Multi-resolution Molecular Dynamics Algorithms for Computational Biology

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Dynamical behaviour of biomolecules has been traditionally studied using molecular dynamics (MD) computer simulations. They describe the time evolution of all atoms in the simulated system, including the biomolecule of interest and surrounding water molecules. Since every atom of the system is explicitly simulated, traditional all-atom MD simulations can only describe relatively small systems (containing a few proteins or DNA segments) over relatively short time intervals. Biological processes which include the transport of molecules between different parts of the cell are out of reach of commonly used MD techniques, even if the atomistic-level information is only needed in parts of the studied system. In this proposal, connections between MD and coarser (less detailed) modelling approaches are investigated. Multi-resolution methodologies, which can use MD together with coarser stochastic models will be developed and analyzed. These multi-resolution methods will enable the modelling of biological processes occurring over multiple spatial and temporal scales, including processes which happen across the whole cell or its significant part. The proposal considers in detail three areas where computational savings can be achieved to incorporate atomistic-level information into large scale models. They include coarse-graining of solvent (water), studying small signalling molecules and multi-resolution methods for large biomolecules. The main mathematical challenges include understanding mathematical limits in which micro processes converge to macro descriptions and the error analysis of multi-resolution methodologies.