Realistic transition paths for large biomolecular systems: A Langevin bridge approach

We introduce a computational framework for generating realistic transition paths between distinct conformations of large biomolecular systems. The method is built on a stochastic integro-differential formulation derived from the Langevin bridge formalism, which constrains molecular trajectories to reach a prescribed final state within a finite time and yields an efficient low-temperature approximation of the exact bridge equation. To obtain physically meaningful protein transitions, we couple this formulation to a new coarse-grained potential, combining a Gō-like term that preserves native backbone geometry with a Rouse-type elastic energy term from polymer physics; we refer to the resulting approach as the Stochastic Integro-Differential Equation (SIDE). We evaluate SIDE on several proteins undergoing large-scale conformational changes and compare its performance with established methods, such as MinActionPath and eBDIMS. SIDE generates smooth, low-energy trajectories that maintain molecular geometry and frequently recover experimentally supported intermediate states. Although challenges remain for highly complex motions-largely due to the simplified coarse-grained potential-our results demonstrate that SIDE offers a powerful and computationally efficient strategy for modeling biomolecular conformational transitions.