Communication: Microsecond peptide dynamics from nanosecond trajectories: A Langevin approach

Abstract

Based on a given time series, the data-driven Langevin equation (dLE) estimates the drift and the diffusion field of the dynamics, which are then employed to reproduce the essential statistical and dynamical features of the original time series. Because the propagation of the dLE requires only local information, the input data are neither required to be Boltzmann weighted nor to be a continuous trajectory. Similar to a Markov state model, the dLE approach therefore holds the promise of predicting the long-time dynamics of a biomolecular system from relatively short trajectories which can be run in parallel. The practical applicability of the approach is shown to be mainly limited by the initial sampling of the system's conformational space obtained from the short trajectories. Adopting extensive molecular dynamics simulations of the unfolding and refolding of a short peptide helix, it is shown that the dLE approach is able to describe microsecond conformational dynamics from a few hundred nanosecond trajectories. In particular, the dLE quantitatively reproduces the free energy landscape and the associated conformational dynamics along the chosen five-dimensional reaction coordinate. C 2014 AIP Publishing LLC. [http://dx

Multidimensional Langevin Modeling of Nonoverdamped Dynamics

“…Given a time series xðtÞ, the basic idea of data-driven Langevin equation (dLE) modeling is to determine the Langevin fields h and D, which together with the properties of the noise constitute the desired dynamical model. The model can then be employed to forecast the essential statistical and dynamical features of the original time series, to predict the system's long-time behavior from many (but short) pieces of input data, and for interpretation purposes [4][5][6][7][8][9][10].…”

“…Otherwise, we may not obtain a consistent dynamical model that correctly reproduces the statistics and dynamics of the input data and satisfies as well the implied assumptions on the noise. As a prime application, the above described approach has been employed to model classical molecular dynamics (MD) simulations [4][5][6][7][8][9][10]. Using a systematic dimensionality reduction method (see below), one can always enforce a system-bath time scale separation at the expense of a higher dimension of the reaction coordinate.…”

Data-driven Langevin modeling of nonequilibrium processes

“…This local information does not require global equilibrium data, but can be readily obtained from short nonstationary data. 31 Secondly, we note that the dLE of time series x(t) in Eq. ( 2) does not involve the mass tensor m, because it is included in the definition of the dLE fields.…”

“…As explained in Section II A, this is possible because dLE fields as well as MSM transition matrices are calculated locally. 31 As short MD trajectories per se represent nonstationary data, there is again the question on the convergence of the dLE model with respect to their number and length (see Sec. III A).…”

“…30 In both cases, a simple Langevin model is constructed that is shown to reproduce well the underlying MD reference data. As a Langevin-based enhanced sampling strategy, 31 we finally consider the construction of a global Langevin model that accounts for the overall kinetics of the system, obtained from massive parallel computing of short MD trajectories that are per se nonstationary. Modeling the conformational dynamics of the helical peptide Aib 9 in five dimensions, 32 we compare the predictions of the resulting dLE to a recently established Markov state model of the system.…”