Reaction Coordinate Diagram

Enzymes Decrease G

Rate Enhancement by Enzymes

How to Lower GEnzymes organize reactive groups into close proximity and proper orientation Uncatalyzed bimolecular reactions two free reactants single restricted transition state conversion is entropically unfavorable Uncatalyzed unimolecular reactions flexible reactant rigid transition state conversion is entropically unfavorable for flexible reactants Catalyzed reactionsEnzyme uses the binding energy of substrates to organize the reactants to a fairly rigid ES complexEntropy cost is paid during bindingRigid reactant complex transition state conversion is entropically OK

How to Lower GEnzymes bind transition states bestThe idea was proposed by Linus Pauling in 1946Enzyme active sites are complimentary to the transition state of the reactionEnzymes bind transition states better than substratesStronger/additional interactions with the transition state as compared to the ground state lower the activation barrierLargely H effect

Illustration of TS Stabilization Idea: Imaginary Stickase

Catalytic Mechanismsacid-base catalysis: give and take protonscovalent catalysis: change reaction pathsmetal ion catalysis: use redox cofactors, pKa shifterselectrostatic catalysis: preferential interactions with TS

General Acid-Base Catalysis

Amino Acids in General Acid-Base Catalysis

Covalent CatalysisA transient covalent bond between the enzyme and the substrateChanges the reaction Pathway

Uncatalyzed:

Catalyzed:

Requires a nucleophile on the enzymeCan be a reactive serine, thiolate, amine, or carboxylate

Metal Ion CatalysisInvolves a metal ion bound to the enzyme

Interacts with substrate to facilitate bindingStabilizes negative charges

Participates in oxidation reactions

Chymotrypsin uses most of the enzymatic mechanisms

Active Site of Chymotrypsin with Substrate

Chymotrypsin Mechanism

Chymotrypsin Mechanism Step 1: Substrate Binding

Chymotrypsin Mechanism Step 2: Nucleophilic Attack

Chymotrypsin Mechanism Step 3: Substrate Cleavage

Chymotrypsin Mechanism Step 4: Water Comes In

Chymotrypsin Mechanism Step 5: Water Attacks

Chymotrypsin Mechanism Step 6: Break-off from the Enzyme

Chymotrypsin Mechanism Step 7: Product Dissociates

What is enzyme kinetics?Kinetics is the study of the rate at which compounds reactRate of enzymatic reaction is affected by:enzymesubstrateeffectorstemperature

Why study enzyme kinetics?Quantitative description of biocatalysisDetermine the order of binding of substratesElucidate acid-base catalysisUnderstand catalytic mechanismFind effective inhibitorsUnderstand regulation of activity

How to Do Kinetic MeasurementsExperiment:Mix enzyme + substrateRecord rate of substrate disappearance/product formation as a function of time (the velocity of reaction)Plot initial velocity versus substrate concentration.Change substrate concentration and repeat

Effect of Substrate Concentration Ideal rate:

Deviations due to: limitation of measurements substrate inhibition substrate prep contains inhibitors enzyme prep contains inhibitors

Effect of Substrate Concentration

Saturation Kinetics: At high [S] velocity does not depend on [S]

Determination of Kinetic ParametersNonlinear Michaelis-Menten plot should be used to calculate parameters Km and Vmax.

Linearized double-reciprocal plot is good for analysis of two-substrate data or inhibition.

Lineweaver-Burk Plot:Linearized, Double-Reciprocal

Derivation of Enzyme Kinetics EquationsStart with a model mechanismIdentify constraints and assumptionsCarry out algebra ...... or graph theory for complex reactions

Simplest Model Mechanism: E + S ES E + POne reactant, one product, no inhibitors

Identify Constraints and AssumptionsTotal enzyme concentration is constantMass balance equation for enzyme: ETot = [E] + [ES]It is also implicitly assumed that: STot = [S] + [ES] [S]

Steady state assumption

What is the observed rate?Rate of product formation

Carry out the algebraThe final form in case of a single substrate is

kcat (turnover number): how many substrate molecules can one enzyme molecule convert per secondKm (Michaelis constant): an approximate measure of substrates affinity for enzymeMicroscopic meaning of Km and kcat depends on the details of the mechanism

