The goal for the research proposed here is to develop mathematical tools for computing three-dimensional structures of large biological molecules. In particular, modeling and large- scale minimization techniques will be devised to predict the conformations of single and doublestranded RNA and DNA molecules. The computational tools involve semi-empirical potential energy minimization and molecular dynamics, executed on the Cray X-MP and aided by interactive computer graphics on the Evans and Sutherland PS-330. The plan is to work on the following four areas of program development: (1) Global optimization strategies; test the determination Tunneling method of Levy and Gomez and a variant of the stochastic Simulated Annealing: (2) Faster manipulation of the pairwise interactions in the energy function; investigate the new method recently proposed by Greengard and Rokhlin which could reduce the order O(N2) computational complexity for an N - particle system to order O(N): (3) Implementation of molecular dynamics: dynamics simulations will enable an examination of the dynamic trajectories of the structures obtained from minimization; and: (4) Incorporation of solvent and metalions into the molecular model; this will provide a more realistic potential field to represent the molecular forces influencing the RNA and DNA in its natural milieu. The developed computational tools will yield the ability to investigate some intriquing problems of three-dimensional molecular structures. These problems include the dependence of DNA conformation on the nucleic acid base sequence and the structure and the complex folding patterns of single-stranded RNA. The minimizations and dynamics results will be used to make 16 mm films and videotapes that will reveal the dynamic range of structures and permit us to relate conformational features with known biological functions. This proposal projects to develop mathematical tools, using state-of-the-art optimization algorithms, for examination of dynamics simulation of solvent and metal-ion interaction in the biologically important molecular RNA and DNA. The Program Director for Computational Science and Engineering recommends support in the sum of $69,370 for a period of one year.
