Michaelis–Menten Kinetics, Even – a Michaelis Complex Is Stabilized by Molecular Though Enzyme Mechanisms Are Interactions (Non-Covalent Interactions)

Home , Enzyme kinetics, Product (chemistry)

Revised 3/21/2017 Reaction Rates (reaction velocities): To measure a reaction rate we monitor the After lectures by disappearance of reactants or appearance of Dr. Loren Williams (GeorgiaTech) products.

e.g., 2NO2 + F2 ĺ122F

initial velocity => [product] = 0, no back reaction

Protein Folding: 1st order reaction

• Rates of enzyme reactions are affected by – Enzymes/catalysts – Substrates – Temperature DNA annealing: 2nd order reaction – Concentrations Why study enzyme kinetics? General Observationsti • Enzymes are able to exert their influence • Quantitative description of biocatalysis at very low concentrations ~ [enzyme] = • Understand catalytic mechanism nM • Find effective inhibitors • The initial rate (velocity) is linear with • Understand regulation of activity [enzyme]. • The initial velocity increases with [substrate] at low [substrate]. • The initial velocity approaches a maximum at high [substrate].

The initial velocity increases with [S] at low [S]. The initial velocity increases with [S] at low [S]. The initial velocity [velocity =d[P]/dt, P=product] approaches a maximum at high [S]. Initial velocity Simplest enzyme mechanism • Start with a mechanistic model • Identify constraints and assumptions - One reactant (S) - One intermediate (ES) • Solve for velocity (d[Product]/dt) - One product (P)

1. First step: The enzyme (E) and the substrate (S) reversibly and quickly form a non-covalent ES The Enzyme-Substrate Complex (ES) complex. 2. Second step: The ES complex undergoes a chemical • The enzyme binds non-covalently to the substrate transformation and dissociates to to form a non-covalent ES complex give product (P) and enzyme (E). – the ES complex is known as the Michaelis 3. v=k2[ES] 4. Many enzymatic reactions follow complex. Michaelis–Menten kinetics, even – A Michaelis complex is stabilized by molecular though enzyme mechanisms are interactions (non-covalent interactions). always more complicated than the Michaelis–Menten model. – Michaelis complexes form quickly and 5. For real enzymatic reactions use dissociate quickly. . kcat instead of k2 kcat andddthdt the reactionti velocityl kcat k o o cat E + S ES o E + P E + S m ES o E + P m • For any enzyme it is possible (pretty easy) to

determine kcat.

• To understand and compare enzymes we need to know how well the enzyme binds to S (i.e, what • The enzyme is either free ([E]) or bound ([ES]): [Eo] = [ES] + [E].

• At sufficiently high [S] all of the enzyme is tied up as ES (i.e., [Eo@§>(6@ happens in the first part of the reaction.) kcat does not according to Le Chatelier's Principle) tell us anything about how well the enzyme binds to • At high [S] the enzyme is working at full capacity (v=v ). max the substrate. • The full capacity velocity is determined only by kcat and [Eo].

•kcat = turnover #: number of moles of substrate produced per time per enzyme active site.

Assumptions

1. k1,k-1>>k2 (i.e., the first step is fast and is always at equilibrium). 2. G>(6@GW§ LHWKHV\VWHPLVDW steady state.)

The time dependence of everything (in a Michaelis-Menten 3. There is a single reaction/dissociation reaction) step (i.e., k2=kcat). 4. STot >6@>(6@§>6@ 5. There is no back reaction of P to ES LH>3@§ 7KLVDVVXPSWLRQDOORZV

us to ignore k-2. We measure initial YHORFLWLHVZKHQ>3@§ KM = [E][S]/[ES]

Now: we derive the Michaelis-Mentens-Menten EquationEquatioti n d[ES]/dt = k1[E][S] –k-1[ES] – k2[ES] = 0 (steady state assumption, see previous graph) solve for [ES] (do the algebra)

[ES] = [E][S] k1/(k-1 + k2)

Define KM (Michealis Constant) KM = (k-1 + k2)/k1 => [ES] = [E][S]/KM rearrange to give KM = [E][S]/[ES]

KM is the substrate concentration required to reach half- maximal velocity (vmax/2). Significance of KM The significance of kcat

•vmax = kcat Etot •KM = [E][S]/[ES] and KM = (k-1 + k2)/k1. •kcat: For the simplest possible mechanism, where ES is the only intermediate, and dissociation is fast, then kcat=k2, the first order rate •KM is the apparent dissociation constant of the ES complex. A constant for the catalytic step. dissociation constant (KD) is the reciprocal of the equilibrium constant • If dissociation is slow then the dissociation rate constant also contributes (K =K -1). K is a measure of a substrate䇻s affinity for the enzyme (but it D A M to kcat. is the reciprocal of the affinity). • If one catalytic step is much slower than all the others (and than the dissociation step), than the rate constant for that step is approximately • If k ,k >>k2, the K =K . 1 -1 M D equal to to kcat.

•kcat is the 䇾turnover number䇿: indicates the rate at which the enzyme •KM is the substrate concentration required to reach half-maximal velocity turns over, i.e., how many substrate molecules one catalytic site (vmax/2). A small KM means the sustrate binds tightly to the enzyme and converts to substrate per second. saturates (max䇻s out) the enzyme. • If there are multiple catalytic steps (see trypsin) then each of those rate

constants contributes to kcat. • The microscopic meaning of K depends on the details of the m • The microscopic meaning of k depends on the details of the mechanism. cat mechanism.

Significance of kcat/KM Data analysis

•k/K is the catalytic efficiency. It is used to rank enzymes. A big cat M • It would be useful to have a linear plot kcat/KM means that an enzyme binds tightly to a substrate (small KM), with a fast reaction of the ES complex. of the MM equation • • Lineweaver and Burk (1934) proposed •kcat/KM is an apparent second order rate constant the following: take the reciprocal of v=k /K [E] [S] cat M 0 both sides and rearrange.

•kcat/KM can be used to estimate the reaction velocity from the total 9 • Collect data at a fixed [E]0. enzyme concentration ([E]0). kcat/KM =10 => diffusion control.

•kcat/KM is the specificity constant. It is used to distinguish and describe various substrates. Lineweaver-Burk-PlotLinewLiL wea

the y (1/v) intercept (1/[S] = 0) is 1/vmax the x (1/[S]) intercept (1/v = 0) is -1/KM the slope is KM/vmax

Competitive Inhibition

Enzyme Inhibition Competitive Inhibition Competitive Inhibition

Figure 12-6

Competitive Inhibition Uncompetitive Inhibition

Figure 12-7 Uncompetitive Inhibition Uncompetitive Inhibition

Figure 12-8

Mixed (competitive and uncompetitive) Inhibition Mixed (competitive and uncompetitive) Inhibition

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