Lecture 2: Protein interactions leading to folding

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The structure of immunoglobulin V-domain, which forms an antiparallel beta barrel; beta sheet strands are in yellow, turns are blue and random coil is white. One short helical segment is shown in red.

Folding of the polypeptide

The simplest structure for a protein to adopt is a single uniform secondary structure:

alpha-keratin is alpha helix

fibroin (a beta keratin) is antiparallel beta sheet

collagen forms a unique triple helical structure, the collagen helix. This is not considered to be a generalized secondary structure, since collagen helix depends on a specific repeating sequence -(Gly-Pro-Pro)n-.

Such structures are rigid, and give the protein an overall fibrous shape, whereas most proteins are globular. A globular shape is the result of folding the polypeptide onto itself and depends on the following:

1) Clearly defined interruptions in the secondary structure;

Myoglobin folds into eight alpha-helical segments representing about 70% of the total sequence, separated by regions of disordered polypeptide or random coil. Although many amino acids are present that otherwise prefer beta sheet, they are scattereed in distribution, so their "vote" is ineffective in determining the secondary structure.cartoon of myoglobin

Secondary structure breaker amino acids Gly, Pro, Ser, Asn Asp interrupt normal secondary structure, especially when present in pairs, creating more flexible turn or loop regions where the polypeptide can fold back on itself.

The figure shows the hairpin formed by helices G and H in myoglobin. Two prolines (green) bracket helix G, defining its limits; several glycines (yellow) mark the loop region between the helices.

2) The folded form clusters almost all the non polar amino acids in the core of the globular shape. The non-polar or hydrophobic amino acids are thus grouped together, away from direct contact with H2O. By default, the outer shell of a folded protein is largely made up of polar amino acids which interact well with the surrounding H2O. The grouping of non-polar amino acids together accounts for about 50% of the energy responsible for stabilizing the folded form.

The figure shows a cutaway section of myoglobin, non polar amino acids colored red and polar amino acids in green.

3) The ideal folded state interlocks like a jigsaw puzzle. This maximizes the number of close atom to atom contacts. Atoms that are in perfect contact bind via the weak van der Waals interaction. This force becomes strongly repulsive if atoms are too close together, and fades to zero if atoms are spaced apart by more than two atom diameters. Since the van der Waals interaction may be weak (0.1 to 1 kJ compared with 26 kJ for a hydrogen bond or 400 kJ for a covalent bond), the overall effect is significant only if a large number of van der Waals contacts exist, i.e. atom to atom contacts at the ideal distance of separation. This can be true for a protein since a protein molecule contains thousands of atoms.
Misfolded arrangements don't fit together well so that only a few van der Waals contacts are made at ideal distances.

4) There's also a contribution from polar interactions such as hydrogen bonding and ion pair formation.

Interactions giving rise to folding

Protein folding is a consequence of intermolecular forces, includingpure ionic interactions
dipole interactions
hydrogen bonds
van der Waals forces
hydrophobic interactions

Pure ionic interactions:

Ion pairs may be + to - (attractive),or + to + and - to - (repulsive).

Strength of the interaction:

E = e2 /D.rAB

Energy is proportional to 1 / rAB, where rAB is distance between charged groups A and B; (force falls off as the inverse square of distance)
D is the dielectric constant of the medium; Dvacuum = 1, but Dwater = 80, which diminishes the net energy in aqueous solution.

In addition ions are extensively solvated in solution:
The solvation layer may increase rAB. Desolvation requires a considerable energy penalty that may negate the benefit of the ionic interaction.

example: C4H9NH3+ CH3CO2- has Kd = 3.2 M

These ions are ions dissociated at all but highest concentration.

In summary, ionic interactions are often thought of as "strong" by virtue of their strength in vacuo, but are relatively weak in an aqueous environment. For a protein molecule, the majority of charged groups are at the surface of the folded protein, where they are solvated and neutralized by counterions of the salts present in the solution.

Occasionally, there are ion pairs buried in the protein interior that can contribute to stabilization of folding because the local dielectric constant D is much lower in the hydrophobic interior of the protein.

Charged amino acids are important for folding as much because they destabilize misfolded states through repulsion between like charges or by desolvation of charged groups that become buried in the interior in an incorrectly folded state.

Dipole interactions:

dipole moment = z . d

where z is the partial charge, and d is the separation between the charge centres. Dipoles are associated with electronegative atoms such as O or N, and in protein structures, in particular with peptide bonds.

Edipole is proportional to 1/ r3 to 1/ r6, depending on alignment and local inductive effects. Dipolar interaction energy is also proportional to 1/ D, the dielectric constant.

