilization
” of enzymes results from a trade-off between biomass allocation to enzy
mes and to metabolites.\n
LOCATION:https://researchseminars.org/talk/MoRN/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maya Mincheva (Northern Illinois University)
DTSTART:20221013T150000Z
DTEND:20221013T153000Z
DTSTAMP:20260421T094423Z
UID:MoRN/53
DESCRIPTION:Title: Ch
emical Reaction Networks with Time Delays\nby Maya Mincheva (Northern
Illinois University) as part of Seminar on the Mathematics of Reaction Net
works\n\n\nAbstract\nDelay mass-action systems provide a model of chemical
kinetics in which past states influence the current dynamics. In this wor
k\, we obtain a graph-theoretic condition for $\\mathit{delay\\\,stabilit
y}$ which is linear stability independent of rate constants and delay par
ameters. The graph-theoretic condition involves cycles in the $\\mathit{di
rected\\\,species}$-$\\mathit{reaction\\\,graph}$ of the network\, which e
ncodes how different species in the system interact. \nSeveral interesting
examples on sequestration networks with delays are presented.\n\nThis is
a joint work with George Craciun\, Casian Pantea and Polly Yu.\n
LOCATION:https://researchseminars.org/talk/MoRN/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shu Wang (Massachusetts Institute of Technology)
DTSTART:20221013T153000Z
DTEND:20221013T160000Z
DTSTAMP:20260421T094423Z
UID:MoRN/54
DESCRIPTION:Title: In
ferring CRN properties from single-cell 'omics data\nby Shu Wang (Mass
achusetts Institute of Technology) as part of Seminar on the Mathematics o
f Reaction Networks\n\n\nAbstract\nIn recent decades\, single-cell 'omics
technology has allowed for measuring the abundance of $10^1$-$10^4$ distin
ct biochemical species in $10^3$-$10^6$ cells from a single experiment. Su
ch large datasets potentially contain rich information about the underlyin
g (bio)chemical reaction networks (CRNs) in cells. We design single-cell '
omics data analysis methods to infer CRN properties\, such as the stoichio
metric subspace of a complex-balanced CRN\, by combining data science tech
niques with algebro-geometric results from CRN theory. \n\nEmail: sw543
@cornell.edu\n
LOCATION:https://researchseminars.org/talk/MoRN/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomislav Plesa (University of Cambridge)
DTSTART:20221027T150000Z
DTEND:20221027T153000Z
DTSTAMP:20260421T094423Z
UID:MoRN/55
DESCRIPTION:Title: In
tegral feedback in synthetic biology: Negative-equilibrium catastrophe
\nby Tomislav Plesa (University of Cambridge) as part of Seminar on the Ma
thematics of Reaction Networks\n\n\nAbstract\nA central goal of synthetic
biology is the design of molecular\ncontrollers that can manipulate the dy
namics of intracellular networks\nin a stable and accurate manner. To addr
ess the fact that detailed knowledge\nabout intracellular networks is unav
ailable\, integral-feedback controllers (IFCs)\n have been put forward for
controlling molecular abundances.\nThese controllers can maintain accurac
y in spite of the uncertainties in the controlled networks.\nHowever\, thi
s desirable feature is achieved only if stability is also maintained.\nIn
this talk\, we show that molecular IFCs can suffer from a hazardous instab
ility called\nnegative-equilibrium catastrophe (NEC)\, whereby\nall nonneg
ative equilibria vanish under the action of the controllers\,\nand some of
the molecular abundances blow up.\nWe analyze the performance of a family
of bimolecular IFCs \nwhen uncertain unimolecular networks are controlle
d\,\nand show that it is possible to safeguard against NECs.\nIn contrast\
, when IFCs are applied on uncertain bimolecular \n(and hence most intrace
llular) networks\,\nwe show that preventing NECs generally becomes an intr
actable problem\nas the number of interacting molecular species increases.
\nNECs therefore place a fundamental limit to\ndesign and control of molec
ular networks.\n
LOCATION:https://researchseminars.org/talk/MoRN/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ugur Cetiner (Harvard Medical School)
DTSTART:20221027T153000Z
DTEND:20221027T160000Z
DTSTAMP:20260421T094423Z
UID:MoRN/56
DESCRIPTION:Title: Re
formulating non-equilibrium steady-states\nby Ugur Cetiner (Harvard Me
dical School) as part of Seminar on the Mathematics of Reaction Networks\n
\n\nAbstract\nMarkov processes are widely used to model stochastic systems
in physics and biology. Their steady-state probabilities are given in ter
ms of their transition rates by the Matrix-Tree theorem (MTT). The MTT use
s spanning trees in a graph-theoretic representation and reveals that\, aw
ay from thermodynamic equilibrium\, steady-state probabilities become glob
ally dependent on all transition rates and the resulting expressions grow
super-exponentially in the graph size. The overwhelming complexity and lac
k of thermodynamic insight have impeded analysis\, despite substantial pro
gress in proving exact fluctuation theorems away from equilibrium. We expl
oit a graph-theoretic representation of Markov processes to reformulate no
n-equilibrium steady state probabilities in a way that makes their descrip
tions independent of system size and gives them thermodynamic meaning. Our
results suggest how we can “follow the energy” to unravel the functio
nal logic of non-equilibrium systems in physics and biology.\n
LOCATION:https://researchseminars.org/talk/MoRN/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Murad Banaji (Middlesex University London)
DTSTART:20221110T160000Z
DTEND:20221110T163000Z
DTSTAMP:20260421T094423Z
UID:MoRN/57
DESCRIPTION:Title: Sp
litting reactions preserves nondegenerate behaviours in chemical reaction
networks\nby Murad Banaji (Middlesex University London) as part of Sem
inar on the Mathematics of Reaction Networks\n\n\nAbstract\nInheritance re
sults attempt to answer the question: which enlargements of a chemical rea
ction network (CRN) preserve its capacity for interesting behaviours such
as multistationarity or oscillation? What are the potential effects on the
dynamics of a CRN of adding new reactions and/or species\, or modifying r
eactions? Such results allow us to make claims about large networks based
on their subnetworks. This talk will focus on a particular inheritance res
ult: under mild assumptions\, splitting reactions and inserting intermedia
te complexes preserves the capacity of a mass action CRN for nondegenerate
multistationarity and oscillation. This allows us to claim\, more general
ly\, that introducing enzymatic mechanisms into mass action systems preser
ves their capacity for these behaviours. The main result is motivated by t
he fact that intermediates are often omitted from CRN models in biology\,
but the effects of leaving out intermediates are not always well understoo
d.\n
LOCATION:https://researchseminars.org/talk/MoRN/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Romain Yvinec (Université de Tours)
DTSTART:20221110T163000Z
DTEND:20221110T170000Z
DTSTAMP:20260421T094423Z
UID:MoRN/58
DESCRIPTION:Title: St
ochastic Becker-Döring model: large population and large time results for
phase transition phenomena\nby Romain Yvinec (Université de Tours) a
s part of Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nW
e present results on a stochastic version of a well-known kinetic nucleati
on model for phase transition phenomena.\nIn the Becker-Döring model\, ag
gregates grow or shrink by addition or removal of one-by-one particle at a
time.\nUnder certain conditions\, very large aggregates emerge and are in
terpreted as a phase transition.\nWe study stationary and quasi-stationary
properties of the stochastic Becker-Döring model in the limit of infinit
e total number of particles\, and compare with results from the determinis
tic nucleation theory.\nOur findings are largely inspired from recent resu
lts from stochastic chemical reaction network theory.\n\nJoint work with E
rwan HINGANT\n
LOCATION:https://researchseminars.org/talk/MoRN/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aidan Howells (University of Wisconsin-Madison)
DTSTART:20221201T163000Z
DTEND:20221201T170000Z
DTSTAMP:20260421T094423Z
UID:MoRN/59
DESCRIPTION:Title: St
ochastic reaction networks within interacting compartments\nby Aidan H
owells (University of Wisconsin-Madison) as part of Seminar on the Mathema
tics of Reaction Networks\n\n\nAbstract\nStochastic reaction networks have
proven to be a useful tool for the understanding of processes\, chemical
and otherwise\, in homogeneous environments. There are multiple avenues fo
r generalizing away from the assumption that the environment is homogeneou
s\, with the proper modeling choice dependent upon the context of the prob
lem being considered. One such generalization\, introduced by Duso and Ze
chner in 2020\, involves a varying number of interacting compartments\, or
cells\, each of which contains an evolving copy of the stochastic reactio
n system. The novelty of the model is that these compartments also interac
t via the merging of two compartments (including their contents)\, the spl
itting of one compartment into two\, and the appearance and destruction of
compartments. We will discuss results pertaining to explosivity\, transie
nce\, recurrence\, and positive recurrence of the model\, and explore a nu
mber of examples demonstrating some possible non-intuitive behaviors.\n\nB
ased on join work with David F. Anderson.\n
LOCATION:https://researchseminars.org/talk/MoRN/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Patrick DeLeenher (Oregon State University)
DTSTART:20221201T160000Z
DTEND:20221201T163000Z
DTSTAMP:20260421T094423Z
UID:MoRN/60
DESCRIPTION:Title: Th
e basic reproduction number for linear semigroups in R^n with an invariant
cone\nby Patrick DeLeenher (Oregon State University) as part of Semin
ar on the Mathematics of Reaction Networks\n\n\nAbstract\nWe consider line
ar ODEs dx/dt=Ax on R^n and first characterize the class of operators A th
at have the property that e^{tA}(K) is contained in K for all non-negative
t. These turn out to be the so-called cross-positive operators on K\, or
equivalently\, the class of resolvent-positive operators (with respect to
K). We then introduce the notion of a basic reproduction number R0 and dis
cuss the trichotomy which says that R0-1 and the spectral abscissa s(A) of
A always have the same sign (positive\, negative or zero). Basic reproduc
tion numbers are often easier to calculate than the spectral abscissa\, wh
ich is why they are so popular in epidemiology and ecology. We shall illus
trate these concepts and results on a simple model of an infectious diseas
e\, and if time permits\, show that controlling R0 one way may have an opp
osite effect on the spectral abscissa. This suggests that one should be (m
ore) careful when lowering R0 in order to control an infectious disease.\n
LOCATION:https://researchseminars.org/talk/MoRN/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruth J. Williams (University of California San Diego)
DTSTART:20230126T163000Z
DTEND:20230126T170000Z
DTSTAMP:20260421T094423Z
UID:MoRN/62
DESCRIPTION:Title: Co
mparison Theorems for Stochastic Chemical Reaction Networks\nby Ruth J
. Williams (University of California San Diego) as part of Seminar on the
Mathematics of Reaction Networks\n\n\nAbstract\nContinuous-time Markov cha
ins are frequently used as stochastic models for chemical reaction network
s\, especially in the growing field of systems biology. A fundamental prob
lem for these Stochastic Chemical Reaction Networks (SCRNs) is to understa
nd the dependence of the stochastic behavior of these systems on the chemi
cal reaction rate parameters. Towards solving this problem\, in this paper
we develop theoretical tools called comparison theorems that provide stoc
hastic ordering results for SCRNs. These theorems give sufficient conditio
ns for monotonic dependence on parameters in these network models\, which
allow us to obtain\, under suitable conditions\, information about transie
nt and steady state behavior. These theorems exploit structural properties
of SCRNs\, beyond those of general continuous-time Markov chains. Further
more\, we derive two theorems to compare stationary distributions and mean
first passage times for SCRNs with different parameter values\, or with t
he same parameters and different initial conditions. These tools are devel
oped for SCRNs taking values in a generic (finite or countably infinite) s
tate space and can also be applied for non-mass-action kinetics models. We
illustrate our results with applications to models of chromatin regulatio
n and enzymatic kinetics.\n\nThis is based on joint work with Felipe Campo
s\, Simone Bruno\, Yi Fu and Domitilla Del Vecchio.\n
LOCATION:https://researchseminars.org/talk/MoRN/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elisenda Feliu (University of Copenhagen)
DTSTART:20230209T160000Z
DTEND:20230209T163000Z
DTSTAMP:20260421T094423Z
UID:MoRN/63
DESCRIPTION:Title: On
the generic dimension and nondegeneracy of steady states of reaction netw
orks\nby Elisenda Feliu (University of Copenhagen) as part of Seminar
on the Mathematics of Reaction Networks\n\n\nAbstract\nIn the context of (
bio)chemical reaction networks\, the dynamics of the concentrations of the
chemical species over time are often modelled by a system of parameter-de
pendent ordinary differential equations\, which are typically polynomial o
r described by rational functions. The dynamics of a reaction network are
also often constrained into invariant linear subspaces called stoichiometr
ic compatibility classes. The study of the steady states of the system tr
anslates then into the study of the positive solutions to a parametric pol
ynomial system. The set of positive solutions lives inside a complex algeb
raic variety and hence tools from algebraic geometry naturally find applic
ation in this field. \n\nIn this talk I will discuss recent results addres
sing the following questions: What is the expected dimension of the algebr
aic variety of steady states? Can the dimension be "wrong" in an open set
of parameters? Under what conditions is the intersection of the algebraic
variety of steady states with the stoichiometric compatibility classes gen
erically finite? \n\nThese are fundamental questions to understand the alg
ebraic nature of the objects under study\, and have been previously brough
t up in the study of reaction networks\, for example in the context of we
akly reversible reaction networks. Additionally\, knowing the answer to th
ese questions in advance is often necessary to be able to apply the mathem
atical machinery coming from complex algebraic geometry. \n\nThis talk is
based on join work in progress with Oskar Henriksson and Beatriz Pascual-E
scudero.\n
LOCATION:https://researchseminars.org/talk/MoRN/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarang Sunil Nath (Technical University of Denmark)
DTSTART:20230209T163000Z
DTEND:20230209T170000Z
DTSTAMP:20260421T094423Z
UID:MoRN/64
DESCRIPTION:Title: Co
nstructing Equivalent Electrical Circuits for (Bio)chemical Reaction Netwo
rks\nby Sarang Sunil Nath (Technical University of Denmark) as part of
Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nIn this wo
rk\, we develop and demonstrate a technique to transform reaction networks
into modular electrical circuits that embody the same dynamic behaviour.
