Interatomic Forces and Protein Structure

Since the form that a protein structure can take and its chemical characteristics are governed by interatomic interactions, it is important to have at least a basic understanding of the interatomic

interactions that play a role in protein structure. Interactions between atoms are physically complicated and to describe them in detail would require a whole other book, which fortunately has already been written by someone else: see the Bibliography. What we hope to give you is a rudimentary knowledge of these forces, to help you understand why computer methods have been developed to measure and calculate particular structural properties of proteins.

Understanding these forces gives us a basis for designing evaluative and predictive methods. Threading methods rely on the ability to discriminate between an amino acid that is in a favorable chemical environment and one that isn't. Homology modeling and structure optimization methods rely on rules for spacing between atoms, bond lengths, bond angles, and other values. These rules can be derived from chemical experiments on small molecules or from the distribution of observed values in known protein structures. However these rules are constructed, though, they reflect energetically favorable interactions between atoms.

Covalent interactions are the very short range (approximately 1 to 1.5 angstroms); they are very strong forces that bind atoms together into a molecule. In covalent bonding, the atoms involved actually share electrons. Unlike other forces encountered in protein structures, covalent bonds actually change the nature of the atoms involved to some extent. Atoms involved in covalent bonds are no longer discrete entities; instead, they combine to form a new molecule.

The protein backbone, including the peptide bond that joins one amino acid to another, is held together by covalent bonds. Amino acids retain some of their chemical individuality within the protein structure, but formally they become part of a new molecule. Atoms within individual amino acid sidechains are also covalently bonded to each other. These covalent bonds place strong constraints on the distance between atoms in a protein structure.

Because covalent interactions are strongly constrained by physicochemical rules, an important part of the verification process for structural quality is making sure that bond lengths, bond angles, and dihedral angles don't vary dramatically from their allowed values. Covalent bond lengths are

determined by the size and type of the atoms involved and by the number of electrons shared between atoms. The more electrons are shared, the shorter and stronger the bond. Bond angles are constrained by the structure of atomic orbitals. Dihedral angles, the angles of rotation of two bonded pairs of atoms with respect to each other around a central bond, are constrained primarily by steric hindrance. These chemical constraints are also used in macromolecular simulation, where they are associated with applied forces that keep the molecule in allowed conformations.

9.2.2.2 Hydrogen bonds

Hydrogen bonds arise when two polar gro ups interact. The two polar groups must be of specific types. One must be a proton donor, a chemical group in which a proton (hydrogen atom) is covalently bonded to a strongly electronegative atom such as oxygen. The bond between the proton and the

electronegative atom is polarized, giving the proton a partial positive charge and the electronegative atom a partial negative charge. The other group must be a proton acceptor, an electronegative atom with a partial negative charge and no attached proton. The positively polarized proton in the first group is attracted to the negatively polarized second group, and the two form a bond that isn't covalent, but is nonetheless, much shorter and stronger than a normal nonbonded interaction. Hydrogen bonds are unusual among nonbonded and electrostatic interactions because they are strongly directional; they weaken if the angle described by the three atoms involved is too large or too small.

Hydrogen bond interactions are one of the most important stabilizing forces in protein structure. The protein backbone contains a proton donor, in its N-H group, and a proton acceptor, in its carbonyl oxygen, spaced at regular intervals along the chain (Figure 9-6). The interaction of these groups stabilizes the two major types of secondary structure, the alpha helix and the beta sheet (Figure 9-7). Therefore, some structure prediction methods attempt to use the presence of potential hydrogen bond pairs to improve the accuracy of predictions.

Figure 9-7. Hydrogen bonding in alpha helices and beta sheets

9.2.2.3 Hydrophobic and hydrophilic interactions

A much-discussed (and frequently wrongly used) concept in protein structure analysis is that of the hydrophobic force. We've already mentioned in passing that amino acids can be classified as hydrophobic or hydrophilic. What exactly does this mean?

Proteins, except for those bound within cell membranes, always exist in aqueous solution. They constantly interact with water molecules. Water is a solution that has some interesting properties, and these properties contribute to the stability of the compact glob ular structures that characterize cellular proteins.

Water is a polar molecule. Individual water molecules in liquid water can each form four hydrogen bonds with neighboring water molecules. Liquid water is an essentially uninterrupted lattice of hydrogen bonded molecules, as seen in Figure 9-8. This unusual property contributes to the high melting and boiling points of water, as well as to such properties as low compres sibility and high surface tension. It also results in interesting interactions of water with soluble proteins.

Figure 9-8. Hydrogen bonding in water

A nonpolar molecule dissolved in water interrupts the regular hydrogen bond lattice of liquid water. Individual water molecules can reorient around a small nonpolar molecule to preserve their network of hydrogen bonds, but this reorientation has a cost in terms of free energy (which is how cost is measured in chemistry). The presence of a nonpolar solute forces water molecules into a more ordered

conformation than they would ordinarily assume. Instead of being able to face any which way and rotate freely, water molecules near the surface of a nonpolar solute have to work around it and form a cage. This is entropically unfavorable.

The larger a nonpolar solute gets, the more water molecules need to reorient to accommodate it, and the higher the energy cost of solvating the molecule becomes. Of course, if the nonpolar solute has some polar groups on its surface, water molecules can use those groups as hydrogen bonding partners instead of other water molecules, and the water lattice is less disturbed. Globular pro teins, which exist in aqueous solution even though they are composed substantially of nonpolar groups, must present a good hydrogen-bonding surface to the world. Hydrophilic amino acids are those whose sidechains offer hydrogen bonding partners to the surrounding medium, while hydrophobic amino acids' sidechains don't. The surface of a globular protein is usually anywhere from 50%-75% polar atoms, and deviations in this pattern can suggest binding or complexation sites.

