Overview of Kinetics

∆ [𝑃 ]∆ 𝑡

=ν=𝑘[𝑆 ]

Rate of reactionM/sec

Rate constantsec-1, M-1 sec-1

Conc. of reactant(s)

Velocity of reaction

1st order reaction-rate depends on concentration of one reactant

S P∆ [𝑃 ]∆ 𝑡

=ν=𝑘[𝑆 ]

2nd order reactions mayDepend on two reactants

S1 + S2 P∆ [𝑃 ]∆ 𝑡

=ν=𝑘[𝑆1] [𝑆2 ]

Review of Kinetics

Most of the time reactions obtain equilibrium

S Pk1

k-1

k1 and k-1 are the rate constants for forwardAnd reverse reactions

𝐾 𝑒𝑞=[𝑃 ]𝑒𝑞[𝑆 ]𝑒𝑞

=𝑘1

𝑘− 1

Kinetic rate constantsare useful in determiningequilibrium chemistry

When equilibrium is reached: rate of forward and reverse reactions are the same.

Determination of rates and rate constants

Method of initial rates (Vo) at different [S]o to determine rate constants

-measure Vo very early in the reaction-very little product has formed (equilibrium is not a factor)

[S]oFigure 7.2

Enzyme Kinetics

E = enzymeS = substrateP = productES = enzyme–substrate complexk1 = rate constant for ES binding

-IF k1 is very large, binding is very favorable

k2 = rate constant for P formation from ES- IF k2 is very large, conversion to product is fast.

This enzymatic reaction depends upon both the [E] and [S]

Enzyme Kinetics

- A more common reaction scheme or mechanism involves a reversible binding of E and S.

E + Sk1

k-1

ES E + Pk2

Define a dissociation constant (Kd), measureof S binding to E.

𝐾 𝑑=𝑘− 1

𝑘1

If k1 >> k-1, S binding is very favorable.

A small value for Kd means binding is favorable

[S] – substrate concentration

Vo – initial velocity of a reaction. A significant amount of substrate has not yet been converted to product.

Vmax – maximal velocity of a reaction. Addition of moresubstrate will not increase the rate of the reaction.

KM – The concentration of substrate at which the rate of the reaction is half-maximal

Enzyme kinetics terminology

A commonly observed behavior for enzyme catalyzed reactionsshowing the change in Vo as [S] is changed

This behavior can be described mathematically by the Michaelis-Menten equation

This region is 1st order in [S]

This region is zero order in [S]

Vo =Vmax [S ]

KM+[S ]

k2 (called kcat) is a measure of the number of substrate molecules converted to product per second per enzyme molecule

kcat is called catalytic constantand is determined at high [S]

ES E + Pkcat (k2)

kcat/KM is a rate measure of catalytic efficiency for the conversion of E + S E + P

Turnover numbers (kcat)

Chymotrypsin catalyzes peptide cleavage(0.01 sec per cleavage)

CO2 + H2O HCO3-

(1.7 microseconds (ms) per reaction)

Experimental method for determining Vmax and KM

Figure 7.5

Plot the reciprocal of The Michaelis-MentenEquation.

A linear equationis generated

Allosteric enzymes and regulation

Figure 7.7

These complex metabolic pathways must be regulated.

Regulation of metabolic pathways

Flux through the pathway is regulated depending on the concentration of Product (K below)

In Feedback Inhibition, high concentration of the product of a pathway controls the rate of its own synthesis by inhibiting an early step

In Allosteric Activation, high concentration of a metabolite early in the pathway activates enzymes for synthesis of the final product.

Flux through the pathway is regulated depending on the concentration of Metabolites (F and I below)

Feed-Forward Activation

- Metabolite early in the pathway activates an enzyme furtherdown the pathway

B is an allosteric activator

Figure 7.11 Effect of regulators on aspartate transcarbamoylase

ATP relaxes the enzyme (R state favored)Binding of substrates more favored

CTP makes enzyme more “tense” (T state favored) binding of substrates less favored

CTP

Regulation by covalent modification

Enzyme activity can be modified by covalent attachmentand removal of groups on the polypeptide chain

reversible phosphorylation

Pyruvate dehydrogenasecatalyzes a reaction that linkglycolysis and the citric acid cycle.

Phosphate is attached to serine residue

Inactive form

Phosphate is removed from serine residue reactivated form

Assignment

Read Chapter 7Read Chapter 8

Topics not covered:Concerted and Sequential models Section 7.4 Enzymes can be studied one molecule at a time.