(470h) Bridging Length Scales: Hierarchical Coarse-Graining of Elastic Biopolymer Models

One of the key challenges in modeling biomolecular systems lies in bridging the gap between length scales at which we have a concrete understanding of the fundamental molecular mechanics and the much larger length scales relevant for biological function. A classic example is the DNA polymer, whose molecular structure gives rise to an elastic rigidity at the nanometer length scale
whereas contour lengths up to several meters must be packaged, processed, and accessed by the cell. A meaningful approach to coarse-graining polymer models is essential for modeling systems of biological relevance. We present here a highly general, straight-forward procedure for generating coarse-grained polymer models. We demonstrate how a polymer may be modeled as a stretchable, shearable wormlike chain on increasingly large length scales while keeping long chain statistics intact.

As an example application for this multiscale modeling approach, we consider the effect of periodically bound DNA-bending proteins on the shape and behavior of the DNA chain. Specifically we study the physical properties of DNA-nucleosome arrays, which form the initial step in the packaging of the eukaryotic genome into a hierarchical chromatin structure.  We employ our coarse-graining procedure to determine looping probabilities for nucleosome arrays on different length scales, examining the effects of linker length and local geometry on the distribution of loops. These looping calculations are then leveraged to investigate the thermodynamics of chromosome condensation via the binding of bridging proteins. In addition, we look at the role of DNA elasticity and nucleosome geometry in the structure of compact fibers. Our multiscale models aim to address how the complex hierarchy of chromatin packing arises from the basic polymer properties of DNA and interacting proteins.

The novel polymer coarse-graining procedure presented here is generally applicable and can be used to systematically zoom out from a detailed polymer model based on localized mechanics to a simple effective model that can be used to calculate large length-scale behavior.