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

A tethering complex drives the terminal stage of SNARE-dependent membrane fusion.

Membrane fusion in eukaryotic cells mediates the biogenesis of organelles, vesicular traffic between them, and exo- and endocytosis of important signalling molecules, such as hormones and neurotransmitters. Distinct tasks in intracellular membrane fusion have been assigned to conserved protein systems. Tethering proteins mediate the initial recognition and attachment of membranes, whereas SNARE (soluble N-ethylmaleimide-sensitive factor attachment protein receptor) protein complexes are considered as the core fusion engine. SNARE complexes provide mechanical energy to distort membranes and drive them through a hemifusion intermediate towards the formation of a fusion pore. This last step is highly energy-demanding. Here we combine the in vivo and in vitro fusion of yeast vacuoles with molecular simulations to show that tethering proteins are critical for overcoming the final energy barrier to fusion pore formation. SNAREs alone drive vacuoles only into the hemifused state. Tethering proteins greatly increase the volume of SNARE complexes and deform the site of hemifusion, which lowers the energy barrier for pore opening and provides the driving force. Thereby, tethering proteins assume a crucial mechanical role in the terminal stage of membrane fusion that is likely to be conserved at multiple steps of vesicular traffic. We therefore propose that SNAREs and tethering proteins should be considered as a single, non-dissociable device that drives fusion. The core fusion machinery may then be larger and more complex than previously thought