6.2 How Enzymes Work in Chapter 6 Enzymes

6.2 How Enzymes Work

The enzymatic catalysis of reactions is essential to living systems. Under biologically relevant conditions, uncatalyzed reactions tend to be slow — most biological molecules are quite stable in the neutral-pH, mild-temperature, aqueous environment inside cells. Reactions required to digest food, send nerve signals, or contract a muscle simply do not occur at a useful rate without catalysis.

The distinguishing feature of an enzyme-catalyzed reaction is that it takes place within the confines of a pocket on the enzyme called the active site (Fig. 6-1). The active site provides a specific environment, customized by evolution, in which a given reaction can occur more rapidly. The molecule that is bound in the active site and acted upon by the enzyme is called the substrate. The surface of the active site is lined with amino acid residues with substituent groups that bind the substrate and catalyze its chemical transformation. Often, the active site encloses a substrate, sequestering it completely from solution. The enzyme-substrate complex is central to the action of enzymes. It is also the starting point for mathematical treatments that define the kinetic behavior of enzyme-catalyzed reactions and for theoretical descriptions of enzyme mechanisms.

A figure shows a bumpy, roughly spherical molecule with a highlighted region in the center labeled, key active-site amino acid residues. This region lies along the side of a pit in the molecule’s surface into which extends a molecule represented by a ball-and-stick structure labeled, substrate. — FIGURE 6-1 Binding of a substrate to an enzyme at the active site. The enzyme chymotrypsin with bound substrate. Some key active-site amino acid residues appear as a red splotch on the enzyme surface. [Data from PDB ID 7GCH, K. Brady et al., *Biochemistry* 29:7600, 1990.]

Enzymes Affect Reaction Rates, Not Equilibria

A simple enzymatic reaction might be written

E + S ⇌ ES ⇌ EP ⇌ E + P

$upper E plus upper S right harpoon over left harpoon ES right harpoon over left harpoon EP right harpoon over left harpoon upper E plus upper P$

(6-1)

where E, S, and P represent the enzyme, substrate, and product; ES and EP are transient complexes of the enzyme with the substrate and with the product.

To understand catalysis, we must first appreciate the important distinction between reaction equilibria and reaction rates. The function of a catalyst is to increase the rate of a reaction. Catalysts do not affect reaction equilibria. (Recall that a reaction is at equilibrium when there is no net change in the concentrations of reactants or products.) Any reaction, such as $mathml alt text39$ $upper S right harpoon over left harpoon upper P$ , can be described by a reaction coordinate diagram (Fig. 6-2), a picture of the energy changes during the reaction. As discussed in Chapter 1, energy in biological systems is described in terms of free energy, G. In the coordinate diagram, the free energy of the system is plotted against the progress of the reaction (the reaction coordinate). The starting point for either the forward reaction or the reverse reaction is called the ground state, the contribution to the free energy of the system by an average molecule (S or P) under a given set of conditions.

A graph plots reaction coordinate on the horizontal axis against free energy, G, on the vertical axis. The figure shows the activation energy and free energy produced by the reaction. — FIGURE 6-2 Reaction coordinate diagram. The free energy of the system is plotted against the progress of the reaction $mathml alt text40$ $upper S right-arrow upper P$ . Such a diagram describes the energy changes during the reaction. 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, $mathml alt text41$ $upper Delta upper G Superscript double-dagger$ , for the $mathml alt text42$ $upper S right-arrow upper P$ and $mathml alt text43$ $upper P right-arrow upper S$ reactions are indicated. $mathml alt text44$ $upper Delta upper G prime degree$ is the overall standard free-energy change in the direction $mathml alt text45$ $upper S right-arrow upper P$ .

FIGURE 6-2 Reaction coordinate diagram. The free energy of the system is plotted against the progress of the reaction $mathml alt text40$ $upper S right-arrow upper P$ . Such a diagram describes the energy changes during the reaction. 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, $mathml alt text41$ $upper Delta upper G Superscript double-dagger$ , for the $mathml alt text42$ $upper S right-arrow upper P$ and $mathml alt text43$ $upper P right-arrow upper S$ reactions are indicated. $mathml alt text44$ $upper Delta upper G prime degree$ is the overall standard free-energy change in the direction $mathml alt text45$ $upper S right-arrow upper P$ .

A curve begins from just below half of the height of the vertical axis, labeled S ground state. A horizontal dotted line extends from this point to near the right vertical axis. The curve moves smoothly upward to a peak and then descends almost symmetrically as a bell curve, except that it ends at a lower level on the vertical axis than its starting point. The ending point is labeled, P ground state, and a second horizontal dotted line extends from the ending point to the right, beneath the dotted horizontal line from the point labeled, S. The peak of the curve is labeled, transition state (double dagger), and a horizontal line extends from it to the right. An arrow labeled, Greek letter delta G prime degree points down from the dotted line beginning at S to the dotted line beginning at P. An arrow pointing upward from the horizontal line from Z to the horizontal line from the transition state is labeled, Greek letter delta G superscript double dagger end superscript subscript S right-facing arrow pointing to P. An arrow pointing upward from the horizontal line from P to the horizontal line from the transition state is labeled, Greek letter delta superscript double dagger end superscript subscript P right-facing arrow pointing to S. All data are approximate.

Key convention

To describe the free-energy changes for reactions, chemists define a standard set of conditions (temperature of 298 K; partial pressure of each gas, 1 atm, or 101.3 kPa; concentration of each solute, 1 m), and express the free-energy change for a reacting system under these conditions as $mathml alt text46$ $bold upper Delta bold-italic upper G Superscript bold degree$ , the standard free-energy change. Because biochemical systems commonly involve $mathml alt text47$ $upper H Superscript plus$ concentrations far below 1 m, biochemists define a biochemical standard free-energy change, $mathml alt text48$ $bold upper Delta bold-italic upper G prime degree$ , the standard free-energy change at pH 7.0; we employ this definition throughout the book. A more complete definition of $mathml alt text49$ $upper Delta upper G prime degree$ is given in Chapter 13.

The equilibrium between S and P reflects the difference in the free energies of their ground states. In the example shown in Figure 6-2, the free energy of the ground state of P is lower than that of S, so $mathml alt text50$ $upper Delta upper G prime degree$ for the reaction is negative (the reaction is exergonic) and at equilibrium there is more P than S (the equilibrium favors P).

