The Polypeptide Model and Potential Energy Function

Proteins require specific three-dimensional conformations to function properly. These “native” conformations result primarily from intramolecular interactions between the atoms in the macromolecule, and also intermolecular interactions between the macromolecule and the surrounding solvent. Although the folding process can be quite complex, the instructions guiding this process are specified by the one-dimensional primary sequence of the protein or nucleic acid: external factors, such as helper (chaperone) proteins, present at the time of folding have no effect on the final state of the protein. Many denatured proteins spontaneously refold into functional conformations once denaturing conditions are removed. Indeed, the existence of a unique native conformation, in which residues distant in sequence but close in proximity exhibit a densely packed hydrophobic core, suggests that this threedimensional structure is largely encoded within the sequential arrangement of these specific amino acids. In any case, the native structure is often the conformation at the global minimum energy (see [1]). In addition to the unique native (minimum energy) structure, other less stable structures exist as well, each with a corresponding potential energy. These structures, in conjunction with the native structure, make up an energy landscape that can be used to characterize various properties of the protein. Over 20 years of research into this “protein folding problem” has resulted in numerous important algorithms that aim to predict native three-dimensional protein structures (see [2], [3], [4], [8], [9], [10], [12], [14], [15], [18], [19], [20], [21], and [22]). Such methods assume that the native structure is a balance of various interactions. These methods invariably use some form of energy minimization technique, such as simulated annealing or genetic algorithms, rather than the computationally more efficient continuous minimization techniques. Each such method correctly predicts a few protein structures, but misses many others, and the process is both slow and limited to structures of relatively small size. The purpose of this paper is to show how one can apply more efficient continuous minimization techniques to the energy minimization problem by using an accurate continuous approximation to the discrete information provided for known protein structures. In addition, we will show how the results of one particular computational method for protein structure prediction (the CGU algorithm), which is based on this continuous minimization technique, can be used both to accurately determine the global minimum of potential energy function and also to offer a quantitative analysis of all of the local (and global) minima on the energy landscape. The CGU method has been extensively tested on a variety of computational platforms including the Intel Paragon, Cray T3D, an 8 workstation Dec Alpha cluster, and a heterogeneous network of 13 Sun SparcStations and 7 SGI Indys. Protein structures with as many as 46 residues have been computed in under 40 hours on the 20 workstation heterogeneous network.