Enzymes (Second Edition)

10 A BRIEF HISTORY OF ENZYMOLOGY

these proteins in the common language of chemical and physical forces. While the vital importance of enzymes in biology cannot be overstated, the understanding of their structures and functions remains a problem of chemistry.

REFERENCES AND FURTHER READING

Rather than providing an exhaustive list of primary references for this historical chapter, I refer the reader to a few modern texts that have done an excellent job of presenting a more detailed and comprehensive treatment of the history of enzymology. Not only do these books provide good descriptions of the history of science and the men and women who made that history, but they are also quite entertaining and inspiring reading — enjoy them!

Friedmann, H. C., Ed. (1981) Enzymes, Hutchinson Ross, Stroudsburg, PA. [This book is part of the series ‘‘Benchmark Papers in Biochemistry.’’ In it, Friedmann has compiled reprints of many of the most influential publications in enzymology from the eighteenth through twentieth centuries, along with insightful commentaries on these papers and their importance in the development of the science.]

Judson, H. F. (1980) T he Eighth Day of Creation, Simon & Schuster, New York. [This extremely entertaining book chronicles the history of molecular biology, including protein science and enzymology, in the twentieth century.]

Kornberg, A. (1989) For the L ove of Enzymes. T he Odyssey of a Biochemist, Harvard University Press, Cambridge, MA. [An autobiographical look at the career of a Nobel Prize—winning biochemist.]

Werth, B. (1994) T he Billion Dollar Molecule, Simon & Schuster, New York. [An interesting, if biased, look at the modern science of structure-based drug design.]

Enzymes: A Practical Introduction to Structure, Mechanism, and Data Analysis.

Robert A. Copeland Copyright 2000 by Wiley-VCH, Inc.

ISBNs: 0-471-35929-7 (Hardback); 0-471-22063-9 (Electronic)

2

CHEMICAL BONDS

AND REACTIONS

IN BIOCHEMISTRY

The hallmark of enzymes is their remarkable ability to catalyze very specific chemical reactions of biological importance. Some enzymes are so well designed for this purpose that they can accelerate the rate of a chemical reaction by as much as 10 -fold over the spontaneous rate of the uncatalyzed

reaction! This incredible rate enhancement results	from the	juxtaposition
of chemically reactive groups within the binding	pocket of	the enzyme

(the enzyme active site) and other groups from the target molecule (substrate), in a way that facilitates the reaction steps required to convert the substrate into the reaction product. In subsequent chapters we shall explore the structural details of these reactive groups and describe how their interactions with the substrate result in the enhanced reaction rates typical of enzymatic catalysis. First, however, we must understand the chemical bonding and chemical reactions that take place both in enzymes and in the simpler molecules on which enzymes act. This chapter is meant as a review of material covered in introductory chemistry courses (basic chemical bonds, some of the reactions associated with these bonds); however, a thorough understanding of the concepts covered here will be essential to understanding the material in Chapters 3—12.

2.1 ATOMIC AND MOLECULAR ORBITALS

2.1.1 Atomic Orbitals

Chemical reactions, whether enzyme-catalyzed or not, proceed mainly through the formation and cleavage of chemical bonds. The bonding patterns seen in molecules result from the interactions between electronic orbitals of individual

11

12 CHEMICAL BONDS AND REACTIONS IN BIOCHEMISTRY

atoms to form molecular orbitals. Here we shall review these orbitals and some properties of the chemical bonds they form.

Recall from your introductory chemical courses that electrons occupy discrete atomic orbitals surrounding the atomic nucleus. The first model of electronic orbitals, proposed by Niels Bohr, viewed these orbitals as a collection of simple concentric circular paths of electron motion orbiting the atomic nucleus. While this was a great intellectual leap in thinking about atomic structure, the Bohr model failed to explain many of the properties of atoms that were known at the time. For instance, the simple Bohr model does not explain many of the spectroscopic features of atoms. In 1926 Erwin Schro¨ dinger applied a quantum mechanical treatment to the problem of describing the energy of a simple atomic system. This resulted in the now-famous Schro¨ dinger wave equation, which can be solved exactly for a simple one-proton, oneelectron system (the hydrogen atom).

Without going into great mathematical detail, we can say that the application of the Schro¨ dinger equation to the hydrogen atom indicates that atomic orbitals are quantized; that is, only certain orbitals are possible, and these have well-defined, discrete energies associated with them. Any atomic orbital can be uniquely described by a set of three values associated with the orbital, known as quantum numbers. The first or principal quantum number describes the effective volume of the orbital and is given the symbol n. The second quantum number, l, is referred to as the orbital shape quantum number, because this value describes the general probability density over space of electrons occupying that orbital. Together the first two quantum numbers provide a description of the spatial probability distribution of electrons within the orbital. These descriptions lead to the familiar pictorial representations of atomic orbitals, as shown in Figure 2.1 for the 1s and 2p orbitals.

