Chapter 13 Enzyme Kinetics

Chapter 13 "There is more to life than increasing its speed." Mahatma Gandhi 1869-1948 The space shuttle must accelerate from zero velocity to a velocity of more than 25,000 miles per hour to escape earth’s gravity.

Essential Questions What are enzymes, and what do they do?

Outline What characteristic features define enzymes? Can the rate of an enzyme-catalyzed reaction be defined in a mathematical way? What equations define the kinetics of enzyme-catalyzed reactions? What can be learned from the inhibition of enzyme activity? What is the kinetic behavior of enzymes catalyzing bimolecular reactions? How can enzymes be so specific? Are all enzymes proteins? Is it possible to design an enzyme to catalyze any desired reaction?

Virtually All Reactions in Cells Are Mediated by Enzymes Enzymes catalyze thermodynamically favorable reactions, causing them to proceed at extraordinarily rapid rates (see Figure 13.1) Enzymes provide cells with the ability to exert kinetic control over thermodynamic potentiality Living systems use enzymes to accelerate and control the rates of vitally important biochemical reactions Enzymes are the agents of metabolic function

Virtually All Reactions in Cells Are Mediated by Enzymes Figure 13.1 Reaction profile showing the large free energy of activation for glucose oxidation. Enzymes lower ΔG‡, thereby accelerating rate.

13.1 What Characteristic Features Define Enzymes? Catalytic power is defined as the ratio of the enzyme-catalyzed rate of a reaction to the uncatalyzed rate Specificity is the term used to define the selectivity of enzymes for their substrates Regulation of enzyme activity ensures that the rate of metabolic reactions is appropriate to cellular requirements Enzyme nomenclature provides a systematic way of naming metabolic reactions Coenzymes and cofactors are nonprotein components essential to enzyme activity.

13.1 What Characteristic Features Define Enzymes? Enzymes can accelerate reactions as much as 1016 over uncatalyzed rates Urease is a good example: Catalyzed rate: 3x104/sec Uncatalyzed rate: 3x10 -10/sec Ratio is 1x1014

Specificity Enzymes selectively recognize proper substrates over other molecules Enzymes produce products in very high yields - often much greater than 95% Specificity is controlled by structure - the unique fit of substrate with enzyme controls the selectivity for substrate and the product yield

Enzymes are the Agents of Metabolic Function Figure 13.2 The breakdown of glucose by glycolysis provides a prime example of a metabolic pathway.

90% yield in each step; 35% over 10 steps Figure 13.3 Yields in biological reactions must be substantially greater than 90%.

Enzyme Nomenclature Provides a Systematic Way of Naming Metabolic Reactions

Coenzymes and Cofactors Are Nonprotein Components Essential to Enzyme Activity

13.2 Can the Rate of an Enzyme-Catalyzed Reaction Be Defined in a Mathematical Way? Kinetics is the branch of science concerned with the rates of reactions Enzyme kinetics seeks to determine the maximum reaction velocity that enzymes can attain and binding affinities for substrates and inhibitors Analysis of enzyme rates yields insights into enzyme mechanisms and metabolic pathways This information can be exploited to control and manipulate the course of metabolic events

Several kinetics terms to understand rate or velocity rate constant rate law order of a reaction molecularity of a reaction

Chemical Kinetics Provides a Foundation for Exploring Enzyme Kinetics Consider a reaction of overall stoichiometry as shown: The rate is proportional to the concentration of A

Chemical Kinetics Provides a Foundation for Exploring Enzyme Kinetics The simple elementary reaction of A→P is a first-order reaction Figure 13.4 shows the course of a first-order reaction as a function of time This is a unimolecular reaction For a bimolecular reaction, the rate law is: v = k[A][B] Kinetics cannot prove a reaction mechanism Kinetics can only rule out various alternative hypotheses because they don’t fit the data

The Time-Course of a First-Order Reaction Figure 13.4 Plot of the course of a first-order reaction. The half-time, t1/2 is the time for one-half of the starting amount of A to disappear.

