Statistically derived amino acid pair-potentials : applications to protein folding and protein-protein interactions

Department of Applied Physics, Stanford University, Stanford, CA 94305, USA.

Abstract

The idea of using empirical amino acid-pair-potentials extracted from proteins of known structure in the protein database was put forward by Wilson and Doniach in 1989. [Ref. 1]. In this approach histograms are created of the incidence of amino acid pairs as a function of their α carbon-α carbon distances or side chain centroid- side chain centroid distances. This is done for all possible amino acid pairs (e.g. Lys-Glu, etc.). Amino acids within plus or minus 3 residues of a given amino acid in the primary chain are excluded. By making the very simplified assumption that the histogram is distributed according to a Boltzman distribution, one can then define amino acid pair-potentials. These potentials are found to carry quite a bit of chemical information: hydrophobic amino acids repel hydrophylic amino acids, etc. They are also found to depend on the local conformation of the amino acids in the primary chain.

We will discuss two classes of algorithms for application of these potentials to problems in protein folding and protein-protein interactions. In the first approach a Monte Carlo procedure is used based on random selection of ø and Ψ angles using statistically collected Ramachandran possibilities. At each selection of a particular (δ, Ψ) pair the total energy of a protein based on the pair-potentials is computed. This then allows the use of a Metropolis algorithm to fold the protein by simulated annealing.

In the second approach, an additional set of potentials for bond angles is created using the Ramachandran tables referred to above. Then Langevin dynamics is performed in the constrained sub-space of (ø, Ψ) angles, using fixed peptides bond lengths. By this means one can perform local heating of part of a more complex protein such as an immunoglobulin. The Langevin dynamics allows an exploration of feasible conformations of the protein chain on a relatively rapid time scale. Finally, interactions between proteins - such as of a protein antigen with an antibody combining site - may be studied as a function of the relative coordinates of the two proteins. The pair-potentials provide an energetic assessment of geometrically feasible docking configurations.