Principal component analysis of fast-folding λ-repressor mutants

Distributions of experimental protein structures on coarse-grained free energy landscapes

Predicting conformational changes of proteins is needed in order to fully comprehend functional mechanisms. With the large number of available structures in sets of related proteins, it is now possible to directly visualize the clusters of conformations and their conformational transitions through the use of principal component analysis. The most striking observation about the distributions of the structures along the principal components is their highly non-uniform distributions. In this work, we use principal component analysis of experimental structures of 50 diverse proteins to extract the most important directions of their motions, sample structures along these directions, and estimate their free energy landscapes by combining knowledge-based potentials and entropy computed from elastic network models. When these resulting motions are visualized upon their coarse-grained free energy landscapes, the basis for conformational pathways becomes readily apparent. Using three well-studied proteins, T4 lysozyme, serum albumin, and sarco-endoplasmic reticular Ca(2+) adenosine triphosphatase (SERCA), as examples, we show that such free energy landscapes of conformational changes provide meaningful insights into the functional dynamics and suggest transition pathways between different conformational states. As a further example, we also show that Monte Carlo simulations on the coarse-grained landscape of HIV-1 protease can directly yield pathways for force-driven conformational changes.

Structural and mechanistic insight into substrate binding from the conformational dynamics in apo and substrate-bound DapE enzyme

Conformational dynamics induced by substrate binding in DapE enzyme.

Near native-state conformational landscape of psychrophilic and mesophilic enzymes: probing the folding funnel model

In recent years, increased interest has been directed to the study of enzyme adaptation to low temperatures. In particular, a peculiar folding funnel model was proposed for the free energy landscape of a psychrophilic alpha-amylase and other cold-adapted enzymes. In the present contribution, the comparison between the near native-state dynamics and conformational landscape in the essential subspace of different cold-adapted enzymes with their mesophilic counterparts, as obtained by more than 0.1 micros molecular dynamics simulations at different temperatures, allows the folding funnel model to be probed. Common characteristics were highlighted in the near native-state dynamics of psychrophilic enzymes belonging to different enzymatic families when compared to the mesophilic counterparts. According to the model, a cold-adapted enzyme in its native-state consists of a large population of conformations which can easily interconvert and result in high structural flexibility.

Cooperativity at different space and time scales in multiscale protein dynamics

A method proposed by Matsunaga [Phys. Rev. Lett. 99, 238103 (2007)] is applied to simple stochastic models and two model proteins composed of 46 amino beads with three different kinds of residues. The method, which is based on the combination of the principal component analysis and the finite size Lyapunov exponent, characterize the coarse-grained dynamics in different spatiotemporal hierarchies in protein dynamics. The application of the method to model proteins reveals that the low-indexed (large-variance) principal components carry less-divergent, regularized dynamics at the coarse-grained scales on a less-frustrated energy landscape, whereas this less-divergent nature is less pronounced for a protein model with a more frustrated energy landscape. It is also revealed that our technique can differentiate the collective motions on the projected principal component space inherent to the system and the apparent collective behavior which can appear even in high-dimensional stochastic systems.

Systematic study of anharmonic features in a principal component analysis of gramicidin A

We use principal component analysis (PCA) to detect functionally interesting collective motions in molecular-dynamics simulations of membrane-bound gramicidin A. We examine the statistical and structural properties of all PCA eigenvectors and eigenvalues for the backbone and side-chain atoms. All eigenvalue spectra show two distinct power-law scaling regimes, quantitatively separating large from small covariance motions. Time trajectories of the largest PCs converge to Gaussian distributions at long timescales, but groups of small-covariance PCs, which are usually ignored as noise, have subdiffusive distributions. These non-Gaussian distributions imply anharmonic motions on the free-energy surface. We characterize the anharmonic components of motion by analyzing the mean-square displacement for all PCs. The subdiffusive components reveal picosecond-scale oscillations in the mean-square displacement at frequencies consistent with infrared measurements. In this regime, the slowest backbone mode exhibits tilting of the peptide planes, which allows carbonyl oxygen atoms to provide surrogate solvation for water and cation transport in the channel lumen. Higher-frequency modes are also apparent, and we describe their vibrational spectra. Our findings expand the utility of PCA for quantifying the essential features of motion on the anharmonic free-energy surface made accessible by atomistic molecular-dynamics simulations.

The pathway of oligomeric DNA melting investigated by molecular dynamics simulations

Details of the reaction coordinate for DNA melting are fundamental to much of biology and biotechnology. Recently, it has been shown experimentally that there are at least three states involved. To clarify the reaction mechanism of the melting transition of DNA, we perform 100-ns molecular dynamics simulations of a homo-oligomeric, 12-basepair DNA duplex, d(A(12)).d(T(12)), with explicit salt water at 400 K. Analysis of the trajectory reveals the various biochemically important processes that occur on different timescales. Peeling (including fraying from the ends), searching for Watson-Crick complements, and dissociation are recognizable processes. However, we find that basepair searching for Watson-Crick complements along a strand is not mechanistically tied to or directly accessible from the dissociation steps of strand melting. A three-step melting mechanism is proposed where the untwisting of the duplex is determined to be the major component of the reaction coordinate at the barrier. Though the observations are limited to the characteristics of the system being studied, they provide important insight into the mechanism of melting of other more biologically relevant forms of DNA, which will certainly differ in details from those here.

Principal component analysis for protein folding dynamics

Protein folding is considered here by studying the dynamics of the folding of the triple beta-strand WW domain from the Formin-binding protein 28. Starting from the unfolded state and ending either in the native or nonnative conformational states, trajectories are generated with the coarse-grained united residue (UNRES) force field. The effectiveness of principal components analysis (PCA), an already established mathematical technique for finding global, correlated motions in atomic simulations of proteins, is evaluated here for coarse-grained trajectories. The problems related to PCA and their solutions are discussed. The folding and nonfolding of proteins are examined with free-energy landscapes. Detailed analyses of many folding and nonfolding trajectories at different temperatures show that PCA is very efficient for characterizing the general folding and nonfolding features of proteins. It is shown that the first principal component captures and describes in detail the dynamics of a system. Anomalous diffusion in the folding/nonfolding dynamics is examined by the mean-square displacement (MSD) and the fractional diffusion and fractional kinetic equations. The collisionless (or ballistic) behavior of a polypeptide undergoing Brownian motion along the first few principal components is accounted for.

Free energy landscape of a biomolecule in dihedral principal component space: sampling convergence and correspondence between structures and minima

Dihedral principal component analysis (dPCA) has recently been developed and shown to display complex features of the free energy landscape of a biomolecule that may be absent in the free energy landscape plotted in principal component space due to mixing of internal and overall rotational motion that can occur in principal component analysis (PCA) [Mu et al., Proteins: Struct Funct Bioinfo 2005;58:45-52]. Another difficulty in the implementation of PCA is sampling convergence, which we address here for both dPCA and PCA using a tetrapeptide as an example. We find that for both methods the sampling convergence can be reached over a similar time. Minima in the free energy landscape in the space of the two largest dihedral principal components often correspond to unique structures, though we also find some distinct minima to correspond to the same structure.