After mathematically proving the equivalence of both representations\, we
illustrate the potential of the electrical framework to analyse oscillator
y or chaotic systems. The approach is then applied to solve for effective
rate constants in heterogeneous catalysis\, to enumerate flux subcycles in
the dihydrofolate reductase (DHFR) reaction pathway\, and to simulate a s
implified model of E. coli glycolysis. In addition to being an elegant ana
logy that bridges separate fields of research\, we believe that the devise
d methodology will be a valuable tool that can be leveraged by (bio)chemis
ts and (bio)chemical engineers to investigate and quantify the dynamics of
their specific reaction systems.\n
LOCATION:https://researchseminars.org/talk/MoRN/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesca Randone (IMT School for Advanced Studies Lucca)
DTSTART:20230223T160000Z
DTEND:20230223T163000Z
DTSTAMP:20260421T094423Z
UID:MoRN/65
DESCRIPTION:Title: Dy
namic Boundary Projection: Refining Deterministic Approximations Of Stocha
stic Reaction Networks Through Dynamic Boundary Projection\nby Frances
ca Randone (IMT School for Advanced Studies Lucca) as part of Seminar on t
he Mathematics of Reaction Networks\n\n\nAbstract\nTo exactly compute the
mean dynamics of stochastic reaction networks\, the solution of the Chemic
al Master Equation (CME) is rarely feasible. Deterministic rate equations
(DRE)\, while proven to converge to the average population dynamics for in
finite individuals\, may exhibit significant discrepancies for finite popu
lations\, especially in the presence of intrinsic noise\, unstable or mult
i-stable dynamics. Therefore\, it is often necessary to resort to computat
ionally expensive simulations. Dynamic Boundary Projection (DBP) is a meth
od that couples together a truncated version of the CME\, describing the e
volution of a subset of states and a set of DREs\, used to shift the obser
ved subset across the state space. I will show how we can apply DBP to SRN
s even when they exhibit oscillatory orbits\, multi-scale populations\, or
multiple stable equilibria. Moreover\, I will present an extension aiming
at reducing the computational costs of the method by suitably defining a
family of rescaled approximating processes. \n\nThe talk is based on joint
work with Mirco Tribastone and Luca Bortolussi.\n
LOCATION:https://researchseminars.org/talk/MoRN/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Muhammad Ali Al-Radhawi (Northeastern University)
DTSTART:20230223T163000Z
DTEND:20230223T170000Z
DTSTAMP:20260421T094423Z
UID:MoRN/66
DESCRIPTION:Title: Gr
aphical characterizations of robust stability in biological interaction ne
tworks\nby Muhammad Ali Al-Radhawi (Northeastern University) as part o
f Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nPrevious
studies have inferred robust stability of reaction networks by utilizing l
inear programs or iterative algorithms. Such algorithms become tedious or
computationally infeasible for large networks. In addition\, they operate
like black-boxes without offering intuition for the structures that are ne
cessary to maintain stability. In this work\, we provide several graphical
criteria for constructing robust stability certificates\, checking robust
non-degeneracy\, verifying persistence\, and establishing global stabil
ity. By characterizing a set of stability-preserving graph modifications t
hat includes the enzymatic modification motif\, we show that the stability
of arbitrarily large nonlinear networks can be examined by simple visual
inspection. We show applications of this technique to ubiquitous motifs i
n systems biology such as Post-Translational Modification (PTM) cycles\,
the Ribosome Flow Model (RFM)\, T-cell kinetic proofreading and others.\n
LOCATION:https://researchseminars.org/talk/MoRN/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:János Tóth (Budapest University of Technology and Economics)
DTSTART:20230126T160000Z
DTEND:20230126T163000Z
DTSTAMP:20260421T094423Z
UID:MoRN/67
DESCRIPTION:Title: Ch
aos in kinetic differential equations: Towards a rigorous approach.\nb
y János Tóth (Budapest University of Technology and Economics) as part o
f Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nA large p
art of theoretical work with kinetic differential equations focuses on con
ditions of exotic behavior like multistationarity and oscillation. Althoug
h experiments and numerical calculations suggest the presence of chaos in
chemical kinetics\, these works use approximations and heuristics. In this
talk\, we will construct a formal chemical reaction network that can rigo
rously be proved to show chaotic behavior.\n
LOCATION:https://researchseminars.org/talk/MoRN/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiaxin Jin (The Ohio State University)
DTSTART:20230309T160000Z
DTEND:20230309T163000Z
DTSTAMP:20260421T094423Z
UID:MoRN/68
DESCRIPTION:Title: Al
gorithm for finding weakly reversible low deficiency realizations of polyn
omial dynamical systems\nby Jiaxin Jin (The Ohio State University) as
part of Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nDif
ferent networks can generate the same dynamical system under mass-action k
inetics. In this talk\, we first show that the problem of identifying an u
nderlying weakly reversible deficiency zero network is well-posed\, in the
sense that the solution is unique whenever it exists. And we design an ef
ficient algorithm for the identification of these networks. Then we genera
lize the idea on identifying a weakly reversible but deficiency one networ
k along with an efficient algorithm. Further\, we prove the uniqueness of
such identification under some conditions. These are joint works with Gheo
rghe Craciun\, Abhishek Deshpande and Polly Yu.\n
LOCATION:https://researchseminars.org/talk/MoRN/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miruna-Stefana Sorea (SISSA Scuola Internazionale Superiore di Stu
di Avanzati)
DTSTART:20230309T163000Z
DTEND:20230309T170000Z
DTSTAMP:20260421T094423Z
UID:MoRN/69
DESCRIPTION:Title: Di
sguised toric dynamical systems\nby Miruna-Stefana Sorea (SISSA Scuola
Internazionale Superiore di Studi Avanzati) as part of Seminar on the Mat
hematics of Reaction Networks\n\n\nAbstract\nWe study families of polynomi
al dynamical systems inspired by biochemical reaction networks. We focus o
n complex balanced mass-action systems\, which have also been called toric
. They are known or conjectured to enjoy very strong dynamical properties\
, such as existence and uniqueness of positive steady states\, local and g
lobal stability\, persistence\, and permanence. We consider the class of d
isguised toric dynamical systems\, which contains toric dynamical systems\
, and to which all dynamical properties mentioned above extend naturally.
By means of (real) algebraic geometry we show that some reaction networks
have an empty toric locus or a toric locus of Lebesgue measure zero in par
ameter space\, while their disguised toric locus is of positive measure. W
e also propose some algorithms one can use to detect the disguised toric l
ocus. This is joint work with Laura Brustenga i Moncusí (University of Co
penhagen) and Gheorghe Craciun (University of Wisconsin-Madison).\n
LOCATION:https://researchseminars.org/talk/MoRN/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jianhua Xing (University of Pittsburgh)
DTSTART:20230323T160000Z
DTEND:20230323T163000Z
DTSTAMP:20260421T094423Z
UID:MoRN/70
DESCRIPTION:Title: Re
constructing cellular dynamics from single cell data\nby Jianhua Xing
(University of Pittsburgh) as part of Seminar on the Mathematics of Reacti
on Networks\n\n\nAbstract\nA grand challenge in single cell studies is to
construct a quantitative\, predictive\, and genome-wide mathematical model
describing cellular dynamics. Single-cell (sc)RNA-seq\, together with RNA
velocity and metabolic labeling\, reveals cellular states and transitions
at unprecedented resolution. A frontier of research is how to extract dyn
amical information from the snapshot data. In this talk I will first discu
ss our recently developed dynamo framework (Qiu et al. Cell\, 2022)\, focu
sing on the underlying mathematical framework. Then I will discuss our rec
ent efforts of reconstructing full dynamical equations using discrete calc
ulus on graphs (Zhang et al. to be submitted). I will conclude with an exa
mple of applying the formalism\, together with transition path analyses or
iginally developed in chemical physics\, to study how epithelial-to-mesenc
hymal transition couples with cell cycle (Wang et al. Sci Adv 2020\, eLife
2022\, Hu et al.\, in preparation).\n
LOCATION:https://researchseminars.org/talk/MoRN/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandru Hening (Texas A&M University)
DTSTART:20230323T163000Z
DTEND:20230323T170000Z
DTSTAMP:20260421T094423Z
UID:MoRN/71
DESCRIPTION:Title: Po
pulation dynamics under environmental and demographic stochasticity\nb
y Alexandru Hening (Texas A&M University) as part of Seminar on the Mathem
atics of Reaction Networks\n\n\nAbstract\nThis work looks at the long term
dynamics of diffusion processes modelling a single species that experienc
es both demographic and environmental stochasticity. In this setting\, the
long term dynamics of the population in the absence of demographic stocha
sticity is determined by the sign of $\\Lambda_0$ \, the external Lyapunov
exponent: $\\Lambda_0<$ implies (asymptotic) extinction and $\\Lambda_0>$
implies convergence to a unique positive stationary distribution $\\mu_0
$. If the system is of size $\\frac{1}{\\epsilon^2}$ for small $\\epsilon>
0$\, the extinction time is finite almost surely. One must therefore analy
ze the quasi-stationary distribution (QSD) $\\mu_\\epsilon$ of the system.
\n\nWe look at what happens when the population size is sent to infinity\,
i.e.\, when $\\epsilon\\to 0$. In contrast to models that only take into
account demographic stochasticity\, our results demonstrate the significan
t effect of environmental stochasticity – it turns an exponentially long
mean extinction time to a sub-exponential one.\n
LOCATION:https://researchseminars.org/talk/MoRN/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carsten Conradi (HTW Berlin)
DTSTART:20230413T150000Z
DTEND:20230413T153000Z
DTSTAMP:20260421T094423Z
UID:MoRN/72
DESCRIPTION:Title: Mo
nomial parameterizations and the dynamics of biochemical reaction networks
\nby Carsten Conradi (HTW Berlin) as part of Seminar on the Mathematic
s of Reaction Networks\n\n\nAbstract\nThe dynamics of biochemical reaction
networks can be described by ODEs with polynomial right hand side. Due to
high measurement uncertainty\, few experimental repetitions and a limited
number of measurable components\, parameters are subject to high uncertai
nty and can vary in large intervals. One therefore effectively has to stud
y families of parametrized polynomial ODEs. In this presentation networks
are considered where the steady state variety can be parameterized by mono
mials. I discuss how one can exploit these parameterizations to derive pol
ynomial conditions for the occurrence of multistationarity or Hopf bifurca
tions.\n
LOCATION:https://researchseminars.org/talk/MoRN/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Máté Telek (University of Copenhagen)
DTSTART:20230413T153000Z
DTEND:20230413T160000Z
DTSTAMP:20260421T094423Z
UID:MoRN/74
DESCRIPTION:Title: Ne
w results on the (dis)connectivity of the parameter region of multistation
arity\nby Máté Telek (University of Copenhagen) as part of Seminar o
n the Mathematics of Reaction Networks\n\n\nAbstract\nDespite recent devel
opments\, describing the set of parameters that enable multistationarity i
n a reaction network is a challenging problem. Under certain assumptions o
n the network\, one can associate a critical polynomial to the network tha
t gives information about multistationarity. Especially\, if the preimage
of the negative real line under the critical polynomial is connected then
the parameter region of multistationarity is connected. In the first part
of the talk\, I will present several new sufficient conditions on the crit
ical polynomial that imply connectivity. I will give several examples of r
eaction networks where our algorithm can be applied. In particular\, we sh
ow that the parameter region of multistationarity of the sequential and di
stributive phosphorylation cycle with up to seven binding sites is connect
ed. In the second part\, I will discuss a reaction network whose parameter
region of multistationarity is not connected.\n
LOCATION:https://researchseminars.org/talk/MoRN/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrés Ortiz-Muñoz (Santa Fe Institute)
DTSTART:20230427T150000Z
DTEND:20230427T153000Z
DTSTAMP:20260421T094423Z
UID:MoRN/75
DESCRIPTION:Title: A
Mathematical Approach to Modeling Complex Structures and their Dynamics\nby Andrés Ortiz-Muñoz (Santa Fe Institute) as part of Seminar on the
Mathematics of Reaction Networks\n\n\nAbstract\nIn this presentation\, we
introduce a novel mathematical approach for modeling complex structures an
d their dynamics using the concept of meronomy. Meronomy allows for a syst
ematic organization of the various types of parts\, or merons\, found with
in a system and their hierarchical relationships. We define complex struct
ures as collections of interconnected parts originating from a meronomy. T
o connect structural theory to quantitative aspects of dynamics\, we propo
se a notion of cardinality for meronomies. We show that the cardinalities
of classes of complex meronomical structures give rise to the probability
and combinatorial generating functions of stochastic chemical reaction net
works.\n
LOCATION:https://researchseminars.org/talk/MoRN/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Radek Erban (University of Oxford)
DTSTART:20230427T153000Z
DTEND:20230427T160000Z
DTSTAMP:20260421T094423Z
UID:MoRN/76
DESCRIPTION:Title: Ch
emical Reaction Networks: Systematic Design\, Noise Control and Limit Cycl
es\nby Radek Erban (University of Oxford) as part of Seminar on the Ma
thematics of Reaction Networks\n\n\nAbstract\nChemical reaction networks d
escribe interactions between biochemical species. Two types of mathematica
l models of reaction systems will be considered: (i) deterministic models
which are written in terms of reaction rate equations (i.e. ordinary diffe
rential equations (ODEs) for concentrations of biochemical species involve
d)\; and (ii) stochastic models of reaction networks\, given in terms of t
he Gillespie stochastic simulation algorithm\, which provides more detaile
d information about the simulated system than ODEs. I will discuss methods
for systematic design of relatively simple reaction systems with exotic d
ynamical behaviour\, including applications to synthetic biology and DNA c
omputing. Considering deterministic models of reaction networks\, I will p
resent examples of reaction systems with multiple oscillating solutions or
systems whose deterministic models (based on reaction rate equations) und
ergo specific bifurcations. Since reaction networks in biological applicat
ions often involve species at low-copy numbers\, stochastic effects may be
come a significant part of the dynamics. In such circumstances\, tools for
controlling the intrinsic noise in the system are needed for a successful
network design. To this end\, the so-called noise control algorithm will
be presented. The algorithm structurally modifies any given reaction netwo
rk under the mass action kinetics\, in such a way that controllable state-
dependent noise is introduced into the stochastic dynamics\, while the det
