Graph-theoretic and algebraic geometric approaches to biochemical reaction networks

Abstract: Under mass-action kinetics, systems of biochemical reactions are modeled by chemical reaction networks (CRNs), a class of graphs that gives rise to polynomial dynamical systems. Approaches in this field include chemical reaction network theory and the more recent linear framework. In this talk, I will focus primarily on the linear framework, a graph-theoretic approach to timescale separation in biochemical systems. I will discuss a graph-theoretic construction within the framework that mimics what would happen if a single parameter in a graph is taken to infinity, producing what we call an asymptotic graph. I consider how properties of the asymptotic graph, such as its steady states, serve as an appropriate representation for a linear framework graph in this limit. Time permitting, I also speculate on some extensions of this construction beyond the scope of the linear framework to parameter identifiability and the steady state varieties of CRNs, suggesting areas for future work at the intersection of graph theory, algebraic geometry, and dynamical systems.

chemical biologychemical kineticsalgebraic geometrydynamical systemsprobability

Audience: researchers in the topic

---

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.

---