CHAPTE R 2 - Biochemistry

The macromolecules that participate

in the structural and functional matrix of life are immense structures held together by strong, covalent bonds. Yet covalent bonding alone cannot begin to describe the complexity of molecular structure in biology. Much weaker interactions are responsible for most of the ele-gant cellular architecture visible in the electron micrographs of Chapter 1. These are the noncovalent interactions, also called noncovalent forces or noncovalent bonds, between ions, molecules, and parts of molecules.

Consider the macromolecules we discussed in Chapter 1. The linear sequence of the nucleotide residues in a strand of DNA is maintained by covalent bonds.

But DNA also has a highly specific three-dimensional structure, which is stabi-lized by noncovalent interactions between different parts of the molecule.

Similarly, every kind of protein is made up of amino acids linked by covalent peptide bonds; but each protein is also folded into a specific molecular conforma-tion that is stabilized by noncovalent interacconforma-tions. Proteins interact with macro-molecules, such as other proteins or nucleic acids or lipids, to form still higher lev-els of organization, ultimately leading to cells, tissues, and whole organisms. All of this complexity is accounted for by a myriad of noncovalent interactions within and between macromolecules.

What makes noncovalent interactions so important in biology and biochem-istry? The key is seen in Figure 2.1, which compares noncovalent and covalent bond energies. The covalent bonds most important in biology (such as C C and C H) have bond energies in the range of 300–400 kJ/mol. Biologically important noncovalent bonds are 10 to 100 times weaker. It is their very weakness that makes noncovalent bonds so essential, for it allows them to be continually broken and re-formed in the dynamic molecular interplay that is life. This interplay depends

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The Matrix of Life:

Weak Interactions in an Aqueous

Environment

THE NATURE OF NONCOVALENT INTERACTIONS

27

10⁴

Combustion of glucose

Covalent bonds found in biomolecules

680 nm light (red)

Hydrolysis of ATP Salt bridges; Hydrogen bonds

Thermal motion @ 37 °C

van der Waals interactions 10³

10²

Energy (kJ/mol) 10

0.1

⎬⎫

⎭

⎬⎫

⎭

⎬⎫

⎭

FIGURE 2.1

Covalent and noncovalent bond energies.Energies typical of noncovalent bonds (0.5–20 kJ/mol; red text) are about one to two orders of magnitude weaker than energies of the covalent bonds commonly found in biochemical compounds (150–600 kJ/mol; blue text).

The energies available from thermal motion, ATP hydrolysis, red light, and aerobic glucose metabolism are also shown as reference points (discussed in detail in later chapters). Note that values are plotted on a log scale.

on rapid exchanges of molecular partners, which could not occur if intermolecular forces were so strong as to lock the molecules in conformation and in place.

If we are to understand life at the molecular level, we must know something about noncovalent interactions. Furthermore, we must know how such interac-tions behave in an aqueous environment, for every cell in every organism on earth is bathed in and permeated by water. This is as true for creatures living in the most arid deserts as for those in the depths of the sea. Water is the major constituent of organisms—70% or more of the total weight, in most cases.

This chapter first describes noncovalent interactions, and then shows that the properties of water have a profound effect on those interactions.

The Nature of Noncovalent Interactions

Molecules and ions can interact noncovalently in a number of different ways, as described in this section and summarized in Figure 2.2. All of these noncovalent interactions are fundamentally electrostatic in nature; thus, they all depend on the forces that electrical charges exert on one another. Table 2.1 lists ranges for the energies of some of the noncovalent interactions prevalent in biomolecules.

Charge–Charge Interactions

The simplest noncovalent interaction is the electrostatic interaction between a pair of charged particles. Such charge–charge interactions are also referred to as ionic bonds or salt bridges. Many of the molecules in cells, including macromole-cules like DNA and proteins, carry a net electrical charge. In addition to these molecules, the cell contains an abundance of small ions, both cations like Na⁺, K⁺, and Mg²⁺and anions like Cl^-and HPO₄^2-. All of these charged entities exert forces on one another (see Figure 2.2a). The force between a pair of charges q₁and q₂, separated in a vacuum by a distance r, is given by Coulomb’s law:

(2.1)

where k is a constant whose value depends on the units used.^*If q₁and q₂have the same sign, F is positive, so a positive value corresponds to repulsion. If one charge is+ and the other -, F is negative, signifying attraction. It is such charge–charge interactions that stabilize a crystal of a salt, like that shown in Figure 2.3.

