Enzymes (Second Edition)

20 CHEMICAL BONDS AND REACTIONS IN BIOCHEMISTRY

for orbital formation. Hence, we find one bond (from the sp hybrid orbitals) and two bonds along the interatomic axis. This triple bond is denoted by drawing three parallel lines connecting the two carbon atoms, as in acetylene:

H C C H

Not all the valence electrons of the atoms in a molecule are shared in the form of covalent bonds. In many cases it is energetically advantageous to the molecule to have unshared electrons that are essentially localized to a single atom; these electrons are often referred to as nonbonding or lone pair electrons. Whereas electrons within bonding orbitals are denoted as lines drawn between atoms of the molecule, lone pair electrons are usually depicted as a pair of dots surrounding a particular atom. (Combinations of atoms and molecules represented by means of these conventions are referred to as Lewis structures.)

2.1.4 Resonance and Aromaticity

Let us consider the ionized form of acetic acid that occurs in aqueous solution at neutral pH (i.e., near physiological conditions). The carbon bound to the oxygen atoms uses sp hybridization: it forms a bond to the other carbon, abond to each oxygen atom, and one bond to one of the oxygen atoms. Thus, one oxygen atom would have a double bond to the carbon atom, while the other has a single bond to the carbon and is negatively charged. Suppose that we could somehow identify the individual oxygen atoms in this molecule — by, for example, using an isotopically labeled oxygen ( O rather thanO) at one site. Which of the two would form the double bond to carbon, and which would act as the anionic center?

Both of these are reasonable electronic forms, and there is no basis on which to choose one over the other. In fact, neither is truly correct, because in reality we find that the bond (or more correctly, the -electron density) is delocalized over both oxygen atoms. In some sense neither forms a single bond nor a double bond to the carbon atom, but rather both behave as if they shared thebond between them. We refer to these two alternative electronic forms of the molecule as resonance structures and sometimes represent this arrangement by

drawing a double-headed arrow between the two forms:

O O

Alternatively, the resonance form is illustrated as follows, to emphasize the delocalization of the -electron density:

O

H C C

O

Now let us consider the organic molecule benzene (C H ). The carbon atoms are arranged in a cyclic pattern, forming a planar hexagon. To account for this, we must assume that there are three double bonds among the carbon—carbon bonds of the molecule. Here are the two resonance structures:

Now a typical carbon—carbon single bond has a bond length of roughly 1.54 Å, while a carbon—carbon double bond is only about 1.35 Å long. When the crystal structure of benzene was determined, it was found that all the carbon— carbon bonds were the same length, 1.45 Å, which is intermediate between the expected lengths for single and double bonds. How can we rationalize this result? The answer is that the orbitals are not localized to the p orbitals of two adjacent carbon atoms (Figure 2.8, left: here the plane defined by the carbon ring system is arbitrarily assigned as the x,y plane); rather, they are delocalized over all six carbon p orbitals. To emphasize this system delocalization, many organic chemists choose to draw benzene as a hexagon enclosing a circle (Figure 2.8, right) rather than a hexagon of carbon with three discrete double bonds.

The delocalization of the system in molecules like benzene tends to stabilize the molecule relative to what one would predict on the basis of three isolated double bonds. This difference in stability is referred to as the resonance energy stabilization. For example, consider the heats of hydrogenation (breaking the carbon—carbon double bond and adding two atoms of hydrogen), using

22 CHEMICAL BONDS AND REACTIONS IN BIOCHEMISTRY

Figure 2.8 Two common representations for the benzene molecule. The representation on the right emphasizes the -system delocalization in this molecule.

H and platinum catalysis, for the series cyclohexene ( H 28.6 kcal/mol), cyclohexadiene, benzene. If each double bond were energetically equivalent, one would expect the H value for cyclohexadiene hydrogenation to be twice that of cyclohexene ( 57.2 kcal/mol), and that is approximately what is observed. Extending this argument further, one would expect the H value for benzene (if it behaved energetically equivalent to cyclohexatriene) to be three times that of cyclohexene, 85.8 kcal/mol. Experimentally, however, the H of hydrogenation of benzene is found to be only 49.8 kcal/mol, a resonance energy stabilization of 36 kcal/mol! This stabilizing effect of -orbital delocalization has an important influence over the structure and chemical reactivities of these molecules, as we shall see in later chapters.

