Optimization problem in biomolecular simulations with DCA-based modeling of transition from a coarse to a fine fidelity

In multiscale modeling of highly complex biomolecular systems, it is desirable to switch the system model either to coarser, or higher fidelity models to achieve the appropriate accuracy and speed. These transitions are achieved by effectively imposing (or releasing) certain systems constraints from a fine scale model to a reduced order model (or vice versa). The transition from a coarse model to a fine one may not result in a unique solution. Therefore, a knowledge-based or physics-based optimization procedure may be used to arrive at the finite number of solutions. In this paper, it is shown that traditional approaches to address and solve the optimization problem such as Lagrange multipliers or changing the constrained optimization problem to an unconstrained one based on coordinate partitioning or basic linear algebra methods are computationally expensive for biomolecular systems. It is demonstrated that using a DCA based approach in modeling the transition can reduce dramatically the computational expense associated with the manipulations performed as part of optimization as well as the ones performed to derive the dynamics of the transition.