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 Rate How?

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 k1, k2, and k3

– Assumption #1: no product reverts to initial substrate (initial state)

– Assumption #2: steady state ([ES] is constant)

• k1[E][S]=k2[ES]+k3[ES], so [ES] = [E][S]/KM ; KM =(k2+k3)/k1

• [E] = [ET] - [ES]; [S] = [ST] - [ES] - [P]

• work under the following condition: [ET] << [ST] ; and at initial time, so [P] is negligible, and so [S] = [ST] [ES] = [ET] [S]/(KM + [S])

so, V = k3 [ES] = k3[ET] [S]/(KM + [S]) = Vmax [S]/(KM + [S])

k1

k2

k3

• Michaelie-Menten equationsexplains the kinetic trendseen for many enzymes

V = Vmax [S]/(KM + [S]):

– When [S] << KM, V = Vmax [S]/KM ,V is directly proportional to [S]

– When [S] >> KM , V = Vmax ,rate is maximal, independent of [S]

– When [S] = KM, V = (1/2) Vmax,

so, KM = [S] when V is 1/2 Vmax

• Determine KM and Vmax

– Experimental Procedure• Set up several reactions with fixed [ET] but increasing [ST] • Experimentally determine V at various [ST] (simplified as [S];

V is initial velocity so [P] is negligible)

– Data Analysis• Using Michaelis-Menten Equation:

V = Vmax [S]/(KM + [S])– Plot V vs. [S]; computer curve fitting to find KM and Vmax

• Lineweaver-Burk Plot

1/V = 1/Vmax + (KM/Vmax) 1/[S]– Plot 1/V vs. 1/[S]

– Y intercept = 1/Vmax; X intercept = -1/KM

Kinetic Perfection in Enzymatic Catalysis• For Enzymes that Obey Michaelis-Menten Model

– When all enzyme molecules are saturated with substrate

• V = Vmax = k3 [ET], rate constant is k3 (= kcat)

– When [S] << KM and so most of the active sites are unoccupied

• V = k3 [ES]= k3 [E][S]/KM

as [S] << KM, so [E] [ET], so V = k3 [ET][S]/KM = (k3/KM)[ET][S]

so V depends on k3 / KM: k3 / KM= k3 k1 / (k2 + k3) < k1

k1 cannot be faster than diffusion controlled encounter of

an enzyme and its substrate, which is 108 to 109 M-1 s-1

So, the upper limit of k3 / KM is 108 to 109 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; kcat k3

– When not all E are saturated with S, rate depends on k cat / KM

• Some enzymes having k3/KM of 108 - 109 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

• 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 k3)

Kinetics of Enzyme Inhibition

• Assume the enzyme exhibits Michaelis-Menten Kinetics

– Set up enzymatic reactions with fixed [ET] but increasing [ST]

– 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)

– KM and KIM are different : KI

M = KM (1 + [I]/KI)

KI = [E][I]/[EI] (for E + I EI)

– 1/V = 1/Vmax + KM/Vmax (1 + [I]/KI) (1/[S])

– KM and KIM can be determined from the Lineweaver-

Burk plot

– KM’ = KM (1 + [I]/KI) allows the determination of KI

– Inhibition can be overcome

by increasing [S]

Kinetics of Enzyme Inhibition

Kinetics of Enzyme Inhibition

• Noncompetitive Inhibition– Same KM in the presence and absence of Inhibitor

– Smaller V max in the presence of Inhibitor

– VI max = V max /(1 + [I]/KI)

– VI max and V max can be determined from the Lineweaver-

Burk plot

– VI max = V max /(1 + [I]/KI)

allows the determination of KI

– Cannot be overcome

by increasing [S]