BEGIN:VCALENDAR
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CALSCALE:GREGORIAN
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BEGIN:VEVENT
SUMMARY:David F. Anderson (University of Wisconsin\, Madison (USA))
DTSTART;VALUE=DATE-TIME:20201112T160000Z
DTEND;VALUE=DATE-TIME:20201112T163000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20201203T160000Z
DTEND;VALUE=DATE-TIME:20201203T163000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20201203T163000Z
DTEND;VALUE=DATE-TIME:20201203T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20201112T163000Z
DTEND;VALUE=DATE-TIME:20201112T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20201210T160000Z
DTEND;VALUE=DATE-TIME:20201210T163000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20201210T163000Z
DTEND;VALUE=DATE-TIME:20201210T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20210114T160000Z
DTEND;VALUE=DATE-TIME:20210114T163000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20210225T160000Z
DTEND;VALUE=DATE-TIME:20210225T163000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20210128T160000Z
DTEND;VALUE=DATE-TIME:20210128T163000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20210211T160000Z
DTEND;VALUE=DATE-TIME:20210211T163000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20210211T163000Z
DTEND;VALUE=DATE-TIME:20210211T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20210114T163000Z
DTEND;VALUE=DATE-TIME:20210114T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20210128T163000Z
DTEND;VALUE=DATE-TIME:20210128T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20210325T160000Z
DTEND;VALUE=DATE-TIME:20210325T163000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20210311T163000Z
DTEND;VALUE=DATE-TIME:20210311T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20210225T163000Z
DTEND;VALUE=DATE-TIME:20210225T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20210311T160000Z
DTEND;VALUE=DATE-TIME:20210311T163000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20210408T153000Z
DTEND;VALUE=DATE-TIME:20210408T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20210422T150000Z
DTEND;VALUE=DATE-TIME:20210422T150000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20210513T150000Z
DTEND;VALUE=DATE-TIME:20210513T153000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20210422T153000Z
DTEND;VALUE=DATE-TIME:20210422T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20210408T150000Z
DTEND;VALUE=DATE-TIME:20210408T150000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20210520T150000Z
DTEND;VALUE=DATE-TIME:20210520T153000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20210520T153000Z
DTEND;VALUE=DATE-TIME:20210520T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20210513T153000Z
DTEND;VALUE=DATE-TIME:20210513T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20211028T153000Z
DTEND;VALUE=DATE-TIME:20211028T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20210923T153000Z
DTEND;VALUE=DATE-TIME:20210923T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20210916T153000Z
DTEND;VALUE=DATE-TIME:20210916T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20210916T150000Z
DTEND;VALUE=DATE-TIME:20210916T153000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20210923T150000Z
DTEND;VALUE=DATE-TIME:20210923T153000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20211118T163000Z
DTEND;VALUE=DATE-TIME:20211118T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20211014T150000Z
DTEND;VALUE=DATE-TIME:20211014T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20220519T153000Z
DTEND;VALUE=DATE-TIME:20220519T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20220127T160000Z
DTEND;VALUE=DATE-TIME:20220127T163000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20211209T163000Z
DTEND;VALUE=DATE-TIME:20211209T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20211028T150000Z
DTEND;VALUE=DATE-TIME:20211028T153000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20211209T160000Z
DTEND;VALUE=DATE-TIME:20211209T163000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20211118T160000Z
DTEND;VALUE=DATE-TIME:20211118T163000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20220210T163000Z
DTEND;VALUE=DATE-TIME:20220210T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20220210T160000Z
DTEND;VALUE=DATE-TIME:20220210T163000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20220127T163000Z
DTEND;VALUE=DATE-TIME:20220127T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20220224T163000Z
DTEND;VALUE=DATE-TIME:20220224T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20220224T160000Z
DTEND;VALUE=DATE-TIME:20220224T163000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20220519T150000Z
DTEND;VALUE=DATE-TIME:20220519T153000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20220310T160000Z
DTEND;VALUE=DATE-TIME:20220310T163000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20220428T150000Z
DTEND;VALUE=DATE-TIME:20220428T153000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20220310T163000Z
DTEND;VALUE=DATE-TIME:20220310T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20220324T163000Z
DTEND;VALUE=DATE-TIME:20220324T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20220324T160000Z
DTEND;VALUE=DATE-TIME:20220324T163000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20220428T153000Z
DTEND;VALUE=DATE-TIME:20220428T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20221013T150000Z
DTEND;VALUE=DATE-TIME:20221013T153000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20221013T153000Z
DTEND;VALUE=DATE-TIME:20221013T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20221027T150000Z
DTEND;VALUE=DATE-TIME:20221027T153000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20221027T153000Z