The biological environment, of course, is not a vacuum. In a cell, charges are always separated by water or by other molecules or parts of molecules. The exis-tence of this dielectric medium between charges has the effect of screening them from one another, so that the actual force is always less than that given by Equation 2.1. This screening effect is expressed by inserting a dimensionless num-ber, the dielectric constant ( ), in Equation 2.1:

(2.2)

Every substance that acts as a dielectric medium has a characteristic value of ; the higher this value, the weaker the force between the separated charges. The dielectric constant of water is high, approximately 80, whereas organic liquids usually have much lower values, in the range of 1 to 10. We shall see presently the reason for the high value ofein water, but its major consequence is that charged e

F= kq₁q₂ er²

F= k q₁q₂ r²

Noncovalent interactions always involve electrical charges.

*In the c.g.s. (centimeter–gram–second) system, with charges in electrostatic units, k is unity.

In this book we use the SI, or international, system of units. Here q1and q2are in coulombs (C), r is in meters (m), and The quantity is the permittivity of a vacuum and has the value 8.85 10^-12J^-1C²m^-1, where J is the energy unit joules. F is in newtons (N).

k= 1/(4pe0).

TABLE2.1 Energies of noncovalent interactions in biomolecules

Type of interaction

Approximate energy (kJ/mol) Charge–charge -13 to -17 Charge–dipole

(H–bond) -13 to -21

Dipole–dipole

(H–bond) -2 to -8

van der Waals -0.4 to -0.8 Values reprinted from Advances in Protein Chemistry 39:125–189, S. K. Burley and G. A. Petsko, Weakly polar interactions in proteins. © 1988, with permis-sion from Elsevier.

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CHAPTER 2 THE MATRIX OF LIFE: WEAK INTERACTIONS IN AN AQUEOUS ENVIRONMENT

particles interact rather weakly with one another in an aqueous environment unless they are very close together (i.e., within 0.4 to 1.0 nm).

Coulomb’s law is an expression of force; that is, it is a quantitative description of an interaction. However, every interaction involves a change in energy, and because we are concerned with the energy changes in biological processes, we are particularly interested in the energy of interaction (E). This is the energy required to separate two charged particles from a distance r to an infinite distance—in other words, to pull them apart working against the electrostatic force. The energy of interaction is given by Equation 2.3, which is similar to Equation 2.2:

(2.3)

As with force, the energy of an oppositely charged pair q₁and q₂is always negative, signifying attraction, but E approaches zero as r becomes very large. For charge–charge interactions, the energy of interaction is inversely proportional to the first power of r; thus, these interactions are relatively strong over greater distances compared to the other noncovalent interactions listed in Figure 2.2.

Charge–charge interactions often occur within or between biomolecules—for example, in the attraction between amino and carboxylate groups, as shown in Figure 2.2a. As will be discussed in Chapter 5, charge–charge interactions can play an important role in the purification of a protein from a complex mixture of cel-lular components.

E = kq₁q₂ er FIGURE 2.2

Types of noncovalent interactions.The induced dipole (d, e) and the dispersion forces (f) depend on a distortion of the electron distribution in a nonpolar atom or molecule. The symbols denote a fraction of an electron or proton charge.d^- and d⁺

(a) Charge–charge

Longest-range force; nondirectional

(b) Charge–dipole

Depends on orientation of dipole

(c) Dipole–dipole

Depends on mutual orientation of dipoles

(d) Charge–induced dipole

Depends on polarizability of molecule in which dipole is induced

(e) Dipole–induced dipole

Depends on polarizability of molecule in which dipole is induced

(f) Dispersion (van der Waals) Involves mutual synchronization of ﬂuctuating charges

(g) Hydrogen bond

Charge attraction + partial covalent bond

1/r

1/r²

1/r³

1/r⁴

1/r⁵

1/r⁶

Length of bond fixed

+ −

+ d⁺

d⁺ d⁻

d⁺ d⁺

d⁻

d⁺

d⁻ d⁻d⁺

d⁺ d⁻

d⁺ d⁻ d⁺

d⁻

d⁺ d⁻

d⁺ d⁺ d⁻

d⁻

d⁺ d⁻

d⁻

d⁻ d⁻

d⁻

Donor Acceptor

O H

H d⁺ NH₃ O

O H

H O

H d⁺ NH₃

NH₃ C

−

Type of Interaction Model Example

Dependence of Energy on Distance

d⁺ d⁻

N H O C

Molecule Formula Dipole Moment (D)^a

Carbon monoxide 0.12

Carbon dioxide 0

Water 1.83

para-Dichlorobenzene 0

ortho-Dichlorobenzene 2.59

Glycine 16.7

Glycylglycine 28.6

aThe common units of dipole moment are debyes; 1 debye (D) equals 3.34 * 10^-30C • m.

