Chapter 8: Enzymes: Basic Concepts and Kinetics Copyright © 2007 by W. H. Freeman and Company Berg Tymoczko Stryer Biochemistry Sixth Edition

Chapter 8 Topics 1.Enzyme properties 2.Enzyme Commission classification 3.Rate enhancement by enzymes 4.Hydrolase enzymes: peptidase/esterase activity 5.Enzyme cofactors 6.Reaction thermodynamics 7.Graphical methods 8.The enzymesubstrate complex 9.Enzyme models: Fisher & Koshland 10. Kinetics: Michaelis-Menton equation and plot 11. Line-Weaver-Burke plot: determine K M and V max 12. k cat, K M and k cat / K M 13. Multisubstrate reactions: Cleland notation 14. Enzyme inhibition

Enzymes Enzymes are typically proteins that serve as catalysts for biochemical reactions. Note that a few RNA catalysts (ribozymes) and antibody catalysts (abzymes) have been observed. Enzymes are characterized by: 1. Catalysis for rate enhancement All do this to some degree 2. Specificity for substrate Varies with the enzyme 3. Regulation of reaction or pathway Some are regulatory, some are not 4.Cofactors Some use cofactors, some do not

Enzyme Classification Enzyme Commission System: Lactate dehydrogenase = EC Know the six main classes and the EC class no.

Rate Enhancement Formation of carbonic acid from CO 2 and H 2 O. Uncatalyzed rate = 1.3 x molecules/sec Catalyzed rate = 1.0 x 10 6 molecules/sec Rate enhancement = 7.7 x 10 6 times Carbonic Anhydrase

Table of Rate Enhancements

Examples of Enzymatic Activity. Proteolytic Activity A protease Catalyzes cleavage of a peptide bond

Esterase Activity Many proteases also manifest esterase activity and catalyze cleavage of an ester bond.

Cleavage of a Peptide Bond Enzymatic cleavage occurs on the carboxyl side of the recognized sidechain. Trypsin

Cofactors (Apoenzyme + Cofactor = Holoenzyme) Some enzymes require cofactors for activity

Thermodynamic Equations  G =  H - T  S  [C eq ][D eq ] = - RT ln [A eq ][B eq ] [C][D]  G =  G o ' + RT ln [A][B] For the reaction:A + B C + D  G o ' = - RT ln K eq ' Free energy Enthalpy Entropy

 G o' and Keq' Keq' = Triosephosphate Isomerase  G o ' = - RT ln K eq ' = (298) ln  G o ' = (-3.05) = 7550 J/mol = 7.55 kJ/mol

Catalyzed vs Uncatayzed Rate Measure formation of product or loss of substrate with time

Reaction Coordinate

Reaction Rate vs [S] E + S ES E + P k1k1 k -1 k2k2 ES is a noncovalent compex

Enzyme Substrate Complex, ES (noncovalent)

Active Site Residues Need not be adjacent in the sequence. 3 o structure must have them all positioned around the active site.

Lock & Key – Fischer (1894) A proposal for ES

Induced Fit – Koshland (1963) A proposal for ES

Enzyme Kinetics E + S ESE + P k1k1 k2k2 k -1 E = enzyme concentration S = Substrate concentration ES = Enzyme-substrate complex concentration P = product concentration k 1 = rate constant for formation of ES from E + S k - 1 = rate constant for decomposition of ES to E + S k 2 = rate constant for decomposition of ES to E + P

Michaelis-Menton Plot Graphical relationship between reaction velocity and substrate concentration E + S ES E + P k1k1 k -1 k2k2 Zero order (High [S]) 1 st order (low [S])

Finding Initial Veocity, V o Rate at the start of an enzyme catalyzed reaction

Enzyme Kinetics Enzyme-substrate complex (ES) - a non-covalent complex formed when specific substrates fit into the enzyme active site When [S] >> [E], every enzyme binds a molecule of substrate (enzyme is saturated with substrate) Under these conditions the rate depends only upon [E], and the reaction is pseudo-first order E + S ESE + P k1k1 k2k2 k -1

The Michaelis-Menton Equation (1) Assume steady-state conditions: Rate of ES formation = Rate of ES decomposition (2) Define Michaelis constant: K M = (k -1 + k 2 ) / k 1 (3) The overall velocity of an enzyme-catalyzed reaction is given by rate of conversion of ES to E + P. v o = k 2 [ES] = k cat [ES]