Solvent accessibility and hydrophobicity play an important role in evaluating model structures. Threading methods for protein fold recognition use amino acid environments in evaluating models. When many hydrophobic amino acids are found in solvent-exposed structural environments or

hydrophilic amino acids buried in the protein interior, it is considered unlikely that the protein model is folded correctly.

9.2.2.4 Charge-charge, charge-dipole, and dipole-dipole interactions

Unlike covalent bonds, the other important interactions in protein structure are nonspecific. They don't change the discrete nature of the interacting atoms. They involve no sharing of electrons. Covalently bonded atoms are married; noncovalently bonded atoms are just shacking up.

Several kinds of important forces can aris e among polar and charged atoms. An ion is an atom that has a net positive or negative charge due to either a surplus or a deficit of electrons. Atoms that carry a positive ionic charge are attracted to atoms that carry a negative ionic charge, with a strength that depends on the size of the charges and the inverse of the distance between the atoms. In proteins, charge-charge interactions occur between the sidechains of acidic and basic amino acids that are negatively charged or positively charged due to loss or gain of a labile proton under normal

physiological conditions. The charge-charge interactions between amino acids in a protein structure are called salt bridges, and they can contribute a significant stabilizing force to a protein structure.

There are other, weaker interactions that occur between charges and groups that don't carry a positive or negative ionic charge. Dipolar molecules are molecules like those involved in hydrogen bonds, in which one end of the molecule has a partial positive charge and the other end has a partial negative charge. The dipole of a molecule is essentially a vector that describes the magnitude of the polarization along a bond. Dipolar molecules can be strongly attracted to other partial charges or to ionic charges. Many amino acid sidechains, as well as the protein backbone, have a strongly dipolar character, so charge-dipole and dipole-dipole interactions play a substantial role in stabilization of protein structure.

9.2.2.5 Van der Waals forces

The van der Waals force is a nonspecific attractive force between molecules. This force is loosely analogous to gravity, in that it exists between every pair of nonbonded atoms, and it's a fairly long- range force. However, it doesn't arise simply from the mass of the atoms involved, but from the transient attractive forces between the instantaneous dipole moments of each atom. The van der Waals force is quite strong, and because van der Waals interactions are nonspecific and numerous they play a significant role in protein folding and protein association.

9.2.2.6 Repulsive forces

Repulsive forces, or steric interactions, are very short range forces that increase sharply as atomic centers approach each other. The radius at which the repulsive force begins to increase sharply defines a spherical boundary around each atom center inside which another atom's spherical boundary (called the van der Waals radius) can't pass. If two nonbonded atoms in a structure get into each other's personal space, the contact is energetically unfavorable. In real molecules, atoms stay out of each other's way. However, in models of molecules, whether derived from NMR or x-ray data or built from scratch, checking for van der Waals bumps between nonbonded atoms is an important part of the structure-refinement process.

9.2.2.7 Relative strength of interatomic forces

The interaction between atoms can be described by a pairpotential, such as the Lennard-Jones

potential (Figure 9-9), which includes both an attractive and a repulsive term. The form of the potential shows that atoms tend to repel each other at very short range (positive potential energy indicating an unfavorable interaction) but to attract each other at slightly longer range. The strength of the attraction decays with distance, depending on the forces modeled.

When making inferences about structural stability or function based on intermolecular interactions, it is important to understand the relative strengths of these interactions, and how they scale with distance (Table 9-1).

Table 9-1. How Interatomic Forces Scale with Distance

Type of Bond Range of Interaction

Covalent Complicated short range

Hydrogen bond Roughly 1/r2

Charge -charge Scales with 1/r

Charge -fixed dipole Scales with 1/r2

Charge -rotating dipole Scales with 1/r4

Fixed dipole-fixed dipole Scales with 1/r3

Rotating dipole-rotating dipole Scales with 1/r6

Charge -nonpolar Scales with 1/r4

Dipole -nonpolar Scales with 1/r6

Nonpolar-nonpolar Scales with 1/r6

In Table 9-1, r represents the distance between two atoms in angstroms. Interactions that decrease in strength with 1/r are effective at a much longer range than those that decrease in strength with higher powers of r. Covalent interactions and hydrogen bonds are strong, and very energetically significant at short distances. Charge-charge interactions have some of the longest-range effects; electrostatic effects on protein activity have been experimentally shown at over 15-angstrom distance, a substantial range in molecular terms. A concentration of charges on a protein surface can create a powerful electrostatic steering effect that can attract ligand molecules or other proteins at even longer range. Hydrogen bonds and charge-dipole interactions are also relatively strong. The effects of these interactions are modeled by computing electrostatic potentials and using the computed potentials as the basis for calculating other molecular properties such as binding constants (via Brownian dynamics) or pKa values. On the other hand, interactions between noncharged and nonpolar atoms are very weak and effective only at short range. However, the effects of these interactions can be cumulative, stabilizing structure and making intermolecular associations more favorable. The effects of these interactions are addressed when you compute the size of intermolecular contact surfaces or enumerate interactions between neighboring interactions in a protein. In the remainder of this chapter, we discuss various methods for