A spatially heterogeneous stochastic model for chemical reaction networks

Abstract: I will present a measure-valued framework for stochastic modelling of chemical reaction networks with spatial heterogeneity. Reactions rates at a spatial location are proportional to the mass of different species present locally, and to a location specific chemical rate that is allowed to be a function of the local or global mass of different species. The benefit of the framework is in rigorous approximation limits that exploit multi-scale aspects of the system. When the mass of all species scales the same way, we get classical deterministic limit 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 type of spatial random evolution process in which discrete mass evolves stochastically and the continuous mass evolves according to PDEs between consecutive jump times of the discrete part. Some useful properties of the limiting process are inherited from the pre-limiting sequence, and could be used in devising simulation algorithms.

This is joint work with Amandine Veber (Paris V, Polytechnique-Saclay)

algebraic geometrydynamical systemsprobability

Audience: researchers in the topic

( video )

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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!

The organizers.

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