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Numerical simulations of protein folding enable the design of protein-based nanomachines and nanorobots by predicting folded three-dimensional protein structures with high accuracy and revealing the protein conformation transitions during folding and unfolding. In the kinetostatic compliance method (KCM) for folding simulations, protein molecules are represented as ensembles of rigid nano-linkages connected by chemical bonds, and the folding process is driven by the kinetostatic influence of nonlinear interatomic force fields until the system converges to a free-energy minimum of the protein. Despite its strengths, the conventional KCM framework demands an excessive number of iterations to reach folded protein conformations, with each iteration requiring costly computations of interatomic force fields. To address these limitations, this work introduces a family of sign gradient descent (SGD) algorithms for predicting folded protein structures. Unlike the heuristic-based iterations of the conventional KCM framework, the proposed SGD algorithms rely on the sign of the free-energy gradient to guide the kinetostatic folding process. Owing to their faster and more robust convergence, the proposed SGD-based algorithms reduce the computational burden of interatomic force field evaluations required to reach folded conformations. Their effectiveness is demonstrated through numerical simulations of KCM-based folding of protein backbone chains.