2.1.5 Different Electronic Configurations Have Different Potential

Energies

We have seen how electrons distribute themselves among molecular orbitals according to the potential energies of those molecular orbitals. The specific distribution of the electrons within a molecule among the different electronic molecular orbitals defines the electronic configuration or electronic state of that molecule. The electronic state that imparts the least potential energy to that molecule will be the most stable form of that molecule under normal conditions. This electronic configuration is referred to as the ground state of the molecule. Any alternative electronic configuration of higher potential energy than the ground state is referred to as an excited state of the molecule.

Let us consider the simple carbonyl formaldehyde (CH O):

H

C O

H

In the ground state electronic configuration of this molecule, the -bonding orbital is the highest energy orbital that contains electrons. This orbital is referred to as the highest occupied molecular orbital (HOMO). The * molecular orbital is the next highest energy molecular orbital and, in the ground state, does not contain any electron density. This orbital is said to be the lowest unoccupied molecular orbital (LUMO). Suppose that somehow we were able to move an electron from the to the * orbital. The molecule would now have a different electronic configuration that would impart to the overall molecule more potential energy; that is, the molecule would be in an excited electronic state. Now, since in this excited state we have moved an electron from a bonding ( ) to an antibonding ( *) orbital, the overall molecule has acquired more antibonding character. As a consequence, the nuclei will occur at a longer equilibrium interatomic distance, relative to the ground state of the molecule.

In other words, the potential energy minimum (also referred to as the zero-point energy) for the excited state occurs when the atoms are further apart from one another than they are for the potential energy minimum of the ground state. Since the electrons are localized between the carbon and oxygen atoms in this molecule, it will be the carbon—oxygen bond length that is most affected by the change in electronic configuration; the carbon—hydro- gen bond lengths are essentially invariant between the ground and excited states. The nuclei, however, are not fixed in space, but can vibrate in both the ground and excited electronic states of the molecule. Hence, each electronic state of a molecule has built upon it a manifold of vibrational substates.

The foregoing concepts are summarized in Figure 2.9, which shows a potential energy diagram for the ground and one excited state of the molecule. An important point to glean from this figure is that even though the potential minima of the ground and excited states occur at different equilibrium interatomic distances, vibrational excursions within either electronic state can bring the nuclei into register with their equilibrium positions at the potential minimum of the other electronic state. In other words, a molecule in the ground electronic state can, through vibrational motions, transiently sample the interatomic distances associated with the potential energy minimum of the excited electronic state, and vice versa.

2.2 THERMODYNAMICS OF CHEMICAL REACTIONS

In freshman chemistry we were introduced to the concept of free energy, G, which combined the first and second laws of thermodynamics to yield the familiar formula:

where G is the change in free energy of the system during a reaction at

24 CHEMICAL BONDS AND REACTIONS IN BIOCHEMISTRY

Figure 2.9 Potential energy diagram for the ground and one excited electronic state of a molecule. The potential wells labeled and * represent the potential energy profiles of the ground and excited electronic states, respectively. The sublevels within each of these potential wells, labeled v , represent the vibrational substates of the electronic states.

constant temperature (T ) and pressure, H is the change in enthalpy (heat), and S is the change in entropy (a measure of disorder or randomness) associated with the reaction. Some properties of G should be kept in mind. First, G is less than zero (negative) for a spontaneous reaction and greater than zero (positive) for a nonspontaneous reaction. That is, a reaction for which G is negative will proceed spontaneously with the liberation of energy. A reaction for which G is positive will proceed only if energy is supplied to drive the reaction. Second, G is always zero at equilibrium. Third, G is a path-independent function. That is, the value of G is dependent on the starting and ending states of the system but not on the path used to go from the starting point to the end point. Finally, while the value of G gives information on the spontaneity of a reaction, it does not tell us anything about the rate at which the reaction will proceed.

