Nonlinear vs. linear biasing in Trp-cage folding simulations.

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.

[1]  Massimiliano Bonomi,et al.  Reconstructing the equilibrium Boltzmann distribution from well‐tempered metadynamics , 2009, J. Comput. Chem..

[2]  W. C. Still,et al.  The GB/SA Continuum Model for Solvation. A Fast Analytical Method for the Calculation of Approximate Born Radii , 1997 .

[3]  M. Parrinello,et al.  From metadynamics to dynamics. , 2013, Physical review letters.

[4]  Marino Arroyo,et al.  Topological obstructions in the way of data-driven collective variables. , 2015, The Journal of chemical physics.

[5]  Vojtěch Spiwok,et al.  Metadynamics in the conformational space nonlinearly dimensionally reduced by Isomap. , 2011, The Journal of chemical physics.

[6]  R. Dror,et al.  How Fast-Folding Proteins Fold , 2011, Science.

[7]  Vojtech Spiwok,et al.  Metadynamics in essential coordinates: free energy simulation of conformational changes. , 2007, The journal of physical chemistry. B.

[8]  H. Berendsen,et al.  Essential dynamics of proteins , 1993, Proteins.

[9]  P. Kollman,et al.  A Second Generation Force Field for the Simulation of Proteins, Nucleic Acids, and Organic Molecules , 1995 .

[10]  Marino Arroyo,et al.  Modeling and enhanced sampling of molecular systems with smooth and nonlinear data-driven collective variables. , 2013, The Journal of chemical physics.

[11]  J. Tenenbaum,et al.  A global geometric framework for nonlinear dimensionality reduction. , 2000, Science.

[12]  William Swope,et al.  Understanding folding and design: Replica-exchange simulations of ``Trp-cage'' miniproteins , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[13]  A. Laio,et al.  Escaping free-energy minima , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[14]  Francesco Luigi Gervasio,et al.  From A to B in free energy space. , 2007, The Journal of chemical physics.

[15]  M. Parrinello,et al.  Well-tempered metadynamics: a smoothly converging and tunable free-energy method. , 2008, Physical review letters.

[16]  A. Laio,et al.  Free-energy landscape for beta hairpin folding from combined parallel tempering and metadynamics. , 2006, Journal of the American Chemical Society.

[17]  Massimiliano Bonomi,et al.  PLUMED: A portable plugin for free-energy calculations with molecular dynamics , 2009, Comput. Phys. Commun..

[18]  Michele Parrinello,et al.  Using sketch-map coordinates to analyze and bias molecular dynamics simulations , 2012, Proceedings of the National Academy of Sciences.

[19]  P. Kollman,et al.  Pathways to a protein folding intermediate observed in a 1-microsecond simulation in aqueous solution. , 1998, Science.

[20]  J. W. Neidigh,et al.  Designing a 20-residue protein , 2002, Nature Structural Biology.

[21]  Shibasish Chowdhury,et al.  Ab initio folding simulation of the Trp-cage mini-protein approaches NMR resolution. , 2003, Journal of molecular biology.

[22]  M. Parrinello,et al.  Canonical sampling through velocity rescaling. , 2007, The Journal of chemical physics.

[23]  A. Laio,et al.  Assessing the accuracy of metadynamics. , 2005, The journal of physical chemistry. B.

[24]  Carsten Kutzner,et al.  GROMACS 4:  Algorithms for Highly Efficient, Load-Balanced, and Scalable Molecular Simulation. , 2008, Journal of chemical theory and computation.

[25]  Lydia E Kavraki,et al.  Low-dimensional, free-energy landscapes of protein-folding reactions by nonlinear dimensionality reduction , 2006, Proc. Natl. Acad. Sci. USA.

[26]  Francesco Luigi Gervasio,et al.  Comparing the Efficiency of Biased and Unbiased Molecular Dynamics in Reconstructing the Free Energy Landscape of Met-Enkephalin , 2010 .

[27]  Vojtěch Spiwok,et al.  Continuous metadynamics in essential coordinates as a tool for free energy modelling of conformational changes , 2008, Journal of molecular modeling.