Key topics about enzyme function: CHAPTER 6 Enzymes Key topics about enzyme function: Physiological significance of enzymes Origin of catalytic power of enzymes Chemical mechanisms of catalysis Description of enzyme kinetics and inhibition

What are enzymes? Enzymes are catalysts Increase reaction rates without being used up Most enzymes are globular proteins However, some RNA (ribozymes and ribosomal RNA) also catalyze reactions Study of enzymatic processes is the oldest field of biochemistry, dating back to late 1700s Study of enzymes has dominated biochemistry in the past and continues to do so

Why biocatalysis over inorganic catalysts? Greater reaction specificity: avoids side products Milder reaction conditions: conducive to conditions in cells Higher reaction rates: in a biologically useful timeframe Capacity for regulation: control of biological pathways Metabolites have many potential pathways of decomposition Enzymes make the desired one most favorable

Enzymatic Substrate Selectivity No binding Binding but no reaction Example: Phenylalanine hydroxylase

Reaction Conditions Compatible with Life pH ≈7

Six Classes of Enzymes: Defined by the Reactions Catalyzed 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 ∆G‡uncat and ∆G‡cat 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.

Enzyme-Substrate Complex Enzymes act by binding substrates The noncovalent enzyme substrate complex is known as the Michaelis complex Description of chemical interactions Development of kinetic equations

Reaction Coordinate Diagram 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.

Enzymes Decrease ΔG‡ 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 ∆G‡uncat and ∆G‡cat 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.

Rate Enhancement by Enzymes

How to Lower G Enzymes 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 reactions Enzyme uses the binding energy of substrates to organize the reactants to a fairly rigid ES complex Entropy cost is paid during binding Rigid reactant complex  transition state conversion is entropically OK

Support for the Proximity Model The rate of anhydride formation from esters and carboxylates shows a strong dependence on proximity of two reactive groups (work by Thomas C. Bruice’s group). FIGURE 6–7 Rate enhancement by entropy reduction. Shown here are reactions of an ester with a carboxylate group to form an anhydride. The R group is the same in each case. (a) For this bimolecular reaction, the rate constant k is second-order, with units of M-1s-1. (b) When the two reacting groups are in a single molecule, and thus have less freedom of motion, the reaction is much faster. For this unimolecular reaction, k has units of s-1. Dividing the rate constant for (b) by the rate constant for (a) gives a rate enhancement of about 105 M. (The enhancement has units of molarity because we are comparing a unimolecular and a bimolecular reaction.) Put another way, if the reactant in (b) were present at a concentration of 1 M, the reacting groups would behave as though they were present at a concentration of 105 M. Note that the reactant in (b) has freedom of rotation about three bonds (shown with curved arrows), but this still represents a substantial reduction of entropy over (a). If the bonds that rotate in (b) are constrained as in (c), the entropy is reduced further and the reaction exhibits a rate enhancement of 108 M relative to (a).

Illustration of TS Stabilization Idea: Imaginary Stickase FIGURE 6–5 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.

Peptidoglycan and Lysozyme Peptidoglycan is a polysaccharide found in many bacterial cell walls Cleavage of the cell wall leads to the lysis of bacteria Lysozyme is an antibacterial enzyme

Peptidoglycan and Lysozyme FIGURE 6–27b Hen egg white lysozyme and the reaction it catalyzes. (b) Reaction catalyzed by hen egg white lysozyme. A segment of a peptidoglycan polymer is shown, with the lysozyme binding sites A through F shaded. The glycosidic C—O bond between sugar residues bound to sites D and E is cleaved, as indicated by the red arrow. The hydrolytic reaction is shown in the inset, with the fate of the oxygen in the H2O traced in red. Mur2Ac is N-acetylmuramic acid; GlcNAc, N-acetylglucosamine. RO— represents a lactyl (lactic acid) group; —NAc and AcN—, an N-acetyl group (see key).

What is enzyme kinetics? Kinetics is the study of the rate at which compounds react Rate of enzymatic reaction is affected by: enzyme substrate effectors temperature

How to Do Kinetic Measurements Experiment: Mix enzyme + substrate Record 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 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 μM/min. The Michaelis constant, Km (explained in the text), is 0.5 μM. 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.

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 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.)

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

Determination of Kinetic Parameters Nonlinear 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 BOX 6-1 FIGURE 1 A double-reciprocal or Lineweaver-Burk plot.

Identify Constraints and Assumptions Total enzyme concentration is constant Mass 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 algebra The final form in case of a single substrate is kcat (turnover number): how many substrate molecules can one enzyme molecule convert per second Km (Michaelis constant): an approximate measure of substrate’s affinity for enzyme

Enzyme efficiency is limited by diffusion: kcat/Km Can gain efficiency by having high velocity or affinity for substrate Catalase vs. acetylcholinesterase

Enzyme Inhibition Inhibitors are compounds that decrease enzyme’s activity Irreversible inhibitors (inactivators) react with the enzyme One inhibitor molecule can permanently shut off one enzyme molecule They are often powerful toxins but also may be used as drugs Reversible inhibitors bind to and can dissociate from the enzyme They are often structural analogs of substrates or products They 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 substrate to the enzyme-substrate complex and prevent the reaction

Competitive Inhibition Competes with substrate for binding Binds active site Does not affect catalysis No change in Vmax; apparent increase in KM Lineweaver-Burk: lines intersect at the y-axis

Competitive Inhibition 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.

Competitive Inhibition BOX 6-2 FIGURE 1 Competitive inhibition.

Uncompetitive Inhibition Only binds to ES complex Does not affect substrate binding Inhibits catalytic function Decrease in Vmax; apparent decrease in Km No change in Km/Vmax Lineweaver-Burk: lines are parallel

Uncompetitive 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.

Uncompetitive Inhibition BOX 6-2 FIGURE 2 Uncompetitive inhibition.

Mixed Inhibition Binds enzyme with or without substrate Binds to regulatory site Inhibits both substrate binding and catalysis Decrease in Vmax; apparent change in Km Lineweaver-Burk: lines intersect left from the y-axis Noncompetitive inhibitors are mixed inhibitors such that there is no change in Km FIGURE 6–15c Mixed inhibitors bind at a separate site, but may bind to either E or ES.

Mixed Inhibition FIGURE 6-15c Three types of reversible inhibition. (c) Mixed inhibitors bind at a separate site, but may bind to either E or ES.

Mixed Inhibition BOX 6-2 FIGURE 3 Mixed inhibition.

Enzyme activity can be regulated Regulation can be: noncovalent modification covalent modification irreversible reversible

Noncovalent Modification: Allosteric Regulators The kinetics of allosteric regulators differ from Michaelis-Menten kinetics. FIGURE 6–34 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. 5–12). 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.

Some Reversible Covalent Modifications FIGURE 6–35 Some enzyme modification reactions.

Zymogens are activated by irreversible covalent modification FIGURE 6–38 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. 6–19).

The blood coagulation cascade uses irreversible covalent modification FIGURE 6–40 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.

Some enzymes use multiple types of regulation FIGURE 6–42 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 6–36. 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.

Chapter 6: Summary In this chapter, we learned: why nature needs enzyme catalysis how enzymes can accelerate chemical reactions how to perform and analyze kinetic studies how to characterize enzyme inhibitors how enzyme activity can be regulated