Onsager-Machlup action-based path sampling and its combination with replica exchange for diffusive and multiple pathways

For sampling multiple pathways in a rugged energy landscape, we propose a novel action-based path sampling method using the Onsager-Machlup action functional. Inspired by the Fourier-path integral simulation of a quantum mechanical system, a path in Cartesian space is transformed into that in Fourier space, and an overdamped Langevin equation is derived for the Fourier components to achieve a canonical ensemble of the path at a finite temperature. To avoid "path trapping" around an initially guessed path, the path sampling method is further combined with a powerful sampling technique, the replica exchange method. The principle and algorithm of our method is numerically demonstrated for a model two-dimensional system with a bifurcated potential landscape. The results are compared with those of conventional transition path sampling and the equilibrium theory, and the error due to path discretization is also discussed.Comment: 20 pages, 5 figures, submitted to J. Chem. Phy

Self-learning Multiscale Simulation for Achieving High Accuracy and High Efficiency Simultaneously

We propose a new multi-scale molecular dynamics simulation method which can achieve high accuracy and high sampling efficiency simultaneously without aforehand knowledge of the coarse grained (CG) potential and test it for a biomolecular system. Based on the resolution exchange simulations between atomistic and CG replicas, a self-learning strategy is introduced to progressively improve the CG potential by an iterative way. Two tests show that, the new method can rapidly improve the CG potential and achieve efficient sampling even starting from an unrealistic CG potential. The resulting free energy agreed well with exact result and the convergence by the method was much faster than that by the replica exchange method. The method is generic and can be applied to many biological as well as non-biological problems.Comment: 14 pages, 6 figure

Directly measuring single molecule heterogeneity using force spectroscopy

One of the most intriguing results of single molecule experiments on proteins and nucleic acids is the discovery of functional heterogeneity: the observation that complex cellular machines exhibit multiple, biologically active conformations. The structural differences between these conformations may be subtle, but each distinct state can be remarkably long-lived, with random interconversions between states occurring only at macroscopic timescales, fractions of a second or longer. Though we now have proof of functional heterogeneity in a handful of systems---enzymes, motors, adhesion complexes---identifying and measuring it remains a formidable challenge. Here we show that evidence of this phenomenon is more widespread than previously known, encoded in data collected from some of the most well-established single molecule techniques: AFM or optical tweezer pulling experiments. We present a theoretical procedure for analyzing distributions of rupture/unfolding forces recorded at different pulling speeds. This results in a single parameter, quantifying the degree of heterogeneity, and also leads to bounds on the equilibration and conformational interconversion timescales. Surveying ten published datasets, we find heterogeneity in five of them, all with interconversion rates slower than 10 s$^{-1}$. Moreover, we identify two systems where additional data at realizable pulling velocities is likely to find a theoretically predicted, but so far unobserved cross-over regime between heterogeneous and non-heterogeneous behavior. The significance of this regime is that it will allow far more precise estimates of the slow conformational switching times, one of the least understood aspects of functional heterogeneity.Comment: Main text: 13 pages, 6 figures; SI: 9 pages, 6 figure

Recurrence quantification analysis as a tool for the characterization of molecular dynamics simulations

A molecular dynamics simulation of a Lennard-Jones fluid, and a trajectory of the B1 immunoglobulin G-binding domain of streptococcal protein G (B1-IgG) simulated in water are analyzed by recurrence quantification, which is noteworthy for its independence from stationarity constraints, as well as its ability to detect transients, and both linear and nonlinear state changes. The results demonstrate the sensitivity of the technique for the discrimination of phase sensitive dynamics. Physical interpretation of the recurrence measures is also discussed.Comment: 7 pages, 8 figures, revtex; revised for review for Phys. Rev. E (clarifications and expansion of discussion)-- addition of the 8 postscript figures previously omitted, but unchanged from version

Monte Carlo, harmonic approximation, and coarse-graining approaches for enhanced sampling of biomolecular structure

The rugged energy landscape of biomolecules and associated large-scale conformational changes have triggered the development of many innovative enhanced sampling methods, either based or not based on molecular dynamics (MD) simulations. Surveyed here are methods in the latter class - including Monte Carlo methods, harmonic approximations, and coarse graining - many of which yield valuable conformational insights into biomolecular structure and flexibility, despite altered kinetics. MD-based methods are surveyed in an upcoming issue of F1000 Biology Reports