Prediction of Peptide Conformation by the Multicanonical Algorithm

We test the effectiveness of the multicanonical algorithm for the tertiary structure prediction of peptides and proteins. As a simple example we study Metenkephalin. The lowest-energy conformation obtained agrees with that determined by other methods such as Monte Carlo simulated annealing. But unlike to simulated annealing the relationship to the canonical ensemble remains exactly controlled. Thermodynamic quantities at various temperature can be calculated from one run. A protein or a peptide is a molecule that consists of a chain of N amino acid residues. There are 20 different amino acids known in nature. When N is large one calls the molecule a protein, otherwise a peptide. The prediction of tertiary structures of proteins, which determine their biological function, from their primary sequences remains one of the long-standing unsolved problems (for recent reviews, see, for example, Refs. [1]). It is widely believed that this structure corresponds to the global minimum in the energy. So the problem amounts to finding the global minimum energy out of a huge number of local minima separated by high tunneling barriers. Within the presently available computer resources, the traditional methods such as molecular dynamics and Monte Carlo simulations at relevant temperatures tend to get trapped in local minima. One of the methods which which seem to alleviate this multiple-minima problem is simulated annealing.[2] However, a disadvantage of simulated annealing is that there is no established protocol for annealing and a certain number (which is not known a priori) of runs are necessary to evaluate the performance. Moreover, the relationship of the obtained conformations to the equilibrium canonical ensemble at a fixed temperature remains unclear. These problems may be overcome by the multicanonical algorithm which was recently proposed by Berg et al.[3] Originally developed to overcome the supercritical slowing down of first-order phase transitions,[4] it has also been tested for systems with conflicting constraints such as spin glasses.[5, 6, 7] The latter systems suffer from a similar multiple-minima problem and it was claimed that the multicanonical algorithm outperforms simulated annealing in these cases.[6] To appear in the Proceedings of the Sixth Annual Workshop on Recent Developments in Computer Simulation Studies in Condensed Matter Physics, 22–26 Feb. 1993, Athens, Georgia. Department of Physics and Supercomputer Computations Research Institute (SCRI), The Florida State University, Tallahassee, FL 32306, USA. Department of Physics, Nara Women’s University,Nara 630, Japan.