M. Reed, J. Best, M. Golubitsky, I. Stewart and F. Nijhout
Analysis of homeostatic mechanisms in biochemical networks
Cell metabolism is an extremely complicated dynamical system that maintains important
cellular functions despite large changes in inputs. This “homeostasis” does not mean that the dynamical
system is rigid and fixed. Typically, large changes in external variables cause large changes
in some internal variables so that, through various regulatory mechanisms, certain other internal
variables (concentrations or velocities) remain approximately constant over a finite range of inputs.
Outside that range, the mechanisms cease to function and concentrations change rapidly with
changes in inputs. In this paper we analyze four different common biochemical homeostatic mechanisms,
feedforward excitation, feedback inhibition, kinetic homeostasis, and parallel inhibition. We
show that all four mechanisms can occur in a single biological network, using folate and methionine
metabolism as an example. Golubitsky and Stewart have proposed a method to find homeostatic
nodes in networks. We show that their method works for two of these mechanisms but not the other
two. We discuss the many interesting mathematical and biological questions that emerge from this
analysis, and we explain why understanding homeostatic control is crucial for precision medicine.