A favorable equilibrium does not mean that the $mathml alt text51$ $upper S right-arrow upper P$ conversion will occur at a rapid or even detectable rate. The rate of a reaction is instead dependent on an entirely different parameter, the energy barrier between S and P. That barrier consists of the energy required for alignment of reacting groups, formation of transient unstable charges, bond rearrangements, and other transformations required for the reaction to proceed in either direction. This is illustrated by the energy “hill” in Figures 6-2 and 6-3. To undergo reaction, the molecules must overcome this barrier and therefore must be raised to a higher energy level. At the top of the energy hill is a point at which decay to the S or P state is equally probable (it is downhill either way). This is called the transition state, often symbolized by a double dagger (‡). The transition state is not a chemical species with any significant stability and should not be confused with a reaction intermediate (such as ES or EP). It is simply a fleeting molecular moment in which events such as bond breakage, bond formation, and charge development have proceeded to the precise point at which decay to substrate and decay to product are equally likely.

The difference between the energy level of the ground state and the energy level of the transition state is the activation energy, $mathml alt text52$ $bold upper Delta bold-italic upper G Superscript bold double-dagger$ . The rate of a reaction reflects this activation energy: a higher activation energy corresponds to a slower reaction. Lowering the activation energy increases the rate of reaction. Reaction rates can be increased by raising the temperature and/or pressure, thereby increasing the number of molecules with sufficient energy to overcome the energy barrier. Alternatively, the activation energy can be lowered, and reaction rate increased, by adding a catalyst (Fig. 6-3).

A graph plots reaction coordinate on the horizontal axis against free energy, G, on the vertical axis to compare an enzyme-catalyzed reaction with an uncatalyzed reaction. — FIGURE 6-3 Reaction coordinate diagram comparing enzyme-catalyzed and uncatalyzed reactions. In the reaction $mathml alt text53$ $upper S right-arrow upper P$ , the ES and EP intermediates occupy minima in the energy progress curve of the enzyme-catalyzed reaction. The terms $mathml alt text54$ $upper Delta upper G Subscript uncat Superscript double-dagger$ and $mathml alt text55$ $upper Delta upper G Subscript cat Superscript double-dagger$ 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.

A curve begins from just below half of the height of the vertical axis, labeled S. A horizontal dotted line extends from this point to near the right vertical axis. The curve moves smoothly upward to a peak and then descends almost symmetrically as a bell curve, except that it ends at a lower level on the vertical axis than its starting point. The ending point is labeled P. The peak of the curve is labeled transition state (double dagger), and a horizontal line extends from it to the right. A second curve begins at S and curves upward slightly, less than one-quarter of the height of the transition state peak. The second curve bends down to meet the dotted horizontal line from S, and this point is labeled highlighted E S. The curve extends up slightly higher than before, and this point is labeled highlighted double dagger with a horizontal dotted line that extends to the right. The curve bends back down to the dotted horizontal line from Z, and this point is labeled highlighted E P. The curve bends up slightly, not as high as the transition state, and then bends down to rejoin the first curve as it crosses the horizontal axis and runs down to end at P. A long upward-pointing arrow extending from the dotted line from S to the dotted line from the transition state is labeled Greek letter delta G superscript double dagger end superscript subscript uncat. A short highlighted upward-pointing arrow extending from the dotted line from S to the dotted horizontal line from the peak labeled double dagger of the second curve is labeled highlighted Greek letter delta superscript double dagger end superscript subscript cat. All data are approximate.

Catalysts do not affect reaction equilibria. The bidirectional arrows in Equation 6-1 make this important point: any enzyme that catalyzes the reaction $mathml alt text56$ $upper S right-arrow upper P$ also catalyzes the reaction $mathml alt text57$ $upper P right-arrow upper S$ . The role of enzymes is to accelerate the interconversion of S and P. The enzyme is not used up in the process, and the equilibrium point is unaffected. However, the reaction reaches equilibrium much faster when the appropriate enzyme is present, because the rate of the reaction is increased.

This relationship between reaction rate and activation energy is illustrated by the process introduced at the beginning of the chapter: the conversion of sucrose and oxygen to carbon dioxide and water:

C_{12} H_{22} O_{11} + 12 O_{2} ⇌ 12 {CO}_{2} + 11 H_{2} O

$upper C Subscript 12 Baseline upper H Subscript 22 Baseline upper O Subscript 11 Baseline plus 12 upper O Subscript 2 Baseline right harpoon over left harpoon 12 CO Subscript 2 Baseline plus 11 upper H Subscript 2 Baseline upper O$

This conversion, which takes place through a series of separate reactions, has a very large and negative $mathml alt text59$ $upper Delta upper G prime degree$ , and at equilibrium the amount of sucrose present is negligible. Yet sucrose is a stable compound, because the activation energy barrier that must be overcome before sucrose reacts with oxygen is quite high. Sucrose can be stored in a container with oxygen almost indefinitely without reacting. In cells, however, sucrose is readily broken down to $mathml alt text60$ $CO Subscript 2$ and $mathml alt text61$ $upper H Subscript 2 Baseline upper O$ in a series of reactions catalyzed by enzymes. These enzymes not only accelerate the reactions, they organize and control them so that much of the energy released is recovered in other chemical forms and made available to the cell for other tasks. The reaction pathway by which sucrose (and other sugars) is broken down is the primary energy-yielding pathway for cells, and the enzymes of this pathway allow the reaction sequence to proceed on a biologically useful (millisecond) time scale.

Any reaction may have several steps, involving the formation and decay of transient chemical species called reaction intermediates.ⁱ A reaction intermediate is any species on the reaction pathway that has a finite chemical lifetime (longer than a molecular vibration, $mathml alt text62$ $tilde 10 Superscript negative 13$ second). When the $mathml alt text63$ $upper S right harpoon over left harpoon upper P$ reaction is catalyzed by an enzyme, the ES and EP complexes can be considered intermediates, even though S and P are stable chemical species (Eqn 6-1); the ES and EP complexes occupy valleys in the reaction coordinate diagram (Fig. 6-3). Additional, less-stable chemical intermediates often exist in the course of an enzyme-catalyzed reaction. The interconversion of two sequential reaction intermediates thus constitutes a reaction step. When several steps occur in a reaction, the overall rate is determined by the step (or steps) with the highest activation energy; this is called the rate-limiting step. In a simple case, the rate-limiting step is the highest-energy point in the diagram for interconversion of S and P. In practice, the rate-limiting step can vary with reaction conditions, and for many enzymes several steps may have similar activation energies, which means they are all partially rate-limiting.

Activation energies are energy barriers to chemical reactions. These barriers are crucial to life itself. Without such energy barriers, complex macromolecules would revert spontaneously to much simpler molecular forms, and the complex and highly ordered structures and metabolic processes of cells could not exist. Over the course of evolution, enzymes have developed to lower activation energies selectively, and thus increase rates, for reactions that are needed for cell survival.