erministic dynamics (based on reaction rate equations) are preserved. I wi
ll present reaction networks with noise-induced oscillations and multi-sta
bility.\n\nReferences:\n[1] Radek Erban and Hye Won Kang\, "Chemical Syste
ms with Limit Cycles"\, submitted\, available as https://arxiv.org/abs/221
1.05755 (2022)\n\n[2] Radek Erban and S. Jonathan Chapman\, "Stochastic M
odelling of Reaction-Diffusion Processes"\, Cambridge Texts in Applied Mat
hematics\, Cambridge University Press (2020)\n\n[3] Tomislav Plesa\, Konst
antinos Zygalakis\, David Anderson and Radek Erban\, "Noise control for mo
lecular computing"\, Journal of the Royal Society Interface\, Volume 15\,
Number 144\, 20180199 (2018)\n
LOCATION:https://researchseminars.org/talk/MoRN/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tian Hong (University of Tennessee\, Knoxville)
DTSTART:20230511T150000Z
DTEND:20230511T153000Z
DTSTAMP:20260421T094423Z
UID:MoRN/77
DESCRIPTION:Title: Ma
ss-action models of regulated degradation\nby Tian Hong (University of
Tennessee\, Knoxville) as part of Seminar on the Mathematics of Reaction
Networks\n\n\nAbstract\nA key goal of systems biology is to use predictive
models to understand complex regulatory networks in living cells. Mathema
tical modeling and analysis have been successful in uncovering dynamics an
d steady-state properties\, such as multistability and oscillation\, of bi
ologically important reactions networks including multisite phosphorylatio
n cycles. However\, it remains unclear how emergent dynamics may arise fro
m other prevalent regulatory networks in nonintuitive ways. In this study\
, we introduce a family of mass-action models for elementary biochemical r
eactions involving only binding\, production\, and degradation. We show th
at altered degradation rate constants of macromolecules upon the formation
of high-order complexes can lead to multistability and limit-cycle oscill
ation. These models can be used to capture dynamics of RNA transcripts for
most human genes\, as well as many proteins. Interestingly\, multistabili
ty and oscillation require the same structurally minimal motif in the cont
ext of this model family. In addition\, oscillations originating from thes
e models have diverging periods\, and we use stochastic simulations to sho
w their utility of robustly generating cell clusters with diverse gene exp
ression patterns in cell populations.\n
LOCATION:https://researchseminars.org/talk/MoRN/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bryan Hernandez (University of the Philippines Diliman)
DTSTART:20230511T153000Z
DTEND:20230511T160000Z
DTSTAMP:20260421T094423Z
UID:MoRN/78
DESCRIPTION:Title: In
dependent decompositions of chemical reaction networks and parametrization
of positive steady states of chemical reaction systems\nby Bryan Hern
andez (University of the Philippines Diliman) as part of Seminar on the Ma
thematics of Reaction Networks\n\n\nAbstract\nA chemical reaction network
(CRN) is composed of reactions that can be seen as interactions among its
units called species. Endowed with kinetics\, the chemical reaction system
(CRN with kinetics) has an associated set of ordinary differential equati
ons (ODEs) that models the dynamics of the system. In chemical reaction ne
twork theory\, we are interested in connections between the CRN and the pr
operties of the associated ODEs. In this talk\, we discuss decompositions
of CRNs into independent subnetworks and how it can be used for parametriz
ation of positive steady states of mass-action systems\, especially for th
ose with complex underlying networks. To facilitate the discussion\, we de
monstrate examples to show how to efficiently get independent decompositio
ns and steady state parametrizations using MATLAB. Independent decompositi
ons could also be used to parametrize positive steady states of non-mass-a
ction systems with considerable independent subnetworks.\n
LOCATION:https://researchseminars.org/talk/MoRN/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gábor Szederkényi (Pazmany Peter Catholic University (PPKE))
DTSTART:20231026T150000Z
DTEND:20231026T153000Z
DTSTAMP:20260421T094423Z
UID:MoRN/79
DESCRIPTION:Title: An
alysis and application of kinetic flow models\nby Gábor Szederkényi
(Pazmany Peter Catholic University (PPKE)) as part of Seminar on the Mathe
matics of Reaction Networks\n\n\nAbstract\nIn this contribution\, nonnegat
ive flow models in kinetic and compartmental form will be studied. The mot
ivation of the research came from the results on ribosome flow models (RFM
s) which are deterministic dynamical systems used to describe ribosome mov
ement during mRNA translation. Over the past 15 years or so\, many of the
advantageous properties and applications of these models have been demonst
rated in the literature. In the talk\, an essential generalization of RFMs
will be presented. The class of systems we propose can handle arbitrary d
irected network (graph) structures and general nonlinear (even time-varyin
g) cell transition rates in contrast to the simpler structures and transit
ion rates studied previously. Under the general assumptions\, important pr
operties of the models (e.g. stability\, monotonicity\, passivity\, Hamilt
onian structure) can be shown\, which can be well exploited in dynamical a
nalysis and control design. The basis of the analysis is the theory of che
mical reaction networks and compartmental systems. Of further interest\, a
special spatial discretization of flow models used in vehicle flow modell
ing can be shown to belong to the generalized RFMs. This opens up an excit
ing opportunity to study the links between biochemical reaction networks a
nd certain transportation models.\n
LOCATION:https://researchseminars.org/talk/MoRN/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhou Fang (ETH Zürich)
DTSTART:20231026T153000Z
DTEND:20231026T160000Z
DTSTAMP:20260421T094423Z
UID:MoRN/80
DESCRIPTION:Title: A
divide-and-conquer method for analyzing high-dimensional noisy gene expres
sion networks\nby Zhou Fang (ETH Zürich) as part of Seminar on the Ma
thematics of Reaction Networks\n\n\nAbstract\nIntracellular gene expressio
n systems are inevitably random due to low molecular counts. Consequently\
, mechanistic models for gene expression should be stochastic\, and centra
l to the analysis and inference of such models is solving the Chemical Mas
ter Equation (CME)\, which characterizes the probability evolution of the
randomly evolving copy-numbers of the reacting species. While conventional
methods such as Monte-Carlo simulations and finite state projections exis
t for estimating CME solutions\, they suffer from the curse of dimensional
ity\, significantly decreasing their efficacy for high-dimensional systems
. Here\, we propose a new computational method that resolves this issue th
rough a novel divide-and-conquer approach. Our method divides the system i
nto a leader system and several conditionally independent follower subsyst
ems. The solution of the CME is then constructed by combining Monte Carlo
estimation for the leader system with stochastic filtering procedures for
the follower subsystems. We develop an optimized system decomposition\, wh
ich ensures the low-dimensionality of the sub-problems\, thereby allowing
for improved scalability with increasing system dimension. The efficiency
and accuracy of the method are demonstrated through several biologically r
elevant examples in high-dimensional estimation and inference problems. We
demonstrate that our method can successfully identify a yeast transcripti
on system at the single-cell resolution\, leveraging mRNA time-course micr
oscopy data\, allowing us to rigorously examine the heterogeneity in rate
parameters among isogenic cells cultured under identical conditions. Furth
ermore\, we validate this finding using a novel noise decomposition techni
que introduced in this study. This technique exploits experimental time-co
urse data to quantify intrinsic and extrinsic noise components\, without r
equiring supplementary components\, such as dual-reporter systems.\n
LOCATION:https://researchseminars.org/talk/MoRN/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:J. Krishnan (Imperial College London)
DTSTART:20231109T160000Z
DTEND:20231109T163000Z
DTSTAMP:20260421T094423Z
UID:MoRN/81
DESCRIPTION:Title: Sy
stems explorations of substrate modification systems\nby J. Krishnan (
Imperial College London) as part of Seminar on the Mathematics of Reaction
Networks\n\n\nAbstract\nThe post-translational modification of proteins i
s a basic way of establishing protein functionality. There are many exampl
es of classes of reversible modification (phosphorylation\, ubiquination\,
acetylation). Typically proteins are reversibly modified at multiple site
by associated enzymes. In some instances\, the same enzymes can perform m
ultiple modifications or demodifications. In such cases\, different types
of chemical mechanisms are possible: distributive\, wherein each modificat
ion is associated with the enzyme binding to the substrate\, and then diss
ociating after the modification\, and processive wherein the enzyme is bou
nd to the substrate as multiple modifications are effected. Substrate modi
fications could also occur in a particular sequence (ordered)\, or could o
ccur in any order (random).\n\nInterest in substrate modification systems
arises from the fact that they are fundamental ingredients of cellular net
works on one hand\, while also being complex molecular information proces
sors in their own right. In this talk\, we discuss various aspects of the
information processing characteristics of substrate modification systems.
We first discuss some aspects of the intrinsic behaviour of these substrat
e modification systems and connect them to basic ingredients (eg. chemical
mechanism\, substrate modification ordering\, commonality of enzymes). Fo
llowing this\, we discuss how such substrate modification systems may beh
ave as part of networks. We discuss the relevance of the results and insig
hts for both systems and synthetic biology\n\n(Joint work with Vaidhiswara
n Ramesh and Thapanar Suwanmajo).\n
LOCATION:https://researchseminars.org/talk/MoRN/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucie Laurence (INRIA)
DTSTART:20231109T163000Z
DTEND:20231109T170000Z
DTSTAMP:20260421T094423Z
UID:MoRN/82
DESCRIPTION:Title: Sc
aling methods for stochastic chemical reaction networks\nby Lucie Laur
ence (INRIA) as part of Seminar on the Mathematics of Reaction Networks\n\
n\nAbstract\nIn this talk we investigate stochastic chemical reaction netw
orks with scaling methods. This approach is used to study the stability pr
operties of the associated Markov processes\, but also to investigate the
transient behavior of these networks. It also gives insight on the impact
of complex features of these networks such as their polynomial rates\, lea
ding to the coexistence of multiple timescales. These methods will be illu
strated by the study of a particular CRN.\n
LOCATION:https://researchseminars.org/talk/MoRN/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elizabeth Gross (University of Hawaiʻi at Mānoa)
DTSTART:20231130T160000Z
DTEND:20231130T163000Z
DTSTAMP:20260421T094423Z
UID:MoRN/83
DESCRIPTION:Title: Mi
xed volumes of networks with binomial steady-states\nby Elizabeth Gros
s (University of Hawaiʻi at Mānoa) as part of Seminar on the Mathematics
of Reaction Networks\n\n\nAbstract\nThe steady-state degree of a chemical
reaction network is the number of complex steady-states for generic rate
constants and initial conditions. One way to bound the steady-state degree
is through the mixed volume of the steady-state system or an equivalent s
ystem. In this work\, we show that for partionable binomial networks compu
ting the mixed volume is equivalent to finding the volume of a single mixe
d cell that is the translate of a parallelotope. We highlight this theorem
by giving a formula for the mixed volume of species-overlapping networks.
This is joint work with Jane Coons and Mark Curiel.\n
LOCATION:https://researchseminars.org/talk/MoRN/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oskar Henriksson (University of Copenhagen)
DTSTART:20231130T163000Z
DTEND:20231130T170000Z
DTSTAMP:20260421T094423Z
UID:MoRN/84
DESCRIPTION:Title: Fi
nding all steady states with tropical geometry\nby Oskar Henriksson (U
niversity of Copenhagen) as part of Seminar on the Mathematics of Reaction
Networks\n\n\nAbstract\nThe point of departure of this talk is the follow
ing seemingly simple question: Suppose we are given a reaction network wit
h (generalized) mass action kinetics\, and a choice of rate constants and
total amounts – how do we find numerical approximations of *all* the pos
itive steady states?\n\nOne possible method is to use numerical algebraic
geometry to completely solve the steady state equations over the complex n
umbers\, and then use interval arithmetic methods to filter out the real p
ositive solutions. This approach has the advantage of finding all positive
steady states with probability 1 (including unstable ones that would be h
ard to find with traditional ODE methods)\, and additionally makes it poss
ible to *certify* in the end that all steady states have been found.\n\nIn
this talk\, I will outline the basic ideas behind this type of numerical
algebraic geometry solvers\, and then describe recent joint work in progre
ss with Feliu\, Helminck\, Ren\, Schröter and Telek\, where we use tropic
al geometry and matroid theory to determine the so-called *steady state de
gree* of a network\, which is needed to ensure efficiency and certifiabili
ty.\n
LOCATION:https://researchseminars.org/talk/MoRN/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniele Cappelletti (Politecnico di Torino)
DTSTART:20231214T160000Z
DTEND:20231214T163000Z
DTSTAMP:20260421T094423Z
UID:MoRN/85
DESCRIPTION:Title: St
ochastic reaction networks in stochastic environment\nby Daniele Cappe
lletti (Politecnico di Torino) as part of Seminar on the Mathematics of Re
action Networks\n\n\nAbstract\nIn the typical definition of stochastic rea
ction networks\, the rate functions only depend on the current state and d
o not change over time. However this is not true in many biological system
s\, where the rate functions change over time. In this study we considered
the more general case of the rates depending on both the current configur
ation and another stochastic process\, which we call "environment" and is
not directly affected by the system of interest. We study the positive rec
urrence of this more general model under the assumption of "monomoleculari
ty"\, and under certain conditions characterize the stationary distributio
n (when it exists) as a mixture of Poisson distributions\, which is unique
ly identified as the law of a fixed point of a stochastic recurrence equat
ion. This recursion can be utilized for numerical computation of moments a
nd other distributional features.\n
LOCATION:https://researchseminars.org/talk/MoRN/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marty Golubitsky (Ohio State University)
DTSTART:20231214T163000Z
DTEND:20231214T170000Z
DTSTAMP:20260421T094423Z
UID:MoRN/86
DESCRIPTION:Title: Ho
meostasis in Input-Output Networks\nby Marty Golubitsky (Ohio State Un
iversity) as part of Seminar on the Mathematics of Reaction Networks\n\n\n
Abstract\nA typical example of homeostasis occurs in warm-blooded mammals
where the animal’s internal body temperature $x_o$ is held approximated
constant on variation of the external ambient temperature I.\n\nOur mathem
atical study of homeostasis focuses on networks of differential equations.
