Chem 438 

Spring 2010 
Lecture Notes: 26 February 


PREVIOUS 
Last time left off with: , 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.
Note predicted consequences of model:
Turnover Number. The rate constant (First order) for the breakdown of the [ES] complex, k_{cat} (k_{3}), 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 secondorder rate constant for the conversion of E + S E + P: v_{o} = (k_{cat} / K_{M})([E][S].
Double Reciprocal or LineweaverBurke Plot: Need in form: y = ax + b , so take reciprocals of both sides and have
. (Figure 5.6)
Other linear plots are also available, and are better in terms of statistics (LB 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).

Three major types of inhibition:
Competitive Inhibition: S & I are mutually exclusive, E can bind to one OR the other. (overhead Horton: T33, 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:
Classically assume binding to same site, but other possibilities also.
Noncompetitive: the inhibitor can bind to either E or ES. S & I do not bind to the same sites!
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):

Last modified 1 March 2010