This problem compares the cooperative (n> 1) and non-cooperative (n = 1) reaction mechanisms dt nS + E = k₁ a) Show that Vmax Sn Km+Sh b) Consider the Hill function f(s) k_1 E, P + E Vmax Sh Km+Sh an inflection point if and only if n > 1. = Show that the function f has c) Find this inflection point (as a function of the substrate S). d) Observe that this inflection point is not exactly at K/", which is wheref (s) = Vmax /2. However, show that, for large n, the inflection point approaches K".

Chemistry
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Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
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This problem compares the cooperative (n> 1) and non-cooperative (n = 1)
reaction mechanisms
dt
nS + E
a) Show that
Vmax S
Km+Sh
b) Consider the Hill function f(s)
=
k₁
E₁ P + B
"max Sh
Km+Sh
an inflection point if and only if n > 1.
c) Find this inflection point (as a function of the substrate S).
d) Observe that this inflection point is not exactly at K", which is
wheref (s) = Vmax /2. However, show that, for large n, the inflection
point approaches K
=
Show that the function f has
Transcribed Image Text:This problem compares the cooperative (n> 1) and non-cooperative (n = 1) reaction mechanisms dt nS + E a) Show that Vmax S Km+Sh b) Consider the Hill function f(s) = k₁ E₁ P + B "max Sh Km+Sh an inflection point if and only if n > 1. c) Find this inflection point (as a function of the substrate S). d) Observe that this inflection point is not exactly at K", which is wheref (s) = Vmax /2. However, show that, for large n, the inflection point approaches K = Show that the function f has
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