Enzyme Kinetics

Chapter 8

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

• 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

Fig. 8-11

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]

Fig. 8-12

Difficult to determine variables from M-M plot

• Hard to measure small changes in V

• Use double reciprocal plot straight line

• Lineweaver-Burk (Box 8-1)

Box 8-1

KM (Table 8-6)

• [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

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

– In real life, system is more complex

Table 8-6

Other kinetics variables (Table 8-7)

• Turnover #

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

– Use when enz is fully sat’d w/ S

– Equals k2

– Can calc from Vmax if know [ET]

Other kinetics variables (cont’d)

• kcat

– Max catalytic rate for E when S saturating

– Equivalent to k of rate limiting step

– For M-M ( E + S <==> ES <==> E + P ), kcat = k2

– Can be complex

– Book = turnover #

Table 8-7

Comparisons of catalytic abilities• Optimum KM, kcat values for each E

• Use ratio to compare catalytic efficiencies

• Max efficiency at kcat / KM = 108 – 109 M-1 sec-1

– Velocity limited by E encounters w/ S

– Called Diffusion Controlled Limit

Table 8-8

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

Fig. 8-13

Fig. 8-13 (cont’d)

Inhibition

• Used by cell to control catalysis in metabolic pathways

• Used to alter catalysis by drugs, toxins

• 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

Fig. 8-16

Reversible inhibition• Inhibitor may bind at active site or some distal

site

• Binding is 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

Fig. 8-15

Reversible inhibition (cont’d)

• Noncompetitive (Mixed)

– When S bound or not

– Bind at site away from active site

– Causes conform’l change in E

– E inactivated 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

Fig. 8-15 (cont’d)

Reversible inhibition (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

Fig. 8-15 (cont’d)

Effect of pH on catalysis

• Optimum pH where maximal activity

• Aa’s impt to catalysis must maintain particular 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)

Fig. 8-17