Homeostasis in Input-Output Networks

Abstract: A 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.

Our mathematical 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 parameter $I$. 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).

We use graph theoretic methods to classify infinitesimal homeostasis. First, we show that there are three kinds of three-node network motif (feedforward loops, substrate inhibition, and negative feedback loops) each of which leads to a different kind of homeostasis. Second, we show that every network leads to a unique set of possible patterns of infinitesimal homeostasis. Where possible, we illustrate our results through example.

algebraic geometrydynamical systemsprobability

Audience: researchers in the topic

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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 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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