Chemical Reaction Networks: Systematic Design, Noise Control and Limit Cycles

Abstract: Chemical reaction networks describe interactions between biochemical species. Two types of mathematical models of reaction systems will be considered: (i) deterministic models which are written in terms of reaction rate equations (i.e. ordinary differential equations (ODEs) for concentrations of biochemical species involved); and (ii) stochastic models of reaction networks, given in terms of the Gillespie stochastic simulation algorithm, which provides more detailed information about the simulated system than ODEs. I will discuss methods for systematic design of relatively simple reaction systems with exotic dynamical behaviour, including applications to synthetic biology and DNA computing. Considering deterministic models of reaction networks, I will present examples of reaction systems with multiple oscillating solutions or systems whose deterministic models (based on reaction rate equations) undergo specific bifurcations. Since reaction networks in biological applications often involve species at low-copy numbers, stochastic effects may become 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 network under the mass action kinetics, in such a way that controllable state-dependent noise is introduced into the stochastic dynamics, while the deterministic dynamics (based on reaction rate equations) are preserved. I will present reaction networks with noise-induced oscillations and multi-stability.

References: [1] Radek Erban and Hye Won Kang, "Chemical Systems with Limit Cycles", submitted, available as arxiv.org/abs/2211.05755 (2022)

[2] Radek Erban and S. Jonathan Chapman, "Stochastic Modelling of Reaction-Diffusion Processes", Cambridge Texts in Applied Mathematics, Cambridge University Press (2020)

[3] Tomislav Plesa, Konstantinos Zygalakis, David Anderson and Radek Erban, "Noise control for molecular computing", Journal of the Royal Society Interface, Volume 15, Number 144, 20180199 (2018)

algebraic geometrydynamical systemsprobability

Audience: researchers in the topic

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Seminar on the Mathematics of Reaction Networks

Series comments: Subscription link: list.ku.dk/postorius/lists/morn.list.ku.dk/

This seminar series focuses on progress in mathematical theory for the study of reaction networks, mainly in biology and chemistry. The scope is broad and accommodates works arising from dynamical systems, stochastics, algebra, topology and beyond.

We aim at providing a common forum for sharing knowledge and encouraging discussion across subfields. In particular we aim at facilitating interactions between junior and established researchers. These considerations will be represented in the choice of invited speakers and we will strive to create an excellent, exciting and diverse schedule.

The seminar runs twice a month, typically on the 2nd and 4th Thursday of the month, at 17:00 Brussels time (observe that this webpage shows the schedule in your current time zone). Each session consists of two 25-minute talks followed by 5-minute questions. After the two talks, longer discussions will take place for those interested. To this end, we will use breakout rooms. For this to work well, you need to have the latest version of Zoom installed (version 5.3.0 or higher), and use the desktop client or mobile app (not supported on ChromeOS).

We look forward hearing about new work and meeting many of you over zoom! Many of the talks are recorded; to see the recording, from Past Talks, open details of the listed talk for a video link.

The organizers.

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