Humboldt State University ® Department of Chemistry

Richard A. Paselk

Chem 431	Biochemistry	Fall 2008
Lecture Notes: 3 October	© R. Paselk 2008
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Introduction to Enzymes

Look at major aspects of enzyme study:

• Specificity
• Molecular mechanisms of catalysis
• Kinetics, including review

Enzyme Specificity

Models for Enzyme Specificity:

• Lock & Key model of Fischer: diagram; Hexokinase example: reaction, methanol and water as ineffective picks. (text Figure 6-4)
• Induced-fit model of Koshland: diagram; space-filling models of HK with and without substrate. (text Figure 6-22){HK}

FYI Types of specificity: Geometric specificity: shape 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. 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:

• First Order: r = k[S] for S P; & r =-d[S]/dt = d[P]/dt.
  • Example - S_N1 from organic chemistry: A + B C + D as 1st order reaction, as in the hydroxylation of t-alkylchloride:

  

  First order because rate depends only on the formation of the carbocation, which in turn depends only on [R₃CCl]

   

• Second order: r = k[A][B] for A + B P; or can have r = k[A]² ;
  • Example - S_N2 from organic chemistry: A + B C + D as 2nd order reaction, as in the hydroxylation of primary alkylchlorides:

  

  Now 2nd order because both RH₂CCl and OH^- (reverse of figure above) are involved in slow step.

   

• Higher order reactions occur, but uncommon.
• Zero order: r = k: Only occurs with catalysts, important in enzyme catalysis. 0 order also only occurs above a minimum [A].

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.

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

Look at simple, one-substrate enzymes:

For simple enzyme, S P get rectangular hyperbola type plot for v_i vs [S] (text Figure 6-11), 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.

Want to come up with a model in expermentally accessible terms, e.g. v_i,

For S P assume[S], etc.

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

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

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

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

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

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

gathering constants: ,

Now define

Then , where K_M 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 3 October 2008