Homeostasis in Input-Output Networks: Structure, Classification and Applications

Fernando Antonelli, EPM-UNIFESP

Abstract:

Homeostasis occurs in a biological or biochemical system when some output variable remains approximately constant as some input parameters vary over some range. Recently, Golubitsky and Stewart [Homeostasis, Singularities and Networks. J. Math. Biol. 74 (2017) 387-407] introduced the notion of 'infinitesimal homeostasis' allowing the use of implicit differentiation and singularity theory to study homeostasis in systems of ordinary differential equations (ODEs). Generally speaking, ODEs appearing in the life sciences are encoded by 'networks of ODEs'. Nodes (vértices) correspond to state variables and links (directed arrows) indicate which nodes are coupled to which. What distinguishes a network of ODEs from a generic system of differential equations is the capability to keep track of the output from each node individually. Hence, infinitesimal homeostasis is related to occurrence of 'singularities' at individual nodes. In this talk we explain a new approach to the study of the combinatorial structure and classification of homeostasis in 'input-output networks', that is, networks of ODES where we keep track of the output from a fixed node, as well as the node(s) that depend on the external input parameters.

Joint work with Martin Golubitsky (Ohio), Ian Stewart (Warwick), Michale C. Reed (Duke), H. Frederick Nijhout (Duke), Janet Best (Ohio), Jiaxin Jin (Louisiana), William Duncan (Simulations Plus), Zhengyuan Huang (Michigan), Yangyang Wang (Iowa) e João Luiz de Oliveira Madeira (Bath).