First\, we assume that the network has an input node $(x_i)$\, an output
node $(x_o)$ \, and a set of n regulatory nodes $(x_{r_1}\, …\, x_{r_n})
$ where only the input node depends explicitly on an external ambient para
meter $I$. Second\, we assume that there exists a stable equilibrium that
leads to an input-output function $x_o(I)$. Third\, we replace homeostasis
(where the output is held approximately constant on variation of $I$) by
infinitesimal homeostasis (where the derivative $(dx_o/dI)$ vanishes).\n\n
We use graph theoretic methods to classify infinitesimal homeostasis. Firs
t\, we show that there are three kinds of three-node network motif (feedfo
rward loops\, substrate inhibition\, and negative feedback loops) each of
which leads to a different kind of homeostasis. Second\, we show that ever
y network leads to a unique set of possible patterns of infinitesimal home
ostasis. Where possible\, we illustrate our results through example.\n
LOCATION:https://researchseminars.org/talk/MoRN/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne Shiu (Texas A&M University)
DTSTART:20240208T160000Z
DTEND:20240208T163000Z
DTSTAMP:20260421T094423Z
UID:MoRN/87
DESCRIPTION:Title: Ab
solute concentration robustness: Algebra and geometry\nby Anne Shiu (T
exas A&M University) as part of Seminar on the Mathematics of Reaction Net
works\n\n\nAbstract\nMotivated by the question of how biological systems m
aintain homeostasis in changing environments\, Shinar and Feinberg introdu
ced in 2010 the concept of absolute concentration robustness (ACR). A bioc
hemical system exhibits ACR in some species if the steady-state value of t
hat species does not depend on initial conditions. Thus\, a system with AC
R can maintain a constant level of one species even as the environment cha
nges. Despite a great deal of interest in ACR in recent years\, the follow
ing basic question remains open: How can we determine quickly whether a gi
ven biochemical system has ACR? This talk presents new methods for decidin
g ACR\, which harness computational algebra.\n\nThis is joint work with Lu
is David García Puente\, Elizabeth Gross\, Heather A Harrington\, Matthew
Johnston\, Nicolette Meshkat\, and Mercedes Pérez Millán.\n
LOCATION:https://researchseminars.org/talk/MoRN/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Diego Rojas La Luz (University of Wisconsin-Madison)
DTSTART:20240208T163000Z
DTEND:20240208T170000Z
DTSTAMP:20260421T094423Z
UID:MoRN/88
DESCRIPTION:Title: Un
veiling Surprising Connections Between the Classical Theory of Reaction Ne
tworks and Generalized Lotka-Volterra Systems\nby Diego Rojas La Luz (
University of Wisconsin-Madison) as part of Seminar on the Mathematics of
Reaction Networks\n\n\nAbstract\nWe explore the relationship between React
ion Networks and Population Dynamics\, with a specific focus on Generalize
d Lotka-Volterra systems. Surprisingly\, we find strong analogies between
classical Mass Action Kinetics results (like the Horn-Jackson theorem and
the deficiency-zero theorem) and new counterparts in Generalized Lotka-Vol
terra systems\, hinting at a deep connection\, where previously none was k
nown. Notably\, in the Generalized Lotka-Volterra setting\, we can prove t
hat “complex-balanced” equilibria (properly defined) are globally attr
active (which corresponds to the “global attractor conjecture" in the Re
action Networks setting). As an example\, we show how to apply this new th
eory to characterize global stability for a large class of cooperative Gen
eralized Lotka-Volterra systems. We can also extend our results to analyze
the properties of variable-k systems\, an area not fully explored in the
context of Generalized Lotka-Volterra systems. This exploration unlocks un
tapped insights into the mathematical foundations of these systems\, shedd
ing light on their connections and paving the way for new avenues of resea
rch and discovery in this field. This is joint work with Gheorghe Craciun
and Polly Yu.\n
LOCATION:https://researchseminars.org/talk/MoRN/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Diego Oyarzun (University of Edinburgh)
DTSTART:20240314T160000Z
DTEND:20240314T163000Z
DTSTAMP:20260421T094423Z
UID:MoRN/89
DESCRIPTION:Title: An
alysis of genetic-metabolic circuits using piecewise affine dynamical syst
ems\nby Diego Oyarzun (University of Edinburgh) as part of Seminar on
the Mathematics of Reaction Networks\n\n\nAbstract\nCell survival depends
on the interplay of biochemical networks that sense\, transmit and process
environmental cues. In particular\, the interplay between metabolism and
gene regulatory networks allows cells to switch on or off specific pathway
s in response to changing environmental conditions. This control strategy
typically appears in the form of feedback loops where key regulatory metab
olites up- or down-regulate enzyme expression. In this talk I will present
some of our work on the analysis and design of coupled genetic-metabolic
networks. I will show how to timescale separation and piecewise constant a
pproximations can be jointly employed to predict the long-term dynamics no
nlinear models with complex combinations of positive and negative feedback
loops. This work results from a long-term collaboration with Madalena Cha
ves at INRIA Sophia Antipolis\, see e.g Chaves & Oyarzún\, Automatica\, 2
019.\n
LOCATION:https://researchseminars.org/talk/MoRN/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eva Loeser (University of California San Diego)
DTSTART:20240222T163000Z
DTEND:20240222T170000Z
DTSTAMP:20260421T094423Z
UID:MoRN/90
DESCRIPTION:Title: Fl
uid Limit for a Stochastic Model of Enzymatic Processing with General Dist
ributions\nby Eva Loeser (University of California San Diego) as part
of Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nIn this
talk\, we consider a stochastic chemical reaction system arising as a mode
l for enzymatic processing in a cell. This can also be thought of as a mul
ti-server multiclass queue with reneging operating under the random order
of service discipline. Stochastic primitives for the model such as product
ion/interarrival times\, processing/service times\, and lifetimes are assu
med to be generally distributed. We establish a fluid limit for a measure-
valued process that keeps track of the remaining lifetime for each entity
in the system. We prove uniqueness for fluid model solutions under mild co
nditions and study the asymptotic behavior of fluid model solutions as tim
e goes to infinity. This talk is based on joint work with Ruth Williams.\n
LOCATION:https://researchseminars.org/talk/MoRN/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mingjian Wen (University of Houston)
DTSTART:20240222T160000Z
DTEND:20240222T163000Z
DTSTAMP:20260421T094423Z
UID:MoRN/91
DESCRIPTION:Title: CR
Ns Enabling Unbiased Exploration of the Reaction Space in Batteries\nb
y Mingjian Wen (University of Houston) as part of Seminar on the Mathemati
cs of Reaction Networks\n\n\nAbstract\nChemical reaction networks (CRNs)\,
when integrated with machine learning (ML) techniques\, can offer unprece
dented opportunities to interrogate complex chemical systems. Here\, as an
example\, I will delve into the use of graph neural networks and CRNs to
facilitate data-driven exploration of the chemical reaction space in Li-io
n batteries\, aiming to find the optimal reaction pathways that lead to th
e formation of the solid-electrolyte interphase. Additionally\, I will tou
ch on other CRN problems where ML holds promising solutions.\n
LOCATION:https://researchseminars.org/talk/MoRN/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Doty (University of California\, Davis)
DTSTART:20240509T150000Z
DTEND:20240509T153000Z
DTSTAMP:20260421T094423Z
UID:MoRN/92
DESCRIPTION:Title: Ex
ecution bounded chemical reaction networks\nby David Doty (University
of California\, Davis) as part of Seminar on the Mathematics of Reaction N
etworks\n\n\nAbstract\nChemical reaction networks (CRNs) model systems whe
re molecules or agents interact according to a finite set of reactions suc
h as A + B → C\, representing that if a molecule of A and B collide\, th
ey disappear and a molecule of C is produced. Although traditionally used
to model natural chemical systems\, CRNs are also studied as a programming
language for describing the desired behavior of synthetic chemical system
s. Synthetic CRNs can compute Boolean-valued predicates $\\phi \\colon \\m
athbb{N}^d \\to \\{0\,1\\}$ and integer-valued functions $f\\colon \\mathb
b{N}^d \\to \\mathbb{N}$\; for instance X1 + X2 → Y can be thought to co
mpute the function min(x1\,x2).\n\nWe study the computational power of exe
cution bounded CRNs\, in which only a finite number of reactions can occur
from the initial configuration (e.g.\, ruling out reversible reactions su
ch as A ⇌ B). Our main negative results\, showing limitations on the com
putational power of execution bounded CRNs\, are based on characterizing e
xecution bounded CRNs as precisely those that have a "linear potential fun
ction": a nonnegative linear function of the network's state\, which every
reaction strictly decreases. This equivalence is proved using a variant o
f Farkas' Lemma and may be of independent interest.\n\n(joint work with Be
n Heckmann)\n
LOCATION:https://researchseminars.org/talk/MoRN/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erik Winfree (California Institute of Technology)
DTSTART:20240509T153000Z
DTEND:20240509T160000Z
DTSTAMP:20260421T094423Z
UID:MoRN/93
DESCRIPTION:Title: Ch
emical reaction networks and stochastic local search: satisfying homeostas
is and self-organization\nby Erik Winfree (California Institute of Tec
hnology) as part of Seminar on the Mathematics of Reaction Networks\n\n\nA
bstract\nWe discuss stochastic chemical reaction networks that do somethin
g when something is wrong\, and do nothing when all is right. Such network
s can solve NP-complete problems such as 3SAT and graph coloring\, sometim
es efficiently. This may be interpreted as a form of homeostasis that aim
s to preserve a set of combinatorial constraints. Moving from well-mixed
to surface-localized contexts reduces network size from polynomial in the
problem instance to constant size\, and suggests re-interpretation in term
s of self-organization instead of homeostasis.\n
LOCATION:https://researchseminars.org/talk/MoRN/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Minjoon Kim (POSTECH)
DTSTART:20240314T163000Z
DTEND:20240314T170000Z
DTSTAMP:20260421T094423Z
UID:MoRN/95
DESCRIPTION:Title: A
path method for non-exponential ergodicity of Markov chains and its applic
ation for chemical reaction systems\nby Minjoon Kim (POSTECH) as part
of Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nWe prese
nt criteria for non-exponential ergodicity of continuous-time Markov chain
s on a countable state space. These criteria can be verified by examining
the ratio of transition rates over certain paths. We applied this path met
hod to explore the non-exponential convergence of microscopic biochemical
interacting systems. Using reaction network descriptions\, we identified s
pecial architectures of biochemical systems for non-exponential ergodicity
. In essence\, we found that reactions forming a cycle in the reaction net
work can induce non-exponential ergodicity when they significantly dominat
e other reactions across infinitely many regions of the state space. Inter
estingly\, special architectures allowed us to construct many detailed bal
anced and complex balanced biochemical systems that are non-exponentially
ergodic. Some of these models are low-dimensional bimolecular systems with
few reactions. Thus this work suggests the possibility of discovering or
synthesizing stochastic systems arising in biochemistry that possess eithe
r detailed balancing or complex balancing and slowly\nconverges to their s
tationary distribution.\n
LOCATION:https://researchseminars.org/talk/MoRN/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Philippe Nghe (CNRS - ESPCI ParisTech)
DTSTART:20240411T150000Z
DTEND:20240411T153000Z
DTSTAMP:20260421T094423Z
UID:MoRN/96
DESCRIPTION:Title: Au
tocatalysis from stoichiometry toward experiments\nby Philippe Nghe (C
NRS - ESPCI ParisTech) as part of Seminar on the Mathematics of Reaction N
etworks\n\n\nAbstract\nMotivated by devising physical-chemical systems tha
t evolve\, we ended up examining the stoichiometric definition of autocata
lysis. We then identified minimal necessary stoichiometric motifs. Then\,
I will shortly present our current progress on kinetic criteria. Finally\,
I will highlight challenges to find experimental autocatalytic systems.\n
LOCATION:https://researchseminars.org/talk/MoRN/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jakob Lykke Andersen (University of Southern Denmark)
DTSTART:20240411T153000Z
DTEND:20240411T160000Z
DTSTAMP:20260421T094423Z
UID:MoRN/97
DESCRIPTION:Title: En
umeration of Autocatalytic Pathways\nby Jakob Lykke Andersen (Universi
ty of Southern Denmark) as part of Seminar on the Mathematics of Reaction
Networks\n\n\nAbstract\nGiven an arbitrary reaction network we are interes
ted in analysing its capabilities\, and in particular if it contains autoc
atalytic pathways. In this presentaion we see how pathways can be formally
modelled as integer hyperflows\, enabling their enumeration through integ
er linear programming (ILP). We then add necessary constraints for pathway
s to be autocatalytic. Finally we look at next steps in refining these con
straints.\n
LOCATION:https://researchseminars.org/talk/MoRN/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Muruhan Rathinam (University of Maryland\, Baltimore County)
DTSTART:20240523T153000Z
DTEND:20240523T160000Z
DTSTAMP:20260421T094423Z
UID:MoRN/98
DESCRIPTION:Title: St
ochastic Filtering of Partially Observed Reaction Networks\nby Muruhan
Rathinam (University of Maryland\, Baltimore County) as part of Seminar o
n the Mathematics of Reaction Networks\n\n\nAbstract\nWe describe recently
developed Sequential Monte Carlo methods for the computation of the condi
tional distribution of the state and/or parameters from the observations o
f the molecular copy numbers of a subset of the species either in continuo
us time or in discrete snapshots in time. In addition to presenting theore
tical justification\, we also provide numerical examples.\n\nThis is joint
work with Dr. Mingkai Yu (UMBC)\n
LOCATION:https://researchseminars.org/talk/MoRN/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David F. Anderson (University of Wisconsin - Madison)
DTSTART:20240425T153000Z
DTEND:20240425T160000Z
DTSTAMP:20260421T094423Z
UID:MoRN/99
DESCRIPTION:Title: Ch
emical mass-action systems as analog computers: implementing arithmetic c
omputations at specified speed\nby David F. Anderson (University of Wi
sconsin - Madison) as part of Seminar on the Mathematics of Reaction Netwo
rks\n\n\nAbstract\nRecent technological advances allow us to view chemical
mass-action systems as analog computers. In this context\, the inputs to
a computation are encoded as initial values of certain chemical species w
hile the outputs are the limiting values of other chemical species. The b
road goal of this nascent field is to develop systems that can operate in
the niche of a (wet) cellular environment\, rather than to directly compet
e with modern digital computers.\n\nThere have been numerous works that de
sign reaction networks that carry out basic arithmetic. However\, in gene
ral\, these constructions have speeds of computation (i.e.\, a rates of co
nvergence) that depend intimately upon the inputs to the computation itsel
f\, sometimes making them unusably slow. In this talk\, I will discuss ho
w we designed a full suite of “elementary” chemical systems that carry
out arithmetic computations (such as inversion\, addition\, roots\, mult
iplication\, rectified subtraction\, absolute difference\, etc.) over the
real numbers\, and that have speeds of computation that are independent of
the inputs to the computations. Moreover\, we proved that finite sequenc
es of such elementary modules\, running in parallel\, can carry out compos
ite arithmetic over real numbers\, also at a rate that is independent of i
nputs. I will close with a number of open questions and directions for fut
ure work.\n\nThis is all joint work with Badal Joshi\, and the relevant pa
per can be found here: https://arxiv.org/abs/2404.04396.\n
LOCATION:https://researchseminars.org/talk/MoRN/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Müller (University of Vienna)
DTSTART:20240425T150000Z
DTEND:20240425T153000Z
DTSTAMP:20260421T094423Z
UID:MoRN/100
DESCRIPTION:Title: F
rom reaction networks to "positive algebraic geometry" - and back\nby
Stefan Müller (University of Vienna) as part of Seminar on the Mathematic
s of Reaction Networks\n\n\nAbstract\nEvery power-law dynamical system (an
d hence every polynomial dynamical system) used in chemistry and biology (
for example\, in ecology and epidemiology) and even in economics and engin
eering can be written as a reaction network with (generalized) mass-action
kinetics. \n\nOver the last 10 years\, we have focused on positive equili
bria that are determined by the underlying graph (complex-balanced equilib
ria). As one highlight\, we have characterized unique existence (in every
