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