MATLAB assignment

5.) Suppose that a substrate can be broken down by two different enzymes with different kinetics. (This happens, for example, in the case of cAMP or cGMIP which can be hydrolyzed by two different forms of phosphodiesterase). (a) Write the reaction scheme and differential equations, and non-dimensionalize, to get the system of equations: dx 1 dy 1 where x and y are the non-dimensional concentrations of the two complexes. Identify all parameters. (b) Apply the quasi-steady-state approximation to find the equation governing the dynamics ofsubstrate . Under what conditions is the quasi-steady state approximation valid (c) Solve the differential equation governing (d) For this system ofequations, show that the solution can never leave the positive octant , x, y 20. By showing that tol lalxt022a2y is decreasing everywhere in the positive octant, show that the solution approaches the origin for large time