invariant set and for all rate constants) using sign vectors of subspaces
arising from the stoichiometric coefficients and the kinetic orders.\n\nRe
cently\, we have turned to general equilibria\, and we study positive solu
tions to parametrized systems of generalized polynomial equations (with re
al exponents) in abstract terms. We identify the relevant geometric object
s of the problem\, namely the coefficient polytope and the monomial differ
ence and monomial dependency subspaces. As our main result\, we rewrite po
lynomial equations in terms of binomial equations (on the coefficient poly
tope). First applications concern real fewnomial and reaction network theo
ry.\n\n(Joint work with Georg Regensburger.)\n
LOCATION:https://researchseminars.org/talk/MoRN/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Philippe Robert (INRIA)
DTSTART:20240523T150000Z
DTEND:20240523T153000Z
DTSTAMP:20260421T094423Z
UID:MoRN/101
DESCRIPTION:Title: A
Stochastic Analysis of Particle Systems with Pairing\nby Philippe Rob
ert (INRIA) as part of Seminar on the Mathematics of Reaction Networks\n\n
\nAbstract\nMotivated by a general principle governing regulation mechanis
ms in biological cells\, we investigate a general interaction scheme betw
een different populations of particles and specific particles\, referred t
o as agents. Particles and agents may bind and form a pair which may have
some specific functional properties. A pair splits after some random amou
nt of time. In a stochastic context\, with a set of J different types of p
articles\, using a Markovian model for the vector of the number of paired
particles\, we study the asymptotic behavior of the time evolution of the
number of paired particles with the total number of particles used as a s
caling parameter. The analysis of the time evolution of this chemical rea
ction network is done via the proof of an averaging principle with three t
imescales. This is a joint work with Vincent Fromion and Jana Zaherddine.\
n
LOCATION:https://researchseminars.org/talk/MoRN/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tung D. Nguyen (University of California\, Los Angeles)
DTSTART:20241010T150000Z
DTEND:20241010T153000Z
DTSTAMP:20260421T094423Z
UID:MoRN/102
DESCRIPTION:Title: R
eaction network operations that double the steady-state capacity\nby T
ung D. Nguyen (University of California\, Los Angeles) as part of Seminar
on the Mathematics of Reaction Networks\n\n\nAbstract\nA great deal of rec
ent research has focused on proving that certain operations on reaction ne
tworks preserve dynamical properties of interest in applications. One such
property is the capability for multistationarity (multiple steady states)
. However\, little is known about how high the number of steady states can
increase after such an operation. Here we construct operations that\, und
er certain conditions\, double a network's steady-state capacity (the maxi
mum number of positive steady states). These operations typically introduc
e one new species and several new reactions.\n\nMoreover\, we establish su
fficient conditions for these operations to increase the number of stable
steady states. This allows for the possibility of turning a monostable (on
e stable steady state) network into a multistable (multiple stable steady
states) one. The operations can also be tuned to control the locations of
the new stable steady states\; in particular it is possible to create new
stable steady states near the location of unstable steady states in the ol
d system.\n\nA joint work with Badal Joshi\, Nidhi Kaihnsa and Anne Shiu.\
n
LOCATION:https://researchseminars.org/talk/MoRN/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ankit Gupta (ETH Zurich)
DTSTART:20241010T153000Z
DTEND:20241010T160000Z
DTSTAMP:20260421T094423Z
UID:MoRN/103
DESCRIPTION:Title: C
omplete characterization of kinetics-independent robust perfect adaptation
in biochemical reaction networks\nby Ankit Gupta (ETH Zurich) as part
of Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nBiologi
cal cells must precisely regulate the levels of key biomolecular species t
o survive and perform their functions. A specific form of this regulation
is Robust Perfect Adaptation (RPA)\, where certain species maintain certai
n levels despite external disturbances\, without the need to fine-tune the
system’s parameters. Although RPA has been extensively studied mathemat
ically\, identifying it in complex\, high-dimensional networks—along wit
h understanding the associated regulatory mechanisms—remains a significa
nt challenge.\n\nThis talk introduces a novel approach to identifying all
RPA properties that emerge independently of the network’s kinetics in ge
neral deterministic reaction networks. The approach demonstrates that each
RPA property corresponds to a subnetwork with specific topological charac
teristics. By leveraging this connection\, we show that these structures g
ive rise to all kinetics-independent RPA properties\, enabling the systema
tic identification of all these properties by enumerating such subnetworks
. Additionally\, we identify the integral feedback controllers responsible
for realizing each RPA property\, framing our findings within the control
-theoretic framework of the Internal Model Principle.\n\nThis is joint wor
k with Prof. Yuji Hirono (Osaka University) and Prof. Mustafa Khammash (ET
H Zürich)\n
LOCATION:https://researchseminars.org/talk/MoRN/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elisa Tonello (Freie Universität Berlin)
DTSTART:20241024T150000Z
DTEND:20241024T153000Z
DTSTAMP:20260421T094423Z
UID:MoRN/104
DESCRIPTION:Title: D
iscrete interaction networks: attractors and cycles\nby Elisa Tonello
(Freie Universität Berlin) as part of Seminar on the Mathematics of React
ion Networks\n\n\nAbstract\nIn a discrete interaction network\, species co
ncentrations are assumed to\ntake on a finite number of values. Interactio
n graphs encode the positive\nand negative influences between species\, an
d can be explored for insights\ninto the network’s dynamics. It is now w
ell-established that in asynchronous dynamics\, multistationarity is only
possible in the presence of positive interaction cycles\, while negative i
nteraction cycles are linked to cyclic attractors. However\, interaction g
raphs often contain many intertwined cycles\, raising the question: which
specific cycles are\nassociated with the network's long-term behavior? How
can we identify and locate them? In this talk\, we will provide an overvi
ew of some answers found in the literature\, as well as discuss new result
s and open problems.\n
LOCATION:https://researchseminars.org/talk/MoRN/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Atsushi Mochizuki (Kyoto University)
DTSTART:20241121T160000Z
DTEND:20241121T163000Z
DTSTAMP:20260421T094423Z
UID:MoRN/105
DESCRIPTION:Title: B
iological functions and functional modules originated in structure of chem
ical reaction network\nby Atsushi Mochizuki (Kyoto University) as part
of Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nIn livi
ng cells\, chemical reactions are connected by sharing their products and
substrates\, and form a complex network system. Biological functions arise
from the dynamics of chemical reaction networks\, and are regulated by ch
anges in the amount/activity of enzymes that catalyze reactions in the sys
tem. In this talk\, I will introduce our recent theoretical approach to de
termine the behaviors of chemical reaction systems caused by changes in th
e amount/activity of enzymes\, based solely on network topology. (1) We fo
und that the qualitative response of chemical concentrations (and reaction
fluxes) to changes in enzyme amount/activity can be determined from the n
etwork structure alone. (2) Non-zero responses are localized to finite ran
ges in a network\, and each range is determined by a subnetwork called a
“buffering structure”. The buffering structure is defined by the follo
wing equation from local topology of a network 𝜒≔−(# of chemicals)+
(# of reactions)−(# of cycles)+(# of conserved quantities)=0 where the i
ndex 𝜒 is analogous to the Euler characteristic. We proved that any per
turbation of a reaction parameter inside a buffering structure only affect
s the concentrations and fluxes inside the buffering structure\, and does
not affect the concentrations and fluxes outside. Finally\, (3) buffering
structures govern the bifurcation of the steady state of a reaction networ
k. The bifurcation behaviors are localized to finite regions within a netw
ork\, and these regions are again determined by buffering structures. Thes
e results imply that the buffering structures may be the origin of the mod
ularity of biological functions derived from reaction networks. We applied
this method to the cell cycle system and demonstrated that the regulation
of different checkpoints is achieved by buffering structures.\n\nReferenc
es\n\nMochizuki A. & Fiedler B. (2015) J. Theor. Biol. 367\, 189-202.\n\nO
kada T. & Mochizuki A. (2016) Phys. Rev. Lett. 117\, 048101\n\nOkada T. &
Mochizuki A. (2017) Phys. Rev. E 96\, 022322\n\nYamauchi\, Hishida\, Okada
\, Mochizuki (2024) Phys. Rev. Research 6\, 023150\n\nYamauchi\, et al. (I
n preparation)\n
LOCATION:https://researchseminars.org/talk/MoRN/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wasiur Khuda Bukhsh (University of Nottingham\, UK)
DTSTART:20241107T160000Z
DTEND:20241107T173000Z
DTSTAMP:20260421T094423Z
UID:MoRN/106
DESCRIPTION:Title: E
nzyme kinetic reactions as interacting particle systems: Stochastic averag
ing and parameter inference\nby Wasiur Khuda Bukhsh (University of Not
tingham\, UK) as part of Seminar on the Mathematics of Reaction Networks\n
\n\nAbstract\nIn this talk\, I will consider a stochastic model of multist
age Michaelis--Menten (MM) type enzyme kinetic reactions describing the co
nversion of substrate molecules to a product through several intermediate
species. The high-dimensional\, multiscale nature of these reaction networ
ks presents significant computational challenges\, especially in statistic
al estimation of reaction rates. This difficulty is amplified when direct
data on system states are unavailable\, and one only has access to a rando
m sample of product formation times. To address this\, we proceed in two s
tages. First\, under certain technical assumptions akin to those made in t
he Quasi-steady-state approximation (QSSA) literature\, we prove a stochas
tic averaging principle that yields a lower-dimensional model. Next\, for
statistical inference of the parameters of the original MM reaction networ
k\, we develop a mathematical framework involving an interacting particle
system (IPS) and prove a propagation of chaos result that allows us to wri
te a product-form likelihood function. The novelty of the IPS-based infere
nce method is that it does not require information about the state of the
system and works with only a random sample of product formation times. We
provide numerical examples to illustrate the efficacy of the theoretical r
esults. Preprint: https://arxiv.org/abs/2409.06565\n
LOCATION:https://researchseminars.org/talk/MoRN/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enrico Bibbona (Politecnico di Torino)
DTSTART:20241024T153000Z
DTEND:20241024T160000Z
DTSTAMP:20260421T094423Z
UID:MoRN/107
DESCRIPTION:Title: N
ew deterministic scaling limits of models of nanoparticle growth\nby E
nrico Bibbona (Politecnico di Torino) as part of Seminar on the Mathematic
s of Reaction Networks\n\n\nAbstract\nWe consider the following nanopartic
le growth model\, where the species $M$\nrepresents monomers\, and $P_i$ a
re nanoparticles of size $i$:\n\\[ \n \\left\\{ \n \\begin{array}{l}\
n mM \\xrightarrow{\\nu N^{1-m}} P_m\, \\\\\n M + P_i \\xr
ightarrow{\\nu N^\\theta} P_{i+1}\, \\quad i \\in \\{1\,\\ldots\, N\\}\n
\\end{array}\n \\right.\n\\]\n$M(0) = N$\, $P_i(0) = 0$ for all $i$. W
e demonstrate that the proportion of particles\, at time $N^αt$\, with a
size within the interval $N^{1−β} [a\, b]$ (for any positive $a$\,\n$b$
)\, approaches a deterministic limit for large $N$. This is subject to the
scaling\nconditions $\\theta + \\alpha + \\beta = 0$ and $1 + \\alpha = \
\beta$. We fully characterize such a scaled size distribution and establis
h its satisfaction\, in terms of Schwartz distributions\, of the Lifshitz-
Slyozov transport partial differential equation (PDE). We remark\nthat the
special case $\\beta = 1$ (which implies $\\alpha = −1$ and $\\theta =
0$) is the so-called classical scaling. In this case the convergence of th
e stochastic model to an infinite system of ODEs\, named after Becker and
Döring\, is a classical result\, see e.g.\n[3]. Moreover\, after a furthe
r coarsening step\, the ODE model was shown to be\nwell approximated by th
e solution of the above mentioned PDE [2\,5]. We show\nin a single step ho
w this PDE solution limit arise directly from the stochastic\nmodel\, both
under the classical scaling and in a wider range of scalings. To\nprove t
he result we use a the framework originally developed for epidemic models
in [1]. Preliminary results based on simulations alone are available at [4
]. This is joint work with Daniele Cappelletti\, Anderson Melchor Hernande
z\, Gabor Lente\, Elena Sabbioni\, Paola Siri\, and Rebeka Szabo.\n\n[1] D
. Cappelletti and G. A. Rempala\, Individual molecules dynamics in reactio
n\nnetwork models\, SIAM Journal on Applied Dynamical Systems\, 22 (2023)\
, pp.\n1344– 1382.\n\n[2] E. Hingant and R. Yvinec\, Deterministic and s
tochastic Becker-Döring equations: Past and recent mathematical developme
nts\, in Stochastic Processes\,\nMultiscale Modeling\, and Numerical Metho
ds for Computational Cellular Biology\, Springer International Publishing\
, 2017\, pp. 175–204.\n\n[3] I. Jeon\, Existence of gelling solutions fo
r coagulation-fragmentation equations\, Communications in Mathematical Phy
sics\, 194 (1998)\, pp. 541–567.\n\n[4] E. Sabbioni\, R. Szabó\, P. Sir
i\, D. Cappelletti\, G. Lente\, and E. Bibbona\,\nFinal nanoparticle size
distribution under unusual parameter regimes. ChemRxiv. 2024.\n\n[5] A. Va
sseur\, F. Poupaud\, J.-F. Collet\, and T. Goudon\, The Becker-D¨oring\ns
ystem and its Lifshitz–Slyozov limit\, SIAM Journal on Applied Mathemati
cs\,\n62 (2002)\, pp. 1488– 1500.\n
LOCATION:https://researchseminars.org/talk/MoRN/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomislav Plesa (University of Cambridge)
DTSTART:20241107T163000Z
DTEND:20241107T170000Z
DTSTAMP:20260421T094423Z
UID:MoRN/108
DESCRIPTION:Title: M
apping dynamical systems into chemical reactions\nby Tomislav Plesa (U
niversity of Cambridge) as part of Seminar on the Mathematics of Reaction
Networks\n\n\nAbstract\nPolynomial dynamical systems are used to model a w
ide range of physical processes. \nA subset of these dynamical systems tha
t can model chemical reactions under mass-action kinetics are called chemi
cal systems. A central problem in synthetic biology is to map general poly
nomial dynamical systems into dynamically similar chemical ones. In this
talk\, I will present a novel map\, called the quasi-chemical map\, that c
an systematically solve this problem. The quasi-chemical map introduces su
itable state-dependent perturbations into any\ngiven polynomial dynamical
system which then becomes chemical under sufficiently large translation of
variables. This map preserves robust dynamical features\, such as generic
equilibria and limit cycles\, as well as temporal properties\, such as pe
riods of oscillations. Furthermore\, the resulting chemical systems are at
most one degree higher than the original\ndynamical systems. I will demon
strate the quasi-chemical map by designing relatively simple chemical syst
ems with exotic dynamics and predefined bifurcations.\n
LOCATION:https://researchseminars.org/talk/MoRN/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jinsu Kim (POSTECH)
DTSTART:20241121T163000Z
DTEND:20241121T170000Z
DTSTAMP:20260421T094423Z
UID:MoRN/109
DESCRIPTION:Title: N
ew path methods for addressing the boundary issues in stochastically model
ed reaction networks\nby Jinsu Kim (POSTECH) as part of Seminar on the
Mathematics of Reaction Networks\n\n\nAbstract\nFoster-Lyapunov criterion
is a popular approach for studying the ergodicity of Markov chains. To ve
rify this criterion\, we examine the infinitesimal behavior of a Markov ch
ain\, specifically up to the first jump from the initial state. However\,
this approach often faces limitations when the dominant jump (usually at t
he boundaries of the state space) is not in a preferred direction. In this
talk\, we introduce two new path methods to address this limitation. Spec
ifically\, we use the probability of a Markov chain following certain path
s to study its (exponential) ergodicity. Using these path methods\, we dem
onstrate how we identified a class of chemical reaction networks whose ass
ociated Markov chains are (exponentially) ergodic.\n
LOCATION:https://researchseminars.org/talk/MoRN/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Polly Yu (University of Illinois Urbana-Champaign)
DTSTART:20241212T163000Z
DTEND:20241212T170000Z
DTSTAMP:20260421T094423Z
UID:MoRN/110
DESCRIPTION:Title: N
ecessary conditions for non-monotonic steady state response\nby Polly