DTEND;VALUE=DATE-TIME:20221027T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20221110T160000Z
DTEND;VALUE=DATE-TIME:20221110T163000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20221110T163000Z
DTEND;VALUE=DATE-TIME:20221110T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20221201T163000Z
DTEND;VALUE=DATE-TIME:20221201T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20221201T160000Z
DTEND;VALUE=DATE-TIME:20221201T163000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20230126T163000Z
DTEND;VALUE=DATE-TIME:20230126T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20230209T160000Z
DTEND;VALUE=DATE-TIME:20230209T163000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20230209T163000Z
DTEND;VALUE=DATE-TIME:20230209T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20230223T160000Z
DTEND;VALUE=DATE-TIME:20230223T163000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20230223T163000Z
DTEND;VALUE=DATE-TIME:20230223T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20230126T160000Z
DTEND;VALUE=DATE-TIME:20230126T163000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20230309T160000Z
DTEND;VALUE=DATE-TIME:20230309T163000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20230309T163000Z
DTEND;VALUE=DATE-TIME:20230309T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20230323T160000Z
DTEND;VALUE=DATE-TIME:20230323T163000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20230323T163000Z
DTEND;VALUE=DATE-TIME:20230323T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20230413T150000Z
DTEND;VALUE=DATE-TIME:20230413T153000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20230413T153000Z
DTEND;VALUE=DATE-TIME:20230413T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20230427T150000Z
DTEND;VALUE=DATE-TIME:20230427T153000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20230427T153000Z
DTEND;VALUE=DATE-TIME:20230427T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20230511T150000Z
DTEND;VALUE=DATE-TIME:20230511T153000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20230511T153000Z
DTEND;VALUE=DATE-TIME:20230511T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20231026T150000Z
DTEND;VALUE=DATE-TIME:20231026T153000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20231026T153000Z
DTEND;VALUE=DATE-TIME:20231026T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20231109T160000Z
DTEND;VALUE=DATE-TIME:20231109T163000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20231109T163000Z
DTEND;VALUE=DATE-TIME:20231109T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20231130T160000Z
DTEND;VALUE=DATE-TIME:20231130T163000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20231130T163000Z
DTEND;VALUE=DATE-TIME:20231130T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20231214T160000Z
DTEND;VALUE=DATE-TIME:20231214T163000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20231214T163000Z
DTEND;VALUE=DATE-TIME:20231214T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20240208T160000Z
DTEND;VALUE=DATE-TIME:20240208T163000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20240208T163000Z
DTEND;VALUE=DATE-TIME:20240208T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20240314T160000Z
DTEND;VALUE=DATE-TIME:20240314T163000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20240222T163000Z
DTEND;VALUE=DATE-TIME:20240222T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20240222T160000Z
DTEND;VALUE=DATE-TIME:20240222T163000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20240509T150000Z
DTEND;VALUE=DATE-TIME:20240509T153000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
UID:MoRN/92
DESCRIPTION:by David Doty (University of California\, Davis) as part of Se
minar on the Mathematics of Reaction Networks\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/MoRN/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erik Winfree (California Institute of Technology)
DTSTART;VALUE=DATE-TIME:20240509T153000Z
DTEND;VALUE=DATE-TIME:20240509T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
UID:MoRN/93
DESCRIPTION:by Erik Winfree (California Institute of Technology) as part o
f Seminar on the Mathematics of Reaction Networks\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/MoRN/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Minjoon Kim (POSTECH)
DTSTART;VALUE=DATE-TIME:20240314T163000Z
DTEND;VALUE=DATE-TIME:20240314T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20240411T150000Z
DTEND;VALUE=DATE-TIME:20240411T153000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20240411T153000Z
DTEND;VALUE=DATE-TIME:20240411T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20240523T153000Z
DTEND;VALUE=DATE-TIME:20240523T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
UID:MoRN/98
DESCRIPTION:by Muruhan Rathinam (University of Maryland\, Baltimore County
) as part of Seminar on the Mathematics of Reaction Networks\n\nAbstract:
TBA\n
LOCATION:https://researchseminars.org/talk/MoRN/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David F. Anderson (University of Wisconsin - Madison)
DTSTART;VALUE=DATE-TIME:20240425T153000Z
DTEND;VALUE=DATE-TIME:20240425T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20240425T150000Z
DTEND;VALUE=DATE-TIME:20240425T153000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
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;VALUE=DATE-TIME:20240523T150000Z
DTEND;VALUE=DATE-TIME:20240523T153000Z
DTSTAMP;VALUE=DATE-TIME:20240423T115935Z
UID:MoRN/101
DESCRIPTION:by Philippe Robert (INRIA) as part of Seminar on the Mathemati
cs of Reaction Networks\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/MoRN/101/
END:VEVENT
END:VCALENDAR