Consider the following reaction:

where G is the free energy for the reaction under standard conditions of all reactants and products at a concentration of 1.0 M (1.0 atm for gases). The terms in brackets, such as [C], are the molar concentrations of the reactants and products of the reaction, the symbol ‘‘ln’’ is shorthand for the natural, or base e, logarithm, and R and T refer to the ideal gas constant (1.98 10 kcal/ mol · degree) and the temperature in degrees Kelvin (298 K for average room temperature, 25°C, and 310 K for physiological temperature, 37°C), respectively. Since, by definition, G 0 at equilibrium, it follows that under equilibrium conditions:

For many reactions, including many enzyme-catalyzed reactions, the values ofG have been tabulated. Thus knowing the value of G one can easily calculate the value of G for the reaction at any displacement from equilibrium. Examples of these types of calculation can be found in any introductory chemistry or biochemistry text.

Because free energy of reaction is a path-independent quantity, it is possible to drive an unfavorable (nonspontaneous) reaction by coupling it to a favorable (spontaneous) one. Suppose, for example, that the product of an unfavorable reaction was also a reactant for a thermodynamically favorable reaction. As long as the absolute value of G was greater for the second reaction, the overall reaction would proceed spontaneously. Suppose that the reaction A B had a G of 5 kcal/mol, and the reaction B C had a G of 8 kcal/mol. What would be the G value for the net reaction A C?

Thus, the overall reaction would proceed spontaneously. In our scheme, B would appear on both sides of the overall reaction and thus could be ignored. Such a species is referred to as a common intermediate. This mechanism of providing a thermodynamic driving force for unfavorable reactions is quite common in biological catalysis.

As we shall see in Chapter 3, many enzymes use nonprotein cofactors in the course of their catalytic reactions. In some cases these cofactors participate directly in the chemical transformations of the reactants (referred to as substrates by enzymologists) to products of the enzymatic reaction. In many other cases, however, the reactions of the cofactors are used to provide the thermodynamic driving force for catalysis. Oxidation and reduction reactions of metals, flavins, and reduced nicotinamide adenine dinucleotide (NADH) are commonly used for this purpose in enzymes. For example, the enzyme cytochrome c oxidase uses the energy derived from reduction of its metal

26 CHEMICAL BONDS AND REACTIONS IN BIOCHEMISTRY

cofactors to drive the transport of protons across the inner mitochondrial membrane, from a region of low proton concentration to an area of high proton concentration. This energetically unfavorable transport of protons could not proceed without coupling to the exothermic electrochemical reactions of the metal centers. Another very common coupling reaction is the hydrolysis of adenosine triphosphate (ATP) to adenosine diphosphate (ADP) and inorganic phosphate (P ). Numerous enzymes drive their catalytic reactions by coupling to ATP hydrolysis, because of the high energy yield of this reaction.

2.2.1 The Transition State of Chemical Reactions

A chemical reaction proceeds spontaneously when the free energy of the product state is lower than that of the reactant state (i.e., G 0). As we have stated, the path taken from reactant to product does not influence the free energies of these beginning and ending states, hence cannot affect the spontaneity of the reaction. The path can, however, greatly influence the rate at which a reaction will proceed, depending on the free energies associated with any intermediate state the molecule must access as it proceeds through the reaction. Most of the chemical transformations observed in enzyme-catalyzed reactions involve the breaking and formation of covalent bonds. If we consider a reaction in which an existing bond between two nuclei is replaced by an alternative bond with a new nucleus, we could envision that at some instant during the reaction a chemical entity would exist that had both the old and new bonds partially formed, that is, a state in which the old and new bonds are simultaneously broken and formed. This molecular form would be extremely unstable, hence would be associated with a very large amount of free energy. For the reactant to be transformed into the product of the chemical reaction, the molecule must transiently access this unstable form, known as the transition state of the reaction. Consider, for example, the formation of an alcohol by the nucleophilic attack of a primary alkyl halide by a hydroxide ion:

RCH Br OH RCH OH Br

We can consider that the reaction proceeds through a transition state in which the carbon is simultaneously involved in partial bonds between the oxygen and the bromine:

RCH Br OH [HO---CH R---Br] RCH OH Br

where the species in brackets is the transition state of the reaction and partial bonds are indicated by dashes. Figure 2.10 illustrates this reaction scheme in terms of the free energies of the species involved. (Note that for simplicity, the various molecular states are represented as lines designating the position of the potential minimum of each state. Each of these states is more correctly

Figure 2.10 Free energy diagram for the reaction profile of a typical chemical reaction, a chemical reaction. The activation energy E is the energetic difference between the reactant state and the transition state of the reaction.

described by the potential wells shown in Figure 2.9, but diagrams constructed according to this convention are less easy to follow.)

