Enzyme Kinetics
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Kinetics of Enzyme-Catalyzed Reactions: Michaelis-Menten KineticsEnzyme Inhibition
Kinetics of Two-Substrate ReactionsRibozymes and Abzymes
How Enzymes Work
?Enzyme-catalyzed reactions are characterized by the formation of a complexbetween the enzyme and its substrate (the ES complex)
?Substrate binding occurs in a pocket on the enzyme called the active site?Enzymes accelerate reactions by lowering the free energy of activation DG?.The equilibrium of the reaction remains unaffected by the enzyme
?Enzymes do this by binding the transition state of the reaction better than thesubstrate
Where Does the Energy Come From?
?Enzyme-substrate interactions are predominantly non-covalent
–ionic–H-bonds–hydrophobic
?The active site is structured so that more of these interactions occur in thetransition state
?These bonds account for a significant part of the energy required to reduce DG??The rest comes from the folding free energy of the enzyme in its ESconformation
The Michaelis-Menten Equation
can we find the relationship between rate and [S]?
Step 1. Formation of the ES complex:forward rate v1 = k1[S][E]backward rate v-1 = k-1[ES]
k1S + E ESk-1
This is an equilibrium where the equilibrium constant K = k1/k-1Step 2. Formation of products:forward rate v2 = k2[ES]backward rate v-2 = k-2[E][P]
k2ES E + Pk-2
Breakdown of ES to form products is assumed to be slower than formation ofES (v1) or breakdown of ES to re-form E and S (v-1)
Assumption 1
?Only consider early times in the reaction–[P] is very small–v-2 is negligible
–step 2 is essentially irreversible
k1k2E + S ES E + Pk-1
?So the initial rate v0 = k2[ES]
?We can easily measure initial rates, but [ES] is very difficult to measure
An Expression for [ES]
?Recall that [E]total = [E] + [ES]
?How fast is the enzyme-substrate complex formed and broken down?
k1k2E + S ES E + Pk-1Step 1: rate of formation of ES = k1[S]([E]total - [ES])
Steps 1 and 2: rate of breakdown of ES = k-1[ES] + k2[ES]
Assumption 2
Briggs-Haldane Steady State Assumptionrate of ES formation = rate of ES breakdown
k1[S]([E]total - [ES]) = k-1[ES] + k2[ES]
[ES] = k1[S][E]total k-1 + k2 + k1[S][ES] = [S][E]total [S] + k-1 + k2
k1
Substitute for [ES] in the initial rate equation
v0 = k2[ES][ES] = [S][E]total [S] + k-1 + k2 k1v0 = k2[S][E]total [S] + k-1 + k2 k1
Assumption 3
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[S] >> [E]total
The enzyme is saturated with substrate[ES] = [E]total
So we can define a maximum rate Vmax where
Vmax = k2[E]totalv0 = Vmax[S] [S] + k-1 + k2 k1
Now group the constants: Km = (k-1 + k2)/k1
v0 = Vmax[S] Km + [S]
?The Michaelis-Menten equation is the rate equation for a one-substrate enzyme-catalyzed reaction
?It quantitatively relates the initial rate, the maximum rate, and the initial substrateconcentration to the Michaelis constant Km
Understanding Km
The \
?Km is a constant with units M
?Km is a constant derived from rate constants
?Km is, under true Michaelis-Menten conditions, an estimate of the dissociationconstant of E from S
?Small Km means tight binding; high Km means weak binding
Understanding Vmax
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theoretical maximal velocity
Vmax is a constant with units s-1
Vmax is the theoretical maximal rate of the reaction - but it is NEVER achievedin reality
To reach Vmax would require that ALL enzyme molecules are tightly bound withsubstrate
Vmax is asymptotically approached as [S] is increased
The Dual Nature of the Michaelis-Menten Equation
combination of zero and 1st-order kinetics
?When [S] is low, the equation for rate is 1st order in [S]?When [S] is high, the equation for rate is zero-order in S
?The Michaelis-Menten equation describes a rectangular hyperbolicdependence of v0 on [S]
The Turnover Number
a measure of 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 = Vmax/Etotal
?Values of kcat range from less than 1/sec to many millions per sec
Enzyme Kinetics - University of Vermont：酶动力学-佛蒙特大学
