7. The MichaelisMenten mechanism describes the catalysis of a biological reaction by an enzyme. The chemical notation for this reaction is E+S:#'ES>E+P Here the enzyme E combines with the substrate .9 to make an intermediate complex, ES, that is converted into product P, releasing the enzyme for another reaction. The notation A i) B refers to the elementary system 5 2 ka, ('1. 2 ka, where b and a are concentrations of species A and B, and k 15 the rate constant. A binary reaction such as A + B > C, corresponds to the nonlinear system c a b= hob. Note that these elementary reactions have conservation laws that reect the conversion of one species into another. For example, in the latter case C(t) + 110'.) =constant and C(t) + Mt} = constant. (a) Convert the MichaelisMenten reaction into a system of four ODEs for the concen- trations c, s, c, and p of the enzyme, substrate, complex, and product, respectively. Each arrow in the reaction diagram above refers to an elementary reaction that adds to the rates