Temporal cooperativity and sensitivity amplification in biological signal transduction.

Sensitivity amplification in signal transduction modules regulated by phosphorylation-dephosphorylation cycles and GTPases results from a new type of cooperativity which is fundamentally different from that of allosterism. This type of cooperativity, termed temporal cooperativity [Qian, H. (2003) Biophys. Chem. 105, 585-593], is analyzed in this paper through stochastic models for molecular interactions. Mathematical analysis is developed through a series of models with different levels of complexity, from which a simple conceptual model based on linear cooperativity is derived. The following are shown: (i) When both kinase and phosphatase are nonsaturating, the distribution of the number of activated substrate molecules is binomial. With increasing kinase activity, the peak of the distribution continuously moves toward 100% activation. (ii) When the kinase is saturated, i.e., zeroth order, the distribution is Poisson. (iii) When both enzymes are saturated, the distribution is geometric. Ultrasensitivity corresponds to an abrupt switching of the peak position of the distribution from 0 to 100%. The theory is applicable to a wide range of processes in cell signaling including the specificity and sensitivity of T-cell activation.