8.3 Enzymes Accelerate Reactions by Facilitating the Formation of the Transition State

The free-energy difference between reactants and products accounts for the equilibrium of the reaction, but enzymes accelerate how quickly this equilibrium is attained. How can we explain the rate enhancement in terms of thermodynamics? To do so, we have to consider not the end points of the reaction but the chemical pathway between the end points.

A chemical reaction of substrate S to form product P goes through a transition state X‡ that has a higher free energy than does either S or P.

The double dagger denotes the transition state. The transition state is a transitory molecular structure that is no longer the substrate but is not yet the product. The transition state is the least-stable and most-seldom-occupied species along the reaction pathway because it is the one with the highest free energy. The difference in free energy between the transition state and the substrate is called the Gibbs free energy of activation or simply the activation energy, symbolized by ΔG‡ (Figure 8.3).

Figure 8.3: Enzymes decrease the activation energy. Enzymes accelerate reactions by decreasing ΔG‡, the free energy of activation.

Note that the energy of activation, or ΔG‡, does not enter into the final ΔG calculation for the reaction, because the energy required to generate the transition state is released when the transition state forms the product. The activation-energy barrier immediately suggests how an enzyme enhances the reaction rate without altering ΔG of the reaction: enzymes function to lower the activation energy, or, in other words, enzymes facilitate the formation of the transition state.

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“I think that enzymes are molecules that are complementary in structure to the activated complexes of the reactions that they catalyze, that is, to the molecular configuration that is intermediate between the reacting substances and the products of reaction for these catalyzed processes. The attraction of the enzyme molecule for the activated complex would thus lead to a decrease in its energy and hence to a decrease in the energy of activation of the reaction and to an increase in the rate of reaction.”

—Linus Pauling

Nature 161:707, 1948

One approach to understanding the increase in reaction rates achieved by enzymes is to assume that the transition state (X‡) and the substrate (S) are in equilibrium.

in which K‡ is the equilibrium constant for the formation of X‡ and v is the rate of formation of product from X‡. The rate of the reaction v is proportional to the concentration of X‡,

v ∝ [X‡],

because only X‡ can be converted into product. The concentration of X‡ at equilibrium is in turn related to the free-energy difference ΔG‡ between X‡ and S; the greater the difference in free energy between these two states, the smaller the amount of X‡. Thus, the overall rate of reaction V depends on ΔG‡. Specifically,

In this equation, k is Boltzmann’s constant, and h is Planck’s constant. The value of kT/h at 25°C is 6.6 × 1012 s−1. Suppose that the free energy of activation is 28.53 kJ mol−1 (6.82 kcal mol−1). If we were to substitute this value of ΔG in equation 7 (as shown in Table 8.3), this free-energy difference would result when the ratio [X‡]/[S] is 10−5. If we assume for simplicity’s sake that [S] = 1 M, then the reaction rate V is 6.2 × 107 s−1. If ΔG‡ were lowered by 5.69 kJ mol−1 (1.36 kcal mol−1), the ratio [X‡]/[S] would then be 10−4, and the reaction rate would be 6.2 × 108 s−1. A decrease of 5.69 kJ mol−1 in ΔG‡ yields a 10-fold larger V. A relatively small decrease in ΔG‡ (20% in this particular reaction) results in a much greater increase in V.

Thus, we see the key to how enzymes operate: enzymes accelerate reactions by decreasing ΔG‡, the activation energy. The combination of substrate and enzyme creates a reaction pathway whose transition-state energy is lower than that of the reaction in the absence of enzyme (Figure 8.3). Because the activation energy is lower, more molecules have the energy required to reach the transition state. Decreasing the activation barrier is analogous to lowering the height of a high-jump bar; more athletes will be able to clear the bar. The essence of catalysis is facilitating the formation of the transition state.

The formation of an enzyme–substrate complex is the first step in enzymatic catalysis

Figure 8.4: Reaction velocity versus substrate concentration in an enzyme-catalyzed reaction. An enzyme-catalyzed reaction approaches a maximal velocity.

