Computational studies on the conformations of some large‐ring cyclodextrins (CDn,n = 20, 21, 22, 23)

Computational studies were carried out on the conformations of large‐ring cyclodextrins with degree of polymerization from 20 to 23. Principal component analysis (PCA) was applied for postprocessing of trajectories from conformational search, based on 100.0 ns molecular dynamics simulations. The dominant PCA modes for concerted motions of the macroring atoms were monitored in a lower‐dimensions subspace. The first six lowest indexed principal components contribute more than 90% of the total atomic motions in all cases, with about 70% (CD21) to 83% (CD22) contribution coming from the three highest‐eigenvalue principal components. Representative average geometries of the cyclodextrin macrorings were also obtained for the whole simulation and for the ten 10.0 ns time intervals of the simulation. We concluded that resemblance exists of the representative conformations of these four cyclodextrins with the circularized three‐turn single helical structure proposed for CD21 from small‐angle X‐ray scattering, as well as with the representative conformations of CD26. Chirality, 2011. © 2011 Wiley‐Liss, Inc.     

Energy landscape of a native protein: Jumping-among-minima model

We have investigated energy landscape of human lysozyme in its native state by using principal component analysis and a model, jumping-among-minima (JAM) model. These analyses are applied to 1 nsec molecular dynamics trajectory of the protein in water. An assumption embodied in the JAM model allows us to divide protein motions into intra-substate and inter-substate motions. By examining intra-substate motions, it is shown that energy surfaces of individual conformational substates are nearly harmonic and mutually similar. As a result of principal component analysis and JAM model analysis, protein motions are shown to consist of three types of collective modes, multiply hierarchical modes, singly hierarchical modes, and harmonic modes. Multiply hierarchical modes, the number of which accounts only for 0.5% of all modes, dominate contributions to total mean-square atomic fluctuation. Inter-substate motions are observed only in a small-dimensional subspace spanned by the axes of multiplyhierarchical and singly hierarchical modes. Inter-substate motions have two notable time components: faster component seen within 200 psec and slower component. The former involves transitions among the conformational substates of the low-level hierarchy, whereas the latter involves transitions of the higher level substates observed along the first four multiply hierarchical modes. We also discuss dependence of the subspace, which contains conformational substates, on time duration of simulation. Proteins 33:496–517, 1998. © 1998 Wiley-Liss, Inc.     

Principal component and clustering analysis on molecular dynamics data of the ribosomal L11·23S subdomain

With improvements in computer speed and algorithm efficiency, MD simulations are sampling larger amounts of molecular and biomolecular conformations. Being able to qualitatively and quantitatively sift these conformations into meaningful groups is a difficult and important task, especially when considering the structure-activity paradigm. Here we present a study that combines two popular techniques, principal component (PC) analysis and clustering, for revealing major conformational changes that occur in molecular dynamics (MD) simulations. Specifically, we explored how clustering different PC subspaces effects the resulting clusters versus clustering the complete trajectory data. As a case example, we used the trajectory data from an explicitly solvated simulation of a bacteria’s L11·23S ribosomal subdomain, which is a target of thiopeptide antibiotics. Clustering was performed, using K-means and average-linkage algorithms, on data involving the first two to the first five PC subspace dimensions. For the average-linkage algorithm we found that data-point membership, cluster shape, and cluster size depended on the selected PC subspace data. In contrast, K-means provided very consistent results regardless of the selected subspace. Since we present results on a single model system, generalization concerning the clustering of different PC subspaces of other molecular systems is currently premature. However, our hope is that this study illustrates a) the complexities in selecting the appropriate clustering algorithm, b) the complexities in interpreting and validating their results, and c) by combining PC analysis with subsequent clustering valuable dynamic and conformational information can be obtained.     

Complexity of free energy landscapes of peptides revealed by nonlinear principal component analysis

Employing the recently developed hierarchical nonlinear principal component analysis (NLPCA) method of Saegusa et al. (Neurocomputing 2004;61:57-70 and IEICE Trans Inf Syst 2005;E88-D:2242-2248), the complexities of the free energy landscapes of several peptides, including triglycine, hexaalanine, and the C-terminal beta-hairpin of protein G, were studied. First, the performance of this NLPCA method was compared with the standard linear principal component analysis (PCA). In particular, we compared two methods according to (1) the ability of the dimensionality reduction and (2) the efficient representation of peptide conformations in low-dimensional spaces spanned by the first few principal components. The study revealed that NLPCA reduces the dimensionality of the considered systems much better, than did PCA. For example, in order to get the similar error, which is due to representation of the original data of beta-hairpin in low dimensional space, one needs 4 and 21 principal components of NLPCA and PCA, respectively. Second, by representing the free energy landscapes of the considered systems as a function of the first two principal components obtained from PCA, we obtained the relatively well-structured free energy landscapes. In contrast, the free energy landscapes of NLPCA are much more complicated, exhibiting many states which are hidden in the PCA maps, especially in the unfolded regions. Furthermore, the study also showed that many states in the PCA maps are mixed up by several peptide conformations, while those of the NLPCA maps are more pure. This finding suggests that the NLPCA should be used to capture the essential features of the systems.     

