Statistical mechanical basis and algorithms for constructing coarse grained models of molecular liquids and biological structures [electronic resource]
Keywords: Chemistry

Computer simulation of condensed phases have been on the forefront of the scientific research in varieties of disciplines including but not limited to chemistry, physics, biophysics and material science. In spite of impressive success, standard computational techniques such as molecular dynamics and Monte Carlo run into serious limitations in the system sizes and temporal durations accessible in simulations when an atomically detailed description of the system is employed, for any given choice of computational technology. One obvious way of surmounting this problem is to construct a reduced representation of the original system of interest with the hope that reduction in number of degrees of freedom will cut down the computational cost at the same time retaining some essential features. This approach, known as coarse-grained modelling, has attracted a great deal of attention in recent years and a varieties of methods have been reported in the literature. The multiscale coarse-graining (MS-CG) method is a method for determining the effective potential energy function for a coarse-grained (CG) model of a system using data obtained from molecular dynamics simulation of the corresponding atomically detailed model. The method has been given a rigorous statistical mechanical basis and the coarse-grained potential obtained using the MS-CG method is an approximate variational solution for the exact many-body potential of mean force for the coarse-grained sites. In this thesis we extend the formal theory behind the method to situations that were not considered in the original version, thereby expanding the applicability of the method. We also develop new algorithms for practical implementation of the MS-CG method. The algorithmic developments consist of introduction of new basis functions for representing the CG potential energy functions and construction of new numerical techniques for the optimization problem associated with the MS-CG method. We apply the MS-CG method, with a new set of basis functions, to study the many body potential of mean force among solutes in a simple model of a solution of Lennard-Jones particles. For this model, pairwise additivity of the many body potential of mean force is a very good approximation when the solute concentration is low, and it becomes less accurate for high concentrations, indicating the importance of many body contributions to the coarse-grained potential. We propose and test a version of the MS-CG method suitable for the isothermal-isobaric ensemble. The method shows how to construct an effective potential energy function for a coarse-grained system that generates the correct volume fluctuations as well as correct distribution functions in the configuration space of the CG sites. We present a new numerical algorithm with automatic basis set selection and noise suppression capabilities for the solution of the MS-CG variational problem. We also develop new basis functions that are similar to multiresolution Haar functions and that have the differentiability properties that are appropriate for representing CG potentials. The new method, allows us to construct a large basis set, and the method automatically chooses a subset of the basis that is most important for representing the MS-CG potential. It provides regularization to mitigate potential numerical problems in the associated linear least squares calculation, and it provides a way to avoid fitting statistical error. We use this technology to construct a systematic method for including three body terms as well as two body terms in the nonbonded part of the CG potential energy. Inclusion of three body terms can lead to significant improvement in the accuracy of CG potentials and hence of CG simulations as shown by the test calculations on two very different model systems. We construct basis functions for representing the CG potential energy functions for molecular systems. We also discuss the problem arising from insufficient sampling of certain parts of the atomistic configuration space and develop methods for surmounting this problem that require very little human intervention. We test our algorithms on a simple but nontrivial test problem that involves constructing coarse grained models of liquid hexane.