Question

the rate equation for the second order reaction of E and S is

what os the diffusion controlled limit in aqueous solution

sapling learning The rate equation for the second-order reaction of E and S is where kcat/KM is the second-order rate constant, which can be used to compare catalytic efficiencies cat What is the diffusion-controlled limit in aqueous solution? O 107 to 108 M s O 108 to 10 M-1s-1 O 10-6 to 10-5 M O 109 to 1010 M s1 O 108 to 10° MIs O 10-7 to 10-8 M s-1 O 10-9 to 10-8 M-'s1

Answer 1

Concepts and reason

Enzyme and substrate collides with each other in enzyme catalyzed reactions. The frequency of enzyme-substrate collision is in the range of ${10^8}{\rm{ to 1}}{{\rm{0}}^9}{\rm{ }}{{\rm{M}}^{ - 1}}{{\rm{s}}^{ - 1}}$ for a second order enzyme catalyzed reaction.

The ratio of ${k_{{\rm{cat}}}}/{K_{\rm{M}}}$ cannot be greater than ${10^8}{\rm{ to 1}}{{\rm{0}}^9}{\rm{ }}{{\rm{M}}^{ - 1}}{{\rm{s}}^{ - 1}}$ for a second order reaction to form${\rm{ES}}$, which is diffusion-controlled limit.

Fundamentals

For a second order reaction between an enzyme (E) and substrate (S) with following mechanism:

${\rm{Initial velocity, }}{V_{\rm{0}}} = \frac{{[{\rm{S}}]}}{{{K_{\rm{M}}} + [{\rm{S}}]}}{V_{\max }}$

Here, ${V_{\max }} = {k_{{\rm{cat}}}}{[{\rm{E}}]_{{\rm{total}}}}$ and ${[{\rm{E}}]_{{\rm{total}}}} = [{\rm{E}}] + [{\rm{ES}}]$ . Michaelis-Menton constant${K_{\rm{M}}} = \frac{{{k_2} + {k_{ - 1}}}}{{{k_1}}}$When $[{\rm{S}}] < < {K_{\rm{M}}}$ then ${K_{\rm{M}}} + {\rm{S }} \approx {K_{\rm{M}}}$ . The expression for ${V_{\rm{0}}}$ becomes as follows:

$\begin{array}{c}\\{V_{\rm{0}}} = \frac{{[{\rm{S}}]}}{{{K_{\rm{M}}} + [{\rm{S}}]}}{V_{\max }}\\\\ = \frac{{{k_{{\rm{cat}}}}}}{{{K_{\rm{M}}}}}{[{\rm{E}}]_{{\rm{total}}}}[{\rm{S}}]\\\end{array}$

The ratio ${k_{{\rm{cat}}}}/{K_{\rm{M}}}$ is the second-order rate constant for the formation of ${\rm{ES}}$.

Following are second rate constants in the given set of rate constants.

$\begin{array}{l}\\{10^8}{\rm{ to 1}}{{\rm{0}}^9}{\rm{ }}{{\rm{M}}^{ - 1}}{{\rm{s}}^{ - 1}}\\\\{10^{ - 9}}{\rm{ to 1}}{{\rm{0}}^{ - 8}}{\rm{ }}{{\rm{M}}^{ - 1}}{{\rm{s}}^{ - 1}}\\\end{array}$

The diffusion-controlled limit in aqueous solution is ${10^8}{\rm{ to 1}}{{\rm{0}}^9}{\rm{ }}{{\rm{M}}^{ - 1}}{{\rm{s}}^{ - 1}}$.

Ans:

The diffusion-controlled limit in aqueous solution is ${10^8}{\rm{ to 1}}{{\rm{0}}^9}{\rm{ }}{{\rm{M}}^{ - 1}}{{\rm{s}}^{ - 1}}$.