Studying adaptation and homeostatic behaviors of kinetic networks by using MATLAB

Organisms have the ability to counteract environmental perturbations and keep certain components within a cell homeostatically regulated. Closely related to homeostasis is the behavior of perfect adaptation where an organism responds to a step-wise perturbation by regulating some of its components, after a transient period, to their original pre-perturbation values. A particular interesting type of model relates to the so-called robust behavior where the homeostatic or perfect adaptation property is independent of the magnitude of the applied step-wise perturbation. It has been shown that this type of behavior is related to the control-theoretic concept of integral feedback (or integral control). Using downloadable MATLAB examples, we demonstrate how robust perfect adaptation sites can be identified in reaction kinetic networks by linearizing the system, applying the Laplace transform and inspecting the transfer function. We also show how the homeostatic set point in perfect adaptation is related to the presence of zero-order fluxes.