= 3.5 Debye units

Hydrogen bonds:

Hydrogen bonds may be regarded as a special case of strong dipolar interaction, and involve dipolar OH and NH groups as donors, and potential bases, O: or N: with an available lone pair of electrons as acceptors. S or F may sometimes be involved in weak hydrogen bonding.

H-bond alignment is critical, with significant weakening if donor D, the H atom and acceptor A are not colinear.

H-bond spacing is indicative of the bond strength:

D --- H - - - - :A

Distance D to H is slightly longer than a normal bond (indicating weakening of the single bond), but H to A is much less than predicted from non-bonded contact radius of the atoms.

D to A separation of 2.8 angstrom represents a hydrogen bond of 28 - 29 kJ mol-1in vacuo; shorter (down to about 2.6 angstrom) hydrogen bonds are stronger. Longer (and thus weaker) H-bonds may be electronically weaker, or may arise because of other geometric constraints of the molecule.

In aqueous solution, hydrogen bond donors and acceptors bond readily to H2O, and the effective strength of H-bonds may be relatively low when the balance between the two possible states is considered:

Induced dipole effects:

Atoms of any kind have fluctuating electron distribution relative to their nuclei, leading to transient dipoles. In addition neighboring charges, or permanent dipoles, may bias the electron distribution to induce dipoles in normally neutral neighbours.

These induced dipole effects give rise to the so called van der Waals interactions, also known as dispersion forces.

Energies are of the order of -0.1 to -1.0 kJ/mol.

The large reciprocal exponents mean that the force falls off rapidly with distance, effectively zero above 5 or 6 angstroms.
Atoms must be in close proximity for the van der Waals interaction to be appreciable, but not so close as to intrude into each other's volume. The so called van der Waals radius of an atom is an expression of the positive (repulsive) branch of the curve, which is very steep due to the inverse 12th power dependency.

There has been a tendency to neglect van der Waals interactions relative to the nominally much stronger ionic and dipolar interactions. This is an error on two counts:

i) the dielectric strength of aqueous media and the effects of solvation considerably diminish the magnitude of long-range electrostatic interaction.

ii) when dealing with macromolecular surfaces making contact, several hundred van der Waals interactions may be involved, between every pair of atoms juxtaposed at optimum separation.

Crystal structures reveal that the interior of proteins are packed at the same density as solids, implying a high number of close contacts are made in the correctly folded form of the protein. The total van der Waals interactions of a protein molecule could therefore sum to hundreds of kJ/mol.

The Hydrophobic effect:

All the effects described so far are electrostatic in origin, and contribute to the enthalpy of protein folding.

The hydrophobic effect is an indirect effect resulting from a peculiarity of water structure. Water molecules exchange hydrogen bonds with neighbours at a rate of about 1011 s-1. At the interface between water and a non-H-bonding group such as CH3, water molecules have fewer opportunities for H-bond exchange, leading to longer than usual lifetime of H-bonds, an ice-like state at the interface, and consequent decrease in entropy.

Negative enthalpy change and positive entropy change give negative, i.e. stabilizing, contributions to Gibbs free energy of protein folding.

Any situation that minimizes the area of contact between H2O and non-polar, i.e. hydrocarbon, regions of the protein results in an increase in entropy. This is achieved by clustering non polar groups together.

100 angstrom2 (e.g. a leucine side chain) of hydrocarbon removed from contact with water contributes about - 8 kJ/mol (about -2 kJ/mol of -CH2-, primarily through gain of entropy in the H2O phase, and with minimal contribution from the leucine itself.

Conformational entropy

In the denatured state, a polypeptide chain has freedom to adopt many different torsional angles through out the molecule. These include:

* the angle phi at each amino acid except proline,
* the angle psi at each amino acid,
* plus free rotation about each non-terminal single bond in the side chain.

If an average amino acid can be in any of 10 states of bond rotation, then the probability that it's in the right state can be written as 0.1 (assuming that all states are equally probable). The probability of a chain of 100 amino acids being in the right state by chance is 0.1100.

This can be related to entropy as follows:

conformational entropy change on folding to a defined state = R ln P

where R is the gas constant, 8.314 J K-1 mol-1 and P is the estimated probability of the folded state. The contribution to the Gibbs free energy of folding is -TdeltaS, and evaluates to about +600 kJ/mol for 100 amino acids in a polypeptide. Since 10 rotational states may be a conservative estimate, this poses a large positive contribution to the Gibbs free energy of folding that must be overcome by the favorable interactions in order to cause a polypeptide to fold.