Framework for the Adaptive Multiscale Modeling of Biopolymers

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The principal objective of the proposed work is to research new methods, which provide a means for the efficient modeling and simulation of the behavior of complex bio-polymeric systems. These systems often have important phenomena taking place at multiple spatial and temporal scales (levels). Systems where fine scale (small and rapid, e.g. motions of individual atoms) phenomena contributes significantly to coarse scale (large and slow; e.g. gene expression depends to significant degree on the shape(conformation) of the molecule) behavior are common in macro-molecular processes and are essential to human health.To gain true insight into the behavior and control of important cellular processes, one must understand the physical principles and mechanisms that underlie them. Physics based modeling and simulation will play a critical role towards gaining such an understanding. Unfortunately, these molecular systems are so computationally costly that they cannot currently be modeled and simulated to an adequate level (in accuracy and duration). Because many of the important aspects of these molecular processes change significantly during the process of interest, the model itself must be similarly able to adapt so that it can accurately represent the important process, while remaining fast and cost effective.The proposed work is devoted to this end. This work involves to production of an adaptive, multi-level modeling strategy, utilizing advanced multibody methods. Physics-based internal metrics guide the division of the system model into regions, each with its own local temporal and spatial set of scales. The region boundaries and model types, which may vary from atomistic (fine scale) to continuum (coarsest scale), are then dynamically (adaptively) adjusted, as needed to capture important system behavior at minimum computational cost. The underlying FDCA and ODCA formulations produce equations which are inherently divided into such regions (subdomains). Additionally, the overall structure of these equations are those of a binary-tree, so the resulting formulation is highly conducive to effective parallel computer implementation. The impact of this work will be a great increase in the rate and extent to which such complex molecular dynamic systems may be modeled and analyzed. This will allow the analyst to treat far more complex systems in a more cost, time, and resource effective manner than is currently possible, thus leading to greater understanding. Examples of such systems where the proposed adaptive multiscale strategy should be particularly suitable are biopolymeric systems which include RNA, DNA, and proteins. The proposed framework is expected to provide a means to obtain greater insight into and understanding of key biomolecular processes, which may contribute greatly to our learning to modify and control such processes in the future. Such understanding and ability could significantly impact human health in many positive respects.