Chapter 6.3: Enzyme Kinetics CHEM 7784 Biochemistry Professor Bensley

CHAPTER 6.3 Enzyme Kinetics –description of enzyme kinetics by examining the Michaelis-Menten theory Today’s Objectives: (To learn and understand the)

What is (are?) Enzyme Kinetics? Kinetics is the study of the rate at which compounds react Rate of enzymatic reaction is affected by –Enzyme –Substrate –Effectors –Temperature

How to Take Kinetic Measurements

Effect of Substrate Concentration Ideal Rate: Deviations due to: –Limitation of measurements –Substrate inhibition –Substrate prep contains inhibitors –Enzyme prep contains inhibitors

Plot V 0 vs. [S] Michaelis-Menten Equation Describes rectangular hyperbolic plot V o = Vmax [S] Km + [S]

K m = ½ Vmax (units moles/L=M) (1/2 of enzyme bound to S) V max = velocity where all of the enzyme is bound to substrate (enzyme is saturated with S)

1)Measurements made to measure initial velocity (v o ). At v o very little product formed. Therefore, the rate at which E + P react to form ES is negligible and k -2 is 0. Therefore Initial Velocity Assumption E + S ESE + P k1k1 k -1 k2k2 E S + E S k -2 E+ P

Steady State Assumption E + S ESE + P k1k1 k -1 k2k2 Steady state Assumption = [ES] is constant. The rate of ES formation equals the rate of ES breakdown E S + E S E+ P

E + S ES k1k1 E S + E S Rate of ES formation Rate = k 1 [E] [S]

ESE + P k2k2 E S E+ P ESE + S k -1 E S + E S Rate of ES breakdown Rate = (k 2 [ES]) + (k -1 [ES]) Rate = [ES](k 2 + k -1 )

Therefore………if the rate of ES formation equals the rate of ES breakdown 1) k 1 [E][S] = [ES](k -1 + k 2 ) 2) (k -1 + k 2 ) / k 1 = [E][S] / [ES] 3) (k -1 + k 2 ) / k 1 = K m (Michaelis constant)

What does K m mean? 1.K m = [S] at ½ V max 2.K m is a combination of rate constants describing the formation and breakdown of the ES complex 3.K m is usually a little higher than the physiological [S]

What does K m mean? 4.K m represents the amount of substrate required to bind ½ of the available enzyme (binding constant of the enzyme for substrate) 5.K m can be used to evaluate the specificity of an enzyme for a substrate (if obeys M-M) 6.Small K m means tight binding; high K m means weak binding GlucoseKm = 8 X AlloseKm = 8 X MannoseKm = 5 X Hexokinase Glucose + ATP Glucose-6-P + ADP

What does k cat mean? E + S ES E + P k1k1 k -1 k cat

What does k cat /K m mean?

Aren’t Enzymes Kinetics Fun?! The final form of M-M equation in the case of a single substrate is k cat (turnover number): how many substrate molecules can one enzyme molecule convert per second K m (Michaelis constant): an approximate measure of substrate’s affinity for enzyme

Limitations of M-M 1.Some enzyme catalyzed rxns show more complex behaviorE + S ES EZ EP E + P With M-M can look only at rate limiting step 2.Often more than one substrate E+S 1 ES 1 +S 2 ES 1 S 2 EP 1 P 2 EP 2 +P 1 E+P 2 Must optimize one substrate then calculate kinetic parameters for the other 3.Assumes k -2 = 0 4.Assume steady state conditions

V max Km K m ~ 1.3 mM V max ~ 0.25

-1/K m = -0.8 K m = 1.23 mM 1/V max = 4.0 V max = /