| Free energy simulations based on molecular dynamics sampling are widely used to evaluate thermodynamic properties. Such simulations have found extensive application in the study of condensed phase phenomena, and arguably form the center of molecular simulation today. For this reason, it is of substantial interest to consider certain problems general to the methodology of these simulations, problems which at present limit its robust application in many cases. Three such problems are considered in this thesis. The first concerns the crossing of energy barriers that exist in the phase space sampled by the hybrid Hamiltonian used to connect the initial and final states of the system. This problem, which exists even for relatively simple (i.e., low-dimensional) systems, is acute in the case of complicated mesoscopic systems, such as biological macromolecules. A solution is offered in which the system is simulated in a generalized ensemble in which energy barriers are effectively reduced, resulting in improved convergence of the free energy calculation. The second problem addressed is the so-called end-point problem, i.e., the weak discrimination of configurations based on energy at the end-points of the calculation, which also leads to poor convergence and in some cases (e.g., in simulations using quantum-mechanical potentials) renders the calculation impossible. A solution to this problem is presented which involves the use of 'chaperones' to guide the configurational sampling of the system near the end-points of the calculation. The third problem considered is the requirement in a free energy simulation to distinguish between the nonequilibrium relaxation of the system that occurs at the start and the equilibrium period which follows it. Only data collected from the latter period are suitable for the calculation of ensemble averages, such as are required to determine the free energy difference. The proposed solution involves evaluating averages starting from the end of the trajectory rather than the beginning, and applying various statistical criteria to examine the normality that is expected for the equilibrium portion of the data. The last chapter of the thesis concerns a problem unrelated to free energy simulations, namely, the placement of functional groups (chemical fragments) in optimal positions in a protein binding site. This problem is examined by comparing two widely used methods, GRID and MCSS, which are found to give qualitatively similar results; the differences observed between the two methods reflect the distinct purposes for which they were developed. |