Application of projection pursuit based robust principal component analysis to ECG enhancement

The paper presents an application of principal component analysis (PCA) to ECG processing. For this purpose the ECG beats are time-aligned and stored in the columns of an auxiliary matrix. The matrix, considered as a set of multidimensional variables, undergoes PCA. Reconstruction of the respective columns on the basis of a low dimensional principal subspace leads to the enhancement of the stored ECG beats. A few modifications of this classical approach to ECG signal filtering by means of a multivariate analysis are introduced. The first one is based on replacing the classical PCA by its robust extension. The second consists in replacing the analysis of the whole synchronized beats by the analysis of shorter signal segments. This creates the background for the third modification, which introduces the concept of variable dimensions of the subspaces corresponding to different parts of ECG beats. The experiments performed show that introduction of the respective modifications significantly improves the classical approach to ECG processing by application of principal component analysis.     

Quantitative analysis of correlations among flower traits in Gerbera hybrida, Compositae. III. Genetic variability and structure of principal component traits

 A sample of 36 flower traits consisting of six morphological categories in the Davis population of gerbera was restructured into phenotypic and genetic principal component traits. The first 5 phenotypic principal component traits accounted for 62% of the total phenotypic variance of the 36 traits and have moderate to high heritablities. The first 5 genetic principal component traits account for 97% of total genetic variance and all have high heritability. Morphological structure of these component traits suggest an underlying process identified by the first genetic principal component involving largely trans and disk floret traits. The results of this study indicate that the quantitative genetic structure of the gerbera flower is controlled by a few independent components and that principal component analysis is a useful tool to reveal variation in this structure. These composite traits are heritable and are expected to respond to selection. Received: 20 September 1997 / Accepted: 19 January 1998     

Principal component analysis of DNA oligonucleotide structural data

The microstructure of a DNA helix is characterized by several base pair and base step parameters such as twist, rise, roll, propeller twist, etc., in addition to conformational parameters such as the backbone and the glycosidic torsion angles. Among these only a few, which are independent of all others and of each other, may be used to precisely characterize the helix. The problem however is to identify these independent parameters. We have used principal component analysis to identify a relatively small set of independent parameters, with which to characterize each DNA helix. We show that these principal components clearly discriminate between A and B DNA helical types. The calculations further suggest that the microstructure of a DNA helix is better characterized using dinucleotides.     

Conformational transition states of a beta-hairpin peptide between the ordered and disordered conformations in explicit water

The conformational transition states of a beta-hairpin peptide in explicit water were identified from the free energy landscapes obtained from the multicanonical ensemble, using an enhanced conformational sampling calculation. The beta-hairpin conformations were significant at 300 K in the landscape, and the typical nuclear Overhauser effect signals were reproduced, consistent with the previously reported experiment. In contrast, the disordered conformations were predominant at higher temperatures. Among the stable conformations at 300 K, there were several free energy barriers, which were not visible in the landscapes formed with the conventional parameters. We identified the transition states around the saddle points along the putative folding and unfolding paths between the beta-hairpin and the disordered conformations in the landscape. The characteristic features of these transition states are the predominant hydrophobic contacts and the several hydrogen bonds among the side-chains, as well as some of the backbone hydrogen bonds. The unfolding simulations at high temperatures, 400 K and 500 K, and their principal component analyses also provided estimates for the transition state conformations, which agreed well with those at 400 K and 500 K deduced from the current free energy landscapes at 400 K and 500 K, respectively. However, the transition states at high temperatures were much more widely distributed on the landscape than those at 300 K, and their conformations were different.     

A multivariate approach for integrating genome-wide expression data and biological knowledge

MOTIVATION: Several statistical methods that combine analysis of differential gene expression with biological knowledge databases have been proposed for a more rapid interpretation of expression data. However, most such methods are based on a series of univariate statistical tests and do not properly account for the complex structure of gene interactions. RESULTS: We present a simple yet effective multivariate statistical procedure for assessing the correlation between a subspace defined by a group of genes and a binary phenotype. A subspace is deemed significant if the samples corresponding to different phenotypes are well separated in that subspace. The separation is measured using Hotelling's T(2) statistic, which captures the covariance structure of the subspace. When the dimension of the subspace is larger than that of the sample space, we project the original data to a smaller orthonormal subspace. We use this method to search through functional pathway subspaces defined by Reactome, KEGG, BioCarta and Gene Ontology. To demonstrate its performance, we apply this method to the data from two published studies, and visualize the results in the principal component space.     

