Interval Constraint Satisfaction and Optimization for Biological Homeostasis and Multistationarity

Abstract

Homeostasis occurs in a biological or chemical system when some output variable remains approximately constant as one or several input parameters change over some intervals. We propose in this paper a new computational method based on interval techniques to find species in biochemical systems that verify homeostasis. A somehow dual and equally important property is multistationarity, which means that the system has multiple steady states and possible outputs, at constant parameters. We also propose an interval method for testing multistationarity. We have tested homeostasis, absolute concentration robustness and multistationarity on a large collection of biochemical models from the Biomodels and DOCSS databases. The codes used in this paper are publicly available at: https://github.com/Glawal/IbexHomeo.