Humboldt State University ® Department of Chemistry

Richard A. Paselk

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 10⁶ to 10¹² 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 8-13, S]
• Induced-fit model of Koshland: diagram; space-filling models of HK with and without substrate. (Figure 14.2, p386) [overhead 8-13, S; 16-5, V&V{HK}]

FYI Types of specificity: Geometric specificity: shape (overhead 12-1, 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:

• 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.

FYI 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], 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 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):

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] = [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.}

Now a couple of tricks: Solve for [ES]:

and recall that k₃[E_t] = V_max and therefore v_i = k₃[ES], and dividing both sides by k₃, v_i/k₃ = [ES]

Substituting: and ,

But maximum possible velocity must = k₃[E_t] = V_max

So, Which is known as the Michaelis-Menten Equation.

Pathway Diagrams

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Last modified 15 February 2006