Harmonic and anharmonic aspects in the dynamics of BPTI: A normal mode analysis and principal component analysis

Abstract

A comparison is made between a 200-ps molecular dynamics simulation in vacuum and a normal mode analysis on the protein bovine pancreatic trypsin inhibitor (BPTI) in order to elucidate the dual aspects of harmonicity and anharmonicity in the dynamics of proteins. The molecular dynamics trajectory is analyzed using principal component analysis, an effective harmonic analysis suited for comparison with the results from the normal mode analysis. The results suggest that the first principal component shows qualitatively different behavior from higher principal components and is associated with apparent barrier crossing events on an anharmonic conformational energy surface. The higher principal components appear to have probability distributions that are well approximated by Gaussians, indicating harmonicity. Eliminating the contribution from the first principal component reveals a great deal of correspondence between the 2 methods. This correspondence, however, involves a factor of 2, as the variances of the distributions of the higher principal components are, on average, roughly twice those found from the normal mode analysis. A model is proposed to reconcile these results with those from previous analyses.

Correlated motions are a fundamental property of β-sheets

“…3, which highlights the regions in which long-range correlations are observed in 12 selected proteins. The first principal component of MD trajectories is known to be the most anharmonic one and is often associated with biologically relevant motions 38,39 . We note that using the first five PCA components gives the same result as using the first normal modes because the first modes concentrate most of the structural variance (Supplementary Table 2).…”

Differential binding of p53 and nutlin to MDM2 and MDMX: Computational studies

“…The technique of principal component analysis (PCA) is the most widely used for this purpose. [54][55][56][57] This technique decomposes the intrinsic flexibility of a protein into motions of different frequencies of vibrations. These are then ordered such that the first component (PC1) characterizes the motion with the largest amplitude and lowest frequency.…”

Global motions exhibited by proteins in micro- to milliseconds simulations concur with anisotropic network model predictions

“…BPTI is a widely studied small protein, with several high-resolution crystal structures resolved since 1975. 16 It served as the subject macromolecule of the first reported MD simulation, 17 and since then its dynamics have been extensively studied by MD, [18][19][20][21][22][23] NMA, [24][25][26][27][28] and experiments. [29][30][31][32][33] We will use its recent Anton trajectory of 1.013 ms, which proved to reproduce numerous experimental findings, 10 as a benchmark for establishing the method for analyzing the output from simulations and comparing the extracted information with ANM predictions.…”