# Biochemistry 301: Enzyme Kinetics

E + S <---> ES <---> E + P
The enzyme grabs a substrate --> ES complex, which then can become enzyme and product, if things are going forward. The reactions can go both ways, but an enzyme biases the direction of the reaction. The rate constants (k's) for each possible reaction are numbered, 1 for forward, -1 for backward, 2 for the reaction that goes ES to E and P. Got it? That's the foundation.

What is the rate equation for an enzyme-catalyzed reaction?
the Michaelis Menten equation

What is the equation for the steady state of the enzyme-substrate complex?
k1[E][S] = k1[E][S] - k-1[ES] + k2[ES]
ie. the rate of ES formation = the rate of ES consumption

What is meant by the "steady state"?
The reaction speed is constant because there is total saturation of the substrate and all enzyme is busy. [S]>>>[E]. The concentration of [ES] remains constant until nearly all [S] has been converted to product [P].

What is the Michaelis Menten equation?
Vo = (Vmax)[S]/Km plus [S]
Discovered in 1913

Km = approximate dissociation constant for [ES], a measure of E's affinity for S

[ ] = concentration of thing inside brackets, molar

Vmax = as fast as the reaction ever goes in the most optimal conditions

The M-M equation is the rate equation for an enzyme-catalyzed reaction. What does its mathematical representation look like? (plot of velocity as a function of [S])

Looks like a climbing curve---hyperbolic if it is a first order reaction and uninhibited.
The curve looks sigmoidal if the enzyme has cooperative binding of 2 or more active sites. This situation is where Kcat becomes useful as a summary of all the rate constants (K's).

Kcat = catalytic constant = Vmax/[E]t = turnover number = number of catalytic cycles each active site undergoes per unit time

[E]t = total enzyme concentration
(approximate: when [ES] = [E]t then Vo = Vmax, is when all the enzyme is involved in reaction, the rate of the reaction is maximal)

Here's some random shit from the lecture:
There are three ways that an enzyme stabilizes the transition state of a reaction:
1) induced fit - the enzyme changes shape to grab the substrate - binds most tightly while in transition state - ex: oxyanion hole in chymotrypsin
2) proximity/orientation - bring the right part of the substrate to the active site of the enzyme - lowers entropy and increases efficiency by 1000x
3) active site isolates reactants from solvent - electrostatic catalysis - no interference so entropy is lowered

Protease Inhibitors act as substrates but are not fully hydrolyzed (competitive inhibitor). A whole class of meds is based on this concept, inhibiting a viral protease, esp in AIDS Tx.

Mechanisms of inhibition:
suicide inhibitor = gets stuck in pocket and never comes out
transition state i =
protein protease i =
chelating agents - chelation = reversible binding

Orders of Rxns
A --> B is first order because only one A
A + B --> C is second order
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