Reaction Rates and Equilibria Have Precise Thermodynamic Definitions

Reaction equilibria are inextricably linked to the standard free-energy change for the reaction, $mathml alt text64$ $upper Delta upper G prime degree$ , and reaction rates are linked to the activation energy, $mathml alt text65$ $upper Delta upper G Superscript double-dagger$ . A basic introduction to these thermodynamic relationships is the next step in understanding how enzymes work.

An equilibrium such as $mathml alt text66$ $upper S right harpoon over left harpoon upper P$ is described by an equilibrium constant, $mathml alt text67$ $bold-italic upper K Subscript bold eq$ , or simply K (p. 23). Under the standard conditions used to compare biochemical processes, an equilibrium constant is denoted $mathml alt text68$ $upper K prime Subscript eq$ (or $mathml alt text69$ $upper K prime Subscript$ ):

K_{eq}^{'} = \frac{[P]}{[S]}

$upper K prime Subscript eq Baseline equals StartFraction left-bracket upper P right-bracket Over left-bracket upper S right-bracket EndFraction$

(6-2)

From thermodynamics, the relationship between $mathml alt text71$ $upper K prime Subscript eq$ and $mathml alt text72$ $upper Delta upper G prime degree$ can be described by the expression

Δ G^{'} ° = - R T ln K_{eq}^{'}

$upper Delta upper G Superscript prime Baseline degree equals minus upper R upper T ln upper K prime Subscript eq$

(6-3)

where R is the gas constant, 8.315 J/mol·K, and T is the absolute temperature, $mathml alt text74$ $298 upper K left-parenthesis 25 Superscript degree Baseline upper C right-parenthesis$ . Equation 6-3 is developed and discussed in more detail in Chapter 13. The important point here is that the equilibrium constant is directly related to the overall standard free-energy change for the reaction (Table 6-4). A large negative value for $mathml alt text75$ $upper Delta upper G prime degree$ reflects a favorable reaction equilibrium (one in which there is much more product than substrate at equilibrium) — but as already noted, this does not mean the reaction will proceed at a rapid rate.

TABLE 6-4 Relationship between $mathml alt text76$ $bold-italic upper K bold prime Subscript bold eq$ and $mathml alt text77$ $bold upper Delta bold-italic upper G bold prime degree$
$mathml alt text78$ $bold-italic upper K bold prime Subscript bold eq$	$mathml alt text79$ $upper Delta bold-italic upper G Superscript bold-italic prime Baseline degree bold left-parenthesis bold kJ slash mol bold right-parenthesis$
$mathml alt text80$ $10 Superscript negative 6$	34.2
$mathml alt text81$ $10 Superscript negative 5$	28.5
$mathml alt text82$ $10 Superscript negative 4$	22.8
$mathml alt text83$ $10 Superscript negative 3$	17.1
$mathml alt text84$ $10 Superscript negative 2$	11.4
$mathml alt text85$ $10 Superscript negative 1$	5.7
1	0.0
$mathml alt text86$ $10 Superscript 1$	−5.7
$mathml alt text87$ $10 squared$	−11.4
$mathml alt text88$ $10 cubed$	−17.1
Note: The relationship is calculated from $mathml alt text89$ $upper Delta upper G Superscript prime Baseline degree equals minus upper R upper T$ ln $mathml alt text90$ $upper K prime Subscript eq$ (Eqn 6-3).

The rate of any reaction is determined by the concentration of the reactant (or reactants) and by a rate constant, usually denoted by k. For the unimolecular reaction $mathml alt text91$ $upper S right-arrow upper P$ , the rate (or velocity) of the reaction, V — representing the amount of S that reacts per unit of time — is expressed by a rate equation:

V = k [S]

$upper V equals k left-bracket upper S right-bracket$

(6-4)

In this reaction, the rate depends only on the concentration of S. This is called a first-order reaction. The factor k is a proportionality constant that reflects the probability of reaction under a given set of conditions (pH, temperature, and so forth). Here, k is a first-order rate constant and has units of reciprocal time, such as $mathml alt text93$ $s Superscript negative 1$ . If a first-order reaction has a rate constant k of $mathml alt text94$ $0.03 s Superscript negative 1$ , this may be interpreted (qualitatively) to mean that 3% of the available S will be converted to P in 1 second. A reaction with a rate constant of $mathml alt text95$ $2 comma 000 s Superscript negative 1$ will be over in a small fraction of a second. If a reaction rate depends on the concentration of two different compounds, or if the reaction is between two molecules of the same compound, the reaction is second order and k is a second-order rate constant, with units of $mathml alt text96$ $upper M Superscript negative 1 Baseline s Superscript negative 1$ . The rate equation then becomes

V = k [S_{1}] [S_{2}]

$upper V equals k left-bracket upper S Subscript 1 Baseline right-bracket left-bracket upper S Subscript 2 Baseline right-bracket$

(6-5)

From transition-state theory we can derive an expression that relates the magnitude of a rate constant to the activation energy:

k = \frac{k T}{h} e^{- Δ G^{‡} / R T}

$k equals StartFraction bold k upper T Over h EndFraction e Superscript minus upper Delta upper G Super Superscript double-dagger Superscript slash upper R upper T$

(6-6)

where k is the Boltzmann constant and h is Planck’s constant. The important point is that the relationship between the rate constant k and the activation energy $mathml alt text99$ $upper Delta upper G Superscript double-dagger$ is inverse and exponential. In simplified terms, this is the basis for the statement that a lower activation energy means a faster reaction rate — and lowering activation energies is what enzymes do.

Now we turn from what enzymes do to how they do it.

A Few Principles Explain the Catalytic Power and Specificity of Enzymes

Enzymes are extraordinary catalysts. The rate enhancements they bring about are in the range of 5 to 17 orders of magnitude (Table 6-5). Enzymes are also very specific, readily discriminating between substrates with quite similar structures. How can these enormous and highly selective rate enhancements be explained? What is the source of the energy for the dramatic lowering of the activation energies for specific reactions?

