Kinetic logic : a boolean analysis of the dynamic behaviour of control circuits

Abstract

In this central chapter I show how a system amenable to boolean description can be analyzed in terms of a set of logical equations. Each equation relates, for any time, the values of a function a, b, c,...(associated with the state, on or off, of a gene, of a chemical reaction, etc.), to the values of input variables, and of memorization variables α, β, γ,...(associated with the presence or absence of the product of a gene, of a chemical reaction, etc.). Time is present in a similar way as in differential equations; in fact, in our logical equations a, b, c,... play essentially the role of the time derivatives of α, β, γ. From the set of logical equations describing a system, one can derive its stable steady states (if any), the pathways (temporal sequences of states) and the conditions determining which pathway will be followed.