Analysis of protein homeostatic regulatory mechanisms in perturbed environments at steady state

Nine different protein homeostatic regulatory mechanisms were analysed for their ability to maintain a generic protein P within a specified range of a set-point steady-state concentration while perturbed by external processes that altered the rates at which P was produced and/or consumed. Steady state regulatory effectiveness was defined by the area within a rectangular region of "perturbation space", where axes correspond to rates of positive and negative perturbations. The size of this region differed in accordance with the regulatory elements composing the homeostatic mechanism. Such elements included basic negative feedback control of transcription (in which P, at some high concentration relative to its set-point value, binds to the gene G that encodes it, thereby inhibiting transcription), multiple sequential binding of a feedback effector (two P's bind sequentially to G), and dimerization of a feedback effector (a P(2) dimer binds to G). Two homeostatic mechanisms included a cascade structure, one with and one without translational feedback control. Another mechanism included feedback control of P degradation. Finally, two mechanisms illustrated the limits of regulatory systems. One lacked all regulatory elements (and included only an invariant rate of P synthesis and degradation) while the other assumed perfect (Boolean) regulation, in which transcription is completely inhibited at [P]>[P](sp) and is fully active at [P]<[P](sp). All of the systems evaluated are known, but the analytical expressions developed here allow quantitative comparisons between them. These expressions were evaluated at values typical of the average protein in Escherichia coli. A method for building regulatory networks by linking semi-independent regulatory modules is discussed.