Variational Methods for Biomolecular Modeling

Structure, function and dynamics of many biomolecular systems can be characterized by the energetic variational principle and the corresponding systems of partial differential equations (PDEs). This principle allows us to focus on the identification of essential energetic components, the optimal parametrization of energies, and the efficient computational implementation of energy variation or minimization. Given the fact that complex biomolecular systems are structurally non-uniform and their interactions occur through contact interfaces, their free energies are associated with various interfaces as well, such as solute-solvent interface, molecular binding interface, lipid domain interface, and membrane surfaces. This fact motivates the inclusion of interface geometry, particular its curvatures, to the parametrization of free energies. Applications of such interface geometry based energetic variational principles are illustrated through three concrete topics: the multiscale modeling of biomolecular electrostatics and solvation that includes the curvature energy of the molecular surface, the formation of microdomains on lipid membrane due to the geometric and molecular mechanics at the lipid interface, and the mean curvature driven protein localization on membrane surfaces. By further implicitly representing the interface using a phase field function over the entire domain, one can simulate the dynamics of the interface and the corresponding energy variation by evolving the phase field function, achieving significant reduction of the number of degrees of freedom and computational complexity. Strategies for improving the efficiency of computational implementations and for extending applications to coarse-graining or multiscale molecular simulations are outlined.Comment: 36 page

Predicting Prokaryotic Ecological Niches Using Genome Sequence Analysis

Automated DNA sequencing technology is so rapid that analysis has become the rate-limiting step. Hundreds of prokaryotic genome sequences are publicly available, with new genomes uploaded at the rate of approximately 20 per month. As a result, this growing body of genome sequences will include microorganisms not previously identified, isolated, or observed. We hypothesize that evolutionary pressure exerted by an ecological niche selects for a similar genetic repertoire in those prokaryotes that occupy the same niche, and that this is due to both vertical and horizontal transmission. To test this, we have developed a novel method to classify prokaryotes, by calculating their Pfam protein domain distributions and clustering them with all other sequenced prokaryotic species. Clusters of organisms are visualized in two dimensions as ‘mountains’ on a topological map. When compared to a phylogenetic map constructed using 16S rRNA, this map more accurately clusters prokaryotes according to functional and environmental attributes. We demonstrate the ability of this map, which we term a “niche map”, to cluster according to ecological niche both quantitatively and qualitatively, and propose that this method be used to associate uncharacterized prokaryotes with their ecological niche as a means of predicting their functional role directly from their genome sequence