Problem Statement:In a catalytic reaction that follows a mechanism known as the Michaelis-Menten kinetics, the reactant (S) combines reversibly with a catalyst (E) to form a complex (ES) with a forward and reverse rate constant of k1 and ki, respectively. The complex then dissociates into product (P) with a reaction rate constant of k2 and the catalyst is regenerated.

k1 k2

E + S <---> ES --> E + P

ki

where

E = enzyme (i.e., catalyst)

S = substrate (i.e., reactant)

ES = enzyme-substrate complex')

P = product

k1, ki, k2 = elementary reaction rate constants

The following ODEs describe how the concentration of each of the four species (E, S, ES, P) changes with time.

dE/dt = -k1*E*S + ki*ES + k2*ES

dS/dt = -k1*E*S + ki*ES

dES/dt = k1*E*S - ki*ES - k2*ES

dP/dt = k2*ES

Integrate the above set of equations with the following rate constants and initial conditions:

k1 = 1

ki = 1

k2 = 10

E(0) = E0 = 0.1

S(0) = S0 = 1.

ES(0) = ES0 = 0.

P(0) = P0 = 0.

1) How do I solve those four in maple?? (tried searching in help, can't write equations correctly keep getting errors even with implicitdiff every example I try works fine.

2) I need to solve and find S(t)

3) How to express S(t) in matchematical rows in maple??