Adaptive Resolution Molecular Dynamics Simulation: Changing the Degrees of Freedom on the Fly

We present a new adaptive resolution technique for efficient particle-based multiscale molecular dynamics (MD) simulations. The presented approach is tailor-made for molecular systems where atomistic resolution is required only in spatially localized domains whereas a lower mesoscopic level of detail is sufficient for the rest of the system. Our method allows an on-the-fly interchange between a given molecule's atomic and coarse-grained level of description, enabling us to reach large length and time scales while spatially retaining atomistic details of the system. The new approach is tested on a model system of a liquid of tetrahedral molecules. The simulation box is divided into two regions: one containing only atomistically resolved tetrahedral molecules, the other containing only one particle coarse-grained spherical molecules. The molecules can freely move between the two regions while changing their level of resolution accordingly. The coarse-grained and the atomistically resolved systems have the same statistical properties at the same physical conditions.Comment: 17 pages, 11 figures, 5 table

Partial differential equations for self-organization in cellular and developmental biology

Understanding the mechanisms governing and regulating the emergence of structure and heterogeneity within cellular systems, such as the developing embryo, represents a multiscale challenge typifying current integrative biology research, namely, explaining the macroscale behaviour of a system from microscale dynamics. This review will focus upon modelling how cell-based dynamics orchestrate the emergence of higher level structure. After surveying representative biological examples and the models used to describe them, we will assess how developments at the scale of molecular biology have impacted on current theoretical frameworks, and the new modelling opportunities that are emerging as a result. We shall restrict our survey of mathematical approaches to partial differential equations and the tools required for their analysis. We will discuss the gap between the modelling abstraction and biological reality, the challenges this presents and highlight some open problems in the field