Yu (University of Illinois Urbana-Champaign) as part of Seminar on the Mat
hematics of Reaction Networks\n\n\nAbstract\nNon-monotonic (or "biphasic")
dose responses are often observed in experimental biology\, which raises
the question of which network motifs might underlie such behaviours. It is
well known that the presence of an incoherent feedforward loop (IFFL) may
give rise to a non-monotonic response\, and it has been informally conjec
tured that this condition is also necessary. We disprove this conjecture w
ith an example. Moreover\, we show that a version of the conjecture does h
old. Towards this aim\, we consider several related notions (infinitesimal
homeostasis\, biphasic response\, and stable biphasic response) and their
underlying network motifs.\n
LOCATION:https://researchseminars.org/talk/MoRN/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ellen Baake (Bielefeld University)
DTSTART:20241212T160000Z
DTEND:20241212T173000Z
DTSTAMP:20260421T094423Z
UID:MoRN/111
DESCRIPTION:Title: G
enetic recombination\, stochastic reaction systems\, and moment closure\nby Ellen Baake (Bielefeld University) as part of Seminar on the Mathema
tics of Reaction Networks\n\n\nAbstract\nWe consider the dynamics of reco
mbination between genetic sequences in a finite population. This nonlinear
system is equivalent to a stochastic reaction network and\, surprisingly\
, it has the property of moment closure. More precisely\, the expectations
of products of frequencies of subsequences follow a closed system of diff
erential equations\, as long as the subsequences do not overlap. We discus
s extensions of the model under which moment closure is conserved or destr
oyed\, and would like to discuss these observations in the context of mome
nt closure in reaction systems.\n
LOCATION:https://researchseminars.org/talk/MoRN/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Badal Joshi (California State University San Marcos)
DTSTART:20250213T160000Z
DTEND:20250213T163000Z
DTSTAMP:20260421T094423Z
UID:MoRN/112
DESCRIPTION:Title: B
ifunctional enzyme action as a source of robustness in biochemical reactio
n networks: a novel hypergraph approach\nby Badal Joshi (California St
ate University San Marcos) as part of Seminar on the Mathematics of Reacti
on Networks\n\n\nAbstract\nSubstrate modification networks are ubiquitous
in living\, biochemical systems. We use a directed hypergraph\, a generali
zation of a directed graph where a directed edge connects a nonempty set o
f nodes to another nonempty set of nodes\, to model the substrate modifica
tions. This substrate ''skeleton'' portrays information about changes to t
he substrates while not showing the detailed reaction steps\, the identity
of enzymes or that of substrate-enzyme compounds. One skeleton can underl
ie multiple different detailed models and reaction mechanisms. We show tha
t certain dynamical properties\, such as the existence of positive steady
states or presence of concentration robustness can be inferred directly fr
om the substrate skeleton. Concentration robustness is the property where
the concentration of one species or a positive-integer linear combination
of species is invariant across all positive steady states. We introduce th
e notion of ''current'' on a directed hypergraph\, which is one of the two
crucial ingredients along with bifunctional enzyme action required to pro
duce concentration robustness. This approach is a departure from previous
deficiency based results as it applies to arbitrary substrate modification
networks. This is joint work with Tung Nguyen.\n
LOCATION:https://researchseminars.org/talk/MoRN/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Grzegorz A. Rempala (The Ohio State University)
DTSTART:20250213T163000Z
DTEND:20250213T170000Z
DTSTAMP:20260421T094423Z
UID:MoRN/113
DESCRIPTION:Title: L
ikelihood Functions for Individual-Level Chemical Reaction Models\nby
Grzegorz A. Rempala (The Ohio State University) as part of Seminar on the
Mathematics of Reaction Networks\n\n\nAbstract\nWhen analyzing chemical re
action systems\, it is often useful to consider the fate of individual mol
ecules. For such systems\, one can construct an individual-level likelihoo
d function—a statistical tool that evaluates how well a specific paramet
ric reaction model fits empirical data. These likelihood functions are typ
ically applied in the context of time series data representing realization
s of reaction network trajectories. In this talk\, I will introduce the co
ncept\, discuss its essential applications\, and explore useful approximat
ions\, particularly in the setting of mass-transfer models. A key example
will be the stochastic SIR network model\, though similar constructions ca
n be applied to enzyme kinetics and other reaction systems.\n
LOCATION:https://researchseminars.org/talk/MoRN/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abhishek Despande (International Institute of Information Technolo
gy\, Hyderabad)
DTSTART:20250410T153000Z
DTEND:20250410T160000Z
DTSTAMP:20260421T094423Z
UID:MoRN/115
DESCRIPTION:Title: D
isguised toric locus of a reaction network\nby Abhishek Despande (Inte
rnational Institute of Information Technology\, Hyderabad) as part of Semi
nar on the Mathematics of Reaction Networks\n\n\nAbstract\nUnder mass-acti
on kinetics\, complex-balanced systems emerge from biochemical reaction ne
tworks and exhibit stable and predictable dynamics. For a reaction network
G\, the associated dynamical system is called disguised toric if it can y
ield a complex- balanced realization on a possibly different network G1. T
his concept extends the robust properties of toric systems to those that a
re not inherently toric. In this work\, we study the disguised toric locus
of a reaction network — i.e.\, the set of positive rate constants that
make the corresponding mass-action system disguised toric. Our primary foc
us is to compute the exact dimension of this locus. We subsequently apply
our results to Thomas-type and circadian clock models.\n
LOCATION:https://researchseminars.org/talk/MoRN/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Takashi Okada (Kyoto University)
DTSTART:20250313T160000Z
DTEND:20250313T163000Z
DTSTAMP:20260421T094423Z
UID:MoRN/116
DESCRIPTION:Title: S
tructural Bifurcation Analysis of Chemical Reaction Networks\nby Takas
hi Okada (Kyoto University) as part of Seminar on the Mathematics of React
ion Networks\n\n\nAbstract\nThis talk is part of a series on the structura
l analysis of chemical reaction networks. In the first talk presented by P
rof. Mochizuki\, we introduced special subnetworks known as buffering stru
ctures (BSs)\, defined by specific topological conditions. A BS has the pr
operty of confining the effect of a parameter perturbation on steady-state
concentrations and fluxes within it. In this talk\, we present another ro
le of BSs\, namely\, confinement of steady-state bifurcation behaviors. Sp
ecifically\, when a bifurcation occurs\, there must be a particular subnet
work that destabilizes the system. It can be shown that such a subnetwork
must be either a BS or the complement of a BS. Furthermore\, depending on
which part of the network destabilizes\, we can identify which parameters
can trigger the bifurcation and which part of the network exhibits bifurca
ting behavior. Our results are based on the network’s structural propert
ies and suggest that certain biological functions may emerge as a direct c
onsequence of network topology.\n
LOCATION:https://researchseminars.org/talk/MoRN/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Florin Avram (Universite de Pau)
DTSTART:20250227T160000Z
DTEND:20250227T163000Z
DTSTAMP:20260421T094423Z
UID:MoRN/117
DESCRIPTION:Title: O
n synergies between mathematical epidemiology(ME)/ecology\, and chemical r
eaction network theory (CRNT)\, and some open questions\nby Florin Avr
am (Universite de Pau) as part of Seminar on the Mathematics of Reaction N
etworks\n\n\nAbstract\nMathematical epidemiology (ME) is both a domain of
great practical interest\, and a huge collection of open problems\, which
are of potential interest to all the mathematical community. A few of thes
e have been tackled in the recent papers of Avram\, Adenane\, Halanay\, Jo
hnston and Vassena [VAA24\, AAN24\, AAHJ]\, using CRN methods like the inh
eritance of bifurcations\, etc\, which were previously unknown in ME.\n\nI
n this paper we further explore the challenging question of finding Lyapun
ov functions for quadratic ME models. The question has already been touche
d upon\, under models governed by matrices with various structures in ME (
multi-group\, multi-patch\, multi-vector and meta-population models)\, eco
logy\, and CRNT\, and it was often found that a Lotka-Volterra type functi
on may be found\, whose coefficients are the left eigenvector of some matr
ix. Our goal is to unify the previous works\, under a general ”eco-epide
miological” SIR-PH model introduced in Avram & al [AAB+23]\, and in part
icular to find conditions which guarantee two remarkable phenomena occurri
ng sometimes in ME/ecology problems:\n\n1. The ”strong (global stability
) threshold property” (STP)\, which ensures the uniqueness of a fixed in
terior point\, and the fact that it is globally stable whenever it exist\,
seems to have originated in ME and ecology Lajmanovich\, Yorke\, Beretta\
, Capasso\, Li and Shuai [LY76\, BC86\, SvdD13].\n\n2. The competitive exc
lusion principle (CEP) – see for example Iggidr\, Kamgang\, Sallet\, Tew
a\,\nBichara\, Souza [IKST06]\, which may be viewed as an extension of the
STP\, to the case when\nseveral boundary points exist.\n
LOCATION:https://researchseminars.org/talk/MoRN/117/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alon Duvall (Northeastern University)
DTSTART:20250227T163000Z
DTEND:20250227T170000Z
DTSTAMP:20260421T094423Z
UID:MoRN/118
DESCRIPTION:Title: I
nterplay between Contractivity and Monotonicity for Reaction Networks\
nby Alon Duvall (Northeastern University) as part of Seminar on the Mathem
atics of Reaction Networks\n\n\nAbstract\nThis work studies relationships
between monotonicity and contractivity\, and applies the results to establ
ish that many reaction networks are weakly contractive\, and thus\, under
appropriate compactness conditions\, globally convergent to equilibria. Ve
rification of these properties is achieved through a novel algorithm that
can be used to generate cones for monotone systems. The results given here
allow a unified proof of global convergence for several classes of networ
ks that had been previously studied in the literature.\n
LOCATION:https://researchseminars.org/talk/MoRN/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlos Floyd (University of Chicago)
DTSTART:20250313T163000Z
DTEND:20250313T170000Z
DTSTAMP:20260421T094423Z
UID:MoRN/119
DESCRIPTION:Title: L
imits on the computational expressivity of non-equilibrium biophysical pro
cesses\nby Carlos Floyd (University of Chicago) as part of Seminar on
the Mathematics of Reaction Networks\n\n\nAbstract\nMany biological decisi
on-making processes can be viewed as performing a classification task over
a set of inputs\, using various chemical and physical processes as "biolo
gical hardware." In this context\, it is important to understand the inher
ent limitations on the computational expressivity of classification functi
ons instantiated in biophysical media. Here\, we model biochemical network
s as Markov jump processes and train them to perform classification tasks\
, allowing us to investigate their computational expressivity. We reveal s
everal unanticipated limitations on the input-output functions of these sy
stems\, which we further show can be lifted using biochemical mechanisms l
ike promiscuous binding. We analyze the flexibility and sharpness of decis
ion boundaries as well as the classification capacity of these networks. A
dditionally\, we identify distinctive signatures of networks trained for c
lassification\, including the emergence of correlated subsets of spanning
trees and a creased "energy landscape" with multiple basins. Our findings
have implications for understanding and designing physical computing syste
ms in both biological and synthetic chemical settings.\n\nThis is joint wo
rk with Suri Vaikuntanathan\, Arvind Murugan\, and Aaron Dinner (https://a
rxiv.org/abs/2409.05827).\n
LOCATION:https://researchseminars.org/talk/MoRN/119/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Software Showcases
DTSTART:20250424T150000Z
DTEND:20250424T163000Z
DTSTAMP:20260421T094423Z
UID:MoRN/120
DESCRIPTION:Title: S
everal software packages relevant for reaction networks analyses\nby S
oftware Showcases as part of Seminar on the Mathematics of Reaction Networ
ks\n\n\nAbstract\nThis week's seminar will take a different format. Four d
ifferent groups will be introducing their software packages that are relev
ant for reaction networks. This will be followed by breakout rooms to lear
n more about these packages.\n\nSpeakers:\n\n$\\color{blue}\\underline{\\t
extbf{1. Herbert Sauro (University of Washington) -- Tellurium}}$\n\n$\\te
xtbf{Keywords:}$ Simulation\, SBML\, High Performance\, reusable library\n
\n$\\textbf{Website:}$ \nhttps://tellurium.analogmachine.org/\, \nhttps:/
/tellurium.readthedocs.io/en/latest/index.html\n\n$\\textbf{Recording:}$ h
ttps://youtu.be/yzVOZlQwM74 \n\n$\\color{blue}\\underline{\\textbf{2. Tork
el Loman (University of Oxford)\; Vincent Du (UNC Chapel Hill) -- Catalyst
}}$\n\n$\\textbf{Keywords:}$ Chemical reaction networks\, ODE Simulations\
, Stochastic simulations\, Network analysis\n\n$\\textbf{Website:}$ https:
//github.com/SciML/Catalyst.jl\n\n$\\textbf{Recording:}$ https://youtu.be/
h9zUQWoyWo0\n\n$\\color{blue}\\underline{\\textbf{3. Marcus Aichmayr (Univ
ersity of Kassel) -- Sign Vector Conditions}}$\n\n$\\textbf{Keywords:}$ ch
emical-reaction-networks\, generalized mass-action systems\, deficiency ze
ro theorem\, robustness\, sign vectors\, SageMath\n\n$\\textbf{Website:}$
\nhttps://github.com/MarcusAichmayr/sign_vector_conditions\n\n$\\textbf{Re
cording:}$ https://youtu.be/H_bYwr1KEi0\n\n\n$\\color{blue}\\underline{\\t
extbf{4. Janos Toth (Budapest University of Technology and Economics) -- R
eactionKinetics.wl}}$\n\n$\\textbf{Keywords:}$ From Exact Stochastic Simu
lation to Qualitative and Structural Analysis of Reactions\, a Wolfram Lan
guage (Mathematica) package\,\nTÓTH\, J.\; NAGY\, A. L.\; PAPP\, D.\, Spr
inger\, 2018.\n\n$\\textbf{Recording:}$ https://youtu.be/8j_7G_tJsb0\n
LOCATION:https://researchseminars.org/talk/MoRN/120/
END:VEVENT
BEGIN:VEVENT
SUMMARY:AmirHosein Sadeghimanesh (Coventry University)
DTSTART:20250410T150000Z
DTEND:20250410T153000Z
DTSTAMP:20260421T094423Z
UID:MoRN/121
DESCRIPTION:Title: D
esigning Machine Learning Tools to Characterize Multistationarity of Fully
Open Reaction Networks\nby AmirHosein Sadeghimanesh (Coventry Univers
ity) as part of Seminar on the Mathematics of Reaction Networks\n\n\nAbstr
act\nChemical Reaction Networks (CRNs) are the mathematical formulation of
how the quantities associated to a set of species (molecules\, proteins\,
cells\, or animals) vary as time passes with respect to their interaction
s with each other. Their mathematics does not describe just chemical react
ions but many other areas of the life sciences such as ecology\, epidemiol
ogy\, and population dynamics. We say a CRN is at a steady state when the
concentration (or number) of species do not vary anymore. Some CRNs do not
attain a steady state while some others may have more than one possible s
teady state. The CRNs in the later group are called multistationary. Multi
stationarity is an important property\, e.g. switch-like behaviour in cell
s needs multistationarity to occur. Existing algorithms to detect whether
a CRN is multistationary or not are either extremely expensive or restrict
ed in the type of CRNs they can be used on\, motivating a new machine lear
ning approach. This talk is about a recent attempt to design machine learn
ing tools to predict multistationarity of reaction networks.\n
LOCATION:https://researchseminars.org/talk/MoRN/121/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Theodore Grunberg
DTSTART:20250508T150000Z
DTEND:20250508T153000Z
DTSTAMP:20260421T094423Z
UID:MoRN/122
DESCRIPTION:Title: E
rror bounds for the linear noise approximation to stationary distributions
of chemical reaction networks\nby Theodore Grunberg as part of Semina
r on the Mathematics of Reaction Networks\n\n\nAbstract\nSpecies interacti
ng according to chemical reactions are often modeled by a continuous time
Markov chain that describes the evolution of counts of the species over ti
me. Such Markov chains typically have a large or infinite number of states
and are thus computationally difficult to analyze. Therefore\, approximat
ions exploiting the fact that the volume and molecular counts are both lar
ge are often used. The most common such approximations are the reaction ra
te equations (RREs)\, which are a deterministic model\, and the linear noi
se approximation (LNA)\, which is a diffusion approximation to fluctuation
s about the solution of the RREs. Limit theorem results\, due to Kurtz (19
71)\, establish the validity of the RREs and of the LNA for finite times.
