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Thread: differential equations in maple

  1. #1
    Apr 2010

    differential equations in maple

    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
    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??
    Last edited by lomkes; April 12th 2010 at 12:14 PM. Reason: betterlooking
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