Humboldt State University ® Department of Chemistry

Richard A. Paselk

Chem 438	Introductory Biochemistry	Spring 2007
Lecture Notes: 19 February	© R. Paselk 2006
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Enzyme Kinetics

For simple, one-substrate enzymes then, have Michaelis-Menten Equation as a model for enzyme activity.

Note predicted consequences of model:

• [S] >> K_M; then v_i = V_max and get Zero order (r = k)
• [S] << K_M; then , and get First order (r = k [S])
• [S] = K_M; then v_i = V_max/2 This is definition of K_M, the substrate concentration at half-saturation.
• Note consequences for a plot: start off with approximately linear slope with y = kx. Then at the limit of high concentrations have a horizontal line. This is exactly what we expect if we look at the general form of the equation: , the formula for a rectangular hyperbola: (Figures 5.4, 5.5; overhead)

Turnover Number. The rate constant (First order) for the breakdown of the [ES] complex, k_cat (k₃), is also known as the turnover number, that is the maximum number of substrate molecules processed/active site (moles substrate/mole active site): k_cat=V_max / [E]_total. Note that this is best determined under saturating conditions. At very low concentrations of [S] can find the second-order rate constant for the conversion of E + S E + P: v_o = (k_cat / K_M)([E][S].

Linear plots for enzyme kinetic studies

Double Reciprocal or Lineweaver-Burke Plot: Need in form: y = ax + b , so take reciprocals of both sides and have

. (Figure 5.6) [overhead 6.6, P]

Other linear plots are also available, and are better in terms of statistics (L-B one of worst, best quality points [high concentration] have least influence on slope, while low precision points [low concentration] are more spread out, and have a large moment, with a strong influence on the slope and the K_M intercept ­ this is not as much of a concern now with computer statistical packages, but you still have to understand the statistics). [overhead: fig 8.2, W et al]

FYI - The Eadie-Hofstee Plot One common plot is shown below. Note that the data points are distributed much more evenly over the plot giving better statistics for the slope. In addition the value of KM is obtained from the slope, giving better precision.

ENZYME KINETICS AND INHIBITION

What's exciting about enzyme inhibition?

• Potential to tell us about enzyme.
• Potential uses as drugs and toxins.
  • Understanding drugs and toxins to counter etc.

Three major types of inhibition:

• Competitive inhibition
• Noncompetitive inhibition
• Uncompetitive inhibition

Competitive Inhibition: S & I are mutually exclusive, E can bind to one OR the other. (overhead Horton: T-33, Fig 5.8)

Plots:

We can model this inhibition with chemical equations, keeping in mind that S & I are mutually exclusive, E can bind to one OR the other:

Model: ; and: ; where .

Classically assume binding to same site, but other possibilities also.

1. steric hindrance between S & I in different sites.
2. overlapping sites for S & I.
3. Partial sharing of sites.
4. Conformational change of enzyme with binding of either such that other can not bind. 

Noncompetitive: the inhibitor can bind to either E or ES. S & I do not bind to the same sites!

Model: ; and .

Note that will have two inhibitor binding constants, they may be the same, as in the equation above, or could be different, leading to more complex behavior.

Plots for classic, simple situation (overhead MvH 11.5):

TEMPERATURE AND pH EFFECTS ON ENZYMES (AND PROTEINS)

Temperature profile reflects two underlying phenomena:

• The effects of temperature on rate due to the fact that as temp. increases more molecules will have the energy required to achieve activation energy, E_a. (Review: Arrhenius equation: , and the Maxwell-Boltzman Distribution.)
• The effects of temperature on protein stability: at high temperatures the protein denatures.

Together these effects lead to the plot below where the rising leg is due to activation energy effects (increasing rate) and the falling leg is due to protein denaturation.

pH EFFECTS ON ENZYME RATE

Papain: inflection at pH 4.2 for cys-25 and at pH 8.2 for his-159.

Note that the two legs represent two pH titration curves (rotate the left leg 90 deg. then flip; rotate the right leg 90 deg. counter clockwise and you can see them), with pK's equal to 4.2 and 8.2 respectively. This is a typical example for an enzyme with titratable groups in the active site. Can also have non-symmetrical curves with only one group. And of course can have curves due to denaturation by titration of charged surface and interior side chains.

Zymogens: define and give examples of trypsin/trypsinogen.

Pathway Diagrams

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Last modified 19 February 2006