| This dissertation presents and applies novel computational techniques applicable for calculating thermodynamic properties of biomolecules and predicting their most probable conformations by isolating low-lying minima of their energy functions.; The first category of methods set forth addresses the problem of "broken ergodicity," shared by a large class of condensed-phase systems such as spin glasses, molecular clusters and proteins. Two novel computational methods, designed to enhance the search of the configurational space, are presented. One method is based on probability density functions derived in a generalization of the statistical mechanics treatment of Tsallis. The other employs a local Monte Carlo sampling scheme together with large global moves in the configurational space using displacement vectors that connect local potential energy minima.; The second category of computational methods is used to find the global minimum of the potential energy function of a system composed of many interacting atoms. One of the most important problems in contemporary molecular biology, protein folding, can be cast in terms of global minimization. Two approaches to global minimization are presented. In the first, a simulated annealing protocol is used, generalized to the case of a system obeying the rules of Tsallis statistics. In the second, a smoothing integral transformation with a cubic kernel is applied to the potential energy hypersurface, with the advantages over similar smoothing methods that the derivatives of the smoothed potential are simple finite-difference formulas and that no approximations to the potential are needed.; For each computational method developed, applications to systems such as atomic clusters, spin systems and peptides are presented. The effectiveness of the conformational sampling and rapid isolation of low-lying energy minima is shown and the success of each method is compared to that of pre-existing algorithms. |