Catalysts Lower the Free Energy of Activation for a Reaction A typical enzyme-catalyzed reaction must pass through a transition state The transition state sits at the apex of the energy profile in the energy diagram The reaction rate is proportional to the concentration of reactant molecules with the transition-state energy This energy barrier is known as the free energy of activation Decreasing ΔG‡ increases the reaction rate The activation energy is related to the rate constant by:

Catalysts Lower the Free Energy of Activation for a Reaction Figure 13.5 Energy diagram for a chemical reaction (A→P) and the effects of (a) raising the temperature from T1 to T2, or (b) adding a catalyst.

Understand the difference between G and G‡ The Transition State Understand the difference between G and G‡ The overall free energy change for a reaction is related to the equilibrium constant The free energy of activation for a reaction is related to the rate constant It is extremely important to appreciate this distinction

13.3 What Equations Define the Kinetics of Enzyme-Catalyzed Reactions? Simple first-order reactions display a plot of the reaction rate as a function of reactant concentration that is a straight line (Figure 13.6) Enzyme-catalyzed reactions are more complicated At low concentrations of the enzyme substrate, the rate is proportional to S, as in a first-order reaction At higher concentrations of substrate, the enzyme reaction approaches zero-order kinetics This behavior is a saturation effect

13.3 What Equations Define the Kinetics of Enzyme-Catalyzed Reactions? Figure 13.6 A plot of v versus [A] for the unimolecular chemical reaction, A→P, yields a straight line having a slope equal to k.

As [S] increases, kinetic behavior changes from 1st order to zero-order kinetics Figure 13.7 Substrate saturation curve for an enzyme-catalyzed reaction.

The Michaelis-Menten Equation is the Fundamental Equation of Enzyme Kinetics Louis Michaelis and Maud Menten's theory It assumes the formation of an enzyme-substrate complex It assumes that the ES complex is in rapid equilibrium with free enzyme Breakdown of ES to form products is assumed to be slower than 1) formation of ES and 2) breakdown of ES to re-form E and S

[ES] Remains Constant Through Much of the Enzyme Reaction Time Course in Michaelis-Menten Kinetics Figure 13.8 Time course for a typical enzyme-catalyzed reaction obeying the Michaelis-Menten, Briggs-Haldane models for enzyme kinetics. The early state of the time course is shown in greater magnification in the bottom graph.

The "kinetic activator constant" Understanding Km The "kinetic activator constant" Km is a constant Km is a constant derived from rate constants Km is, under true Michaelis-Menten conditions, an estimate of the dissociation constant of E from S Small Km means tight binding; high Km means weak binding

The theoretical maximal velocity Understanding Vmax The theoretical maximal velocity Vmax is a constant Vmax is the theoretical maximal rate of the reaction - but it is NEVER achieved in reality To reach Vmax would require that ALL enzyme molecules are tightly bound with substrate Vmax is asymptotically approached as substrate is increased

The dual nature of the Michaelis-Menten equation Combination of 0-order and 1st-order kinetics When S is low, the equation for rate is 1st order in S When S is high, the equation for rate is 0-order in S The Michaelis-Menten equation describes a rectangular hyperbolic dependence of v on S The relation of the “rectangular hyperbola” to the enzyme kinetics profile is described in references at the end of the chapter

Table 13.3 gives the Km values for some enzymes and their substrates

The Turnover Number Defines the Activity of One Enzyme Molecule A measure of catalytic activity kcat, the turnover number, is the number of substrate molecules converted to product per enzyme molecule per unit of time, when E is saturated with substrate. If the M-M model fits, k2 = kcat = Vmax/Et Values of kcat range from less than 1/sec to many millions per sec

The Turnover Number Defines the Activity of One Enzyme Molecule

The Ratio kcat/Km Defines the Catalytic Efficiency of an Enzyme The catalytic efficiency: kcat/Km An estimate of "how perfect" the enzyme is kcat/Km is an apparent second-order rate constant It measures how the enzyme performs when S is low The upper limit for kcat/Km is the diffusion limit - the rate at which E and S diffuse together

The Ratio kcat/Km Defines the Catalytic Efficiency of an Enzyme

Linear Plots Can Be Derived from the Michaelis-Menten Equation Be able to derive these equations Lineweaver-Burk: Begin with v = Vmax[S]/(Km + [S]) and take the reciprocal of both sides Rearrange to obtain the Lineweaver-Burk equation: A plot of 1/v versus 1/[S] should yield a straight line

Linear Plots Can Be Derived from the Michaelis-Menten Equation Figure 13.9 The Lineweaver-Burk double-reciprocal plot.