Enzyme efficiency is limited by diffusion:kcat/KMCan gain efficiency by having high velocity or affinity for substrateCatalase vs. acetylcholinesterase

Two-Substrate ReactionsKinetic mechanism: the order of binding of substrates and release of products

When two or more reactants are involved, enzyme kinetics allows to distinguish between different kinetic mechanismsSequential mechanismPing-Pong mechanism

Sequential Kinetic MechanismWe cannot easily distinguish random from orderedRandom mechanisms in equilibrium will give intersection point at y-axisLineweaver-Burk: lines intersect

Ping-Pong Kinetic MechanismLineweaver-Burk: lines are parallel

Enzyme InhibitionInhibitors are compounds that decrease enzymes activity

Irreversible inhibitors (inactivators) react with the enzymeOne inhibitor molecule can permanently shut off one enzyme moleculeThey are often powerful toxins but also may be used as drugs

Reversible inhibitors bind to and can dissociate from the enzymeThey are often structural analogs of substrates or productsThey are often used as drugs to slow down a specific enzyme

Reversible inhibitor can bind: to the free enzyme and prevent the binding of the substrateto the enzyme-substrate complex and prevent the reaction

Competes with substrate for binding Binds active siteDoes not affect catalysis

No change in Vmax; apparent increase in KMLineweaver-Burk: lines intersect at the y-axis

Competitive Inhibition

Competitive Inhibition

Competitive Inhibition

Uncompetitive InhibitionOnly binds to ES complex Does not affect substrate bindingInhibits catalytic function

Decrease in Vmax; apparent decrease in KMNo change in KM/VmaxLineweaver-Burk: lines are parallel

Uncompetitive Inhibition

Uncompetitive Inhibition

Mixed InhibitionBinds enzyme with or without substrateBinds to regulatory siteInhibits both substrate binding and catalysisDecrease in Vmax; apparent change in KMLineweaver-Burk: lines intersect left from the y-axisNoncompetitive inhibitors are mixed inhibitors such that there is no change in KM

Mixed Inhibition

Mixed Inhibition

Enzyme activity can be regulatedRegulation can be:noncovalent modificationcovalent modificationirreversiblereversible

Noncovalent Modification: Allosteric RegulatorsThe kinetics of allosteric regulators differ from Michaelis-Menten kinetics.

Some Reversible Covalent Modifications

Zymogens are activated by irreversible covalent modification

The blood coagulation cascade uses irreversible covalent modification

Some enzymes use multiple types of regulation

Chapter 6: Summarywhy nature needs enzyme catalysishow enzymes can accelerate chemical reactionshow chymotrypsin breaks down peptide bonds how to perform and analyze kinetic studieshow to characterize enzyme inhibitors how enzyme activity can be regulated

In this chapter, we learned:

