9.10 Enzyme Kinetics and Inhibition

k

Unit of rate constant; Units of k=M^1-order/S

Enzyme substrate reaction equation

Pre-steady state

Initial period where [ES] builds up

Steady state

Period where [ES] and other intermediates remain constant

Steady-state kinetics, understand kinetics charts

Equilibrium assumption

Assume P is produced more slowly than ES dissociates; meaning k₂«k_-1 and that ES formation reaches equilibrium quickly

Steady-state assumption

Probability of P → S is very low and can be ignored; Therefore, steady-state assumes ES formation equals ES loss (Either to reverse reaction or product formation)

Initial rate and formula

Initial velocity (V₀); Stays constant no matter concentration (Because S is regarded as constant at the beginning); V₀ = k₂[ES]

Low S vs High S effect on V₀

Low S, increases linearly as most E spots are empty; High S, increases until plateau as most E spots are filled

Michaelis and Mentee Theory

E + S forms reversible ES, ES breaks down to yield free enzyme and product (Slower, irreversible); Because P formation is slower, it limits overall reaction rate to be proportional to [ES] formation

Total enzyme concentration formula

[E_t] = [E] + [ES]; rearranging terms can help determine other values (ex. V₀)

Michaelis constant

K_m, point in which reaction velocity is V_max/2, Smaller is better (Less S needed to reach V_max/2)

k_cat; V₀ equation using k_cat

Limiting rate constant for a general catalysis reaction, max # of S an enzyme can convert to product per unit of time; k_cat=k₂; considering this… (Refer to image*); Higher k_cat faster turnover;

k_cat = V_max/[E_t]

Michaelis-Menten Equation

At low [S] concentrations, K_m + [S] = K_m

V_max

Point at which enzyme is saturated and [ES] = [E_t]; Means V_max = k_cat[E_t]

Visual representation of K_m, V₀, and V_max

K_d

Dissociation constant; rate of reverse reaction/rate of forward reaction; K_d = k_-1/k₁; K_m = K_d when k_-1»k₂

k_cat/K_m

Specificity constant for different E same S or different S same E; Higher value = higher efficiency

Upper limit of enzyme activity

10⁸ - 10⁹ M^-1s^-1 (Limited by diffusion rate of E and S)

experimental procedure to determine K_m and V_max

Lineweaver-Burk Plots

Double reciprocal;

Factors that affect enzyme activity

pH, number and types of substrate

Types and subtypes of inhibitions

Noncovalent (Reversible) inhibition

1. Non-competitive: Reversibly binds at alternate site

2. Competitive: Binds at active site, can be made based on knowledge of E reaction mechanism

3. Uncompetitive: Binds at alternate site to interfere with catalysis, only on ES

4. Mixed competitive: Combination of the types of activity above

Covalent (Irreversible) inhibition: Completely kills enzyme.

Competitive inhibitor

Reversible; aK_m = apparent K_m; more inhibitor = less enzyme activity; Uses substrate site; Higher slope = Stronger inhibition

Uncompetitive inhibitor

Does not use substrate site (Hence entire slope shift); Higher slope = Stronger inhibition

Mixed inhibition

Substrate vs transition-state analogs designs: What about noncompetitive and uncompetitive inhibitors

Substrate is based on structure of substrate and predicted interaction with proteins/ES structure

Transition-state binds better than substrate

Other inhibitors are harder to design and are often discovered rather than created

Ternary vs tertiary complex

Ternary is Inhibitor + E + S

Tertiary is just E + S

Suicide inactivator

Mechanism-based inactivators that undergoes the first few steps of the reaction before forming covalent bond with the enzyme.

Irreversible enzyme for chymotrypsin

Diisopropyl fluorophosphate (DIFP)

Irreversible enzyme

Binds covalently with/destroys functional group of protein or forms high stable noncovalent association