Linear Plots Can Be Derived from the Michaelis-Menten Equation Hanes-Woolf: Begin with Lineweaver-Burk and divide both sides by [S] to obtain: Hanes-Woolf is best - why? Because Hanes-Woolf has smaller and more consistent errors across the plot

Linear Plots Can Be Derived from the Michaelis-Menten Equation Figure 13.11 A Hanes-Woolf plot of [S]/v versus [S]

Enzymatic Activity is Strongly Influenced by pH Enzyme-substrate recognition and catalysis are greatly dependent on pH Enzymes have a variety of ionizable side chains that determine its secondary and tertiary structure and also affect events in the active site Substrate may also have ionizable groups Enzymes are usually active only over a limited range of pH The effects of pH may be due to effects on Km or Vmax or both

Enzymatic Activity is Strongly Influenced by pH Figure 13.11 The pH activity profiles of four different enzymes.

The Response of Enzymatic Activity to Temperature is Complex Rates of enzyme-catalyzed reactions generally increase with increasing temperature However, at temperatures above 50° to 60° C, enzymes typically show a decline in activity Two effects here: Enzyme rate typically doubles in rate for ever 10°C as long as the enzyme is stable and active At higher temperatures, the protein becomes unstable and denaturation occurs

The Response of Enzymatic Activity to Temperature is Complex Figure 13.12 The effect of temperature on enzyme activity.

13.4 What Can Be Learned from the Inhibition of Enzyme Activity? Enzymes may be inhibited reversibly or irreversibly Reversible inhibitors may bind at the active site or at some other site Enzymes may also be inhibited in an irreversible manner Penicillin is an irreversible suicide inhibitor

Reversible Inhibitors May Bind at the Active Site or at Some Other Site

Competitive Inhibitors Compete With Substrate for the Same Site on the Enzyme Figure 13.13 Lineweaver-Burk plot of competitive inhibition, showing lines for no I, [I], and 2[I].

Succinate Dehydrogenase – a Classic Example of Competitive Inhibition Figure 13.14 Structures of succinate, the substrate of succinate dehydrogenase (SDH), and malonate, the competitive inhibitor. Fumarate is also shown.

Pure Noncompetitive Inhibition – where S and I bind to different sites on the enzyme Figure 13.15 Lineweaver-Burk plot of pure noncompetitive inhibition. Note that I does not alter Km but that it decreases Vmax.

Mixed Noncompetitive Inhibition: binding of I by E influences binding of S by E Figure 13.16 Lineweaver-Burk plot of mixed noncompetitive inhibition. Note that both intercepts and the slope change in the presence of I.

Uncompetitive Inhibition, where I combines only with E, but not with ES Figure 13.17 Lineweaver-Burk plot of uncompetitive inhibition. Note that both intercepts change but the slope (Km/Vmax) remains constant in the presence of I.

Enzymes Can Be Inhibited Irreversibly Figure 13.18 Penicillin is an irreversible inhibitor of the enzyme glycoprotein peptidease, which catalyzes an essential step in bacterial cell all synthesis.

Enzymes often catalyze reactions involving two (or more) substrates 13.5 - What Is the Kinetic Behavior of Enzymes Catalyzing Bimolecular Reactions? Enzymes often catalyze reactions involving two (or more) substrates Reactions may be sequential or single-displacement reactions These can be of two distinct classes: Random, where either substrate may bind first, followed by the other substrate Ordered, where a leading substrate binds first, followed by the other substrate

13.5 - What Is the Kinetic Behavior of Enzymes Catalyzing Bimolecular Reactions? Figure 13.19 Single-deplacement bisubstrate mechanism.

Viagra – An Unexpected Outcome in a Program of Drug Design Note the similarities in the structures of cGMP (left) and Viagra (right). Viagra produces an increase in [cGMP] in penile vascular tissue, allowing vascular muscle relaxation, improved blood flow, and erection.