TABLE 6-5 Some Rate Enhancements Produced by Enzymes
Cyclophilin	$mathml alt text100$ $10 Superscript 5$
Carbonic anhydrase	$mathml alt text101$ $10 Superscript 7$
Triose phosphate isomerase	$mathml alt text102$ $10 Superscript 9$
Carboxypeptidase A	$mathml alt text103$ $10 Superscript 11$
Phosphoglucomutase	$mathml alt text104$ $10 Superscript 12$
Succinyl-CoA transferase	$mathml alt text105$ $10 Superscript 13$
Urease	$mathml alt text106$ $10 Superscript 14$
Orotidine monophosphate decarboxylase	$mathml alt text107$ $10 Superscript 17$

The answer to these questions has two distinct but interwoven parts. The first lies in the noncovalent interactions between enzyme and substrate. What really sets enzymes apart from most other catalysts is the formation of a specific ES complex. The interaction between substrate and enzyme in this complex is mediated by the same forces that stabilize protein structure, including hydrogen bonds, ionic interactions, and the hydrophobic effect (Chapter 4). Formation of each weak interaction in the ES complex is accompanied by release of a small amount of free energy that stabilizes the interaction. The energy derived from noncovalent enzyme-substrate interaction is called binding energy, $mathml alt text108$ $bold upper Delta bold-italic upper G Subscript bold upper B$ . Its significance extends beyond a simple stabilization of the enzyme-substrate interaction. As we will see, binding energy is a major source of free energy used by enzymes to lower the activation energies of reactions.

The second part of the explanation lies in covalent interactions between enzyme and substrate, plus a few additional chemical catalytic mechanisms. Chemical reactions of many types take place between substrates and enzymes’ functional groups (specific amino acid side chains, metal ions, and coenzymes). Catalytic functional groups on an enzyme may form a transient covalent bond with a substrate and activate it for reaction, or a group may be transiently transferred from the substrate to the enzyme. In many cases, these reactions occur only in the enzyme active site. Covalent interactions between enzymes and substrates lower the activation energy (and thereby accelerate the reaction) by providing an alternative, lower-energy reaction path. Metal ions facilitate additional mechanisms of catalysis that do not involve covalent interactions.

We now consider noncovalent contributions to catalysis and the additional chemical mechanisms in turn.

Noncovalent Interactions between Enzyme and Substrate Are Optimized in the Transition State

How does an enzyme use noncovalent binding energy to lower the activation energy for a reaction? Formation of the ES complex is not the explanation in itself, although some of the earliest considerations of enzyme mechanisms began with this idea. Studies on enzyme specificity carried out by Emil Fischer led him to propose, in 1894, that enzymes were structurally complementary to their substrates, so that they fit together like a lock and key (Fig. 6-4). This elegant idea, that a specific (exclusive) interaction between two biological molecules is mediated by molecular surfaces with complementary shapes, has greatly influenced the development of biochemistry. However, the “lock and key” hypothesis can be misleading when applied to enzymatic catalysis. An enzyme completely complementary to its substrate would be a very poor enzyme, as we can demonstrate.

A figure shows the change in shape of an enzyme, dihydrofolate reductase, as a substrate, N A D P plus, binds. — FIGURE 6-4 Complementary shapes of a substrate and its binding site on an enzyme. The enzyme dihydrofolate reductase with its substrate $mathml alt text109$ $NADP Superscript plus$ , unbound and bound; another bound substrate, tetrahydrofolate, is also visible. In this model, the $mathml alt text110$ $NADP Superscript plus$ binds to a pocket that is complementary to it in shape and ionic properties, an illustration of Emil Fischer’s “lock and key” hypothesis of enzyme action. In reality, the complementarity between protein and ligand (in this case, substrate) is rarely perfect, as we saw in Chapter 5. [Data from PDB ID 1RA2, M. R. Sawaya and J. Kraut, *Biochemistry* 36:586, 1997.]

FIGURE 6-4 Complementary shapes of a substrate and its binding site on an enzyme. The enzyme dihydrofolate reductase with its substrate $mathml alt text109$ $NADP Superscript plus$ , unbound and bound; another bound substrate, tetrahydrofolate, is also visible. In this model, the $mathml alt text110$ $NADP Superscript plus$ binds to a pocket that is complementary to it in shape and ionic properties, an illustration of Emil Fischer’s “lock and key” hypothesis of enzyme action. In reality, the complementarity between protein and ligand (in this case, substrate) is rarely perfect, as we saw in Chapter 5. [Data from PDB ID 1RA2, M. R. Sawaya and J. Kraut, *Biochemistry* 36:586, 1997.]

Consider an imaginary reaction, the breaking of a magnetized metal stick. The uncatalyzed reaction is shown in Figure 6-5a. Let’s examine two imaginary enzymes — two “stickases” — that could catalyze this reaction, both of which employ magnetic forces as a paradigm for the binding energy used by real enzymes. We first design an enzyme perfectly complementary to the substrate (Fig. 6-5b). The active site of this stickase is a pocket lined with magnets. To react (break), the stick must reach the bent transition state of the reaction. However, the snug fit of the stick in this active site means that magnets hinder the required bending. Such an enzyme impedes the reaction, stabilizing the substrate instead. In a reaction coordinate diagram (Fig. 6-5b), this kind of ES complex would correspond to an energy trough from which the substrate would have difficulty escaping. Such an enzyme would be useless.

A three-part figure, a, b, and c, shows a reaction without an enzyme in part a, with an enzyme complementary to the substrate in part b, and with an enzyme complementary to the transition state in part c. — 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). $mathml alt text111$ $upper Delta upper G Subscript upper M$ , 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 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). $mathml alt text111$ $upper Delta upper G Subscript upper M$ , 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.