A principal component analysis of the dynamics of subdomains and binding sites in human serum albumin

The conformational dynamics of human serum albumin (HSA) was investigated by principal component analysis (PCA) applied to three molecular dynamics trajectories of 200 ns each. The overlap of the essential subspaces spanned by the first 10 principal components (PC) of different trajectories was about 0.3 showing that the PCA based on a trajectory length of 200 ns is not completely convergent for this protein. The contributions of the relative motion of subdomains and of the subdomains (internal) distortion to the first 10 PCs were found to be comparable. Based on the distribution of the first 3 PC, 10 protein conformers are identified showing relative root mean square deviations (RMSD) between 2.3 and 4.6 Å. The main PCs are found to be delocalized over the whole protein structure indicating that the motions of different protein subdomains are coupled. This coupling is considered as being related to the allosteric effects observed upon ligand binding to HSA. On the other hand, the first PC of one of the three trajectories describes a conformational transition of the protein domain I that is close to that experimentally observed upon myristate binding. This is a theoretical support for the older hypothesis stating that changes of the protein onformation favorable to binding can precede the ligand complexation. A detailed all atoms PCA performed on the primary Sites 1 and 2 confirms the multiconformational character of the HSA binding sites as well as the significant coupling of their motions. © 2013 Wiley Periodicals, Inc. Biopolymers 101: 561–572, 2014.     

Conformational fluctuations of the AXH monomer of Ataxin‐1

In this paper, we report the results of molecular dynamics simulations of AXH monomer of Ataxin‐1. The AXH domain plays a crucial role in Ataxin‐1 aggregation, which accompanies the initiation and progression of Spinocerebellar ataxia type 1. Our simulations involving both classical and replica exchange molecular dynamics, followed by principal component analysis of the trajectories obtained, reveal substantial conformational fluctuations of the protein structure, especially in the N‐terminal region. We show that these fluctuations can be generated by thermal noise since the free energy barriers between conformations are small enough for thermally stimulated transitions. In agreement with the previous experimental findings, our results can be considered as a basis for a future design of ataxin aggregation inhibitors that will require several key conformations identified in the present study as molecular targets for ligand binding. Proteins 2016; 84:52–59. © 2015 Wiley Periodicals, Inc.     

Conformational studies of a monoclonal antibody, IgG1, by chemical oxidation: structural analysis by ultrahigh-pressure LC-electrospray ionization time-of-flight MS and multivariate data analysis

We describe the development of a method in which protein oxidation by H₂O₂ followed by ultrahigh-pressure liquid chromatography (UHPLC) coupled with electrospray ionization time-of-flight mass spectrometry (ESI-ToFMS) and multivariate analysis are used to detect alterations in conformational states of proteins. In the study reported here, an IgG1 monoclonal antibody in native and denatured conformational states was oxidized by treatment with hydrogen peroxide. Peptide fragments generated by tryptic digestion were then analyzed by UHPLC-ESI-ToFMS. After reducing noise and extracting peaks from the LC–MS data using MzExplorer, software developed in-house and based on Matlab, we were able to distinguish peptides arising from the native and denatured states of the oxidized protein by principal component analysis. Peptides containing residues, which are inclined to undergo oxidation, such as methionine, are founded to be particularly important in this approach. We believe that the methodology could facilitate attempts to characterize the conformational states of recombinant monoclonal antibodies and other proteins.     

Essential dynamics of reversible peptide folding: memory-free conformational dynamics governed by internal hydrogen bonds

A principal component analysis has been applied on equilibrium simulations of a beta-heptapeptide that shows reversible folding in a methanol solution. The analysis shows that the configurational space contains only three dense sub-states. These states of relatively low free energy correspond to the "native" left-handed helix, a partly helical intermediate, and a hairpin-like structure. The collection of unfolded conformations form a relatively diffuse cloud with little substructure. Internal hydrogen-bonding energies were found to correlate well with the degree of folding. The native helical structure folds from the N terminus; the transition from the major folding intermediate to the native helical structure involves the formation of the two most C-terminal backbone hydrogen bonds. A four-state Markov model was found to describe transition frequencies between the conformational states within error limits, indicating that memory-effects are negligible beyond the nanosecond time-scale. The dominant native state fluctuations were found to be very similar to unfolding motions, suggesting that unfolding pathways can be inferred from fluctuations in the native state. The low-dimensional essential subspace, describing 69% of the collective atomic fluctuations, was found to converge at time-scales of the order of one nanosecond at all temperatures investigated, whereas folding/unfolding takes place at significantly longer time-scales, even above the melting temperature.     

