Signal amplification ϕ, φ ≡ 〈C*/A* − 1〉 ( A and C), and signal magnitude θ, θ ≡ 〈C*/ 0〉 ( B and D) are considered as a function of scaffold binding affinity, E. Low basal phosphatase levels are considered ( E 4 = 6). Scaffold proteins attenuate signals that would otherwise strongly amplify. Note that this amplification of signal propagation occurs even when phosphatases can act on scaffold-bound kinases.įig. Thus, when phosphatase activity is sufficiently high, a scaffold allows for the effective propagation of a signal that would otherwise be significantly quenched. Amplification is also evident in the absolute magnitude of the signal output ( Fig. For reasonable parameter values, a ≈100% increase in signal output (ϕ ∼ 1) with respect to the first member of the cascade can result. In this circumstance, assembling kinases on a scaffold allows for significant signal amplification. We find that, when phosphatase activity is high, and the initiating stimulus is strong, assembling kinases onto the scaffold results in a sharp increase in the number of active kinases as the signal propagates along the cascade ( Fig. When the affinity is sufficiently strong, available kinases are bound to their corresponding binding sites on the scaffold, and this scenario can be interpreted as having a scaffold present. When the affinity of the kinases to the scaffold increases, kinases begin to assemble onto the scaffold. Other important issues that we examined with this model are the consequences of whether kinases bound to the scaffold can phosphorylate downstream kinases that are in solution and whether phosphatases in solution can act on proteins bound to the scaffold. Schematics of how signaling occurs in solution and on a scaffold are shown in Fig. We studied how scaffolds influence signal propagation for different physiological conditions determined by values of these parameters.
1) can be characterized by the following small number of parameters: the rate at which an active kinase can phosphorylate a downstream kinase, the rate at which phosphatases can remove a phosphate group from a kinase, the binding affinity of kinases to the scaffold or exchange rate, the relative concentration of scaffolds and kinases, and the parameters characterizing the mobility of the various protein kinases. The signaling module that we studied ( Fig. We investigated how scaffolds can influence protein motion, phosphorylation of downstream kinases by an active kinase, and phosphatase-mediated deactivation of kinases.