Enzyme Kinetics

Chapter 6

Kinetics

• Study of rxn rates, changes with changes in experimental conditions

• Simplest rxn: S P

– Rate meas’d by V = velocity (M/sec)

– Depends on k, [S]

Michaelis-Menten Kinetics• Gen’l theory rxn rate w/

enzymatic catalysis

• Add E, ES to rxn:

E + S ES E + P

• Assume little reverse rxn E + P ES

So E + S ES E + P

• Assign rate constants k1, k-1, k2

• Assume: Vo condition -- [S] >>> [E]

– Since S used up during rxn, can’t be limiting

• Assume: All E goes to ES

• Assume: Fixed amt enzyme

– If all E ES, will see max rate of P formed

– At steady state

rate form’n ES = rate breakdown ES

Exper’l Findings:

– As incr [S], V incr’s linearly up to some max V

– At max V, little V incr regardless of [S] added

M-M Relates [E], [S], [P] Exper’ly Provable Variables

• New constant:

KM = (k2 + k-1) / k1

• M-M eq’n:

Vo = (Vmax [S]) / (KM + [S])

• Quantitative relationship between

– Initial velocity

– Max rate of rxn

– Initial [S]

Exper’l Definition of KM

• At ½ Vmax (substitute ½ Vmax for Vo)

• Divide by Vmax

• Solve for KM

• KM = [S]

• So when Vo = ½ Vmax , KM = [S]

Difficult to Determine Variables from M-M Plot

• Hard to measure small changes in V

• Use double reciprocal plot straight line

• Lineweaver-Burk (Box 6-1)

KM

• [S] at which ½ enz active sites filled

• Related to rate constants

• In living cells, value close to [S] for that E

– Commonly enz active sites NOT saturated w/ S

• May describe affinity of E for S ONLY if k-1 >>> k2

– Right half of rxn equation negligible

– KM = k-1 / k1

– Describes rate form’n, breakdown of ES

• Considered dissociation constant of ES complex

– Here, KM value indicates strength of binding E-S

– In real life, system is more complex

Other Kinetics Variables

• Turnover #

– kcat

– # S molecules converted P by 1 enz molecule per unit time

– Use when enz is fully sat’d w/ S

Comparisons of Catalytic Abilities• Optimum KM, kcat values for each E

• Use ratio to compare catalytic efficiencies

• Max efficiency at kcat / KM = 107– 108 M-1 sec-1

– Velocity limited by E encounters w/ S

– Called Diffusion Controlled Limit

Kinetics When>1 Substrate• Random order = E can accept

either S1 or S2 first

• Ordered mechanism = E must accept S1 first, before S2 can bind

• Double displacement (or ping-pong) = S1 must bind and P1 must be released before S2 can bind and P2 is released

Inhibition• Used by cell to control catalysis

in metabolic pathways

• Drugs, toxins alter catalysis by inhib’n

• Used as tools to study mechanisms

• Irreversible

• Reversible

– Includes competitive, noncompetitive, uncompetitive

Irreversible Inhibition

• Inhibitor binds tightly to enz

• Dissociates slowly or not at all

• Book example: DIFP

• Includes suicide substrate inhibitors

Reversible Inhibition

• Inhibitor may bind at active site or some distal site

• Binding reversible

• Temporarily inhibits E, S binding or proper rxn

• Can calculate KI

• Competitive

– “Appear as S”

– Bind active site

•So compete w/ S for active site

– Overcome w/ incr’d [S]

– Affects KM, not Vmax

Reversible Inhib’n (cont’d)• Uncompetitive

– Binds only when S already bound (so ES complex)

– Bind at site away from active site

– Causes conform’l change, E inactivated

– Not overcome w/ incr’d [S]

– Affects both KM, Vmax

– Common when S1 + S2

Reversible Inhib’n (cont’d)• Noncompetitive (Mixed)

– When S bound or not

– Bind at site away from active site

– Conform’l change in E

– E inact’d when I bound

– Decr’d E avail for binding S, rxn catalysis

– Not overcome w/ incr’d [S]

– Affects both KM, Vmax

– Common when S1 + S2

Effect of pH on Catalysis• Optimum pH where max activity

• Aa’s impt to catalysis must maintain partic ionization

• Aa’s in other parts of enz impt to maintain folding, structure must also maintain partic ionization

• Can predict impt aa’s by activity changes at different pH’s (use pKa info)