Reaction Constituents

Michaelis-Menton Derivation 1. The overall rate of product formation: v = k 2 [ES] 2. Rate of formation of [ES]:v f = k 1 [E][S] 3. Rate of decomposition of [ES]: v d = k -1 [ES] + k 2 [ES] 4. Rate of ES formation = Rate of ES decomposition (steady state) 5. So: k 1 [E][S] = k -1 [ES] + k 2 [ES] E + S ESE + P k1k1 k2k2 k -1

Michaelis-Menton Derivation 6. In solving for [ES], use the enzyme balance to eliminate [E]. E T = [E] + [ES] 7. k 1 (E T - [ES])[S] = k -1 [ES] + k 2 [ES] k 1 E T [S] - k 1 [ES][S] = k -1 [ES] + k 2 [ES] 8. Rearrange and combine [ES] terms: k 1 E T [S] = (k -1 + k 2 + k 1 [S])[ES] k 1 E T [S] 9. Solve for [ES] = (k -1 + k 2 + k 1 [S])

Michaelis-Menton Derivation E T [S] 10. Divide through by k 1 : [ES] = (k -1 + k 2 )/k 1 + [S] 11. Defined Michaelis constant: K M = (k -1 + k 2 ) / k Substitute K M into the equation in step Then substitute [ES] into v = k 2 [ES] from step1 and replace V max with k 2 E T to give: V max [S] v o = K M + [S]

Michaelis-Menton Plot Relates reaction velocity and substrate concentration V max [S] v o = K M + [S]

Lineweaver-Burke Plot Also called a double reciprocal plot 1 K M = v o V max [S] V max

k cat In an enzyme catalyzed reaction, the overall rate of product formation is v = k 2 [ES]. If all of the enzyme molecules are complexed with substrate (excess [S]) then the maximum velocity occurs and V max = k cat E T where k cat is the overall reaction rate constant. This can also be written as k cat = V max /E T. k cat is called the turnover number (TON). E + S ESE + P k1k1 k2k2 k -1

KMKM When K M = [S] when v o = 1/2 Vmax. K M  k -1 / k 1 = K s (the enzyme-substrate dissociation constant) when k cat is small (<< either k 1 or k -1 ). Generally, the lower the numerical value of K M, the tighter the substrate binding. K M is used as a measure of the affinity of E for S.

= k cat (s -1 )

k cat /K M k cat /K M is taken to be a measure of the efficiency of an enzyme. Rewriting k cat /K M in terms of the kinetic constants gives: k cat k 1 k = K M k -1 + k 2 So, where k 2 is small, the denominator becomes k -1 and k cat /K M is small.

k cat /K M k cat k 1 k = K M k -1 + k 2 And where k 2 is large, the denominator becomes k 2 and k cat /K M is limited by the value of k 1 or formation of the ES complex. This formation is in turn limited by the rate of diffusion of S into the active site of E. So, the maximum value for this second-order rate constant (k cat /K M ) is the rate of diffusion (~10 9 sec -1 M -1 ).

k cat /K M

Multisubstrate Reactions Ordered Sequential Ordered = all reactants in before reaction occurs

Cleland Notation Ordered Sequential

Multisubstrate Reactions Ordered Random

Cleland Notation Ordered Random

Multisubstrate Reactions Ping Pong Substrate and product alternate in and out

Cleland Notation Ping Pong

An allosteric enzyme

Enzyme Inhibition Noncovalent binding: Competitive (I binds only to E) Uncompetitive (I binds only to ES) Noncompetitive (I binds to E or ES) Covalent binding – irreversible Group Specific Substrate Analogs Suicide

Competitive Inhibition

(I binds only to E)

1 K M (1 + I/K i ) = x v V M S V M K M raised; V M same

Uncompetitive Inhibition

(I binds only to ES)

1 K M / (1 + I/K i ) = x v V M / (1 + I/K i ) S V M / (1 + I/K i ) K M & V M lowered

Noncompetitive Inhibition

(I binds to E or ES)

1 K M = x v V M / (1 + I/K i ) S V M / (1 + I/K i ) K M same; V M lowered

Irreversible - Group Specific

Irreversible - Substrate Analog

Irreversible - Suicide

Transition State Analog

End of Chapter 8 Copyright © 2007 by W. H. Freeman and Company Berg Tymoczko Stryer Biochemistry Sixth Edition