Conversion of AEB to PEQ is the Rate-Limiting Step in Random, Single-Displacement Reactions In this type of sequential reaction, all possible binary enzyme-substrate and enzyme-product complexes are formed rapidly and reversibly when enzyme is added to a reaction mixture containing A, B, P, and Q.

Creatine Kinase Acts by a Random, Single-Displacement Mechanism The overall direction of the reaction will be determined by the relative concentrations of ATP, ADP, Cr, and CrP and the equilibrium constant for the reaction.

Creatine Kinase Acts by a Random, Single-Displacement Mechanism Figure 13.21 The structures of creatine and creatine phosphate, guanidinium compounds that are important in muscle energy metabolism.

In an Ordered, Single-Displacement Reaction, the Leading Substrate Must Bind First The leading substrate (A) binds first, followed by B. Reaction between A and B occurs in the ternary complex and is usually followed by an ordered release of the products, P and Q.

An Alternative way of Portraying the Ordered, Single-Displacement Reaction

The Double Displacement (Ping-Pong) Reaction Double-Displacement (Ping-Pong) reactions proceed via formation of a covalently modified enzyme intermediate. Reactions conforming to this kinetic pattern are characterized by the fact that the product of the enzyme’s reaction with A (called P in the above scheme) is released prior to reaction of the enzyme with the second substrate, B.

An Alternative Presentation of the Double-Displacement (Ping-Pong) Reaction

The Double Displacement (Ping-Pong) Reaction Figure 13.22 Double-displacement (ping-pong) bisubstrate mechanisms are characterized by parallel lines.

Glutamate:aspartate Aminotransferase Figure 13.23 An enzyme conforming to a double-displacement bisubstrate mechanism.

13.7 – How Can Enzymes Be So Specific? The “Lock and key” hypothesis was the first explanation for specificity The “Induced fit” hypothesis provides a more accurate description of specificity Induced fit favors formation of the transition-state Specificity and reactivity are often linked. In the hexokinase reaction, binding of glucose in the active site induces a conformational change in the enzyme that causes the two domains of hexokinase to close around the substrate, creating the catalytic site

13.7 – How Can Enzymes Be So Specific? Figure 13.24 A drawing, roughly to scale, of H2O, glycerol, glucose, and an idealized hexokinase molecule. Binding of glucose in the active site induces a conformational change in the enzyme that causes the two domains of hexokinase to close around the substrate, creating the catalytic site.

13.7 – Are All Enzymes Proteins? Ribozymes - segments of RNA that display enzyme activity in the absence of protein Examples: RNase P and peptidyl transferase Abzymes - antibodies raised to bind the transition state of a reaction of interest For a good review of abzymes, see Science, Vol. 269, pages 1835-1842 (1995) Transition states are covered in more depth in in Chapter 14

RNA Molecules That Are Catalytic Have Been Termed “Ribozymes” Figure 13.25 RNA splicing in Tetrahymena rRNA maturation.

RNA Molecules That Are Catalytic Have Been Termed “Ribozymes” Figure 13.26 (a) The 50S subunit from H. marismortui. (b) The aminoacyl-tRNA (yellow) and the peptidyl-tRNA (orange) in the peptidyl transferase active site.

RNA Molecules That Are Catalytic Have Been Termed “Ribozymes” Figure 13.27 The peptidyl transferase reaction.

Antibody Molecules Can Have Catalytic Activity Figure 13.28 (a) Intramolecular hydrolysis of a hydroxy ester yields a δ-lactone. (b) The cyclic phosphonate ester analog of the cyclic transition state.

13.8 Is It Possible to Design An Enzyme to Catalyze Any Desired Reaction? A known enzyme can be “engineered” by in vitro mutagenesis, replacing active site residues with new ones that might catalyze a desired reaction Another approach attempts to design a totally new protein with the desired structure and activity This latter approach often begins with studies “in silico” – i.e., computer modeling Protein folding and stability issues make this approach more difficult And the cellular environment may provide complications not apparent in the computer modeling

13.8 Is It Possible to Design An Enzyme to Catalyze Any Desired Reaction? Figure 13.29 cis-1,2-Dichloroethylene (DCE) is an industrial solvent that poses hazards to human health. Site-directed mutations have enabled the conversion of a bacterial epoxide hydrolase to catalyze the chlorinated epoxide hydrolase reaction.