Each figure shows a reaction on the left and a graph on the right that plots free energy, G, on the vertical axis against reaction coordinate on the horizontal axis. Part a, no enzyme, shows a horizontal cylinder labeled S and substrate (metal stick). An arrow points to show the same stick bent into an inverted V with a green top vertex and a green double dagger symbol beneath it. This is labeled transition state (bent stick). An arrow points to show two brown halves of the stick labeled brown P and products (broken stick). On the graph, a curve begins from about one-quarter of the height of the vertical axis, labeled S. A horizontal dotted line extends from this point to near the right vertical axis. The curve moves smoothly upward to a peak labeled green double dagger, from which a dotted horizontal line extends to the right. The curve descends more steeply than it rose and continues beneath the starting level to level off and end about one-eighth of the height of the vertical axis at brown P. An upward arrow pointing from the dotted line extending from S to the dotted line extending from the green double dagger is labeled Greek letter delta G superscript double dagger end superscript subscript uncat. Part b, enzyme complementary to substrate, shows the same metal stick surrounded by a C-shaped ring of small green bars labeled magnets within a larger molecule labeled enzyme that is wider above and curves with the magnets along the left and right sides. The bottom side of the iron bar is not enclosed. The entire structure is labeled E S. An arrow points to the words few products. On the graph, a dotted curve begins at S just below half of the height of the vertical axis and follows a similar path upward as in part a to reach a peak labeled green double dagger, from which a second dotted line continues horizontally to the right. A dotted horizontal line extends from the vertical axis at S across the graph. A blue curve begins at S and curves slightly upward just after the dotted line curves upward, but it has a very small peak before dropping rapidly down to E S near the horizontal axis. A dotted line extends to the right from E S. The curve bends rapidly upward and extends almost vertically to meet the dotted curve at the point labeled green double dagger. The curve bends downward more gradually, following a similar path to the curve in part a before ending at brown P at about one-third of the height of the vertical axis. As in part a, an arrow pointing upward from the dotted line from S to the top dotted line extending from the green double dagger is labeled Greek letter delta superscript double dagger end superscript subscript uncat. A blue arrow pointing upward from the dotted line from E S to the dotted line from the green double dagger is labeled blue Greek letter delta G superscript double dagger end superscript subscript cat. A green arrow pointing upward from the dotted line from E S to the dotted line from S is labeled Greek letter delta G superscript uppercase M. In part c, enzyme complementary to the transition state, shows a similar structure to that shown in part b, except that the magnets and bottom of the enzyme are bent upward so that there is a space between them and the metal rod in the middle, while the iron bar is still contained on the left and the right. This structure is labeled E S. An arrow points to show the same structure with the metal rod bent into an inverted V shape so the vertex of the bend is now adjacent to the center of the enzyme with the magnets. This is labeled green double dagger. An arrow points to show the same structure, labeled E, with two brown pieces of metal stick beneath labeled brown P. The graph shows a dotted line resembling the curve from part a with green double dagger at its peak and a dotted horizontal line extending from the peak to the right. A horizontal dotted line also extends from S, which is at about one-quarter of the height of the vertical axis. A blue curve begins from S and rises slightly to the right of the dotted peak, then lowers almost to the dotted horizontal line from S. This is labeled E S. The line extends up almost to half of the height of the peak of the dotted curve, where it is labeled with a green double dagger, then curves down to join with the dotted curve near its end at brown P. A dotted horizontal line extends from the peak labeled with a green double dagger. A long arrow pointing upward from the dotted line from S to the dotted line from the top peak of the dotted curve is labeled Greek delta G superscript double dagger end superscript subscript uncat. A short blue arrow pointing upward from the dotted line from S to the dotted line from the green double dagger of the blue peak is labeled Greek letter delta G superscript double dagger. A green arrow pointing downward from the dotted line from the top peak of the dotted curve, labeled with a green double dagger, to the dotted line extending from the blue peak labeled with a green double dagger, is labeled Greek letter delta G subscript uppercase M. All data are approximate.

The modern notion of enzymatic catalysis, first proposed by Michael Polanyi (1921) and J. B. S. Haldane (1930), was elaborated by Linus Pauling in 1946 and by William P. Jencks in the 1970s: in order to catalyze reactions, an enzyme must be complementary to the reaction transition state. This means that optimal interactions between substrate and enzyme occur only in the transition state. Figure 6-5c demonstrates how such an enzyme can work. The metal stick binds to the stickase, but only a few of the possible magnetic interactions are used in forming the ES complex. The bound substrate must still undergo the increase in free energy needed to reach the transition state. Now, however, the increase in free energy required to draw the stick into a bent and partially broken conformation is offset, or “paid for,” by the magnetic interactions that form between our imaginary enzyme and substrate (analogous to the binding energy in a real enzyme) in the transition state. Many of these interactions involve parts of the stick that are distant from the point of breakage; thus, interactions between the stickase and nonreacting parts of the stick provide some of the energy needed to catalyze stick breakage. This “energy payment” translates into a lower net activation energy and a faster reaction rate.

Real enzymes work on an analogous principle. Some weak interactions are formed in the ES complex, but the full complement of such interactions between substrate and enzyme is formed only when the substrate reaches the transition state. The free energy (binding energy) released by the formation of these interactions partially offsets the energy required to reach the top of the energy hill. The summation of the unfavorable (positive) activation energy $mathml alt text112$ $upper Delta upper G Superscript double-dagger$ and the favorable (negative) binding energy $mathml alt text113$ $upper Delta upper G Subscript upper B$ results in a lower net activation energy (Fig. 6-6). Even on the enzyme, the transition state is not a stable species but a brief point in time that the substrate spends atop an energy hill. However, the enzyme-catalyzed reaction is much faster than the uncatalyzed process because the hill is much smaller. The important principle is that weak binding interactions between the enzyme and the substrate provide a substantial driving force for enzymatic catalysis. The groups on the substrate that are involved in these weak interactions can be at some distance from the bonds that are broken or changed. The weak interactions formed only in the transition state are those that make the primary contribution to catalysis.

A graph plots reaction coordinate on the horizontal axis against free energy, G, on the vertical axis to show the role of binding energy. — FIGURE 6-6 Role of binding energy in catalysis. To lower the activation energy for a reaction, the system must acquire an amount of energy equivalent to the amount by which $mathml alt text114$ $upper Delta upper G Superscript double-dagger$ is lowered. Much of this energy comes from binding energy, $mathml alt text115$ $upper Delta upper G Subscript upper B$ , contributed by formation of weak noncovalent interactions between substrate and enzyme in the transition state. The role of $mathml alt text116$ $upper Delta upper G Subscript upper B$ is analogous to that of $mathml alt text117$ $upper Delta upper G Subscript upper M$ in Figure 6-5.

FIGURE 6-6 Role of binding energy in catalysis. To lower the activation energy for a reaction, the system must acquire an amount of energy equivalent to the amount by which $mathml alt text114$ $upper Delta upper G Superscript double-dagger$ is lowered. Much of this energy comes from binding energy, $mathml alt text115$ $upper Delta upper G Subscript upper B$ , contributed by formation of weak noncovalent interactions between substrate and enzyme in the transition state. The role of $mathml alt text116$ $upper Delta upper G Subscript upper B$ is analogous to that of $mathml alt text117$ $upper Delta upper G Subscript upper M$ in Figure 6-5.

A curve begins from just below half of the height of the vertical axis, labeled S. A horizontal dotted line extends from this point to near the right vertical axis. The curve moves smoothly upward to a peak labeled with a double dagger and then descends almost symmetrically as a bell curve, except that it ends at a lower level than it began. The ending point is labeled P. A dotted horizontal line extends from the top peak to the right. A blue curve extends from S to form a small peak, then descends to E S just above the dotted line from S, then has another small peak labeled double dagger, then descends to E P just above the dotted line from S, then has a small peak before descending to join with the first curve where it crosses the dotted line from S before ending at P. A long upward arrow from the dotted line from S to the dotted line from the top peak labeled with a double dagger is labeled Greek letter delta G superscript double dagger end superscript subscript uncat. A bright green downward arrow extending from the dotted line from the top peak labeled with a double dagger to the dotted line from the smaller peak labeled light green double dagger is labeled bright green Greek letter delta subscript uppercase B. A short upward light green arrow extending from the dotted line from S to the dotted line from the peak labeled light green double dagger is labeled light green Greek letter delta G superscript double dagger end superscript subscript cat. All data are approximate.