Global and Local Structural Properties of the Principal Neutralizing Determinant of the HIV-1 Envelope Protein gp120

Abstract

The model of spatial structure for the principal neutralizing determinant (PND) of the HIV-1 envelope protein gpl20 is proposed in terms of two-dimensional nuclear Overhauser effect (NOE) spectroscopy data. To build the model, the NMR-based theoretical conformational analysis of synthetic PND peptides of length 40, 24, and 12 residues is carried out. The modeling of the molecular spatial structures is performed by a new approach to research of conformationally mobile peptides using the algorithms of the restrained molecular mechanics method developed earlier. The following major conclusions are made based on the analysis of the simulated peptide conformations: i) there is not unique PND structure in solution, ii) there are seven different PND structures each of which agrees with the experimental data and stereochemical criteria used in computing its spatial model, iii) the PND is characterized by irregular conformation containing a number of reverse turns, iv) all of the selected conformations are conserved in the Gly-Pro-Gly-Arg-Ala-Phe stretch, the most provable viral immunodominant epitope. These data allow to suppose that binding properties of this site are determined by the structural motif which forms the conformation of a double β-turn and appears common for all hexapeptide structures.     

Global and local structural properties of the principal neutralizing determinant of the HIV-1 envelope protein gp120

The model of spatial structure for the principal neutralizing determinant (PND) of the HIV-1 envelope protein gp120 is proposed in terms of two-dimensional nuclear Overhauser effect (NOE) spectroscopy data. To build the model, the NMR-based theoretical conformational analysis of synthetic PND peptides of length 40, 24, and 12 residues is carried out. The modeling of the molecular spatial structures is performed by a new approach to research of conformationally mobile peptides using the algorithms of the restrained molecular mechanics method developed earlier. The following major conclusions are made based on the analysis of the simulated peptide conformations: i) there is not unique PND structure in solution, ii) there are seven different PND structures each of which agrees with the experimental data and stereochemical criteria used in computing its spatial model, iii) the PND is characterized by irregular conformation containing a number of reverse turns, iv) all of the selected conformations are conserved in the Gly-Pro-Gly-Arg-Ala-Phe stretch, the most probable viral immunodominant epitope. These data allow to suppose that binding properties of this site are determined by the structural motif which forms the conformation of a double beta-turn and appears common for all hexapeptide structures.     

Exploration of the Dynamic Properties of Protein Complexes Predicted from Spatially Constrained Protein-Protein Interaction Networks

Protein complexes are not static, but rather highly dynamic with subunits that undergo 1-dimensional diffusion with respect to each other. Interactions within protein complexes are modulated through regulatory inputs that alter interactions and introduce new components and deplete existing components through exchange. While it is clear that the structure and function of any given protein complex is coupled to its dynamical properties, it remains a challenge to predict the possible conformations that complexes can adopt. Protein-fragment Complementation Assays detect physical interactions between protein pairs constrained to ≤8 nm from each other in living cells. This method has been used to build networks composed of 1000s of pair-wise interactions. Significantly, these networks contain a wealth of dynamic information, as the assay is fully reversible and the proteins are expressed in their natural context. In this study, we describe a method that extracts this valuable information in the form of predicted conformations, allowing the user to explore the conformational landscape, to search for structures that correlate with an activity state, and estimate the abundance of conformations in the living cell. The generator is based on a Markov Chain Monte Carlo simulation that uses the interaction dataset as input and is constrained by the physical resolution of the assay. We applied this method to an 18-member protein complex composed of the seven core proteins of the budding yeast Arp2/3 complex and 11 associated regulators and effector proteins. We generated 20,480 output structures and identified conformational states using principle component analysis. We interrogated the conformation landscape and found evidence of symmetry breaking, a mixture of likely active and inactive conformational states and dynamic exchange of the core protein Arc15 between core and regulatory components. Our method provides a novel tool for prediction and visualization of the hidden dynamics within protein interaction networks.     

Interpreting principal components in biomechanics: Representative extremes and single component reconstruction

Principal component analysis is a powerful tool in biomechanics for reducing complex multivariate datasets to a subset of important parameters. However, interpreting the biomechanical meaning of these parameters can be a subjective process. Biomechanical interpretations that are based on visual inspection of extreme 5th and 95th percentile waveforms may be confounded when extreme waveforms express more than one biomechanical feature. This study compares interpretation of principal components using representative extremes with a recently developed method, called single component reconstruction, which provides an uncontaminated visualization of each individual biomechanical feature. Example datasets from knee joint moments, lateral gastrocnemius EMG, and lumbar spine kinematics are used to demonstrate that the representative extremes method and single component reconstruction can yield equivalent interpretations of principal components. However, single component reconstruction interpretation cannot be contaminated by other components, which may enhance the use and understanding of principal component analysis within the biomechanics community.     

Principal component analysis for protein folding dynamics

Protein folding is considered here by studying the dynamics of the folding of the triple β-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.