A menagerie of interactions

Protein folding, assembly and interactions are largely governed by the non-covalent interactions between residue side chains. In order to capture computationally the molecular details of such interactions, for the purposes of precise interface defini- tion, it is first necessary to understand their physico-chemical origins. These will be reviewed briefly here for a series of such non-covalent interactions, broadly in order of their significance to protein-protein interactions.

2.1.4.1 van der Waals

Van der Waals interactions are a consequence of quantum dynamics inducing fluc- tuating polarizations in the electron cloud of nearby particles. They are composed of a short-range repulsive component, due to steric hindrance when neighbouring atoms have overlapping electron clouds, and a longer-range attractive term, due to the coupling of dipoles in the electron cloud of neighbouring atoms, known as London dispersion forces. The two components are usually combined and, although many different functional forms have been suggested, they are most commonly described by the so-called Lennard-Jones potential shown in Equation

2.1 Introduction

Figure 2.1: Lennard Jones potential for an Argon dimer. Short range repulsions

are mediated by the r−12component whereas London dispersion-attraction forces

are accounted for by the r−6 term.

V (r) = 4[(σ/r)12− (σ/r)6_{] (2.1)}

where r is the interatomic distance,  is the depth of the potential well and σ is the distance at which the potential between the atoms is zero.

Figure2.1 indicates a weak attraction at large distances and strong repulsion

at very close distance. Van der Waals interactions are typically around 2.8˚A

to 4.0˚A in length. The difference between sum of the van der Waals radii of

the two atoms and the point of lowest energy is of the order of 0.3˚A to 0.5˚A .

2.1 Introduction

Waals interactions are individually very low (typically < 1 kcal/mol), but the large number of such interactions makes them significant for protein folding and binding.

2.1.4.2 Hydrogen bonds

A hydrogen bond is an attractive interaction between two electronegative atoms competing for the same hydrogen atom. A hydrogen atom is formally covalently bound to the donor and aligned between the donor and acceptor atoms. The strength of the hydrogen bond varies broadly depending on various factors in- cluding the linearity of the interaction, but typically ranges from 2-10 kcal/mol.

2.1.4.3 Hydrophobic interactions

The increase in entropy gained by removing surfaces of hydrophobic side chains from ordered solvent is amongst the most significant factors for protein folding. A convenient handle for characterizing this phenomenon is to consider the effect in terms of favourable interactions between hydrophobic side chains. However, it should be borne in mind that it is not the interactions between these side chains that is the source of the favourable interactions, rather the entropic gain from exclusion of solvent. As such, hydrophobic residues tend to cluster in the protein core and hydrophilic residues on the surface (Tsai et al. (1997)). Based on experimental data Kyte and Doolittle (Kyte & Doolittle (1982)) derived a hydropathy scale to describe the differing hydrophobic capacity of each residue type.

2.1.4.4 Ionic interactions

In electrostatic interactions charges on nuclei and electrons interact according to the Coulomb equation:

V = qiqj

4π0rrij

(2.2)

where qi and qj are the magnitude of the charges, rij is their separation, 0the

2.1 Introduction

Estimates of the free energy of formation of a solvent exposed salt bridge on the protein’s surface vary but values of the order of -1.0 kcal/mol have been suggested (Schulz & Schirmer (1996)).

2.1.4.5 Aromatic interactions

In the side chains of aromatic amino acids π-electron orbital systems are delocal- ized on both sides of a planar ring, generating a small partial negative charge on each face, and a small partial positive charge on the peripheral hydrogens. 60% of aromatic side chains in protein domains are involved in aromatic pairings (Burley & Petsko (1985)). It is commonly perceived that aromatic groups stack on top of one another in a face-to-face manner. In fact, detailed analysis of protein struc- tures (Hunter et al. (1991)) backed up the results of previous molecular modelling studies (Hunter & Sanders (1990)) suggesting that such a stacking arrangement is disfavoured due to π-electron repulsion. Instead, offset stacked interactions and edge-to-face interactions are marginally favoured. Analysis of thermodynamic cy- cles (Horovitz (1996)) indicates that the contribution to protein stability by the interaction energy between two aromatic groups is 1.3 kcal/mol, only marginally higher than the stabilization expected from the hydrophobic contribution from burying the surface area between them.

2.1.4.6 π-cation

The π-cation interaction is increasingly recognized as an important non-covalent binding interaction. The effect arises from the electrostatic interaction of a cation with the negative face of an aromatic π-system. A survey of high resolution struc- tures (Gallivan & Dougherty (1999)) indicated that one out of every 77 residues is involved in an energetically meaningful π-cation interaction. Of the cationic residues, arginine participates in almost twice as many π-cation interactions as lysine; of the aromatics, tryptophan participates more commonly than pheny- lalanine or tyrosine. Interestingly 26% of tryptophans were involved in π-cation interactions, with the preferred geometry being the cation positioned over the 6-atom ring. The free energy contribution of π-cation interactions across protein-

2.1 Introduction

protein interfaces has been estimated as around 3 kcal/mol on average (Crowley & Golovin (2005)).

2.1.4.7 Disulphide

Disulphide bonds are formed by the oxidation of two cysteine residues to form a covalent sulphur-sulphur bond coupling the two thiol groups. Calculations suggest that a disulphide bond should give rise to 2.5 - 3.5 kcal/mol of stabilization but experimental values vary greatly (Thornton (1981)).

2.1.4.8 Aromatic sulphur interactions

Interactions between the non-polar aromatic and sulphur-containing amino acids occur most frequently in the interior of proteins. About half of all side-chain sulphur atoms are in contact with aromatic groups (Zauhar et al. (2000)). The geometry of such interactions suggests that sulphur atoms, unlike carbon and nitrogen, predominantly approach the edge of aromatic rings rather than inter- acting in a planar stacking fashion (Pal & Chakrabarti (2001); Reid et al. (1985)). Aromatic-sulphur interactions have been predicted to provide between -0.7 and -2.6 kcal/mol of free energy, depending on local geometry (Ringer et al. (2007)).