Homeostasis Patterns and Infinitesimal Homeostasis in Reaction Networks

Abstract: Homeostasis is a regulatory mechanism that keeps a specific variable close to a prescribed value as other variables fluctuate. This notion can be formulated rigorously when a system is modeled as an input-output network with distinguished input and output nodes, where the dynamics determine the corresponding input-output function. In this setting, homeostasis can be defined infinitesimally, namely when the derivative of the input-output function vanishes at an isolated point. Combined with graph-theoretic ideas from combinatorial matrix theory, this provides a framework for computing homeostasis points and classifying homeostasis types.

In the first part of the talk, we introduce the notion of a homeostasis pattern, a set of nodes that are simultaneously infinitesimally homeostatic, and show that all such patterns can be described using a combinatorial structure associated with the network, called the homeostasis pattern network. In the second part, we study infinitesimal homeostasis in chemical reaction networks, where conservation laws complicate the standard analysis. We present criteria for the existence of infinitesimal homeostasis with and without conservation, and introduce the notion of infinitesimal concentration robustness, where the output remains nearly constant under perturbations of conserved quantities.

chemical biologychemical kineticsalgebraic geometrydynamical systemsprobability

Audience: researchers in the topic

( video )

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Seminar on the Mathematics of Reaction Networks

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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 approximately every other week on Thursdays, 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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