Much of the catalytic power of enzymes comes from their binding to and then altering the structure of the substrate to promote the formation of the transition state. Thus, the first step in catalysis is the formation of an enzyme–substrate (ES) complex. Substrates bind to a specific region of the enzyme called the active site. Most enzymes are highly selective in the substrates that they bind. Indeed, the catalytic specificity of enzymes depends in part on the specificity of binding.

What is the evidence for the existence of an enzyme–substrate complex?

  1. The first clue was the observation that, at a constant concentration of enzyme, the reaction rate increases with increasing substrate concentration until a maximal velocity is reached (Figure 8.4). In contrast, uncatalyzed reactions do not show this saturation effect. The fact that an enzyme-catalyzed reaction has a maximal velocity suggests the formation of a discrete ES complex. At a sufficiently high substrate concentration, all the catalytic sites are filled, or saturated, and so the reaction rate cannot increase. Although indirect, the ability to saturate an enzyme with substrate is the most general evidence for the existence of ES complexes.

  2. 223

    The spectroscopic characteristics of many enzymes and substrates change on the formation of an ES complex. These changes are particularly striking if the enzyme contains a colored prosthetic group (Problem 39).

  3. X-ray crystallography has provided high-resolution images of substrates and substrate analogs bound to the active sites of many enzymes (Figure 8.5). In Chapter 9, we will take a close look at several of these complexes.

    Figure 8.5: Structure of an enzyme–substrate complex. (Left) The enzyme cytochrome P450 is illustrated bound to its substrate camphor. (Right) Notice that, in the active site, the substrate is surrounded by residues from the enzyme. Note also the presence of a heme cofactor.
    [Drawn from 2CPP.pdb.]

The active sites of enzymes have some common features

Figure 8.6: Active sites may include distant residues. (A) Ribbon diagram of the enzyme lysozyme with several components of the active site shown in color. (B) A schematic representation of the primary structure of lysozyme shows that the active site is composed of residues that come from different parts of the polypeptide chain.
[Drawn from 6LYZ.pdb.]

The active site of an enzyme is the region that binds the substrates (and the cofactor, if any). It also contains the amino acid residues that directly participate in the making and breaking of bonds. These residues are called the catalytic groups. In essence, the interaction of the enzyme and substrate at the active site promotes the formation of the transition state. The active site is the region of the enzyme that most directly lowers the ΔG‡ of the reaction, thus providing the rate-enhancement characteristic of enzyme action. Recall from Chapter 2 that proteins are not rigid structures, but are flexible and exist in an array of conformations. Thus, the interaction of the enzyme and substrate at the active site and the formation of the transition state is a dynamic process. Although enzymes differ widely in structure, specificity, and mode of catalysis, a number of generalizations concerning their active sites can be stated:

Figure 8.7: Hydrogen bonds between an enzyme and substrate. The enzyme ribonuclease forms hydrogen bonds with the uridine component of the substrate.
[Information from F. M. Richards, H. W. Wyckoff, and N. Allewell. In The Neurosciences: Second Study Program, F. O. Schmidt, Ed. (Rockefeller University Press, 1970), p. 970.]

  1. The active site is a three-dimensional cleft, or crevice, formed by groups that come from different parts of the amino acid sequence: indeed, residues far apart in the amino acid sequence may interact more strongly than adjacent residues in the sequence, which may be sterically constrained from interacting with one another. In lysozyme, an enzyme that degrades the cell walls of some bacteria, the important groups in the active site are contributed by residues numbered 35, 52, 62, 63, 101, and 108 in the sequence of 129 amino acids (Figure 8.6).

