General Features of Enzymes Most biological reactions are catalyzed by enzymes Most enzymes are proteins Highly specific (in reaction & reactants) Involvement of cofactor or coenzyme in some enzymes (prosthetic groups, holoenzyme, apoenzyme) Activity regulated through –Feedback inhibition –Regulatory proteins (e.g. calmodulin) –Covalent modification (e.g. phosphorylation) –Precursor to mature form transition (proteolytic activation)

How Enzymes Work Substrate binding is the first step of enzymatic catalysis –Substrate –Active site Binds substrate (by multiple weak interactions) A 3-dimensional entity complementary to substrate Contains catalytic residues Size and location: Small; located at clefts or crevices Source of binding specificity

Enzyme-substrate interaction: Lock-and-key model Induced fit model

Enzymes Accelerate Reaction RateHow? Enzymes accelerate reaction rate but do not alter equilibrium! Rate of reaction = (Ae -  G‡/RT )[S] Accelerate reaction rate by stabilizing transition states (  G‡) Essence of catalysis: specific binding of the transition state

Michaelis-Menten Model Accounts for Kinetic Properties of many Enzyme Kinetic properties of many enzymes (V vs. [S] plot) Michaelis-Menten Model E + S ES E + P –Purpose: using the model to derive an expression relating rate of reaction to [E] and [S] and k 1, k 2, and k 3 –Assumption #1: no product reverts to initial substrate (initial state) –Assumption #2: steady state ([ES] is constant) k 1 [E][S]=k 2 [ES]+k 3 [ES], so [ES] = [E][S]/K M ; K M =(k 2 +k 3 )/k1 [E] = [E T ] - [ES]; [S] = [S T ] - [ES] - [P] work under the following condition: [E T ] << [S T ] ; and at initial time, so [P] is negligible, and so [S] = [S T ]  [ES] = [E T ] [S]/(K M + [S]) so, V = k 3 [ES] = k 3 [E T ] [S]/(K M + [S]) = V max [S]/(K M + [S]) k1k1 k2k2 k3k3

Michaelie-Menten equations explains the kinetic trend seen for many enzymes V = V max [S]/(K M + [S]): –When [S] << K M, V = V max [S]/K M, V is directly proportional to [S] –When [S] >> K M, V = V max, rate is maximal, independent of [S] –When [S] = K M, V = (1/2) V max, so, K M = [S] when V is 1/2 V max

Determine K M and V max –Experimental Procedure Set up several reactions with fixed [E T ] but increasing [S T ] Experimentally determine V at various [S T ] (simplified as [S]; V is initial velocity so [P] is negligible) –Data Analysis Using Michaelis-Menten Equation: V = V max [S]/(K M + [S]) –Plot V vs. [S]; computer curve fitting to find K M and V max Lineweaver-Burk Plot 1/V = 1/V max + (K M /V max ) 1/[S] –Plot 1/V vs. 1/[S] –Y intercept = 1/V max ; X intercept = -1/K M

Kinetic Perfection in Enzymatic Catalysis For Enzymes that Obey Michaelis-Menten Model –When all enzyme molecules are saturated with substrate V = V max = k 3 [E T ], rate constant is k 3 (= k cat ) –When [S] << K M and so most of the active sites are unoccupied V = k 3 [ES]= k 3 [E][S]/K M as [S] << K M, so [E]  [E T ], so V = k 3 [E T ][S]/K M = (k 3 /K M )[E T ][S] so V depends on k 3 / K M: k 3 / K M = k 3 k 1 / (k 2 + k 3 ) < k 1 k 1 cannot be faster than diffusion controlled encounter of an enzyme and its substrate, which is 10 8 to 10 9 M -1 s -1 So, the upper limit of k 3 / K M is 10 8 to 10 9 M -1 s -1. For Enzymes that Do not Obey Michaelis-Menten Model –When all E are saturated with S, rate depends on k cat ; k cat  k 3 –When not all E are saturated with S, rate depends on k cat / K M Some enzymes having k 3 /K M of M -1 s -1  reached kinetic perfection! Their catalytic velocity is limited by the rate at which they encounter substrate in the solution.

Enzyme Inhibition Irreversible Inhibition –Inhibitor destroys a functional group on the enzyme –Or inhibitor binds to the enzyme very tightly (covalently or noncovalently)  dissociates very slowly from enzyme Reversible Inhibition

–Inhibitor binds and dissociate rapidly from the enzyme –Competitive inhibitor Inhibitor binds at active site; compete for binding with substrate; exist as either ES or EI; no ESI Inhibitor structure resembles that of substrate Overcome competitive inhibition by increasing [S] –Noncompetitive inhibitor Inhibitor binds at a site other than active site Binding of noncompetitive inhibitor decreases turnover number (reduces k 3 )

Kinetics of Enzyme Inhibition Assume the enzyme exhibits Michaelis-Menten Kinetics –Set up enzymatic reactions with fixed [E T ] but increasing [S T ] –One set without inhibitor and another set with inhibitor –Plot 1/V vs. 1/[S] (Lineweaver-Burk Plot)

Competitive Inhibition –The two lines on the plot have the same Y intercept (Same V max ) –K M and K I M are different : K I M = K M (1 + [I]/K I ) K I = [E][I]/[EI] (for E + I EI) –1/V = 1/V max + K M /V max (1 + [I]/K I ) (1/[S]) –K M and K I M can be determined from the Lineweaver-Burk plot – K M ’ = K M (1 + [I]/K I ) allows the determination of K I –Inhibition can be overcome by increasing [S] Kinetics of Enzyme Inhibition

Noncompetitive Inhibition –Same K M in the presence and absence of Inhibitor –Smaller V max in the presence of Inhibitor –V I max = V max /(1 + [I]/K I ) –V I max and V max can be determined from the Lineweaver- Burk plot –V I max = V max /(1 + [I]/K I ) allows the determination of K I –Cannot be overcome by increasing [S]