6| Enzymes
CHAPTER 6 Enzymes topics about enzyme function:
– Physiological significance of enzymes – Origin of catalytic power of enzymes – Chemical mechanisms of catalysis – Mechanisms of chymotrypsin and lysozyme – 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 • We will celebrate my inspiration, the Biochemist Louis Pasteur.
Why do cells evolve 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
- - COO COO
NH2 • Metabolites have many - O COO - potential pathways of COO OH decomposition
- O COO Chorismate - - COO COO OH mutase - OOC • Enzymes make the O desired one most favorable OH NH2 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
k [E][S] v cat Km [S] Enzyme-Substrate Complex
• Binding of a substrate to an enzyme at the active site. The enzyme chymotrypsin with bound substrate (PDB ID 7GCH). • Some key active-site amino acid residues appear as a red splotch on the enzyme surface.
Enzymatic Catalysis • Enzymes do not affect equilibrium (ΔG) • Slow reactions face significant activation barriers (ΔG‡) that must be surmounted during the reaction • Enzymes increase reaction rates (k) by decreasing ΔG‡
kBT G k exp h RT
Reaction Coordinate Diagram
• 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‡
• 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. From previous slide; 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). How to Lower G Enzymes bind transition states best
• The idea was proposed by Linus Pauling in 1946 – Enzyme active sites are complimentary to the transition state of the reaction – Enzymes bind transition states better than substrates – Stronger/additional interactions with the transition state as compared to the ground state lower the activation barrier Illustration of TS Stabilization Idea: Imaginary Stickase 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. Catalytic Mechanisms
– acid-base catalysis: give and take protons – covalent catalysis: change reaction paths
– metal ion catalysis: use redox cofactors, pKa shifters – electrostatic catalysis: preferential interactions with TS General Acid-Base Catalysis
• 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.
Amino Acids in General Acid-Base Catalysis • 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. Covalent Catalysis
• A transient covalent bond between the enzyme and the substrate • Changes the reaction Pathway
H2O – Uncatalyzed: A — B A B
H2O – Catalyzed: A — B X : A — X B A X : B
• Requires a nucleophile on the enzyme – Can be a reactive serine, thiolate, amine, or carboxylate Metal Ion Catalysis
• Involves a metal ion bound to the enzyme
• Interacts with substrate to facilitate binding – Stabilizes negative charges
• Participates in oxidation reactions Chymotrypsin uses most of the enzymatic mechanisms
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).
Active Site of Chymotrypsin with Substrate
• 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 6–22. 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. Chymotrypsin Mechanism Step 1: Substrate Binding
(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.
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 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
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).
General Acid-Base + Covalent Catalysis: Cleavage of Peptidoglycan by Lysozyme X-ray structures of lysozyme with bound substrate analogs show that the C-1 carbon is located between Glu 35 and Asp 52 residues. From previous slide; Lysozyme reaction.
• In this reaction, the water introduced into the product at C-1 of Mur2Ac is in the same configuration as the original glycosidic bond. The reaction is thus a molecular substitution with retention of configuration. (b) A surface rendering of the lysozyme active site with the covalent enzyme-substrate intermediate shown as a ball-and-stick structure. Side-chains of active-site residues are shown as ball-and-stick structures protruding from ribbons (PDB ID 1H6M). Cleavage of Peptidoglycan by Lysozyme: Two
Successive SN2 Steps Model • Asp 52 acts as a nucleophile to attack the anomeric
carbon in the first SN2 step • Glu 35 acts as a general acid and protonates the leaving group in the transition state • Water hydrolyzes the covalent glycosyl-enzyme intermediate • Glu 35 acts as a general base to deprotonate water in
the second SN2 step
Experimental work I am no longer allowed to enjoy! 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 • We will celebrate my inspiration, the Biochemist Louis Pasteur.
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
- - COO COO
NH2 • Metabolites have many - O COO - potential pathways of COO OH decomposition
- O COO Chorismate - - COO COO OH mutase - OOC • Enzymes make the O desired one most favorable OH NH2 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 Why study enzyme kinetics?
• Quantitative description of biocatalysis • Determine the order of binding of substrates • Elucidate acid-base catalysis • Understand catalytic mechanism • Find effective inhibitors • Understand regulation of activity How to Do Kinetic Measurements Experiment: 1)Mix enzyme + substrate 2)Record rate of substrate disappearance/product formation as a function of time (the velocity of reaction) 3)Plot initial velocity versus substrate concentration. 4)Change substrate concentration and repeat From previous slide; 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
V [S] • Ideal rate: v max K S m
• Deviations due to: – limitation of measurements – substrate inhibition – substrate prep contains inhibitors – enzyme prep contains inhibitors Effect of Substrate Concentration
• 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.)
Saturation Kinetics: At high [S] velocity does not depend on [S]
• 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 Derivation of Enzyme Kinetics Equations
• Start with a model mechanism • Identify constraints and assumptions • Carry out algebra ... – ... or graph theory for complex reactions
• Simplest Model Mechanism: E + S ES E + P – One reactant, one product, no inhibitors
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
d[ES ] rateof formationof ES rateof breakdownofES 0 dt
dP • What is the observed rate? v k[ES] – Rate of product formation net dt
Carry out the algebra
• The final form in case of a single substrate is k [E ][S] v cat tot
Km [S]
• 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
• Microscopic meaning of Km and kcat depends on the details of the mechanism Enzyme efficiency is limited by diffusion:
kcat/KM • Can gain efficiency by having high velocity or affinity for substrate – Catalase vs. acetylcholinesterase Two-Substrate Reactions
• Kinetic 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 mechanisms – Sequential mechanism – Ping-Pong mechanism • 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 can bind 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.
Sequential Kinetic Mechanism • We cannot easily distinguish random from ordered • Random mechanisms in equilibrium will give intersection point at y-axis • Lineweaver-Burk: lines intersect
• 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.
Ping-Pong Kinetic Mechanism
Lineweaver-Burk: lines are parallel • 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.
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 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 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 Mixed Inhibition 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.
Aspartate transcarbamylase; From previous slide
• 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. 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 Zymogens are activated by irreversible covalent modification From previous slide; 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
• 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 • 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.