Network Dynamics and Homeostasis
speaker: Marty Golubitsky (The Ohio State University)abstract: A typical example of homeostasis occurs in warm-blooded mammals where the animal’s internal body temperature xo 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 (xi), an output node (xo) , and a set of n regulatory nodes (x{r1}, …, x{rn}) 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 xo(I). Third, we replace homeostasis (where the output is held approximately constant on variation of I) by infinitesimal homeostasis (where the derivative (dxodI) 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 input-output network leads to a unique
set of possible patterns of infinitesimal homeostasis.
timetable:
Wed 31 May, 15:50 - 16:40, Aula Dini
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