Dynamic responses of protein homeostatic regulatory mechanisms to perturbations from steady state.

Nineteen hypothetical protein homeostatic regulatory mechanisms were constructed and analysed in terms of the rate at which they recovered from a perturbation in the steady-state concentration of any component. Systems were constructed to symbolize transcription/translation processes of the average protein from Escherichia coli (1000 copies of protein P along with 1 gene G per cell). In some model systems, G catalysed the synthesis of P directly, while in others G catalysed the synthesis of mRNA (called M), and M catalysed the synthesis of P in a subsequent step. Recovery rates for each regulatory mechanism were obtained by generating the corresponding system of differential equations, linearizing the system about the steady state, and determining eigenvalues of the associated coefficient matrix. The optimal rate of recovery for a given mechanism, R(D), was determined by combining random and gradient search approaches to find rate constants for which the system recovered fastest. Regulatory elements that improved dynamic regulation were identified. These consisted of negative feedback relationships that involved P binding to either G (to shut off the synthesis of P) or M (to stimulate its degradation). Regulation improved as increasing numbers of P's bound to either G or M; however, the binding to M was more effective. In other mechanisms PP dimers bound G. Dimer-binding mechanisms were roughly twice as effective in terms of regulation as those that bound P monomers. The effect of linking two regulatory "modules" was also investigated. Linking had no effect on R(D), but optimal rate constants for the linked system were similar to those of the unlinked modules, suggesting that it may be feasible to construct regulatory networks by linking individual modules of this type.