Distance Estimation between Coarsened Regions of Biopolymers for Far Field Force Approximation

Abstract

Current strategies to simulate dynamic behavior of large molecular systems involve computationally expensive fully atomistic models, or lower resolution models that have been coarsened. Coarsening is accomplished by grouping tightly bonded atoms, with little relative motion, in two main ways: spherical beads, and rigid bodies. The latter method, which preserves system geometry, has been shown to better capture the system physics by including rotational equations of motion of the coarsened region. This can have a significant effect on the system dynamics. The most advanced of these methods adaptively determine the regions that should be coarsened, and approach O(log(n)) computational performance (n is the number of coarsened regions in the system). Low computational order methods are limited by the pairwise force computation at each time step, which is required for biochemical systems. Thus, an approximation has been proposed for use with these methods that reduce the computational complexity of the force computation to O(nlog(n)).This approximation method (constructed similarly to the Fast Multipole Method) requires that the minimum distance between coarsened regions be computed. Intuitively obvious strategies, such as tracking the exact system geometry, are often so expensive that they negate the benefits of using a reduced order method. To this end, pseudo-radius of gyration is proposed that is computed from a tensor quantity similar to the inertia tensor, but describes the charge distribution of the coarsened region. The mechanisms for manipulating this quantity during the assembly and disassembly of coarsened regions would be similar to what is done for the actual inertia tensor in the current dynamics model. This quantity will be computationally inexpensive to store and manipulate, therefore will preserve the overall low computational cost of the force approximation, while allowing for a more accurate coarsening strategy.