TABLE 2.2 Dipole moments of some molecules

THE NATURE OF NONCOVALENT INTERACTIONS

29 Permanent and Induced Dipole Interactions

Molecules that carry no net charge may nevertheless have an asymmetric internal distribution of charge. For example, the electron distribution of the uncharged carbon monoxide molecule is such that the oxygen end is slightly more negative than the carbon end (Figure 2.4a). Such a molecule is called polar, or a permanent dipole, and is said to have a permanent dipole moment The dipole moment expresses the magnitude of a molecule’s polarity. If a linear molecule like CO has fractional charges and separated by a distance x, the dipole moment is a vector directed toward whose magnitude is

(2.4)

where q is the magnitude of the charge (or fractional charge). In molecules with a more complex shape, like water, the dipole moment for the entire molecule is a vector sum of the dipole moments along each polar bond (Figure 2.4b). Water has a significant because electrons are drawn from the hydrogen atoms toward the oxygen atom, due to the much greater electronegativity of the oxygen atom.

Some dipole moment values are given in Table 2.2. Notice the large values for glycine and glycylglycine. At neutral pH, the amino acid glycine exists as the ion

+NH₃CH₂COO^-, which has both a positive ammonium group and a negative car-boxylate group. Thus, whole electron charges are separated by the length of the molecule, accounting for the large In glycylglycine, which is made by cova-lently linking two glycine molecules, the dipole moment is nearly twice as large because the charge separation is almost doubled. Molecules with large dipole moments are said to be highly polar.

m . m ,

m = qx

d⁺, d^-, d⁺

(m).

FIGURE 2.3

Charge–charge interactions in an ionic crystal.

Ionic crystals are held together by charge–charge inter-actions between positive and negative ions. In a sodium chloride crystal, each sodium ion is surrounded by six chloride ions, and each chloride ion is surrounded by six sodium ions.

Marcel Clemens/Shutterstock.

Cl⁻ Na⁺

Some molecules interact because they possess dipole moments.

FIGURE 2.4

Dipolar molecules. (a) Carbon monoxide: the partial negative charge on the oxygen together with cor-responding partial positive charge on the carbon produces a dipole moment directed along the OiC axis. (b) Water: the partial negative charge on O together with the partial positive charge on each H pro-duces two moments, and directed along the OiH bonds. Their vector sum represents the net dipole moment of the molecule.

(m) m2, m1

(d⁺) (d^-)

d⁺

d⁺ H H

(a) Carbon monoxide d⁻ C

x O

d⁻

(b) Water O

m1 m₂

C O

O C O

O H

CI CI

H₃N⁺ CH₂ COO⁻

H₃N⁺ CH₂ C O

N CH₂COO⁻ H

Note also in Table 2.2 that molecules must possess an appropriate geometry to have dipole moments: compare with O C O, or o-dichlorobenzene with p-dichlorobenzene. In carbon dioxide and p-dichlorobenzene, the dipole vectors are equal in magnitude but oppositely directed so that their effects cancel each other, leaving no net dipole moment.

In the aqueous environment of a cell, a permanent dipole can be attracted by a nearby ion (a charge–dipole interaction) or by another permanent dipole (a dipole–dipole interaction). These permanent dipole interactions are described in Figure 2.2b and c. Unlike the simple charge–charge interactions described ear-lier, dipole interactions depend on the orientation of the dipoles. Furthermore, they are shorter-range interactions: The energy of a charge–dipole interaction is proportional to 1/r²and that of a dipole–dipole interaction to 1/r³. Thus, a pair of permanent dipoles must be quite close together before the interaction becomes strong.

Molecules that do not have permanent dipole moments can become dipolar in the presence of an electric field. The field may be externally imposed, as in a laboratory instrument, or it may be produced by a neighboring charged or dipo-lar particle. A molecule in which a dipole can be so induced is said to be polarizable. Aromatic rings, for example, are very polarizable because the elec-trons can easily be displaced in the plane of the ring, as shown in Figure 2.5a.

Interactions of polarizable molecules are called induced dipole interactions. An anion or a cation may induce a dipole in a polarizable molecule and thereby be attracted to it (a charge–induced dipole interaction, Figure 2.2d), or a permanent dipole may do the same (a dipole–induced dipole interaction, Figure 2.2e). These induced dipole interactions are even shorter range than permanent dipole inter-actions, with energies of interaction proportional to 1/r⁴and 1/r⁵, respectively.