*FIGURE 6-2 Reaction coordinate diagram. The free energy of the system is plotted against the progress of the reaction S P. A diagram of this kind is a description of the energy changes during the reaction, and the horizontal axis (reaction coordinate) reflects the progressive chemical changes (e.g., bond breakage or formation) as S is converted to P. The activation energies, G, for the S P and P S reactions are indicated. G is the overall standard free-energy change in the direction S P.*FIGURE 6-3 Reaction coordinate diagram comparing enzyme-catalyzed and uncatalyzed reactions. In the reaction S P, the ES and EP intermediates occupy minima in the energy progress curve of the enzymecatalyzed reaction. The terms Guncat and Gcat correspond to the activation energy for the uncatalyzed reaction and the overall activation energy for the catalyzed reaction, respectively. The activation energy is lower when the enzyme catalyzes the reaction.***FIGURE 65 An imaginary enzyme (stickase) designed to catalyze breakage of a metal stick. (a) Before the stick is broken, it must first be bent (the transition state). In both stickase examples, magnetic interactions take the place of weak bonding interactions between enzyme and substrate. (b) A stickase with a magnet-lined pocket complementary in structure to the stick (the substrate) stabilizes the substrate. Bending is impeded by the magnetic attraction between stick and stickase. (c) An enzyme with a pocket complementary to the reaction transition state helps to destabilize the stick, contributing to catalysis of the reaction. The binding energy of the magnetic interactions compensates for the increase in free energy required to bend the stick. Reaction coordinate diagrams (right) show the energy consequences of complementarity to substrate versus complementarity to transition state (EP complexes are omitted). GM, the difference between the transition-state energies of the uncatalyzed and catalyzed reactions, is contributed by the magnetic interactions between the stick and stickase. When the enzyme is complementary to the substrate (b), the ES complex is more stable and has less free energy in the ground state than substrate alone. The result is an increase in the activation energy.**FIGURE 68 How a catalyst circumvents unfavorable charge development during cleavage of an amide. The hydrolysis of an amide bond, shown here, is the same reaction as that catalyzed by chymotrypsin and other proteases. Charge development is unfavorable and can be circumvented by donation of a proton by H3O+ (specific acid catalysis) or HA (general acid catalysis), where HA represents any acid. Similarly, charge can be neutralized by proton abstraction by OH (specific base catalysis) or B: (general base catalysis), where B: represents any base.*FIGURE 69 Amino acids in general acid-base catalysis. Many organic reactions that are used to model biochemical processes are promoted by proton donors (general acids) or proton acceptors (general bases). The active sites of some enzymes contain amino acid functional groups, such as those shown here, that can participate in the catalytic process as proton donors or proton acceptors.*FIGURE 6-19c Structure of chymotrypsin. (PDB ID 7GCH) (c) The polypeptide backbone as a ribbon structure. Disulfide bonds are yellow; the three chains are colored as in part (a). **FIGURE 6-19d Structure of chymotrypsin. (PDB ID 7GCH) (d) A close-up of the active site with a substrate (white and yellow) bound. The hydroxyl of Ser195 attacks the carbonyl group of the substrate (the oxygens are red); the developing negative charge on the oxygen is stabilized by the oxyanion hole (amide nitrogens from Ser195 and Gly193, in blue), as explained in Figure 622. The aromatic amino acid side chain of the substrate (yellow) sits in the hydrophobic pocket. The amide nitrogen of the peptide bond to be cleaved (protruding toward the viewer and projecting the path of the rest of the substrate polypeptide chain) is shown in white.**FIGURE 6-22 (step 1) Hydrolytic cleavage of a peptide bond by chymotrypsin. The reaction has two phases. In the acylation phase (steps 1 to 4), formation of a covalent acyl-enzyme intermediate is coupled to cleavage of the peptide bond. In the deacylation phase (steps 5 to 7), deacylation regenerates the free enzyme; this is essentially the reverse of the acylation phase, with water mirroring, in reverse, the role of the amine component of the substrate.*FIGURE 6-22 (step 2) Hydrolytic cleavage of a peptide bond by chymotrypsin. The reaction has two phases. In the acylation phase (steps 1 to 4), formation of a covalent acyl-enzyme intermediate is coupled to cleavage of the peptide bond. In the deacylation phase (steps 5 to 7), deacylation regenerates the free enzyme; this is essentially the reverse of the acylation phase, with water mirroring, in reverse, the role of the amine component of the substrate.