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BIOL 382 Applied Mathematics

Recall the derivation of the Michaelis-Menten rate law for an enzyme-catalysed reaction,
which began with the scheme:
a) [1] Write a dierential equation model for the system dynamics (not assuming kc) [2] Determine the overall reaction rate (i.e. the net rate of production of product) as a
function of the concentrations of substrate and product.
d) [1] Confirm that when ka) [1] Simulate the system from initial conditions (in mM) (s1, s2) = (1, 1).
b) [2] Based on the results of your simulation, which of reaction rates 1-3 could be accurately
described by a zeroth-order approximation? Which could be accurately described by a first-
order approximation?
c) [1] Construct an accurate approximate model in which one of the reaction rates 1-3 is
replaced by a zeroth-order approximation. Generate a simulation of the approximate model,
with initial conditions (in mM) (s1, s2) = (1, 1).
d) [1] Construct an accurate approximate model in which one of the reaction rates 1-3 is
replaced by a first-order approximation. Generate a simulation of the approximate model,
with initial conditions (in mM) (s1, s2) = (1, 1).
e) [1] Compare the approximations in (c) and (d). Which is more accurate?
f) [1] Which of the approximations in (c) and (d) will still be accurate if the simulation is
run from initial conditions (in mM) (s1, s2) = (10, 10)? Explain why.A