An iterative solution of the Michaelis-Menten equations

A new approach is developed for the study of the Michaelis-Menten kinetic equations in all times t, based on their solution in the limit of large t. The linear terms in concentration of the substrate and the intermediate complex are more dominant than their product in this limit and the quadratic term can therefore be treaded iteratively. The proper behavior of the analytical solutions we give, in the small and large time limit, leads for the first time to a remarkable indistinguishability between the analytical and the numerical results in all times and for a large region of the parameters of the problem. Enlargement of the region of imperceptibility is found going from the zeroth to the first order iteration. The analytical description of the steady state where the concentration of the intermediate complex becomes maximum, permits the exploration of the conditions of both fast and slow transient to this region.