Biased simulations have great potential for the study of slow processes, including protein folding. Atomic motions in molecules are nonlinear, which suggests that simulations with enhanced sampling of collective motions traced by nonlinear dimensionality reduction methods may perform better than linear ones. In this study, we compare an unbiased folding simulation of the Trp-cage miniprotein with metadynamics simulations using both linear (principle component analysis) and nonlinear (Isomap) low dimensional embeddings as collective variables. Folding of the mini-protein was successfully simulated in 200 ns simulation with linear biasing and non-linear motion biasing. The folded state was correctly predicted as the free energy minimum in both simulations. We found that the advantage of linear motion biasing is that it can sample a larger conformational space, whereas the advantage of nonlinear motion biasing lies in slightly better resolution of the resulting free energy surface. In terms of sampling efficiency, both methods are comparable.

Department of Biochemistry and Microbiology University of Chemistry and Technology Prague Technická 3 Prague 6 166 28 Czech Republic

Institute of Computer Science Masaryk University Botanická 554 68a 602 00 Brno Czech Republic

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