The requirement for multiple weak interactions to drive catalysis is one reason why enzymes (and some coenzymes) are so large. An enzyme must provide functional groups for ionic, hydrogen-bond, and other interactions, and also must precisely position these groups so that binding energy is optimized in the transition state. Adequate binding is accomplished most readily by positioning a substrate in a cavity (the active site) where it is effectively removed from water. The size of proteins reflects the need for superstructure to keep interacting groups properly positioned and to keep the cavity from collapsing.

Can we demonstrate quantitatively that binding energy accounts for the huge rate accelerations brought about by enzymes? Yes. As a point of reference, Equation 6-6 allows us to calculate that $mathml alt text118$ $upper Delta upper G Superscript double-dagger$ must be lowered by about 5.7 kJ/mol to accelerate a first-order reaction by a factor of 10, under conditions commonly found in cells. The energy available from formation of a single weak interaction is generally estimated to be 4 to 30 kJ/mol. The overall energy available from many such interactions is therefore sufficient to lower activation energies by the 60 to 100 kJ/mol required to explain the large rate enhancements observed for many enzymes.

The same binding energy that provides energy for catalysis also gives an enzyme its specificity, the ability to discriminate between a substrate and a competing molecule. Conceptually, specificity is easy to distinguish from catalysis, but this distinction is much more difficult to make experimentally, because catalysis and specificity arise from the same phenomenon. If an enzyme active site has functional groups arranged optimally to form a variety of weak interactions with a particular substrate in the transition state, the enzyme will not be able to interact to the same degree with any other molecule. For example, if the substrate has a hydroxyl group that forms a hydrogen bond with a specific Glu residue on the enzyme, any molecule lacking a hydroxyl group at that particular position will be a poorer substrate for the enzyme. In general, specificity is derived from the formation of many weak interactions between the enzyme and its specific substrate molecule.

The importance of binding energy to catalysis can be readily demonstrated. For example, the glycolytic enzyme triose phosphate isomerase catalyzes the interconversion of glyceraldehyde 3-phosphate and dihydroxyacetone phosphate:

A figure shows the interconversion of glyceraldehyde 3-phosphate and dihydroxyacetone phosphate.

This reaction rearranges the carbonyl and hydroxyl groups on carbons 1 and 2. However, more than 80% of the enzymatic rate acceleration has been traced to enzyme-substrate interactions involving the phosphate group on carbon 3 of the substrate. This was determined by comparing the enzyme-catalyzed reactions with glyceraldehyde 3-phosphate and with glyceraldehyde (no phosphate group at position 3) as substrate.

The general principles outlined above can be illustrated by a variety of recognized catalytic mechanisms. These mechanisms are not mutually exclusive, and a given enzyme might incorporate several catalytic strategies in its overall mechanism of action.

Consider what needs to occur for a reaction to take place. Prominent physical and thermodynamic factors contributing to $mathml alt text119$ $upper Delta upper G Superscript double-dagger$ , the barrier to reaction, might include (1) the entropy of molecules in solution, which reduces the possibility that they will react together; (2) the solvation shell of hydrogen-bonded water that surrounds and helps to stabilize most biomolecules in aqueous solution; (3) the distortion of substrates that must occur in many reactions; and (4) the need for proper alignment of catalytic functional groups on the enzyme. Binding energy can be used to overcome all these barriers.

First, a large restriction in the relative motions of two substrates that are to react, or entropy reduction, is one obvious benefit of binding them to an enzyme. Binding energy constrains the substrates in the proper orientation to react — a substantial contribution to catalysis, because productive collisions between molecules in solution can be exceedingly rare. Substrates can be precisely aligned on the enzyme, with many weak interactions between each substrate and strategically located groups on the enzyme clamping the substrate molecules into the proper positions. Studies have shown that simply constraining the motion of two reactants can produce rate enhancements of many orders of magnitude (Fig. 6-7).

A three-part figure, a, b, and c, shows the rate enhancement of three reactions with different rate enhancements. The reaction in part a has a rate enhancement of 1, the reaction in part b has a rate enhancement of 10 superscript 5 M, and the reaction in part c has a rate enhancement of 10 superscript 8 M. — 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 $mathml alt text120$ $upper M Superscript negative 1 Baseline s Superscript negative 1$ . (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 $mathml alt text121$ $s Superscript negative 1$ . Dividing the rate constant for (b) by the rate constant for (a) gives a rate enhancement of about $mathml alt text122$ $10 Superscript 5 Baseline upper M$ . (The enhancement has units of molarity because we are comparing a unimolecular reaction 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 $mathml alt text123$ $10 Superscript 5 Baseline upper M$ . 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 $mathml alt text124$ $10 Superscript 8 Baseline upper M$ relative to (a).

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 $mathml alt text120$ $upper M Superscript negative 1 Baseline s Superscript negative 1$ . (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 $mathml alt text121$ $s Superscript negative 1$ . Dividing the rate constant for (b) by the rate constant for (a) gives a rate enhancement of about $mathml alt text122$ $10 Superscript 5 Baseline upper M$ . (The enhancement has units of molarity because we are comparing a unimolecular reaction 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 $mathml alt text123$ $10 Superscript 5 Baseline upper M$ . 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 $mathml alt text124$ $10 Superscript 8 Baseline upper M$ relative to (a).