Even two molecules that have neither a net charge nor a permanent dipole moment can attract one another if they are close enough (Figure 2.2f). The distri-bution of electronic charge in a molecule is never static, but fluctuates. When two molecules approach very closely, they synchronize their charge fluctuations so as to give a net attractive force. Such intermolecular forces, which can be thought of as mutual dipole induction, are called van der Waals, or dispersion, forces. Their attractive energy varies as the inverse sixth power of the distance, so van der Waals forces are significant only at very short range. They can become particularly strong when two planar molecules can stack on one another, as shown in Figure 2.5b and c. We shall encounter many examples of such interactions in the internal packing of molecules like proteins and nucleic acids. As discussed in Chapter 6, van der Waals forces are individually weak; but, collectively they make significant contributions to the stability of biomolecules.

Molecular Repulsion at Extremely Close Approach:

The van der Waals Radius

When molecules or atoms that do not have covalent bonds between them come so close together that their outer electron orbitals begin to overlap, there is a mutual repulsion. This repulsion increases very steeply as the distance between their cen-ters (r) decreases; it can be approximated as proportional to r^-12. If we combine this repulsive energy with one or more of the kinds of attractive energy described previously, we see that the total energy of noncovalent interaction (E) for a pair of atoms, molecules, or ions will vary with distance of their separation (r) in the manner depicted in Figure 2.6. Two points on the graph should be noted. First, there is a minimum in the energy curve, at position r₀. This minimum corre-sponds to the most stable distance between the centers of the two particles. If we allow them to approach each other, this is how close they will come. Second, the repulsive potential rises so steeply at shorter distances that it acts as a “wall,” effec-tively barring approach closer than the distance r_v. This distance defines the

w w C{ O

30

CHAPTER 2 THE MATRIX OF LIFE: WEAK INTERACTIONS IN AN AQUEOUS ENVIRONMENT

Dispersion forces between two benzene molecules

Space-filling model of molecules in (b) Induction of a dipole in benzene by a positively charged ion

H H

H H H

d⁺ d⁻

d⁻ d⁺

H C

0.34 nm

H +

H H

d⁺ d⁻

(a)

(b)

(c) FIGURE 2.5

Induced dipoles and dispersion forces. (a) Benzene has neither a net charge nor a permanent dipole moment, but a nearby charge can induce a redistribution of electrons within the benzene ring, producing an induced dipole moment ( ). (b) Planar molecules like benzene have a strong tendency to stack because fluctu-ations in the electron clouds of the stacked rings interact with one another, producing a dispersion force.

(c) Although the molecules approach closely, they do not interpenetrate.

Molecules may attract one another by nonco-valent forces but cannot interpenetrate: van der Waals radii determine molecular surfaces.

so-called van der Waals radius, R, the effective radius for closest molecular pack-ing. For a pair of identical spherical molecules, r_v= 2R; for molecules with van der Waals radii R₁and R₂, r_v= R1+ R2.

Real molecules, of course, are not spherical objects like those depicted in Figure 2.6. Because large biological molecules all have complicated shapes, it is useful to extend the concept of the van der Waals radius to atoms or groups of atoms within a molecule. The values for van der Waals radii given in Table 2.3 rep-resent the distances of closest approach for another atom or group. When we depict complex molecules in a so-called “space filling” manner, we represent each atom by a sphere with its appropriate van der Waals radius (see Figure 2.5c). In this case, the van der Waals radii of the carbon atoms (0.17 nm) mean that the planes of the two stacked rings cannot be closer than 0.34 nm.

Hydrogen Bonds

One specific kind of noncovalent interaction, the hydrogen bond, is of the greatest importance in biochemistry. The structure and properties of many biological mole-cules and of water, the universal biological solvent, are determined largely by this type of bond. A hydrogen bond is an interaction between a covalently bonded hydrogen atom on a donor atom (e.g., O H or N H) and a pair of nonbonded electrons on an acceptor atom (e.g., O C or N ), as shown in Figure 2.2g and Figure 2.7. The atom to which hydrogen is covalently bonded is called the hydrogen-bond donor, and the atom with the nonbonded electron pair is called the hydrogen-bond acceptor. The interaction between the donor and acceptor is typi-cally represented by a dotted line between the acceptor atom and the shared H.

