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The Michaelis-Menton reaction mechanism usually assumed for enzymatic reactions is: S + E = E-S (1) E-S Æ P + E (2) a. Consider a well-mixed batch reactor with initial enzyme concentration [E]0 and initial substrate concentration [S]0. Write expressions for the rate of change of concentration of [S], [ES], [E], and [P] in terms of k1, k2, and Keq,1, and concentration variables. b. Write a Matlab function that solves this set of differential equations for the concentration of all species in time given inputs k1, k2, Keq,1, [E]0, [S]0. c. The pseudo-steady approximation may be applied on the reactive intermediate species [ES]. This approximation is: 0 dt d[ES] ˜ . Using this pseudo-steady approximation, verify that the rate of change of [S] is given by the expression: [S]K [S]v dt d[S] M max + -= . What are and in terms of the other constants in this problem: k vmax KM 1, k2, Keq,1, [E]0, [S]0? d. What does the rate dt d[S] simplify to in the limit ? What about the limit ? >> K[S] M M >> [S]K e. Consider the following conditions: k1=109 liter/mole-s, k2=1 s-1, Keq,1= 1 liter/mole, [E]0=10-6 M, [S]0=0.01 M. Find analytical solutions for [S](t), [ES](t),
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