Multiscale modeling of biological and soft matter

Abstract

The large range of spatial and temporal scales inherent in biological and soft matter is a challenge to modeling. To understand the physics of a cell membrane, one needs to start from Ångström-sized atoms and their motions in the femtosecond range, and go all the way to whole cells, whose diameters can be tens of micrometers and lifetimes of the order of days. All these scales can neither be probed by a single experimental technique, nor modeled using one simulation approach. What is needed is a range of techniques.

Describing matter by a hierarchy of computational models, systematically linking the models at lower resolution to those at higher resolution, is termed multiscale modeling. Depending on the phenomenon one wishes to study, one may choose atomic-level models and algorithms, opt for a simplified or coarse-grained description, or decide on a combination of these. The aim of this Thesis is to describe modeling at atomic scale and mesoscale, i.e., at scales in the range 1-1000 nm and 1-1000 ns. We also focus on the systematic linking; how to reduce the degrees of freedom in an atomic-scale model to arrive at a coarse-grained description. Further, use of hybrid models that combine atomic and coarse-grained descriptions is discussed.

We approach multiscale modeling through examples from biological and soft matter physics. Atomic-scale modeling is illustrated through molecular dynamics simulations of phospholipid/cholesterol bilayers. The effect of cholesterol on the free volume, packing, and diffusive properties of bilayers is investigated. We then link the atomic-scale model to one allowing us to reach length scales significantly larger than those reached in current-day state-of-the-art atomic-level simulations: the new model offers an eight-order-of-magnitude speed-up, enabling us to study the lateral structure of bilayers at length scales up to hundreds of nanometers at a modest computational cost. The simulation results point at the existence of cholesterol-rich domains with sizes in the ten-nanometer-range.

From membrane systems we move to the realm of complex fluids. We use polymer chains and colloids in solution as examples of systems where hybrid models should be used. The solutes are modeled in microscopic detail, while the solvent is coarse-grained. The solvent model is cost-effective, yet correctly describes the hydrodynamic interactions between the solute particles. Using these models we are able to resolve a long-standing debate about dynamic scaling of two-dimensional polymers in solution, and obtain interesting results for collective diffusion in colloidal suspensions.