Each part shows the reaction on the left and the rate enhancement on the right. Part a shows the addition of two molecules. The first molecule has a central C that is double bonded to O above, bonded to O R on the right, and bonded to C H 3 on the left. The second molecule is similar except that C is bonded to O minus on the right. An arrow points to the right above text reading, lowercase K open parenthesis M superscript minus 1 end superscript lowercase S superscript minus 1 close parenthesis. An arrow shows that superscript minus end superscript O R leaves during the reaction. The product has the central carbons of both molecules connected by O. The first molecule is the same, except that it is now bonded to O on the right and below instead of to O R. The same O bonds to C of the second molecule below and to the left, where it is further double bonded to O below and single bonded to C H 3 on the left. The rate enhancement is 1. Part b shows a single C-shaped molecule that rotates. The molecule has C on top that is double bonded to O above, bonded to O R on the right, and bonded to a chain of two carbons to the left that link down to another C that is double bonded to O below and bonded to O minus on the right. The bonds connecting the top C double bonded to O to the first C of the chain, the first to the second C of the chain, and the second C of the chain to the second C double bonded to O each have an arrow curving from the outside to the inside of the area enclosed by the overall molecule (the open area of the C). An arrow points to the right above text reading, lowercase K open parenthesis lowercase S superscript minus 1 close parenthesis. A curved arrow shows that superscript minus end superscript O R leaves during the reaction. This produces a five-membered ring with O forming the right vertex, C double bonded to O above at the top right vertex, and C double bonded to O below at the bottom right vertex. The rate enhancement is 10 superscript 5 M. Part c shows a molecule with a complex ring structure. It has a six-carbon ring with a double bond on the far left side. The bonds from the rear and front C forming this double bond angle upward to the rear and front central vertices, which are each joined to a single O above the ring. From these central vertices, the bonds angle down to the rear and front right vertices. The rear right vertex is further bonded to C that is double bonded to O above and bonded to O R on the right. The front right vertex is further bonded to C that is double bonded to O above and single bonded to O minus on the right. An arrow points to the right above text reading lowercase K open parenthesis lowercase S superscript minus 1 close parenthesis. A curved arrow shows that superscript minus end superscript O R leaves during the reaction. This produces a similar molecule in which the rear C double bonded to O is now bonded to an O to the right instead of to O R. The same O is further bonded to the left to C that is now double bonded to O below instead of above. The rate enhancement is 10 superscript 8 end superscript M.

Second, in water, many organic molecules are surrounded by a solvation shell of structured water that can hinder reactions (see Fig. 2-8). Formation of weak bonds between substrate and enzyme results in desolvation of the substrate. Enzyme-substrate interactions replace most or all of the hydrogen bonds between the substrate and water that would otherwise impede reaction.

Third, binding energy involving weak interactions that are formed only in the reaction transition state helps to compensate thermodynamically for the unfavorable free-energy change associated with any distortion, primarily electron redistribution, that the substrate must undergo to react.

Finally, the enzyme itself usually undergoes a change in conformation when the substrate binds, induced by multiple weak interactions with the substrate. This is referred to as induced fit, a mechanism postulated by Daniel Koshland in 1958. The motions can affect a small part of the enzyme near the active site or can involve changes in the positioning of entire domains. Typically, a network of coupled motions occurs throughout the enzyme that ultimately brings about the required changes in the active site. Induced fit serves to bring specific functional groups on the enzyme into the proper position to catalyze the reaction. The conformational change also permits formation of additional weak bonding interactions in the transition state. In either case, the new enzyme conformation has enhanced catalytic properties. As we have seen, induced fit is a common feature of the reversible binding of ligands to proteins (Chapter 5). Induced fit is also important in the interaction of almost every enzyme with its substrate.

Covalent Interactions and Metal Ions Contribute to Catalysis

In most enzymes, noncovalent binding energy is just one of several contributors to the overall catalytic mechanism. Once a substrate is bound to an enzyme, properly positioned catalytic functional groups aid in the cleavage and formation of bonds by a variety of mechanisms, including general acid-base catalysis, covalent catalysis, and metal ion catalysis. The first two of these mechanisms are distinct from those based on binding energy, because they generally involve transient covalent interaction with a substrate or group transfer to or from a substrate.

General Acid-Base Catalysis

Transfer of a proton from one molecule to another is the single most common reaction in biochemistry. One or, often, many proton transfers occur in the course of most reactions that take place in cells. Many biochemical reactions occur through the formation of unstable charged intermediates that tend to break down rapidly to their constituent reactant species, impeding the forward reaction (Fig. 6-8). Charged intermediates can often be stabilized by the transfer of protons to form a species that breaks down more readily to products. These protons are transferred between an enzyme and a substrate or intermediate.

A figure shows the role of a catalyst in a reaction that produces an unstable intermediate that rapidly breaks down if the catalyst is not present. — FIGURE 6-8 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 $mathml alt text125$ $upper H Subscript 3 Baseline upper O Superscript plus$ (specific acid catalysis) or HA (general acid catalysis), where HA represents any acid. Similarly, charge can be neutralized by proton abstraction by $mathml alt text126$ $OH Superscript minus$ (specific base catalysis) or B: (general base catalysis), where B: represents any base.

FIGURE 6-8 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 $mathml alt text125$ $upper H Subscript 3 Baseline upper O Superscript plus$ (specific acid catalysis) or HA (general acid catalysis), where HA represents any acid. Similarly, charge can be neutralized by proton abstraction by $mathml alt text126$ $OH Superscript minus$ (specific base catalysis) or B: (general base catalysis), where B: represents any base.

The top part of the figure shows the reactants. A central carbon is bonded to R superscript 1 above, H on the left R superscript 2 below, and O on the right with a pair of red electrons below and a red H to the right. This is added to a second molecule with a central C bonded to R superscript 3 above, double bonded to O to the right, and bonded to N below that is further bonded to H to the right and to R superscript 4 below. A red arrow points from the pair of electrons on O to the C of the other molecule. Another red arrow points from the double bond connecting that C to O to the O. A vertical double-headed arrow below has a short arrow pointing down and a long arrow pointing up. Text reads, without catalysis, unstable (charged) intermediate breaks down rapidly to form reactants. Beneath the arrow, a molecule has O in the center with plus below, red H above, C on the left that is further bonded to R superscript 1 above, H on the left and R superscript 2 below, and C on the right that is further bonded to R superscript 3 above, O minus to the right, and N below that is further bonded to H on the right and to R superscript 4 below. Two arrows point downward accompanied by text that reads, proton transfers to and from either water or weak acids and bases stabilize the intermediate and accelerate the reaction. The left-hand arrow is accompanied by a curved arrow showing the addition of O H minus and H 2 O blue highlighted H plus and the departure of H O red H and H O H. The right-hand arrow is accompanied by a curved arrow showing the addition of B with a red pair of electrons and blue H black A and the departure of B positive red H and A minus. The product below has a central carbon on the left bonded to R superscript 1 above, H to the left, R superscript 2 below, and O to the right that is further bonded to a central C that is bonded to R superscript 3 above, O minus on the right, and N positive below that is further bonded to blue H on the right, R superscript 4 below, and H on the left. An arrow points down to two molecules labeled products. The first molecule has a central carbon on the left bonded to R superscript 1 above, H to the left, R superscript 2 below, and O to the right that is further bonded to a central C that is bonded to R superscript 3 above and double bonded to O on the right. The second molecule has a central N that is bonded to blue H to the upper left, H to the upper right, and R superscript 4 below.

