A theoretical model for the collective motion of proteins by means of principal component analysis

Abstract

Abstract:A coarse grained model in the frame work of principal component analysis is presented. We used a bath of harmonic oscillators approach, based on classical mechanics, to derive the generalized Langevin equations of motion for the collective coordinates. The dynamics of the protein collective coordinates derived from molecular dynamics simulations have been studied for the Bovine Pancreatic Trypsin Inhibitor. We analyzed the stability of the method by studying structural fluctuations of the C α atoms obtained from a 20 ns molecular dynamics simulation. Subsequently, the dynamics of the collective coordinates of protein were characterized by calculating the dynamical friction coefficient and diffusion coefficients along with time-dependent correlation functions of collective coordinates. A dual diffusion behavior was observed with a fast relaxation time of short diffusion regime 0 2 − 0 4 ps and slow relaxation time of long diffusion about 1 − 2 ps. In addition, we observed a power law decay of dynamical friction coefficient with exponent for the first five collective coordinates varying from −0 746 to −0 938 for the real part and from −0 528 to −0 665 for its magnitude. It was found that only the first ten collective coordinates are responsible for configuration transitions occurring on time scale longer than 50 ps.

Computation of the memory functions in the generalized Langevin models for collective dynamics of macromolecules

“…[10][11][12][13] The model, which in theory could describe a system far from equilibrium, 13 has been considered by many researchers over the years. [14][15][16][17][18][19][20][21][22][23] The MZ projection procedure, when the conditional expectation is used as projector, yields an averaged force, which is consistent with that in the PMF approach. 11,18,24 In addition, the formalism gives rise to a history-dependent term, which with reasonable approximations, simplifies to a linear convolutional term with a memory function, and a random noise term, which is consistent with the memory function via the second fluctuation-dissipation theorem (FDT).…”

“…(A7) obtained from (35) and (17). The correspondence with the average force in GLE (41), −∇ q W (q, k B T ), is more subtle.…”

“…This has been the approach followed by many other groups. 17,18,20 In general, the calculation of VACF tends to be expensive due to the large size of the system. More importantly, the sampling of the random noise is still a challenge.…”

Symbolic Information Flow Measurement (SIFM): A Software for Measurement of Information Flow Using Symbolic Analysis

“…We have discussed in details the PCA algorithm in Ref. [21] In this study, we aim to introduce a new algorithm, which is an improved version of the auto-encoder machine learning approach [22] to the algorithm of determining the collective variables from higher dimensionality data. Machine Learning (ML) approach provides a potential method to predict the properties of a system using decision-making algorithms, based on some predefined features characterizing these properties of the system.…”

Calculating Transfer Entropy from Variance–Covariance Matrices Provides Insight into Allosteric Communication in ERK2

“…5,6,13 One significant drawback of these approximate methods is that, because there is no sensitivity to side chain identity or motions, there is limited utility for these methods in mutation studies, which are often of great interest in biomolecular systems. 5,14 Here we demonstrate a method that balances these two considerations: one that is fast enough for practical use but sensitive enough to the chemical nature of the protein to be capable of studying the effects of amino acid mutations on the information transfer and allosteric behavior of the protein. In this method, the transfer entropy is extracted from the variancecovariance matrix derived from short simulations (which converge on a timescale of 5-20ns 15 ) and computed using the formalism of the dynamic Gaussian Network Model (dGNM), since the covariance matrix is known to be inversely proportional to the contact (Kirchoff) matrix used as the basis for the GNM method.…”