This mathematical model help us to understand the dynamics of our modified Saccharomyces cerevisiae (Yeast). Our model is based on the yeast MAPK pathway.By using this model,we hope it can help us analyze the possible problems will be occur in the lab, For instance, How long will it take from IL-8/CXCR 1 binding to get the highest concentration of the output signal — GFP .

For a biochemical reaction system, We use to present the dynamic of reaction by a set of ordinary differential equations (ODEs) to describe the changes in the concentration of a biochemical substances. In a system of m biochemical species with the concentration ci (i = 1, ..,m) and r biochemical reactions with the rates vj (j = 1, .., r), one may write:
dc1/dt = f1(c1, c2, .., cm) = n11v1 + n12v2 +…+n1r vr
dc2/dt= f2(c1, c2, .., cm) = n21v1 + n22v2 +….+n2r vr
dcm / dt = fm(c1, c2, .., cm) = nm1v1 + nm2v2 +….+nmr vr


Our model was based on a mathematical model for the pheromone pathway. By changing some of the parameter,We got some results. there is the modified system of ODE’s for our model as follows :







The conclusions that can be made from our analysis of the modelcas follows :