Multi-resolution Molecular Dynamics Algorithms for Computational Biology

生物分子的动力学行为传统上是用分子动力学（MD）计算机模拟来研究的。它们描述了模拟系统中所有原子的时间演化，包括感兴趣的生物分子和周围的水分子。由于系统的每个原子都被明确地模拟，传统的全原子MD模拟只能在相对较短的时间间隔内描述相对较小的系统（包含少量蛋白质或DNA片段）。包括细胞不同部分之间分子运输在内的生物过程是常用的MD技术无法达到的，即使只需要所研究系统的部分原子级信息。在这个建议中，MD和更粗的（不太详细的）建模方法之间的联系进行了研究。将开发和分析多分辨率方法，这些方法可以将MD与更粗的随机模型结合使用。这些多分辨率方法将能够模拟发生在多个空间和时间尺度上的生物过程，包括发生在整个细胞或其重要部分的过程。该提案详细考虑了将原子级信息合并到大型模型中可以实现计算节省的三个领域。它们包括溶剂（水）的粗粒化，小信号分子的研究和大生物分子的多分辨率方法。主要的数学挑战包括理解微观过程收敛于宏观描述的数学极限和多分辨率方法的误差分析。

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.