In the free energy diagram of Figure 2.10, the x axis is referred to as the reaction coordinate and tracks the progressive steps in going from reactant to product. This figure makes it clear that the transition state represents an energy barrier that the reaction must overcome in order to proceed. The higher the energy of the transition state in relation to the reactant state, the more difficult it will be for the reaction to proceed. Once, however, the system has attained sufficient energy to reach the transition state, the reaction can proceed effortlessly downhill to the final product state (or, alternatively, collapse back to the reactant state). Most of us have experienced a macroscopic analogy of this situation in riding a bicycle. When we encounter a hill we must pedal hard, exerting energy to ascend the incline. Having reached the crest of the hill, however, we can take our feet off the pedals and coast downhill without further exertion.

The energy required to proceed from the reactant state to the transition state, which is known as the activation energy or energy barrier of the reaction, is the difference in free energy between these two states. The activation energy

28 CHEMICAL BONDS AND REACTIONS IN BIOCHEMISTRY

is given the symbol E or G‡. This energy barrier is an important concept for our subsequent discussions of enzyme catalysis. This is because the height of the activation energy barrier can be directly related to the rate of a chemical reaction. To illustrate, let us consider a unimolecular reaction in which the reactant A decomposes to B through the transition state A‡. The activation

The transition state will decay to product with the same frequency as that of the stretching vibration of the bond that is being ruptured to produce the product molecule. It can be shown that this vibrational frequency is given by:

where is the vibrational frequency, k is the Boltzmann constant, and h is Planck’s constant. The rate of loss of [A] is thus given by:

and the first-order rate constant for the reaction is thus given by the Arrhenius equation:

From Equations 2.6 and 2.7 it is obvious that as the activation energy barrier increases (i.e., E becomes larger), the rate of reaction will decrease in an exponential fashion. We shall see in Chapter 6 that this concept relates directly to the mechanism by which enzymes achieve the acceleration of reaction rates characteristic of enzyme-catalyzed reactions.

It is important to recognize that the transition state of a chemical reaction is, under most conditions, an extremely unstable and short-lived species. Some chemical reactions go through intermediate states that are more long-lived and stable than the transition state. In some cases, these intermediate species exist long enough to be kinetically isolated and studied. When present, these intermediate states appear as local free energy minima (dips) in the free energy diagram of the reaction, as illustrated in Figure 2.11. Often these intermediate states structurally resemble the transition state of the reaction (Hammond,

Figure 2.11 Free energy diagram for a chemical reaction that proceeds through the formation of a chemical intermediate.

1955). Therefore, when they can be trapped and studied, these intermediates provide a glimpse at what the true transition state may look like. Enzymecatalyzed reactions go through intermediate states like this, mediated by the specific interactions of the protein and/or enzyme cofactors with the reactants and products of the chemical reaction being catalyzed. We shall have more to say about some of these intermediate species in Chapter 6.

2.3 ACID‒BASE CHEMISTRY

In freshman chemistry we were introduced to the common Lewis definition of acids and bases: a L ewis acid is any substance that can act as an electron pair acceptor, and a L ewis base is any substance that can act as an electron pair donor. In many enzymatic reactions, protons are transferred from one chemical species to another, hence the alternative Brønsted—L owry definition of acids and bases becomes very useful for dealing with these reactions. In the Brønsted—Lowry classification, an acid is any substance that can donate a proton, and a base is any substance that can accept a proton by reacting with a Brønsted—Lowry acid. After donating its proton, a Brønsted—Lowry acid is converted to its conjugate base.