*FIGURE 6-22 (step 3) Hydrolytic cleavage of a peptide bond by chymotrypsin. The reaction has two phases. In the acylation phase (steps 1 to 4), formation of a covalent acyl-enzyme intermediate is coupled to cleavage of the peptide bond. In the deacylation phase (steps 5 to 7), deacylation regenerates the free enzyme; this is essentially the reverse of the acylation phase, with water mirroring, in reverse, the role of the amine component of the substrate.*FIGURE 6-22 (step 4) Hydrolytic cleavage of a peptide bond by chymotrypsin. The reaction has two phases. In the acylation phase (steps 1 to 4), formation of a covalent acyl-enzyme intermediate is coupled to cleavage of the peptide bond. In the deacylation phase (steps 5 to 7), deacylation regenerates the free enzyme; this is essentially the reverse of the acylation phase, with water mirroring, in reverse, the role of the amine component of the substrate.*FIGURE 6-22 (step 5) Hydrolytic cleavage of a peptide bond by chymotrypsin. The reaction has two phases. In the acylation phase (steps 1 to 4), formation of a covalent acyl-enzyme intermediate is coupled to cleavage of the peptide bond. In the deacylation phase (steps 5 to 7), deacylation regenerates the free enzyme; this is essentially the reverse of the acylation phase, with water mirroring, in reverse, the role of the amine component of the substrate.*FIGURE 6-22 (step 6) Hydrolytic cleavage of a peptide bond by chymotrypsin. The reaction has two phases. In the acylation phase (steps 1 to 4), formation of a covalent acyl-enzyme intermediate is coupled to cleavage of the peptide bond. In the deacylation phase (steps 5 to 7), deacylation regenerates the free enzyme; this is essentially the reverse of the acylation phase, with water mirroring, in reverse, the role of the amine component of the substrate.*FIGURE 6-22 (step 7) Hydrolytic cleavage of a peptide bond by chymotrypsin. The reaction has two phases. In the acylation phase (steps 1 to 4), formation of a covalent acyl-enzyme intermediate is coupled to cleavage of the peptide bond. In the deacylation phase (steps 5 to 7), deacylation regenerates the free enzyme; this is essentially the reverse of the acylation phase, with water mirroring, in reverse, the role of the amine component of the substrate.*FIGURE 6-10 Initial velocities of enzyme-catalyzed reactions. A theoretical enzyme catalyzes the reaction S P, and is present at a concentration sufficient to catalyze the reaction at a maximum velocity, Vmax, of 1 M/min. The Michaelis constant, Km (explained in the text), is 0.5 M. Progress curves are shown for substrate concentrations below, at, and above the Km. The rate of an enzyme-catalyzed reaction declines as substrate is converted to product. A tangent to each curve taken at time = 0 defines the initial velocity, V0, of each reaction.*FIGURE 6-11 Effect of substrate concentration on the initial velocity of an enzyme-catalyzed reaction. The maximum velocity, Vmax, is extrapolated from the plot because V0 approaches but never quite reaches Vmax. The substrate concentration at which V0 is half maximal is Km, the Michaelis constant. The concentration of enzyme in an experiment such as this is generally so low that [S] >> [E] even when [S] is described as low or relatively low. The units shown are typical for enzyme-catalyzed reactions and are given only to help illustrate the meaning of V0 and [S]. (Note that the curve describes part of a rectangular hyperbola, with one asymptote at Vmax. If the curve were continued below [S] = 0, it would approach a vertical asymptote at [S] = Km.)*FIGURE 6-12 Dependence of initial velocity on substrate concentration. This graph shows the kinetic parameters that define the limits of the curve at high and low [S]. At low [S], Km >> [S] and the [S] term in the denominator of the Michaelis-Menten equation (Eqn 6-9) becomes insignificant. The equation simplifies to V0 = Vmax[S]/Km and V0 exhibits a linear dependence on [S], as observed here. At high [S], where [S] >> Km, the Km term in the denominator of the Michaelis-Menten equation becomes insignificant and the equation simplifies to V0 = Vmax; this is consistent with the plateau observed at high [S]. The Michaelis-Menten equation is therefore consistent with the observed dependence of V0 on [S], and the shape of the curve is defined by the terms Vmax/Km at low [S] and Vmax at high [S].*BOX 6-1 FIGURE 1 A double-reciprocal or Lineweaver-Burk plot.*FIGURE 613 Common mechanisms for enzyme-catalyzed bisubstrate reactions. (a) The enzyme and both substrates come together to form a ternary complex. In ordered binding, substrate 1 must bind before substrate 2 can bind productively. In random binding, the substrates canbind in either order. (b) An enzyme-substrate complex forms, a product leaves the complex, the altered enzyme forms a second complex with another substrate molecule, and the second product leaves, regenerating the enzyme. Substrate 1 may transfer a functional group to the enzyme (to form the covalently modified E), which is subsequently transferred to substrate 2. This is called a Ping-Pong or double-displacement mechanism.