Coarse-grained modeling is a key component in the field of multiscale simulation. Many biomolecular and otherwise complex systems require the characterization of phenomena over multiple length and time scales in order to fully resolve and understand their behavior. These different scales range from atomic to near macroscopic dimensions, and they are generally not independent of one another, but instead coupled. That is, phenomena occurring at atomic length scales have an effect at macroscopic dimensions and vice versa. Systematic transfer of information between these different scales represents a core challenge in the field of multiscale simulation. Coarse-grained modeling works at an intermediate resolution that can bridge the very high resolution (atomic) scale to the very low resolution (macroscopic) scale. As such, a significant challenge is the development of a systematic methodology whereby coarse-grained models can be derived from their high-resolution atomistic-scale counterpart. Here, a systematic theoretical and computational methodology will be described for developing coarse-grained representations of biomolecular and other soft-matter systems. At the heart of the methodology is a variational statistical mechanical algorithm that uses force-matching of atomistic molecular dynamics data to a coarse-grained representation. A theoretical analysis of the coarse-graining methodology will be presented, along with illustrative applications to membranes, peptides, and carbohydrates.
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