Chapter 9 - Multistationarity in Biochemical Networks: Results, Analysis, and Examples

Abstract

Biochemical networks are complex objects, almost always containing nonlinear interactions among a usually large number of chemical species. The smallest activation or inhibition interactions involve two components (a gene and its protein, or an inhibitor and an enzyme), are well understood biologically, and have simple stable long-term behavior that can be inferred straight from the interaction diagram. But if the interaction involves a larger number of components, or if feedback loops are present, then the dynamics may become far more complicated, and understanding it requires strategies more subtle than chasing paths in the interaction diagram. Instabilities of different kinds are possible even for small biological structures and are associated with signaling events. One key class of instabilities is those leading to multiple positive steady states, also known as multistationarity, and seen experimentally as irreversible switch-like behavior. There is significant theoretical evidence, backed by experiment, that important pathways may exhibit multistationarity as response to chemical signaling. This phenomenon is particularly relevant in crucial cell behaviors, including generating sustained oscillatory responses, remembering transitory stimuli, differentiation, or apoptosis. Multistationarity occurs in chemistry and chemical engineering as well, but is much less common. There is, in fact, a great deal of stable behavior in networks of chemical reactions, and (to a lesser degree) in biological networks. This can be explained in part by the fact that the possibility of exotic behavior places rather delicate constraints on the structure of an interaction network. A seminal remark is due to Thomas who conjectured that positive feedbacks in the logical structure of an interaction network are necessary for multistationarity. Much theoretical and simulation work followed, and proposed a series of increasingly refined design principles for pathways allowing multistationarity. Building on this effort, multistationarity has been demonstrated experimentally in bacterial synthetic genetic networks.