Control theory of regulatory cascades

We have extended Metabolic Control Theory to include cascades consisting of several modules controlling each other solely via regulatory effects. We derive several theorems that determine how the control properties of a cascade derive from (1) the control properties of each module, taken in isolation and (2) the regulatory interactions between the modules. Two cases are treated explicitly. The first concerns cascades in the absence of feed-back: in this case the internal control behaviour of each module is unaffected by external regulatory interactions. The second includes one feed-back loop and gives a quantitative expression of how feed-back modifies control properties: the internal control matrix within one module can be calculated as if the elasticity matrix of this module was the sum of its intrinsic elasticity matrix and a cyclic regulation matrix. More complex cascades can be analysed recursively by subdividing them into simpler modules, which can be treated individually. The theoretical framework developed here should facilitate quantitative experimental analysis of the control of cell physiology where the latter involves regulatory cascades.