Optimization problem and efficient partitioning algorithm for transitions to finer-scale models in adaptive resolution simulation of articulated biopolymers

Adaptive coarse graining of highly complex biomolecular systems is conducted by either imposing constraints on the system model to generate a coarser model, or releasing certain constraints from it to create a higher fidelity one. This paper addresses some of the challenges of transitions to finer-scale models. It is shown that the kinetic energy associated with ignored modes of motion during the coarse graining process must be estimated and put back into the simulation. As such, unlike real mechanical systems, transitioning back to a finer biomolecular model may result in an infinite number of solutions. Herein, an optimization-based approach subject to the satisfaction of impulse–momentum balance and desired kinetic energy is presented to arrive at a physically meaningful state of the system immediately after the transition. In order to reduce the cost of formulating and solving this optimization problem, generalized velocities of the system are partitioned into two categories: independent joint velocities associated with the released joints, and dependent joint velocities associated with the rest of the joints. This paper further develops a divide-and-conquer algorithm to efficiently perform this partitioning process and express dependent velocities in terms of independent ones. The presented method is highly parallelizable and avoids the construction of the mass and Jacobian matrices of the entire system, resulting in a significant improvement in computational efficiency.