The ability of an atom to function as a hydrogen-bond donor depends greatly on its electronegativity. The more electronegative the donor atom, the more

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THE NATURE OF NONCOVALENT INTERACTIONS

31

FIGURE 2.6

Noncovalent interaction energy of two approach-ing particles.The interaction energy of two atoms, molecules, or ions is graphed versus the distance between their centers, r. The total interaction energy (E) at any distance is the sum of the energy of attrac-tion and the energy of repulsion. As the distance between the particles decreases (reading right to left along the x-axis), both the attractive energy (60) and the repulsive energy (70) increase, but at different rates. At first the longer-range attraction dominates, but then the repulsive energy increases so rapidly that it acts as a barrier, defining the distance of closest approach (rv) and the van der Waals radii (R, described by the orange spheres). The position of minimum energy (r0) is usually very close to rv.

van der Waals radii

Energy of repulsion (+)

(−) 0

Energy of interaction

Total energy of interaction, E

Energy of attraction

Distance of minimum energy, r₀

Distance between centers of particles, r

Distance of closest approach, r_v

R R

R (nm) Atoms

H 0.12

O 0.14

N 0.15

C 0.17

S 0.18

P 0.19

Groups

OH 0.14

NH2 0.15

CH₂ 0.20

CH3 0.20

Half-thickness of aromatic 0.17 ring

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TABLE 2.3 van der Waals radii of some atoms and groups of atoms

negative charge it withdraws from the hydrogen to which it is bonded; thus, the hydrogen becomes more positive and is more strongly attracted to the electron pair of the acceptor. Among the atoms encountered in biological compounds, only O and N have appropriate electronegativities to serve as strong donors. Thus,

C H groups do not form strong hydrogen bonds, but O H groups do.

The hydrogen bond has features in common with both covalent and noncova-lent interactions. In part, it is like a charge–charge interaction between the partial positive charge on H and the negative charge of the electron pair. But it is also true that there is electron sharing (as in a covalent bond) between H and the acceptor.

This double character is reflected in the bond length of the hydrogen bond. The distance between the hydrogen atom and the acceptor atom in a hydrogen bond is considerably less than would be expected from their van der Waals radii. For example, the distance between H and O in the bond N H . . . O C is only about 0.19 nm, whereas we would predict about 0.26 nm from the sum of the van der Waals radii given in Table 2.2. On the other hand, a covalent H O bond has a length of only 0.10 nm. The distance between the hydrogen-bond donor and acceptor is about 0.29 nm. The donor–acceptor distances of some particularly strong hydrogen bonds are listed in Table 2.4. Note that these distances are fixed, as they are for covalent (but not for other noncovalent) bonds.

The energy of hydrogen bonds is considerably higher than that of most other noncovalent bonds, in keeping with their partially covalent character (see Figure 2.1). Hydrogen bonds are also like covalent bonds in being highly direc-tional. Computational studies predict that hydrogen bonds are strongest when the angle defined by the donor atom, the shared H atom, and the acceptor atom is 180° (i.e., the three atoms are colinear). The majority of hydrogen bond angles in proteins are within 30° of 180°. The importance of this directionality is seen in the role that hydrogen bonds play in organizing a regular biochemical structure such as the -helix in proteins (Figure 2.8, discussed in greater detail in Chapter 6).

This is but one example of many we shall encounter in which hydrogen bonds sta-bilize ordered structure in large molecules.

We finish this section by reiterating the important point that the various noncovalent interactions we have described are individually weak, but when many are present within a given macromolecule, or between macromolecules, their energies can sum to an impressive total—often several hundreds of

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CHAPTER 2 THE MATRIX OF LIFE: WEAK INTERACTIONS IN AN AQUEOUS ENVIRONMENT

C O δ⁻

δ⁻ δ⁺

δ⁺ Donor

Acceptor O

FIGURE 2.7

The hydrogen bond.The figure shows an idealized H bond that might exist, for example, between an alcohol (the donor) and a keto compound (the acceptor). The H bond is represented by a dotted line between the H and the acceptor atom, and a solid line between the H and the donor atom.

Distance between Donor

Donor… Acceptor and Acceptor (nm) Comment

0.28 0.01 H bond formed in water

0.28 0.01

Bonding of water to other 0.29 0.01

molecules often involves

冧

^these

0.29 0.01

Very important in protein and 0.31 0.02

nucleic acid structures

冧

0.37 Relatively rare; weaker than above

;

TABLE 2.4 Major types of hydrogen bonds found in biomolecular interactions

H O

O C

H O

N C

H O

H N

H S

N Hydrogen bonds are among the strongest,

most specific, noncovalent interactions.

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