  2. The active site takes up a small part of the total volume of an enzyme. Although most of the amino acid residues in an enzyme are not in contact with the substrate, the cooperative motions of the entire enzyme help to correctly position the catalytic residues at the active site. Experimental attempts to reduce the size of a catalytically active enzyme show that the minimum size requires about 100 amino acid residues. In fact, nearly all enzymes are made up of more than 100 amino acid residues, which gives them a mass greater than 10 kDa and a diameter of more than 25 Å, suggesting that all amino acids in the protein, not just those at the active site, are ultimately required to form a functional enzyme.

  3. Active sites are unique microenvironments. In all enzymes of known structure, active sites are shaped like a cleft, or crevice, to which the substrates bind. Water is usually excluded unless it is a reactant. The nonpolar microenvironment of the cleft enhances the binding of substrates as well as catalysis. Nevertheless, the cleft may also contain polar residues, some of which may acquire special properties essential for substrate binding or catalysis. The internal positions of these polar residues are biologically crucial exceptions to the general rule that polar residues are located on the surface of proteins, exposed to water.

  4. 224

    Substrates are bound to enzymes by multiple weak attractions. The noncovalent interactions in ES complexes are much weaker than covalent bonds, which have energies between −210 and −460 kJ mol−1 (between −50 and −110 kcal mol−1). In contrast, ES complexes usually have equilibrium constants that range from 10−2 to 10−8 M, corresponding to free energies of interaction ranging from about −13 to −50 kJ mol−1 (from −3 to −12 kcal mol−1). As discussed in Section 1.3, these weak reversible contacts are mediated by electrostatic interactions, hydrogen bonds, and van der Waals forces. Van der Waals forces become significant in binding only when numerous substrate atoms simultaneously come close to many enzyme atoms through the hydrophobic effect. Hence, the enzyme and substrate should have complementary shapes. The directional character of hydrogen bonds between enzyme and substrate often enforces a high degree of specificity, as seen in the RNA-degrading enzyme ribonuclease (Figure 8.7).

  5. The specificity of binding depends on the precisely defined arrangement of atoms in an active site. Because the enzyme and the substrate interact by means of short-range forces that require close contact, a substrate must have a matching shape to fit into the site. Emil Fischer proposed the lock-and-key analogy in 1890 (Figure 8.8), which was the model for enzyme–substrate interaction for several decades. We now know that enzymes are flexible and that the shapes of the active sites can be markedly modified by the binding of substrate, a process of dynamic recognition called induced fit (Figure 8.9). Moreover, the substrate may bind to only certain conformations of the enzyme, in what is called conformation selection. Thus, the mechanism of catalysis is dynamic, involving structural changes with multiple intermediates of both reactants and the enzyme.

Figure 8.8: Lock-and-key model of enzyme–substrate binding. In this model, the active site of the unbound enzyme is complementary in shape to the substrate.
Figure 8.9: Induced-fit model of enzyme–substrate binding. In this model, the enzyme changes shape on substrate binding. The active site forms a shape complementary to the substrate only after the substrate has been bound.

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The binding energy between enzyme and substrate is important for catalysis

Enzymes lower the activation energy, but where does the energy to lower the activation energy come from? Free energy is released by the formation of a large number of weak interactions between a complementary enzyme and its substrate. The free energy released on binding is called the binding energy. Only the correct substrate can participate in most or all of the interactions with the enzyme and thus maximize binding energy, accounting for the exquisite substrate specificity exhibited by many enzymes. Furthermore, the full complement of such interactions is formed only when the substrate is converted into the transition state. Thus, the maximal binding energy is released when the enzyme facilitates the formation of the transition state. The energy released by the interaction between the enzyme and the substrate can be thought of as lowering the activation energy. The interaction of the enzyme with the substrate and reaction intermediates is fleeting, with molecular movements resulting in the optimal alignment of functional groups at the active site so that maximum binding energy occurs only between the enzyme and the transition state, the least-stable reaction intermediate. However, the transition state is too unstable to exist for long. It collapses to either substrate or product, but which of the two accumulates is determined only by the energy difference between the substrate and the product—that is, by the ΔG of the reaction.