The third quantum number, m , describes the orbital angular momentum associated with the electronic orbital and can be thought of as describing the orientation of that orbital in space, relative to some arbitrary fixed axis. With these three quantum numbers, one can specify each particular electronic orbital of an atom. Since each of these orbitals is capable of accommodating two electrons, however, we require a fourth quantum number to uniquely identify each individual electron in the atom.

The fourth quantum number, m , is referred to as the electron spin quantum number. It describes the direction in which the electron is imagined to spin with respect to an arbitrary fixed axis in a magnetic field (Figure 2.2). Since no two electrons can have the same values for all four quantum numbers, it follows that two electrons within the same atomic orbital must be spin-paired;

that is, if one is spinning clockwise (m				), the other must be spinning
counterclockwise (m
		). This concept,			known as the Pauli exclusion

principle, is often depicted graphically by representing the spinning electron as

an arrow pointing either up or down, within an atomic orbital.

Thus we see that associated with each atomic orbital is a discrete amount of potential energy; that is, the orbitals are quantized. Electrons fill these

ATOMIC AND MOLECULAR ORBITALS

13

Figure 2.1 Spatial representations of the electron distribution in s and p orbitals.

Figure 2.2 Electron spin represented as rotation of a particle in a magnetic field. The two spin ‘‘directions’’ of the electron are represented as clockwise (m ) and counterclockwise (m ) rotations. The coil-bearing rectangles schematically represent the magnetic fields.

14 CHEMICAL BONDS AND REACTIONS IN BIOCHEMISTRY

Figure 2.3 The aufbau principle for the order of filling of atomic orbitals, s, p, d, and f.

orbitals according to the potential energy associated with them; low energy orbitals fill first, followed by higher energy orbitals in ascending energetic order (the aufbau principle). By schematizing the energetic order of atomic orbitals, as illustrated in Figure 2.3, we can inventory the electrons in the orbitals of an atom. For example, each atom of the element helium contains two electrons; since both electrons occupy the 1s orbital, we designate this by the shorthand notation 1s . Lithium contains 3 electrons and, according to Figure 2.3, has the configuration 1s 2s . When dealing with nonspherical orbitals, such as the p, d, and f orbitals, we must keep in mind that more than one atomic orbital is associated with each orbital set that is designated by a combination of n and l quantum numbers. For example, the 2p orbital set consists of three atomic orbitals: 2p , 2p , and 2p . Hence, the 2p orbital set can accommodate 6 electrons. Likewise, a d orbital set can accommodate a total of 10 electrons (5 orbitals, with 2 electrons per orbital), and an f orbital set can accommodate 14 electrons.

A survey of the biological tissues in which enzymes naturally occur indicates that the elements listed in Table 2.1 are present in highest abundance. Because of their abundance in biological tissue, these are the elements we most often encounter as components of enzyme molecules. For each of these atoms, the highest energy s and p orbital electrons are those that are capable of participating in chemical reactions, and these are referred to as valence electrons (the electrons in the lower energy orbitals are chemically inert and are referred to as closed-shell electrons). In the carbon atom, for example, the two

	ATOMIC AND MOLECULAR ORBITALS			15
Table 2.1 Electronic configurations of the elements most
commonly found in biological tissues
Element	Number of Electrons	Orbital Configuration
Hydrogen	1	1s
Carbon	6	1s 2s 2p
Nitrogen	7	1s 2s 2p
Oxygen	8	1s 2s 2p
Phosphorus	15	1s 2s 2p 3s 3p
Sulfur	16	1s 2s 2p 3s 3p

1s electrons are the closed-shell type, while the four electrons in the 2s and 2p orbitals are valence electrons, and are thus available for bond formation.

2.1.2 Molecular Orbitals

If two atoms can approach each other at close enough range, and if their valence orbitals are of appropriate energy and symmetry, the two valence atomic orbitals (one from each atom) can combine to form two molecular orbitals: a bonding and an antibonding molecular orbital. The bonding orbital occurs at a lower potential energy than the original two atomic orbitals; hence electron occupancy in this orbital promotes bonding between the atoms because of a net stabilization of the system (molecule). The antibonding orbital, in contrast, occurs at a higher energy than the original atomic orbitals; electron occupancy in this molecular orbital would thus be destabilizing to the molecule.

Let us consider the molecule H . The two 1s orbitals from each hydrogen atom, each containing a single electron, approach each other until they overlap to the point that the two electrons are shared by both nuclei (i.e., a bond is formed). At this point the individual atomic orbital character is lost and the two electrons are said to occupy a molecular orbital, resulting from the mixing of the original two atomic orbitals. Since there were originally two atomic orbitals that mixed, there must result two molecular orbitals. As illustrated in Figure 2.4, one of these molecular orbitals occurs at a lower potential energy than the original atomic orbital, hence stabilizes the molecular bond; this orbital is referred to as a bonding orbital (in this case a -bonding orbital, as discussed shortly). The other molecular orbital occurs at higher potential energy (displaced by the same amount as the bonding orbital). Because the higher energy of this orbital makes it destabilizing relative to the atomic orbitals, it is referred to as an antibonding orbital (again, in this case a-antibonding orbital, *). The electrons fill the molecular orbitals in order of potential energy, each orbital being capable of accommodating two electrons.

