Analysis of Protein Dynamics Simulations by a Stochastic Point Process Approach

Abstract

MD simulations can now explore the complex dynamics of proteins and their associated solvent in atomic detail on a millisecond time scale. Among the phenomena that thereby become amenable to detailed study are intermittent conformational transitions where the protein accesses transient high-energy states that often play key roles in biology. Here, we present a coherent theoretical framework, based on the stochastic theory of stationary point processes, that allows the essential dynamical characteristics of such processes to be efficiently extracted from the MD trajectory without assuming Poisson statistics. Since the complete information content of a point process is contained in the sequence of residence or interevent times, the experimentally relevant survival correlation function can be computed several orders of magnitude more efficiently than with the conventional approach, involving averaging over initial times. We also present a detailed analysis of the statistical and binning errors, of particular importance when MD results are compared with experiment. As an illustration of the general theoretical framework, we use a 1 ms MD trajectory of the protein BPTI to analyze the exchange kinetics of an internal water molecule and the dynamics of the rare conformational fluctuations that govern the rate of this exchange process.

Transient Access to the Protein Interior: Simulation versus NMR

“…In analyzing the quasi-continuous MD trajectory, we can therefore model internalwater exchange as a stationary point process. 36−38 A comprehensive account of this rather general stochastic approach can be found elsewhere; 39 here we merely sketch the key points.…”

“…The RT and ST statistics presented here are subject to a systematic binning error and a random statistical error. 39 The binning error is due to the replacement of the quasi-continuous RT probability density by a discrete RT histogram and to the possibility that exchange events can escape detection when the trajectory is sampled at a finite resolution Δτ. 39 Because the STs of interest here are much longer than Δτ, the binning error is unimportant.…”

“…39 The binning error is due to the replacement of the quasi-continuous RT probability density by a discrete RT histogram and to the possibility that exchange events can escape detection when the trajectory is sampled at a finite resolution Δτ. 39 Because the STs of interest here are much longer than Δτ, the binning error is unimportant. The statistical error arises because the RT ensemble is incompletely sampled by a trajectory of finite length.…”

“…A comprehensive tretament of the binning and statistical errors in point process analysis of MD trajectories has been presented. 39 Multiexponential deconvolution of the SCF was performed with the non-negative least-squares (NNLS) algorithm, 43,44 which is more robust than nonlinear optimization methods and does not require an a priori assumption about the number of exponentials. So as not to place undue weight on long τ values, we resampled the SCF by selecting 100 points uniformly spaced along the curve in a semilog plot.…”

Point processes with Gaussian boson sampling

“…Similarly, point process analysis is a quantitative statistical method for analyzing such point patterns to provide information that can be used for prediction and planning purposes [10]. This finds applications in a variety of fields such as finance [11][12][13][14], seismology [15][16][17], biology [18][19][20], medicine [21][22][23], ecology [24][25][26][27][28], physics [29][30][31][32], and chemistry [33][34][35][36][37].…”