Normal mode partitioning of Langevin dynamics forbiomolecules

• Published in: The Journal of chemical physics Vol. 128; no. 14
• Main Authors: Sweet, Christopher R, Petrone, Paula, Pande, Vijay S, Izaguirre, Jesús A
• Format: Journal Article
• Language: English
• Published: Melville American Institute of Physics 14.04.2008
• Subjects: Alanine; Biomolecules; Eigenvalues; Eigenvectors; Hessian matrices; Integrators; Propagation modes; Sampling; Trypsin inhibitors
• ISSN: 0021-9606; 1089-7690
• DOI: 10.1063/1.2883966

We propose a novel normalmode multiple time stepping Langevin dynamics integrator called NML. The aim is toapproximate the kinetics or thermodynamics of a biomolecule by a reduced model based on anormal modedecomposition of the dynamical space. Our basis set uses the eigenvectors of a massreweighted Hessian matrix calculated with a biomolecular force field. This particularchoice has the advantage of an ordering according to the eigenvalues, which have aphysical meaning of being the square of the mode frequency. Low frequency eigenvalues correspond to morecollective motions, whereas the highest frequency eigenvalues are the limitingfactor for the stability of the integrator. In NML, the higher frequency modes areoverdamped and relaxed near their energy minimum while respecting the subspace of low frequencydynamical modes. Our numerical results confirm that both sampling and rates are conservedfor an implicitly solvated alanine dipeptide model, with only 30% of the modes propagated,when compared to the full model. For implicitly solvated systems, NML gives a twofoldimprovement in efficiency over plain Langevin dynamics for sampling a small 22 atom (alaninedipeptide) model and in excess of an order of magnitude for sampling an 882 atom (bovinepancreatic trypsin inhibitor) model, with good scaling with system size subject to thenumber of modes propagated. NML has been implemented in the open source softwarePROTOMOL.