Thus for H both electrons from the 1s orbitals of the atoms will occupy the

-bonding molecular orbital in the molecule.

16 CHEMICAL BONDS AND REACTIONS IN BIOCHEMISTRY

Figure 2.4 (A) Schematic representation of two s orbitals on separate hydrogen atoms combining to form a bonding molecular orbital. (B) Energy level diagram for the combination of two hydrogen s orbitals to form a bonding and antibonding molecular orbital in the H2 molecule.

Now let us consider the diatomic molecule F . The orbital configuration of the fluorine atom is 1s 2s 2p . The two s orbitals and two of the three p orbitals are filled and will form equal numbers of bonding and antibonding molecular orbitals, canceling any net stabilization of the molecule. The partially filled p orbitals, one on each atom of fluorine, can come together to form one bonding and one antibonding molecular orbital in the diatomic molecule F . As illustrated in Figure 2.5, the lobes of the two valence p orbitals overlap end to end in the bonding orbital; molecular orbitals that result from such end-to-end overlaps are referred to as sigma orbitals ( ). The bonding orbital is designated by the symbol , and the accompanying antibonding orbital is designated by the symbol *. The bond formed between the two atoms in the

F molecules is therefore referred to as a sigma bond. Because the orbital is

lower in energy than the * orbital, both the electrons from the valence atomic

ATOMIC AND MOLECULAR ORBITALS

17

Figure 2.5 Combination of two p atomic orbitals by end-to-end overlap to form a -type molecular orbital.

orbit will reside in the molecular orbital when the molecule is at rest (i.e., when it is in its lowest energy form, referred to as the ground state of the molecule).

2.1.3 Hybrid Orbitals

For elements in the second row of the periodic table (Li, Be, C, N, O, F, and Ne), the 2s and 2p orbitals are so close in energy that they can interact to form orbitals with combined, or mixed, s and p orbital character. These hybrid orbitals provide a means of maximizing the number of bonds an atom can form, while retaining the greatest distance between bonds, to minimize repulsive forces. The hybrid orbitals formed by carbon are the most highly studied, and the most germane to our discussion of enzymes.

From the orbital configuration of carbon (1s 2s 2p ), we can see that the similar energies of the 2s and 2p orbital sets in carbon provide four electrons that can act as valence electrons, giving carbon the ability to form four bonds to other atoms. Three types of hybrid orbital are possible, and they result in three different bonding patterns for carbon. The first type results from the combination of one 2s orbital with three 2p orbitals, yielding four hybrid orbitals referred to as sp3 orbitals (the exponent reflects the number of p orbitals that have combined with the one s orbital to produce the hybrids). The four sp orbitals allow the carbon atom to form four bonds that lie along

18 CHEMICAL BONDS AND REACTIONS IN BIOCHEMISTRY

Figure 2.6 Spatial electron distributions of hybrid orbitals: (A) sp hybridization, (B) sp hybridization, and (C) sp hybridization.

the apices of a tetrahedron, as shown in Figure 2.6C. The second type of hybrid orbital, sp2, results from the mixing of one 2s orbital and two 2p orbitals. These hybrid orbitals allow for three trigonal planar bonds to form (Figure 2.6B). When a single 2p orbital combines with a 2s orbital, the resulting single hybrid orbital is referred to as an sp orbital (Figure 2.6A).

Let us look at the sp hybrid case in more detail. We have said that the 2p orbital set consists of three p orbitals that can accommodate a total of six electrons. With sp hybridization, we have accounted for two of the three p orbitals available in forming three trigonal planar bonds, as in the case of ethylene (Figure 2.7A). On each carbon atom, this hybridization leaves one orbital, of pure p character, which is available for bond formation. These orbitals can interact with one another to form a bond by edge-to-edge orbital overlap, above and below the plane defined by the sp bonds (Figure 2.7B). This type of edge-to-edge orbital overlap results in a different type of molecular orbital, referred to as a orbital. As illustrated in Figure 2.7B, the overlap of

ATOMIC AND MOLECULAR ORBITALS

19

Figure 2.7 Hybrid bond formation in ethylene. (A) The bonds are illustrated as lines, and the remaining p orbitals lobes form edge-to-edge contacts. (B) The p orbitals combine to form a bond with electron density above and below the interatomic bond axis defined by the bond between the carbon atoms.

the p orbitals provides for bonding electron density above and below the interatomic axis, resulting in a pi bond ( ). Of course, as with bonds, for everyorbital formed, there must be an accompanying antibonding orbital at higher energy, which is denoted by the symbol *. Thus along the interatomic axis of ethylene we find two bonds: one bond, and one bond. This combination is said to form a double bond between the carbon atoms. A shorthand notation for this bonding situation is to draw two parallel lines connecting the carbon atoms:

HH

C C

HH

A similar situation arises when we consider sp hybridization. In this case we have two mutually perpendicular p orbitals on each carbon atom available