Effect of Phosphorylation on the Circadian Clock of Drosophila by Analytical and Graph Theory Matrix Approach

The system of nonlinear differential equations in steady state conditions for phosphorylation on Drosophila’s circadian clock is solved analytically. Approximate analytical expressions of concentrations of phosphorylate in the abundance of mRNA, unphosphorylated PER protein, phosphorylated protein within domain A, phosphorylated protein within domain B, and its nuclear variants respectively are discussed. Using homotopy perturbation method, the steady state condition for phosphorylation on Drosophila’s circadian clock is solved analytically. The influence of kinetic parameters inhibition constant, maximum rate of degradation, Michaelis constant for degradation of mRNA, phosphorylated protein within domain A and within domain B over the concentrations are obtained. The numerical result and the analytical results are compared, and a satisfactory agreement is observed.