Humboldt State University ® Department of Chemistry

Richard A. Paselk

Chem 438

Introductory Biochemistry

Spring 2010

Lecture Notes: 24 February

© R. Paselk 2006


Enzymes, cont.


Models for Enzyme Specificity:

Enzyme Kinetics


Gives information on dynamic systems.

Sets the parameters for catalytic mechanisms such as:

A right arrow C + X;

B + X right arrow D etc.

Review some Kinetics from General Chemistry:

We have now reviewed kinetics as tools. Before we go to enzymes a few comments:


Plots of vi = d[P]/dt vs. [S] for 0 - 3rd order

reaction order plot

Look at simple, one-substrate enzymes:

For simple enzyme, S right arrow P get rectangular hyperbola type plot for vi vs [S], similar to Mb binding curve.

M-M plot

Let's look at a mathematical model and attempt to generate curve. This was first done by Michaelis and Menten for an equilibrium model. Better is the steady state model of Haldane and Briggs (more general), which we will derive.

For S P assume

chemical equation for  E +S in equilibrium with [ES] (showing rate constants k1 and k2) in equilibrium with E + P  (with rate constants k3 and k4)

And for initial reaction conditions [P] = 0 & therefore k4 = 0, so have

chemical equation for  E +S in equilibrium with [ES] (showing rate constants k1 and k2) decaying to E + P  (with rate constants k3)

Now vi = d[P]/dt = k3[ES] (Note that kcat is often used instead of k3);

Assume steady state (steady state assumption: d[ES]/dt= 0):

d[ES]/dt= 0; Thus: 0 = d[ES]/dt= k1[E][S] - k2[ES] - k3[ES].

Continuing we can now substitute for E (free enzyme), because hard to find, and gather constants:

[E] = [Et] - [ES]; then

d[ES]/dt= k1([Et] [S] - [ES][S]) - k2[ES] - k3[ES],

gathering constants: mathematical equation: (k2 + k3)/k1 = [S]([Et] - [ES])/[ES],

Now define mathematical equation: (k2 + k3)/k1 = Km

Then mathematical equation: Km = [S]([Et] - [ES])/[ES], where KM is the Michaelis-Menten constant.

{Note that if k2 >> k3 (that is the equil. of E+S with ES is rapid compared to breakdown of ES to P), then M-M const = 1/(affinity)= the dissociation constant, but only in these special conditions.}
Pathway Diagrams

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Last modified 24 February 2006