*FIGURE 6-14a Steady-state kinetic analysis of bisubstrate reactions. In these double-reciprocal plots (see Box 6-1), the concentration of substrate 1 is varied while the concentration of substrate 2 is held constant. This is repeated for several values of [S2], generating several separate lines. (a) Intersecting lines indicate that a ternary complex is formed in the reaction.*FIGURE 6-14b Steady-state kinetic analysis of bisubstrate reactions. In these double-reciprocal plots (see Box 6-1), the concentration of substrate 1 is varied while the concentration of substrate 2 is held constant. This is repeated for several values of [S2], generating several separate lines. (b) parallel lines indicate a Ping-Pong (double-displacement) pathway.**FIGURE 6-15a Three types of reversible inhibition. (a) Competitive inhibitors bind to the enzyme's active site; KI is the equilibrium constant for inhibitor binding to E.*BOX 6-2 FIGURE 1 Competitive inhibition.**FIGURE 6-15b Three types of reversible inhibition. (b) Uncompetitive inhibitors bind at a separate site, but bind only to the ES complex; KI is the equilibrium constant for inhibitor binding to ES.*BOX 6-2 FIGURE 2 Uncompetitive inhibition.*FIGURE 615c Mixed inhibitors bind at a separate site, but may bind to either E or ES. *FIGURE 6-15c Three types of reversible inhibition. (c) Mixed inhibitors bind at a separate site, but may bind to either E or ES.*BOX 6-2 FIGURE 3 Mixed inhibition.FIGURE 634 Substrate-activity curves for representative allosteric enzymes. Three examples of complex responses of allosteric enzymes to their modulators. (a) The sigmoid curve of a homotropic enzyme, in which the substrate also serves as a positive (stimulatory) modulator, or activator. Note the resemblance to the oxygen-saturation curve of hemoglobin (see Fig. 512). The sigmoidal curve is a hybrid curve in which the enzyme is present primarily in the relatively inactive T state at low substrate concentration, and primarily in the more active R state at high substrate concentration. The curves for the pure T and R states are plotted separately in color. ATCase exhibits a kinetic pattern similar to this. (b) The effects of several different concentrations of a positive modulator (+) or a negative modulator (-) on an allosteric enzyme in which K0.5 is altered without a change in Vmax. The central curve shows the substrate-activity relationship without a modulator. For ATCase, CTP is a negative modulator and ATP is a positive modulator. *FIGURE 635 Some enzyme modification reactions.*FIGURE 638 Activation of zymogens by proteolytic cleavage. Shown here is the formation of chymotrypsin and trypsin from their zymogens, chymotrypsinogen and trypsinogen. The bars represent the amino acid sequences of the polypeptide chains, with numbers indicating the positions of the residues (the amino-terminal residue is number 1). Residues at the termini of the polypeptide fragments generated by cleavage are indicated below the bars. Note that in the final active forms, some numbered residues are missing. Recall that the three polypeptide chains (A, B, and C) of chymotrypsin are linked by disulfide bonds (see Fig. 619).*FIGURE 640 The coagulation cascades. The interlinked intrinsic and extrinsic pathways leading to the cleavage of fibrinogen to form active fibrin are shown. Active serine proteases in the pathways are shown in blue. Green arrows denote activating steps, and red arrows indicate inhibitory processes.*FIGURE 642 Regulation of muscle glycogen phosphorylase activity by phosphorylation. The activity of glycogen phosphorylase in muscle is subjected to a multilevel system of regulation involving much more than the covalent modification (phosphorylation) shown in Figure 636. Allosteric regulation, and a regulatory cascade sensitive to hormonal status that acts on the enzymes involved in phosphorylation and dephosphorylation, also play important roles. The activity of both forms of the enzyme is allosterically regulated by an activator (AMP) and by inhibitors (glucose 6-phosphate and ATP) that bind to separate sites on the enzyme. The activities of phosphorylase kinase and phosphorylase phosphatase 1 (PP1) are also regulated by covalent modification, via a short pathway that responds to the hormones glucagon and epinephrine. One path leads to the phosphorylation of phosphorylase kinase and phosphoprotein phosphatase inhibitor 1 (PPI-1). The phosphorylated phosphorylase kinase is activated and in turn phosphorylates and activates glycogen phosphorylase. At the same time, the phosphorylated PPI-1 interacts with and inhibits PP1. PPI-1 also keeps itself active (phosphorylated) by inhibiting phosphoprotein phosphatase 2B (PP2B), the enzyme that dephosphorylates (inactivates) it. In this way, the equilibrium between the a and b forms of glycogen phosphorylase is shifted decisively toward the more active glycogen phosphorylase a. Note that the two forms of phosphorylase kinase are both activated to a degree by Ca2+ ion (not shown). This pathway is discussed in more detail in Chapters 14, 15, and 23.*