Model of Kinase Fluctuations and Intrinsic Noise

A model describing how fluctuations around a steady state, due to kinase fluctuations and intrinsic noise, are distributed between two reactions with substrates phosphorylated by a shared kinase. The formalism uses a realistic set of biological constants to illustrate various features of fluctuations and relaxation times to a steady state. The model shows that the steady-state response determines the size and range in enzyme concentration of phosphorylated substrate fluctuations, and that the choice of an operating point can have a large impact on how shared kinase noise is distributed among two available pathways. ( Shared kinase fluctuations between two enzymatic reactions, Viswanathan, Ganesh A., Jayaprakash Ciriyam, Sealfon Stuart C., and Hayot Fernand , Physical Biology 5(4), p.046002, (2008))

Below is a schematic of reactions for the phosphorylation of two substrates X and Y by a common kinase E and dephosphorylation by different phosphatases P1 and P2.

The equation describing the model are: