L16 Enzyme Kinetics (Ch14)

7/29/2019 L16 Enzyme Kinetics (Ch14)

http://slidepdf.com/reader/full/l16-enzyme-kinetics-ch14 1/28

Chapter 14Rates of Enzymatic Reactions

Reading:

V&V pp. 472-487

Chymotrypsin with bound substrate



Enzyme Kinetics

Several terms to know:

• rate or velocity

• rate constant

• rate law

• order of a reaction

• molecularity of a reaction

• Enzymes accelerate reactions by lowering thefree energy of activation

• Enzymes do this by binding the transition state

of the reaction better than the substrate



The Michaelis-Menten Equation

• Louis Michaelis and Maude Menten's theory

• It assumes the formation of an enzyme-substrate complex

• It assumes that the ES complex is in rapidequilibrium with free enzyme

• Breakdown of ES to form products is assumed

to be slower than(1) formation of ES and

(2) breakdown of ES to re-form E and S



The dual nature of the Michaelis-Menten equation

Combination of zero-order and 1st-order kinetics



E + S ES E + P

k1

k-1

k2

Vo = k2 [ES]

Rate of ES formation = k1 [E][S] = k1 ([Etotal] - [ES]) [S]

Rate of ES breakdown = k-1 [ES] + k2 [ES]

k1 ([Etotal] - [ES]) [S] = k-1 [ES] + k2 [ES](steady state assumption)

(k-2 is insignificant early in rxn)



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

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

[ES] =[Etotal][S]

________________________

[S] + (k2 + k-1 ) ___________

k1

=[Etotal][S]

____________

KM + [S]

Vo = k2 [ES] Vo =k2 [Etotal][S] ____________

KM + [S]

Vo = Vmax when [Etotal] = [ES](at saturation)

Therefore Vmax = k2 [Etotal]

Vo =Vmax[S]

____________

KM + [S]



The dual nature of the

Michaelis-Menten equation

Combinat ion o f zero-order and f i rs t -order kinet ics

• When [S] is low, the equation for rate is first order in [S]

• When [S] is high, the equation for rate is zero-order in [S]

• The Michaelis-Menten equation describes a rectangular hyperbolic

dependence of Vo on [S]

Vo = Vmax[S] _________

Km + [S]



Vmax[S]Vo = ____________

KM + [S]

KM = [S]

when Vo

= Vmax _____

2

Enzyme Kinetics: Michaelis-Menton Equation

From LehningerPrinciples of Biochemistry



The following data were obtained in a study of an enzyme known to follow

Michaelis Menten kinetics:

V 0

Substrate added

(mmol/min) (mmol/L)

—————————————

216 0.9

323 2

435 4

489 6647 2,000

—————————————

Calculate the K m for this enzyme.

Without graphing

Vmax = 647

Vmax /2 = 647 / 2 = 323.5

Km = 2 mmol/L

Km is the substrate

concentration that

corresponds to Vmax

2





Understanding Km

• Km is a constant • Km is a constant derived from rate constants

• Km is, under true Michaelis-Menten conditions,

an estimate of the dissociation constant of Efrom S

• Small Km means tight binding; high Km means

weak binding

Enzyme Substrate Km (mM)Glutamate dehydrogenase NH4

+ 57

Glutamate 0.12

Carbonic anhydrase CO2 12



Understanding Vmax

The theoretical maximal velocity

• Vmax is a constant

• Vmax is the theoretical maximal rate of thereaction - but it is NEVER achieved in reality

• To reach Vmax would require that ALLenzyme molecules are tightly bound with

substrate• Vmax is asymptotically approached assubstrate is increased



The turnover number (also known as the molecular activity of the enzyme)

A measure of its maximal catalytic activity • kcat, the turnover number , is the number of

substrate molecules converted to product per enzyme molecule per unit of time, when E is

saturated with substrate.• If the M-M model fits, k2 = kcat

kcat = Vmax/Et

• Values of kcat range from less than 1/sec to many millions per sec

Turnover number comparison

Catalase 40,000,000 sec-1

Lysozyme 0.5 sec-1



Catalytic efficiency of an enzymeName for k cat /K m

• An estimate of "how perfect" the enzyme is • kcat/Km is an apparent second-order rate constant

• It measures how the enzyme performs when S islow

• Catalytic efficiency cannot exceed the diffusionlimit - the rate at which E and S diffuse together

• WT and a mutant protein k cat /K m comparision

WT sulfite oxidase 1.1

Mutant R160K 0.015





Double-Reciprocal or Lineweaver-Burk Plot

1 KM

1 ______ = _______ + ______

Vo Vmax[S] Vmax


Use linear plot and intercepts to

determine Km and Vmax



pH must be specified!



Enzyme Inhibitors

Reversible versus Irreversible

• Reversible inhibitors interact with an

enzyme via noncovalent associations

• Irreversible inhibitors interact with an

enzyme via covalent associations



Classes of Inhibition

Two real, one hypothetical

• Competitive inhibition - inhibitor (I) binds

only to E, not to ES

• Uncompetitive inhibition - inhibitor (I) binds

only to ES, not to E. This is a hypotheticalcase that has never been documented for a

real enzyme, but which makes a useful

contrast to competitive inhibition• Noncompetitive (mixed) inhibition - inhibitor

(I) binds to E and to ES



Inhibitor (I) binds only to E, not to ES

Inhibitor (I) binds only to ES, not to E.

This is a hypothetical case that hasnever been documented for a realenzyme, but which makes a usefulcontrast to competitive inhibition

Inhibitor (I) binds to E and to ES. Enzyme Inhibition




Competitive Uncompetitive NoncompetitiveInhibition Inhibition (Mixed) Inhibition

Kmchangeswhile Vmax does not

Km and Vmax both change

Km and Vmax both change




Succinate dehydrogenase is a classic example of competitive inhibition


Malonate is a strong

competitive inhibitor of

succinate dehydrogenase

C titi I hibiti



1/[S]

1/V

+ I

No I

-1 / Km

-1 / Kmapp

Competitive Inhibition

Km

changes whileVmax does not

Where Kmapp = a Km a = 1 + [I]

KI



1/[S]

1/V+ I

No I

-a’ / Km

-1 / Km

a‘ = 1 + [I]

KI

Uncompetitive inhibition

a’/Vmax

1/Vmax



Type of inhibition Vmaxapp KM

app

No inhibitor Vmax KM

Competitive Vmax aKM

Uncompetitive Vmax/a’ KM/a’

Noncompetitive (Mixed) Vmax/a’ aKM/a’

a = 1 + [I] a’ = 1 + [I]

KI KI’

Effects of Inhibitors on the parameters of Michaelis-Menten Equation

R l ti f ti ti it



Regulation of enzymatic activity

Two ways that this may occur:

1) Control of enzyme availability

Depends on rate of enzyme synthesis & degradation

2) Control of enzyme activityEnzyme-substrate binding affinity may vary with

binding of small molecules called allosteric effectors(ex: BPG for Hb)

Allosteric mechanisms can cause large changes in

enzymatic activity



Regulatory Enzymes

important in controlling flux through metabolic pathways

2. Regulation by covalent modification

1. Allosteric enzymes




Conversion of L-threonine toL-isoleucine catalyzed by asequence five enzymes, E1-E5

L-isoleucine is an inhibitoryallosteric modulator of E1

Regulation by Feedback Inhibition

From Lehninger

Documents

L16 Enzyme Kinetics (Ch14)