However\, such results do not justify approximating the stationary distrib
ution of a chemical reaction network using the RREs or LNA. The validity o
f these approximations for the stationary distribution has only been inves
tigated for special cases\, such as when the Markov chain’s state space
is bounded in concentration\, or when the chemical reaction network has a
special structure. Here\, we use Stein’s method to derive bounds on the
approximation error for the LNA applied to the stationary distribution of
a chemical reaction network. Specifically\, we give a non-asymptotic bound
on the 1-Wasserstein distance between an appropriately scaled Markov chai
n and its LNA\, under certain technical conditions\, that decays to zero w
ith increasing system size. Our results do not require that the Markov ch
ain’s state space be bounded\, nor do they require that the chemical rea
ction network have a special structure. We further show how global stabili
ty properties of an equilibrium point of the RREs are sufficient to obtain
such error bounds. Our results can be used to check when the LNA is a sui
table approximation of the stationary distribution of a chemical reaction
network without having to perform computationally costly simulations.\n
LOCATION:https://researchseminars.org/talk/MoRN/122/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jakob Ruess (INRIA)
DTSTART:20250508T153000Z
DTEND:20250508T160000Z
DTSTAMP:20260421T094423Z
UID:MoRN/123
DESCRIPTION:Title: F
rom single cells to microbial consortia and back: stochastic chemical kine
tics coupled to population dynamics\nby Jakob Ruess (INRIA) as part of
Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nAt the sin
gle-cell level\, biochemical processes are inherently stochastic. Such pro
cesses are typically studied using models based on stochastic chemical kin
etics\, governed by a chemical master equation (CME). The CME describes th
e time evolution of the probability distribution over system states and ha
s been a tremendously helpful tool in shedding light on the functioning of
cellular processes. However\, single cells are not living in isolation bu
t are part of a growing population or community. In such contexts\, stocha
sticity at the single-cell scale leads to population heterogeneity and cel
ls may be subject to population processes\, such as selection\, that drive
the population distribution away from the probability distribution of the
single-cell process.\n\nHere\, I will introduce a multi-scale modeling fr
amework that allows one to capture coupled stochastic single-cell and popu
lation process. I will show that the expected population distribution of s
uch multi-scale models can be calculated by solving a modified version of
the CME that is of the same dimensionality as the standard CME. I will the
n show how such models can be used to explain experimental data on plasmid
copy number fluctuations and population growth in media that selects agai
nst cells that have lost the plasmid. Finally\, I will present an optogene
tic recombination system that allows one to partition yeast populations in
to different cell types via external application of blue light to cells an
d show how our modeling framework can be used to predict and control emerg
ing dynamics of the population composition in response to time-varying lig
ht stimuli.\n
LOCATION:https://researchseminars.org/talk/MoRN/123/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Johnston (Lawrence Technological University)
DTSTART:20251009T150000Z
DTEND:20251009T153000Z
DTSTAMP:20260421T094423Z
UID:MoRN/124
DESCRIPTION:Title: E
xtending the Basic Reproduction Number to Biochemical Reaction Networks\nby Matthew Johnston (Lawrence Technological University) as part of Semi
nar on the Mathematics of Reaction Networks\n\n\nAbstract\nWe extend the n
ext generation matrix method for computing the basic reproduction number i
n mathematical epidemiology to computing an analogous number for establish
ing the stability of boundary faces in biochemistry. In epidemiology\, the
basic reproduction number indicates whether a disease can invade a popula
tion\, with values below one leading to disease-free stability and values
above one signaling an outbreak. In biochemistry\, the number determines w
hether certain chemical species persist or go extinct\, with values greate
r than one leading to persistence. The next generation matrix method appro
ach is typically significantly more computationally tractable than standar
d Jacobian or Routh-Hurwitz methods for establishing stability\; consequen
tly\, the method could have significant applications for understanding met
abolic function.\n
LOCATION:https://researchseminars.org/talk/MoRN/124/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carles Checa Nualart (University of Copenhagen)
DTSTART:20251106T160000Z
DTEND:20251106T163000Z
DTSTAMP:20260421T094423Z
UID:MoRN/126
DESCRIPTION:Title: A
n effective criterion for multiple positive solutions of vertical systems<
/a>\nby Carles Checa Nualart (University of Copenhagen) as part of Seminar
on the Mathematics of Reaction Networks\n\n\nAbstract\nWe present a crite
rion for determining when a vertically parametrized polynomial system admi
ts multiple positive zeros for some parameter values. Our approach is base
d on the higher deficiency algorithms from chemical reaction network theor
y. Under certain assumptions\, these algorithms reduce the problem to chec
king the feasibility of a linear system of equalities and inequalities (po
lyhedral cones). Our criterion requires that the linear part of the system
(stoichiometric matrix) has a row reduction whose underlying graph is a f
orest\, implying a highly structured pattern of zeros\, which is often rea
lized in steady state varieties. Using the same polyhedral cones\, we also
provide sufficient conditions to derive connectivity of the parameter reg
ion yielding multiple positive solutions and to guarantee the existence of
a pair of distinct nondegenerate positive zeros. This is joint work with
Elisenda Feliu.\n
LOCATION:https://researchseminars.org/talk/MoRN/126/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sabina J Haque (University of Michigan)
DTSTART:20251120T160000Z
DTEND:20251120T163000Z
DTSTAMP:20260421T094423Z
UID:MoRN/127
DESCRIPTION:Title: G
raph-theoretic and algebraic geometric approaches to biochemical reaction
networks\nby Sabina J Haque (University of Michigan) as part of Semina
r on the Mathematics of Reaction Networks\n\n\nAbstract\nUnder mass-action
kinetics\, systems of biochemical reactions are modeled by chemical react
ion networks (CRNs)\, a class of graphs that gives rise to polynomial dyna
mical systems. Approaches in this field include chemical reaction network
theory and the more recent linear framework. In this talk\, I will focus p
rimarily on the linear framework\, a graph-theoretic approach to timescale
separation in biochemical systems. I will discuss a graph-theoretic const
ruction within the framework that mimics what would happen if a single par
ameter in a graph is taken to infinity\, producing what we call an asympto
tic graph. I consider how properties of the asymptotic graph\, such as its
steady states\, serve as an appropriate representation for a linear frame
work graph in this limit. Time permitting\, I also speculate on some exten
sions of this construction beyond the scope of the linear framework to par
ameter identifiability and the steady state varieties of CRNs\, suggesting
areas for future work at the intersection of graph theory\, algebraic geo
metry\, and dynamical systems.\n
LOCATION:https://researchseminars.org/talk/MoRN/127/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marc Roussel (University of Lethbridge)
DTSTART:20251204T160000Z
DTEND:20251204T163000Z
DTSTAMP:20260421T094423Z
UID:MoRN/128
DESCRIPTION:Title: E
very qualitative stability analysis method implies model reduction procedu
res\nby Marc Roussel (University of Lethbridge) as part of Seminar on
the Mathematics of Reaction Networks\n\n\nAbstract\nA qualitative stabilit
y analysis method will typically give us necessary\,\nand sometimes suffic
ient\, conditions for a dynamical system to display\nparticular behaviors
such as oscillations\, multistability or patterning.\nOnce we have identif
ied how a network satisfies those conditions\, we can\nsimplify a model by
eliminating components that do not contribute to the\nbehavior. In the co
ntext of chemical reaction networks\, this might mean\neliminating chemica
l species\, often by combining reactions. I will\nillustrate this idea usi
ng the Ivanova criterion for multistability and a\nmodel for the control o
f Hmp\, an NO detoxifying enzyme\, in Streptomyces\ncoelicolor.\n
LOCATION:https://researchseminars.org/talk/MoRN/128/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jingyi Ma (University of Wisconsin–Madison)
DTSTART:20251023T153000Z
DTEND:20251023T160000Z
DTSTAMP:20260421T094423Z
UID:MoRN/129
DESCRIPTION:Title: M
athematical Analysis for a Class of Stochastic Copolymerization Processes<
/a>\nby Jingyi Ma (University of Wisconsin–Madison) as part of Seminar o
n the Mathematics of Reaction Networks\n\n\nAbstract\nIn this talk\, I wan
t to present a rigorous mathematical framework for analyzing a class of st
ochastic copolymerization processes\, where finitely many types of monomer
s attach and detach at the tip of a polymer chain. These dynamics are mode
led as a continuous-time Markov chain on an infinite tree-like state space
. The sharp criteria for transience\, null recurrence\, and positive recu
rrence in terms of the attachment and detachment rates will be established
. In the transient regime\, explicit formulas for the almost sure asymptot
ic composition of the polymer and its growth velocity are provided. We exp
ect that the mathematical methods used and developed will also enable the
study of even more complex models in the future.\n
LOCATION:https://researchseminars.org/talk/MoRN/129/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Müller (University of Vienna)
DTSTART:20251023T150000Z
DTEND:20251023T153000Z
DTSTAMP:20260421T094423Z
UID:MoRN/130
DESCRIPTION:Title: E
xistence\, uniqueness\, and stability of equilibria in (generalized) mass-
action systems\nby Stefan Müller (University of Vienna) as part of Se
minar on the Mathematics of Reaction Networks\n\n\nAbstract\nWe report on
several recent results for reaction networks with (generalized) mass-actio
n kinetics\, short (G)MAK.\n\n1. In the setting of MAK\, complex-balanced
equilibria are asymptotically stable. We further clarify the binomial stru
cture of mass-action systems\, and extend the stability result to 'binomia
l differential inclusions'\, a very general class of dynamical systems.\n\
n2. For GMAK\, complex-balanced equilibria need not be stable. We provide
sufficient (sign) conditions for linear stability.\n\nFor both results\, w
e use a new decomposition of the graph Laplacian and monomial evaluation o
rders (inducing 'banana' regions or 'wedges' in log coordinates).\n\nFor t
wo more results\, we use our new framework for parametrized systems of gen
eralized polynomial equations\, which covers equilibria of reaction networ
ks with (G)MAK.\n\n3. In full generality\, we characterize the unique exis
tence of solutions for all parameters. As a sufficient condition\, we prov
ide a 'genuine' multivariate Descartes rule of signs.\n\n4. For MAK\, we e
xtend the deficiency one theorem (from deficiency one to *dependency* one
and from single to multiple terminal linkage classes).\n\nThis is joint wo
rk with Georg Regensburger and Abhishek Deshpande.\n
LOCATION:https://researchseminars.org/talk/MoRN/130/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicola Vassena (Leipzig University)
DTSTART:20251009T153000Z
DTEND:20251009T160000Z
DTSTAMP:20260421T094423Z
UID:MoRN/131
DESCRIPTION:Title: I
nstability and Oscillations in Reaction Networks\nby Nicola Vassena (L
eipzig University) as part of Seminar on the Mathematics of Reaction Netwo
rks\n\n\nAbstract\nIn the past two decades\, much mathematical research on
reaction \nnetworks has focused on multistationarity\, both under mass-ac
tion and \nmore general kinetics. Multistationarity typically arises in pa
rameter \nspace when a stable steady state loses stability through a real-
zero \neigenvalue crossing. More recently\, attention has turned also to \
nstability loss via purely imaginary eigenvalues (Hopf bifurcation)\, \nwh
ich is associated with periodic oscillations.\n\nIn this talk\, based on e
stablished results from dynamical systems \ntheory developed in late 1970s
and 1980s\, I will first clarify that \nfor monostationary networks\, in
essence\, any loss of stability \nnecessarily leads to oscillations. I wil
l then present sufficient \nconditions for oscillations expressed as algeb
raic criteria (for \nmass-action kinetics) and as minimal network motifs (
for general \nkinetics). In turn\, excluding Hopf bifurcations in monostat
ionary \nnetworks with a stable steady state is equivalent to 'universal
’ \nstability\, meaning that the unique steady state is locally stable f
or \nall parameter choices. I will conclude with a conjecture \ncharacteri
zing universal stability for reaction networks with general \nkinetics. Th
is is ongoing joint work with Peter F. Stadler and Alex \nBlokhuis.\n
LOCATION:https://researchseminars.org/talk/MoRN/131/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Balázs Boros (Bolyai Institute\, University of Szeged)
DTSTART:20251106T163000Z
DTEND:20251106T170000Z
DTSTAMP:20260421T094423Z
UID:MoRN/132
DESCRIPTION:Title: B
ifurcations in small mass-action systems\nby Balázs Boros (Bolyai Ins
titute\, University of Szeged) as part of Seminar on the Mathematics of Re
action Networks\n\n\nAbstract\nWe give an overview of the recent developme
nts on the smallest quadratic mass-action reaction networks that admit And
ronov-Hopf\, Bautin\, Bogdanov-Takens\, fold\, or cusp bifurcations. Then\
, we discuss the analogous questions in the class of bimolecular mass-acti
on reaction networks. Finally\, we briefly discuss the inheritance theory
of mass-action reaction networks\, which allows us to lift nondegenerate b
ehaviors from a network to its enlargement.\n
LOCATION:https://researchseminars.org/talk/MoRN/132/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Casian Pantea (West Virginia University)
DTSTART:20251120T163000Z
DTEND:20251120T170000Z
DTSTAMP:20260421T094423Z
UID:MoRN/133
DESCRIPTION:Title: W
eakly reversible deficiency zero realizations of polynomial ODE systems wi
th parameters\nby Casian Pantea (West Virginia University) as part of
Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nWeakly reve
rsible deficiency zero (WR0) mass-action systems are known to have remarka
bly stable dynamics\, with a unique positive asymptotically stable steady
state in each compatibility class. Suppose we have an ODE polynomial sys
tem whose coefficients depend affinely on a set of parameters (for example
\, mass-action systems). We present an algorithm which outputs the region
of parameters where our ODE system is identical with that of a weakly reve
rsible\, deficiency zero mass-action system\, whose nice dynamical propert
ies it inherits. The algorithm is based on computations on polyhedra\, and
was developed in polymake. This is joint work with Neal Buxton (WVU).\n
LOCATION:https://researchseminars.org/talk/MoRN/133/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lea Popovic (Concordia University)
DTSTART:20251204T163000Z
DTEND:20251204T170000Z
DTSTAMP:20260421T094423Z
UID:MoRN/134
DESCRIPTION:Title: S
ensitivity of dynamics in Autocatalytic Reaction Networks of Togashi-Kanek
o type\nby Lea Popovic (Concordia University) as part of Seminar on th
e Mathematics of Reaction Networks\n\n\nAbstract\nThe Togashi–Kaneko (TK
) model is a prototypical example of an auto- catalytic reaction network e
xhibiting dramatic switching behavior that is a result of the stochastic d
ynamics at small volumes. I will present a study of the TK model with addi
tional mutations\, using a stochastic averaging principle to make use of t
he multi-scale feature of its dynamics. I will demonstrate a sensitivity o
f the model to even slight departures from symmetry in the autocatalytic r
eactions\, using a detailed analysis of the stationary distribution of the
fast process when the state of the slow process is fixed. This is joint w
ork with Yi Fu\, HyeWon Kang\, Wasiur Khudabukhsh\, Greg Rempala and Ruth
Williams.\n
LOCATION:https://researchseminars.org/talk/MoRN/134/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nidhi Kaihnsa (University of Copenhagen)
DTSTART:20260409T150000Z
DTEND:20260409T153000Z
DTSTAMP:20260421T094423Z
UID:MoRN/135
DESCRIPTION:Title: C
onnectivity in Parameter Regions of Reaction Networks\nby Nidhi Kaihns
a (University of Copenhagen) as part of Seminar on the Mathematics of Reac
tion Networks\n\n\nAbstract\nI will discuss the general problem of connect
ivity in the parameter regions of reactions networks. In particular for di
fferent phosphorylation networks. The talk will be based on multiple joint
works with Feliu\, Telek\, de Wolff\, Yürük\, and Wang. I will conclude
with some open problems in this direction.\n
LOCATION:https://researchseminars.org/talk/MoRN/135/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hyukpyo Hong (University of Wisconsin-Madison)
DTSTART:20260226T163000Z
DTEND:20260226T170000Z
DTSTAMP:20260421T094423Z
UID:MoRN/136
DESCRIPTION:Title: U
biquitous Asymptotic Robustness in Biochemical Systems\nby Hyukpyo Hon
g (University of Wisconsin-Madison) as part of Seminar on the Mathematics
of Reaction Networks\n\n\nAbstract\nLiving systems maintain stable interna
