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: K M = (k2 + k-1) / k1 M-M eq’n: Vo = (V max [S]) / (K M + [S]) Quantitative relationship between –Initial velocity –Max rate of rxn –Initial [S]

Exper’l definition of K M At ½ V max (substitute ½ V max for Vo) Divide by V max Solve for K M K M = [S] So when Vo = ½ V max, K M = [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

K M (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 –K M = k-1 / k1 –Describes rate form’n, breakdown of ES –Here, K M 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 V max if know [E T ]

Other kinetics variables (cont’d) k cat –Max catalytic rate for E when S saturating –Equivalent to k of rate limiting step –For M-M ( E + S ES E + P ), k cat = k2 –Can be complex –Book = turnover #

Table 8-7

Comparisons of catalytic abilities Optimum K M, k cat values for each E Use ratio to compare catalytic efficiencies Max efficiency at k cat / K M = 10 8 – 10 9 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 (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 K I Competitive –“Appear as S” – Bind active site So compete w/ S for active site –Overcome w/ incr’d [S] –Affects K M, not V max

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 K M, V max –Common when S1 + S2

Fig (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 K M, V max –Common when S1 + S2

Fig (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