The effects of catalysis by acids and bases are often studied using nonenzymatic model reactions, in which the proton donors or acceptors are either the constituents of water alone or other weak acids and bases. Catalysis of the type that uses only the $mathml alt text127$ $upper H Superscript plus Baseline left-parenthesis upper H Subscript 3 Baseline upper O Superscript plus Baseline right-parenthesis$ or $mathml alt text128$ $OH Superscript minus$ ions present in water is referred to as specific acid-base catalysis. However, a further increase in rate can often be afforded by the addition of weak acids and bases to the reaction. Many weak organic acids can supplement water as proton donors, or weak organic bases can supplement water as proton acceptors. The term general acid-base catalysis refers to proton transfers mediated by weak acids and bases other than water.

General acid-base catalysis becomes crucial in the active site of an enzyme, where water may not be available as a proton donor or acceptor. Several amino acid side chains can and do take on the role of proton donors and acceptors (Fig. 6-9). These groups can be precisely positioned in an enzyme active site to allow proton transfers, providing rate enhancements of the order of $mathml alt text129$ $10 squared$ to $mathml alt text130$ $10 Superscript 5$ . This type of catalysis occurs on the vast majority of enzymes.

A table shows the general acid forms and general base forms of eight amino acid residues: G l u, A s p, L y s, A r g, C y s, H i s, S e r, and T y r. — FIGURE 6-9 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.

The table has three columns and six rows. The column headers are amino acid residues, general acid form (proton donor), and general base form (proton acceptor). The rows are as follows with each containing the amino acid name followed by the general acid form and then the general base form. G l u, A s p: R bonded to C O O highlighted H, R bonded to C O O minus; L y s, A r g: R bonded to N positive bonded to H above, highlighted H to the right, and H below, R bonded to N H 2 with a pair of highlighted electrons above N; C y s: R bonded to S highlighted H, R bonded to S minus; H i s: five-membered ring with R bonded to the top left vertex, C H at the top right vertex, N positive highlighted H substituted for C at the bottom right vertex, C H at the bottom vertex, N H substituted for C at the bottom left vertex, and double bonds at the top and lower right sides, similar molecule with N positive highlighted H replaced by N with a pair of highlighted electrons; S e r: R bonded to O highlighted H, R bonded to O minus; T y r: benzene ring with R and O highlighted H at para positions, benzene ring with R and O minus at para positions.

Covalent Catalysis

In covalent catalysis, a transient covalent bond is formed between the enzyme and the substrate. Consider the hydrolysis of a bond between groups A and B:

A — B \overset{H_{2} O}{\to} A + B

$upper A em-dash upper B right-arrow Overscript upper H Subscript 2 Baseline upper O Endscripts upper A plus upper B$

In the presence of a covalent catalyst (an enzyme with a nucleophilic group X:) the reaction becomes

A — B + X : \to A — X + B \overset{H_{2} O}{\to} A + X : + B

$upper A em-dash upper B plus upper X colon right-arrow upper A em-dash upper X plus upper B right-arrow Overscript upper H Subscript 2 Baseline upper O Endscripts upper A plus upper X colon plus upper B$

Formation and breakdown of a covalent intermediate creates a new pathway for the reaction, but catalysis results only when the new pathway has a lower activation energy than the uncatalyzed pathway. Both of the new steps must be faster than the uncatalyzed reaction. Several amino acid side chains, including all those in Figure 6-9, and the functional groups of some enzyme cofactors can serve as nucleophiles in the formation of covalent bonds with substrates. These covalent complexes always undergo further reaction to regenerate the free enzyme. The covalent bond formed between the enzyme and the substrate can activate a substrate for further reaction in a manner that is usually specific to the particular group or coenzyme.

Metal Ion Catalysis

Metals, whether tightly bound to the enzyme or taken up from solution along with the substrate, can participate in catalysis in several ways. Ionic interactions between an enzyme-bound metal and a substrate can help orient the substrate for reaction or stabilize charged reaction transition states. This use of weak bonding interactions between metal and substrate is similar to some of the uses of enzyme-substrate binding energy described earlier, and it can contribute to enzyme–transition state complementarity. Metals can also mediate oxidation-reduction reactions by reversible changes in the metal ion’s oxidation state. Nearly a third of all known enzymes require one or more metal ions for catalytic activity.

Most enzymes combine several catalytic strategies to bring about a rate enhancement. A good example is the use of covalent catalysis, general acid-base catalysis, and transition-state stabilization in the reaction catalyzed by chymotrypsin, detailed in Section 6.4.

SUMMARY 6.2 How Enzymes Work

Enzymes are highly effective catalysts, commonly enhancing reaction rates by a factor of $mathml alt text133$ $10 Superscript 5$ to $mathml alt text134$ $10 Superscript 17$ . Enzyme-catalyzed reactions are characterized by the formation of a complex between substrate and enzyme (an ES complex). Substrate binding occurs in a pocket on the enzyme called the active site.
The function of enzymes and other catalysts is to lower the activation energy, $mathml alt text135$ $upper Delta upper G Superscript double-dagger$ , for a reaction and thereby enhance the reaction rate. The equilibrium of a reaction is unaffected by the enzyme.
Reaction equilibria are described by equilibrium constants, $mathml alt text136$ $upper K Subscript eq$ , which are related to the biochemical standard free-energy change $mathml alt text137$ $upper Delta upper G prime degree$ . Reaction rates are described by rate constants, k, which are related to the activation energy $mathml alt text138$ $upper Delta upper G Superscript double-dagger$ .
The extraordinary rate accelerations provided by enzymes are due to noncovalent binding energy supplemented by covalent interactions or metal ion catalysis.
Noncovalent binding energy, $mathml alt text139$ $upper Delta upper G Subscript upper B$ , is maximized in the transition state of the catalyzed reaction. Enzyme–transition state complementarity is a fundamental principle of enzymatic catalysis. Noncovalent interactions may facilitate the path to the transition state, offsetting the energy required for activation, $mathml alt text140$ $upper Delta upper G Superscript double-dagger$ , by lowering substrate entropy, causing substrate desolvation, or causing a conformational change in the enzyme (induced fit). Binding energy also accounts for the exquisite specificity of enzymes for their substrates.
General acid-base catalysis and covalent catalysis mechanisms contribute to the catalytic power of enzymes. Covalent interactions between the substrate and the enzyme, group transfers to and from the enzyme, and interactions with metal ions can provide a new, lower-energy reaction path.