l states despite environmental fluctuations. Absolute concentration robust
ness (ACR) is a striking homeostatic phenomenon in which the steady-state
concentration of a species remains invariant despite changes in total supp
ly. In this talk\, we introduce a previously underappreciated phenomenon\
, namely asymptotic ACR (aACR): approximate robustness can emerge solely f
rom the network structure\, without requiring exact ACR motifs or negligib
le parameters. We find that aACR is more pervasive than classical ACR and
prove that this ubiquity stems solely from network structure. This notion
of aACR would provide a rigorous and practical tool to analyze robust resp
onses in broad biochemical systems. This is joint work with Diego Rojas La
Luz and Gheorge Craciun.\n
LOCATION:https://researchseminars.org/talk/MoRN/136/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oskar Henriksson (Max Planck Institute of Molecular Cell Biology a
nd Genetics\, Dresden)
DTSTART:20260212T160000Z
DTEND:20260212T163000Z
DTSTAMP:20260421T094423Z
UID:MoRN/137
DESCRIPTION:Title: T
he polyhedral structure of the disguised toric locus\nby Oskar Henriks
son (Max Planck Institute of Molecular Cell Biology and Genetics\, Dresden
) as part of Seminar on the Mathematics of Reaction Networks\n\n\nAbstract
\nThe disguised toric locus of a reaction network is the set of rate const
ants for which the associated mass action system is dynamically identical
to a complex-balanced mass action system. The starting point of this talk
is a recent result from joint work with Boros\, Craciun\, Jin\, and Rojas
La Luz (2510.03621)\, showing that the disguised toric locus is homeomorph
ic to a prism over the disguised toric flux locus\, which is a polyhedral
cone with a rich combinatorial structure. This result has both theoretical
and practical consequences: it leads to new results on the geometry of th
e disguised toric locus\, and provides a computational strategy for explic
itly computing the disguised toric locus for networks that were out of rea
ch with previous methods.\n
LOCATION:https://researchseminars.org/talk/MoRN/137/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yong-Jin Huang (Kyoto University)
DTSTART:20260312T160000Z
DTEND:20260312T163000Z
DTSTAMP:20260421T094423Z
UID:MoRN/138
DESCRIPTION:Title: A
Structural Approach to Identifying Indicator Species in Chemical Reaction
Networks\nby Yong-Jin Huang (Kyoto University) as part of Seminar on
the Mathematics of Reaction Networks\n\n\nAbstract\nCellular phenotypes di
splay high diversity\, reflecting the complex functional states of individ
ual cells. While transcriptomics has traditionally been used to determine
these states\, recent advances in single-cell technologies are shifting in
terest toward more detailed classification via metabolomic phenotyping\, w
hich directly reflects cellular function. However\, the large number of me
tabolites poses challenges for both measurement and computational clusteri
ng in the task of phenotypic classification. A fundamental question theref
ore arises: which subset of species suffices to represent the system's ove
rall state?\n\nThis talk introduces a novel theory that\, based solely on
the structural information of chemical reaction networks\, identifies indi
cator species—whose concentrations uniquely determine all others and thu
s distinguish multistable equilibria. An implementing algorithm is applied
to biochemical pathway databases. Numerical experiments demonstrate that
classification based solely on these indicator species matches or surpasse
s full-set accuracy\, with superior robustness under measurement noise. Th
ese results provide a rigorous\, topology-based foundation for selecting i
ndicator species\, advancing metabolic phenotyping and biomarker discovery
.\n
LOCATION:https://researchseminars.org/talk/MoRN/138/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucie Laurence (University of Bern)
DTSTART:20260212T163000Z
DTEND:20260212T170000Z
DTSTAMP:20260421T094423Z
UID:MoRN/139
DESCRIPTION:Title: N
oise induced stabilization in stochastic chemical reaction network\nby
Lucie Laurence (University of Bern) as part of Seminar on the Mathematics
of Reaction Networks\n\n\nAbstract\nChemical reaction networks (CRNs) are
commonly analyzed through deterministic or stochastic models that track m
olecular populations over time. In regimes with large molecule counts\, st
ochastic dynamics are typically approximated by deterministic mass-action
kinetics. We present a CRN that defies this expectation: while the determi
nistic system is unstable\, exhibiting finite-time blow-up of trajectories
within the interior of the state space\, its stochastic counterpart is po
sitive recurrent.\n
LOCATION:https://researchseminars.org/talk/MoRN/139/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giulio Cuniberti (Politecnico di Torino)
DTSTART:20260312T163000Z
DTEND:20260312T170000Z
DTSTAMP:20260421T094423Z
UID:MoRN/140
DESCRIPTION:Title: S
tochastic ordering tools for reaction network models\nby Giulio Cunibe
rti (Politecnico di Torino) as part of Seminar on the Mathematics of React
ion Networks\n\n\nAbstract\nStochastic reaction networks are mathematical
models with a wide range of applications in biochemistry\, ecology\, and e
pidemiology\, and are often complex to analyze. Except for some special ca
ses\, it is generally difficult to predict how the abundances of all consi
dered species evolve over time. A possible approach to address this issue
is to develop tools to compare the model under study with a similar one wh
ose behavior is better understood. The main contribution of our work is to
provide direct and computable conditions that can be used to ensure the e
xistence of an ordered coupling between two stochastic reaction networks a
nd to identify which parameter changes in a given model lead to an increas
e or decrease in the count of certain species. We also make an algorithm a
vailable that implements our theory and we illustrate it with several appl
ications. This is joint work with Daniele Cappelletti and Paola Siri.\n
LOCATION:https://researchseminars.org/talk/MoRN/140/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiaxin Jin (University of Louisiana at Lafayette)
DTSTART:20260326T160000Z
DTEND:20260326T163000Z
DTSTAMP:20260421T094423Z
UID:MoRN/141
DESCRIPTION:Title: H
omeostasis Patterns and Infinitesimal Homeostasis in Reaction Networks
\nby Jiaxin Jin (University of Louisiana at Lafayette) as part of Seminar
on the Mathematics of Reaction Networks\n\n\nAbstract\nHomeostasis is a re
gulatory mechanism that keeps a specific variable close to a prescribed va
lue as other variables fluctuate. This notion can be formulated rigorously
when a system is modeled as an input-output network with distinguished in
put and output nodes\, where the dynamics determine the corresponding inpu
t-output function. In this setting\, homeostasis can be defined infinitesi
mally\, namely when the derivative of the input-output function vanishes a
t an isolated point. Combined with graph-theoretic ideas from combinatoria
l matrix theory\, this provides a framework for computing homeostasis poin
ts and classifying homeostasis types. \n\nIn the first part of the talk\,
we introduce the notion of a homeostasis pattern\, a set of nodes that are
simultaneously infinitesimally homeostatic\, and show that all such patte
rns can be described using a combinatorial structure associated with the n
etwork\, called the homeostasis pattern network. In the second part\, we s
tudy infinitesimal homeostasis in chemical reaction networks\, where conse
rvation laws complicate the standard analysis. We present criteria for the
existence of infinitesimal homeostasis with and without conservation\, an
d introduce the notion of infinitesimal concentration robustness\, where t
he output remains nearly constant under perturbations of conserved quantit
ies.\n
LOCATION:https://researchseminars.org/talk/MoRN/141/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Faul (University of Fribourg)
DTSTART:20260226T160000Z
DTEND:20260226T163000Z
DTSTAMP:20260421T094423Z
UID:MoRN/142
DESCRIPTION:Title: O
n the abelian structure of noncompetitive chemical reaction networks\n
by Louis Faul (University of Fribourg) as part of Seminar on the Mathemati
cs of Reaction Networks\n\n\nAbstract\nCRNs of interest in biochemistry an
d systems biology are embedded in complex networks so that local CRNs have
to respond to internal and environmental cues. We describe the network’
s response to such perturbations using a Markov chain whose state space is
the set of CRN’s static states\, from where no reaction is possible.
We study noncompetitive CRNs\, a class of networks whose static states are
rate-independent\, and is a special instance of Abelian networks. One c
an thus use a unified algebraic and probabilistic framework for analyzing
their long-term behavior.\n
LOCATION:https://researchseminars.org/talk/MoRN/142/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rebeka Szabo (University of Pécs)
DTSTART:20260326T163000Z
DTEND:20260326T170000Z
DTSTAMP:20260421T094423Z
UID:MoRN/143
DESCRIPTION:Title: D
iscrete state deterministic approach\nby Rebeka Szabo (University of P
écs) as part of Seminar on the Mathematics of Reaction Networks\n\n\nAbst
ract\nChemical reaction networks are typically modeled using two approache
s: deterministic models\, which are suitable for large systems\, and stoch
astic descriptions\, which are accurate at smaller scales. However\, the t
ransition between these two models has been unclear. We introduce a contin
uous-time\, discrete-state deterministic (CDD) approach that bridges this
gap by using a newly introduced concept called reaction extent. A reaction
is considered complete when its coordinate reaches an integer value. Nume
rical simulations demonstrate the stepwise changes in concentration and th
e underlying dynamics. Additionally\, this method shows potential for appl
ication to various types of chemical reaction systems. Joint work with Gá
bor Lente.\n
LOCATION:https://researchseminars.org/talk/MoRN/143/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hye-Won Kang (University of Maryland Baltimore)
DTSTART:20260409T153000Z
DTEND:20260409T160000Z
DTSTAMP:20260421T094423Z
UID:MoRN/144
DESCRIPTION:Title: M
ultiscale Approximation and Parameter Estimation in Stochastic Models of t
he Glycolytic Pathway\nby Hye-Won Kang (University of Maryland Baltimo
re) as part of Seminar on the Mathematics of Reaction Networks\n\n\nAbstra
ct\nIn this talk\, I will introduce a glycolytic pathway that includes mul
tiple enzyme-catalyzed reactions. We assume that some enzymes are present
in low copy numbers and thus adopt a continuous-time Markov chain framewo
rk to capture stochastic effects. To further reduce network complexity\, w
e apply a multiscale approximation method and derive a reduced ODE model t
hat describes the system's behavior on a slow timescale.\n\nThe reduced mo
del involves two key species and contains fewer parameters—expressed as
functions of those in the full model--which facilitates more tractable par
ameter estimation. Assuming that only the reduced species are observable\,
we generate synthetic data from the full model and use it to estimate the
parameters in the reduced model. This approach demonstrates how time-seri
es data from a subset of species can enable effective estimation of compos
ite parameters in a reduced system.\n\nThis is joint work with Arnab Gangu
ly.\n
LOCATION:https://researchseminars.org/talk/MoRN/144/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carsten Wiuf (University of Copenhagen)
DTSTART:20260423T153000Z
DTEND:20260423T160000Z
DTSTAMP:20260421T094423Z
UID:MoRN/145
DESCRIPTION:Title: Q
SDs for one-species reaction networks\nby Carsten Wiuf (University of
Copenhagen) as part of Seminar on the Mathematics of Reaction Networks\n\n
\nAbstract\nThis talk is concerned with quasi-stationary distributions (QS
Ds) on $\\mathbb{N}_0$ for one-species stochastic reaction networks concei
ved as continuous time Markov chains (CTMCs). A QSD describes the long ti
me behaviour of the CTMC before absorption. \n Examples arise in ecology
\, epidemiology\, cellular biology and chemistry. \n\n Let $(X_t)_{t\\ge
0}$\, $X_t\\in \\mathbb{N}_0$\, describe the species count of a one-speci
es reaction network that eventually is absorbed into a trapping set $A\\su
bseteq\\mathbb{N}_0$. For example\, $S\\to 2S$ and $S\\to 0$\, here $A=\\{
0\\}$. A probability distribution $\\nu$ with support on $A^c=\\mathbb
{N}_0\\!\\setminus\\! A$ is a QSD\, if the following holds:\n\n$\\bullet$
If the initial count $X_0$ is chosen from $\\nu$\, then $X_t$\, $t>0$\,
remains distributed as $\\nu$\, provided the chain is not absorbed.\n\n\n
Formulated in math terms:\n$$\\mathbb{P}_\\nu(X_t\\in B\\\, |\\\, t<\\tau_
A)=\\nu(B)\,\\quad B\\subseteq A^c\,\\quad\\text{for all}\\quad t\\ge 0\,$
$\n where $ \\tau_A=\\inf\\{t\\ge0 \\colon X_t\\in A\\}$ is the time until
absorption\, and $\\mathbb{P}_{\\nu}$ is the distribution of the process
before absorption with initial distribution $\\nu$. \n\nWe start by looki
ng at some examples to shape the intuition. Then\, we characterise all QSD
s $\\nu$ in terms of a finite number of generating terms $\\nu(J)=(\\nu(
i_1)\,\\ldots\,\\nu(i_d))$\, $J=\\{i_1\,\\ldots\,i_d\\}$ and a correspondi
ng eigenvalue $\\theta\\in\\R$. This is to say\, $\\nu(n)=\\sum_{j\\in J}R
_j(n\,\\theta)\\nu(j)$\, where \nthe coefficients $R_j(n\,\\theta)$ are g
iven recursively in $n$. Based on this and relying on Perron-Frobenius the
ory for infinite matrices\, we prove existence of an extremal QSD for King
man's parameter $\\theta_K>0$\, provided the CTMC is ultimately absorbed.
Furthermore\, we show the existence of a series of polynomials of increas
ing degree\, $ \\rho_n(\\theta)$\, such that $\\theta(n)\\downarrow\\theta
_K$\, where $\\theta(n)$ is the smallest real root of $ \\rho_n(\\theta)$
. These results mimic results for birth-death processes (seminal work b
y Karlin and McGregor). \n\nWe further discuss numerial means to find the
generator and to determine Kingman's parameter. The results are illustr
ated with numerical examples from stochastic reaction network theory.\n\n
This is joint work with Chuang Xu (University of Hawaii) and Mads Chr Hans
en (formerly at University of Copenhagen).\n
LOCATION:https://researchseminars.org/talk/MoRN/145/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aidan Howells (Politecnico di Torino)
DTSTART:20260507T153000Z
DTEND:20260507T160000Z
DTSTAMP:20260421T094423Z
UID:MoRN/146
DESCRIPTION:by Aidan Howells (Politecnico di Torino) as part of Seminar on
the Mathematics of Reaction Networks\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/MoRN/146/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gábor Szederkényi (Pazmany Peter Catholic University)
DTSTART:20260423T150000Z
DTEND:20260423T153000Z
DTSTAMP:20260421T094423Z
UID:MoRN/147
DESCRIPTION:Title: C
ompartmental discretization and simulation of gene regulation networks (GR
Ns)\nby Gábor Szederkényi (Pazmany Peter Catholic University) as par
t of Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nGene e
xpression is a fundamental biological process of actually realizing DNA in
formation in the form of proteins in living organisms. It is widely accept
ed that the stochastic nature of gene expression has to be taken into cons
ideration during quantitative modeling due to uncertainties coming from e.
g.\, both translational and transcriptional bursting. In (Friedman\, 2006)
a model in partial integro-differential equation (PIDE) form was proposed
for the description of the temporal evolution of protein distribution. Th
is model was generalized to multiple dimensions in (Pájaro\, 2017). To ma
ke numerical solution and analysis easier\, a finite volume discretization
scheme in the space of molecule numbers was proposed in (Vághy\, 2024) w
hich gives a non-homogeneous master equation which is essentially a linear
time-varying compartmental model. In this presentation\, I will show rece
nt results on the simulation and control of GRNs using the discretized com
partmental model form. Existence and uniqueness of equilibria (i.e.\, stat
ionary distributions) and stability of solutions will be studied using the
theory of non-autonomous master equations (see\, e.g. Diblík\, 2024).\n\
nCoauthors: Irene Otero-Muras\, Mihály A. Vághy\, Manuel Pájaro\, Chris
tian Fernandez Perez\, Mihály Pituk\, Josef Diblík\n\nReferences:\n\nFri
edman\, N.\, Cai\, L.\, & Xie\, X. S. (2006). Linking stochastic dynamics
to population Distribution: an analytical framework of gene expression. Ph
ysical Review Letters\, 97(16)\, 168302.\n\nPájaro\, M.\, Alonso\, A. A.\
, Otero-Muras\, I.\, & Vázquez\, C. (2017). Stochastic modeling and numer
ical simulation of gene regulatory networks with protein bursting. Journal
of Theoretical Biology\, 421\, 51-70.\n\nVághy\, M. A.\, Otero-Muras\, I
.\, Pájaro\, M.\, & Szederkényi\, G. (2024). A kinetic finite volume dis
cretization of the multidimensional PIDE model for gene regulatory network
s. Bulletin of Mathematical Biology\, 86(2)\, 22.\n\nDiblík\, J.\, Pituk\
, M.\, & Szederkényi\, G. (2024). Large time behavior of nonautonomous li
near differential equations with Kirchhoff coefficients. Automatica\, 161\
, 111473.\n
LOCATION:https://researchseminars.org/talk/MoRN/147/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maya Mincheva (Northern Illinois University)
DTSTART:20260507T150000Z
DTEND:20260507T153000Z
DTSTAMP:20260421T094423Z
UID:MoRN/148
DESCRIPTION:by Maya Mincheva (Northern Illinois University) as part of Sem
inar on the Mathematics of Reaction Networks\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/MoRN/148/
END:VEVENT
END:VCALENDAR