Adaptive Coarse-Graining Framework to Model Non-Equilibrium Dynamic Behavior of Biopolymers

Abstract

In this paper, an adaptive framework to model and simulate the non-equilibrium dynamic behavior of complex macro-biomolecular systems such as RNAs, DNAs, and proteins is presented. It is demonstrated that given the coupling and nonlinearity of biopolymers, it is expected that factors such as geometric and dynamic boundary conditions, as well as the applied forces will greatly affect the system's dynamic behavior. Consequently, static (time-invariant) coarse-grained models are not always able to fully sample the conformational space of the molecule. In the adaptive multiscale strategy presented here, some degrees of freedom of the system (internal coordinates) have their definitions/meanings adjusted “on-the-fly” at different instants and different locations of the system based on the values of knowledge-base (derived empirically), math-based (derived from strictly mathematical relations), and/or physics-based (derived directly from physical laws) metrics. This paper investigates the appropriate metrics to steer the model transitions during the simulation. Within each model transition towards the lower or higher fidelity system's model (which may be viewed as the instantaneous application or release of system's internal constraints), the generalized momentum of the system must be conserved to arrive at the physically meaningful post-transition system's states. It is also demonstrated that within the transitions to the finer-scale models, some issues arise which are associated with the proper amount and place of the energy within the system. Given the central role that multibody dynamics plays in the presented framework, a suite of Generalized Divide-and-Conquer Algorithms-based approaches is employed to this end, since these methods offer a good combination of computational efficiency and modular structure. The computational complexity of the algorithm is O(n) and O(logn) in serial and parallel implementations, respectively, where denotes the number of degrees of freedom of the system.