Chem 438 
Introductory Biochemistry 
Spring 2007 
Lecture Notes: 15 February 
© R. Paselk 2006 

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INTRODUCTION TO ENZYMES
Enzymes are the heart of Biochemistry
 protein based catalysts (for us RNA based catalysts are Ribozymes)
 enormously effective catalysts: typically enhance rates by 10^{6} to 10^{12} fold
 operate under mild conditions: 0  100 °C (or perhaps even 300+ °C for some bacteria in deep ocean), 20 40 °C for most organisms; and low pressures (atmospheric)
 very specific: generally catalyze reaction for a very restricted group of molecules, sometimes for a single naturally occurring molecule of a single chirality.
Enzymes generally have a cleft for active site, generally <5%of surface: look like pac man. Need large structure to maintain shape etc. with many weak bonds.
Look at major aspects of enzyme study:
 Specificity
 Molecular mechanisms of catalysis
 Kinetics, including review
Specificity
Models for Enzyme Specificity:
 Lock & Key model of Fischer: diagram; Hexokinase example: reaction, methanol and water as ineffective picks. [overhead 813, S]
 Inducedfit model of Koshland: diagram; spacefilling models of HK with and without substrate. (Figure 14.2, p386) [overhead 813, S; 165, V&V{HK}]
FYI
Types of specificity:
 Geometric specificity: shape (overhead 121, V&V]
 Chiral specificity: most chirally specific enzymes are absolutely stereospecific.
 Prochirality, because of their own chiral nature enzymes can often hold substrates in such a way that on one chiral product is made, distinguishing between seemingly identical groups. [overhead 12.3, V&V]
 Chemical specificity: functional groups, types of chemical reaction.

Enzyme Kinetics
CHEMICAL REACTION KINETICS
Gives information on dynamic systems.
Sets the parameters for catalytic mechanisms such as:
 Number of species in rate determining step.
 Which species involved in Transition State.
 Order of steps: Thus for A + B C + D can have many mech.:
A C + X;
B + X D etc.
Review some Kinetics from General Chemistry:
We have now reviewed kinetics as tools. Before we go to enzymes a few comments:
 Note: r = d[S]/dt = d[P]/dt
 Note that for all cases with fixed initial concentrations (except zero order) as [A] decreases r decreases, so need to look at initial rates, that is rate of reaction before a significant amount of reactant is used up.
 Biochem v_{i} = r_{i}
 With enzymes can get very high apparent orders due to allosteric effects.
FYI
Plots of v_{i} = d[P]/dt vs. [S] for 0  3rd order

Look at simple, onesubstrate enzymes:
For simple enzyme, S P get rectangular hyperbola type plot for v_{i} vs [S], similar to Mb binding curve.
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
And for initial reaction conditions [P] = 0 & therefore k_{4} = 0, so have
Now v_{i} = d[P]/dt = k_{3}[ES] (Note that k_{cat} is often used instead of k_{3});
Assume steady state (steady state assumption: d[ES]/dt= 0):
d[ES]/dt= 0; Thus: 0 = d[ES]/dt= k_{1}[E][S]  k_{2}[ES]  k_{3}[ES].
Continuing we can now substitute for E (free enzyme), because hard to find, and gather constants:
[E] = [E_{t}]  [ES]; then
d[ES]/dt= k_{1}([E_{t}] [S]  [ES][S])  k_{2}[ES]  k_{3}[ES],
gathering constants: ,
Now define
Then , where K_{M} is the MichaelisMenten constant.
{Note that if k_{2} >> k_{3} (that is the equil. of E+S with ES is rapid compared to breakdown of ES to P), then MM const = 1/(affinity)= the dissociation constant, but only in these special conditions.}
Now a couple of tricks: Solve for [ES]:
and recall that k_{3}[E_{t}] = V_{max} and therefore v_{i} = k_{3}[ES], and dividing both sides by k_{3}, v_{i}/k_{3} = [ES]
Substituting: and ,
But maximum possible velocity must = k_{3}[E_{t}] = V_{max}
So, Which is known as the MichaelisMenten Equation.
Last modified 15 February 2006