Quantitative Assessment of Molecular Dynamics Sampling for Flexible Systems

Molecular dynamics (MD) simulation is a natural method for the study of flexible molecules but at the same time is limited by the large size of the conformational space of these molecules. We ask by how much the MD sampling quality for flexible molecules can be improved by two means: the use of diverse sets of trajectories starting from different initial conformations to detect deviations between samples and sampling with enhanced methods such as accelerated MD (aMD) or scaled MD (sMD) that distort the energy landscape in controlled ways. To this end, we test the effects of these approaches on MD simulations of two flexible biomolecules in aqueous solution, Met-Enkephalin (5 amino acids) and HIV-1 gp120 V3 (a cycle of 35 amino acids). We assess the convergence of the sampling quantitatively with known, extensive measures of cluster number <i>N</i>_c and cluster distribution entropy <i>S</i>_c and with two new quantities, conformational overlap <i>O</i>_conf and density overlap <i>O</i>_dens, both conveniently ranging from 0 to 1. These new overlap measures quantify self-consistency of sampling in multitrajectory MD experiments, a necessary condition for converged sampling. A comprehensive assessment of sampling quality of MD experiments identifies the combination of diverse trajectory sets and aMD as the most efficient approach among those tested. However, analysis of <i>O</i>_dens between conventional and aMD trajectories also reveals that we have not completely corrected aMD sampling for the distorted energy landscape. Moreover, for V3, the courses of <i>N</i>_c and <i>O</i>_dens indicate that much higher resources than those generally invested today will probably be needed to achieve convergence. The comparative analysis also shows that conventional MD simulations with insufficient sampling can be easily misinterpreted as being converged

Odds-ratio plot and Tartan plot for visualization of statistical associations.

<p><b>A</b> Odds-ratio plot, based on an alignment of region of HIV-1 gp120 around the V3 loop (C296-C331). Here, the feature is the predicted co-receptor tropism of HIV-1 [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0146409#pone.0146409.ref017" target="_blank">17</a>] (R5 vs. X4 tropic). Bar heights and colors indicate logarithms of odds ratios and negative logarithms of <i>p</i> values, respectively. A reference sequence and sequence positions can be added in the top and bottom rows for orientation. <b>B</b> Tartan plot for the synopsis of two alignment pair association measures, here: −log <i>p</i> from association test between alignment position pairs (upper right triangle) vs. Direct Information between these pairs (lower left triangle). Association strengths are color coded (color legend on the right). For orientation, axes can be annotated and sequence substructures can be indicated by lines.</p

SearchXLinks. A Program for the Identification of Disulfide Bonds in Proteins from Mass Spectra

We present the computer program SearchXLinks that analyzes mass spectra with the aim of identifying disulfide bonds and other modifications in proteins of known amino acid sequence. Disulfide bonds can be intra- or intermolecular. To decrease the number of false positives, the analysis of in-source decay and tandem mass spectra are coupled into the program. The steps taken during a SearchXLinks run are outlined, and the computational costs are discussed. The application of the program is illustrated by the analysis of data from recent studies on bovine ribonuclease A and bovine serum albumin. The software can be used free of charge on the Internet at http://www.searchxlinks.de

Comparison of statistical indicators of association.

<p>200 random contingency tables with total count <i>N</i> = 100, a typical order of magnitude for analyses of sequence-feature association in practice, are analyzed by Fisher’s exact test, yielding <i>p</i> values for the rejection of independence (horizontal axis, not corrected for multiple testing), and by four different BF models, namely <i>K</i> = 1, <i>K</i> = 100, <i>K</i>_<i>D</i>, and uniform model, with corresponding BFs on vertical axis. Solid horizontal black line at <i>BF</i> = 1 and dashed vertical line at <i>p</i> = 0.05 for orientation.</p

Comparison of frequentist approach and Bayes factors (BF).

<p>Discovery of association of alignment positions of HBV core proteins with patient HLA types, here: A*01 (top row) and B*44 (bottom row). Sequence numbers in panel titles are feature-carrying fractions of the total of 148 sequences included in the alignment. Association of sequences with feature HLA were analyzed by Fisher’s exact test (panels A, D), BF with <i>K</i> = 1 (panels B, E), and BF with <i>K</i>_<i>D</i> (panels C, F). Alignment positions with association above certain thresholds (horizontal dashed lines) are marked by red stars and vertical dashed lines, namely <i>p</i> < 0.01 (A, D), or <i>BF</i> > 10 (B, C, E, F). The <i>p</i> values and BFs shown are the best for each alignment position (lowest <i>p</i> values, highest <i>BF</i>s).</p

Phylogenetic distribution of feature-carrying sequences and phylogenetic bias indicator <i>B</i>.

<p>The distance-based phylogenetic tree in all six panels was computed for the same set of 788 East Asian HIV-1 gag protein sequences obtained from the HIV sequence database at <a href="http://www.hiv.lanl.gov" target="_blank">http://www.hiv.lanl.gov</a>. In each panel, those branches are colored red that correspond to sequences that carry an amino acid substitution apparently associated with a certain HLA type. The numbers to the upper right of each tree are the corresponding values of the bias indicator <i>B</i>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0146409#pone.0146409.e005" target="_blank">Eq (4)</a>.</p

Partial Reduction and Two-Step Modification of Proteins for Identification of Disulfide Bonds

An experimental protocol was established to combine partial reduction, cyanylation, and a second modification step for the assignment of disulfide bonds in proteins that are resistant to proteolysis under native conditions. After proteolysis, disulfide bonds were assigned via MALDI mass spectrometry with subsequent semiautomatic interpretation using the program SearchXLinks, which enumerates all possible combinations of proteolytic fragments for all observed monoisotopic masses. The putative assignment of disulfide bonds was confirmed by ISD and PSD fragmentation of the corresponding protonated molecules

Partial Reduction and Two-Step Modification of Proteins for Identification of Disulfide Bonds

An experimental protocol was established to combine partial reduction, cyanylation, and a second modification step for the assignment of disulfide bonds in proteins that are resistant to proteolysis under native conditions. After proteolysis, disulfide bonds were assigned via MALDI mass spectrometry with subsequent semiautomatic interpretation using the program SearchXLinks, which enumerates all possible combinations of proteolytic fragments for all observed monoisotopic masses. The putative assignment of disulfide bonds was confirmed by ISD and PSD fragmentation of the corresponding protonated molecules

Partial Reduction and Two-Step Modification of Proteins for Identification of Disulfide Bonds

An experimental protocol was established to combine partial reduction, cyanylation, and a second modification step for the assignment of disulfide bonds in proteins that are resistant to proteolysis under native conditions. After proteolysis, disulfide bonds were assigned via MALDI mass spectrometry with subsequent semiautomatic interpretation using the program SearchXLinks, which enumerates all possible combinations of proteolytic fragments for all observed monoisotopic masses. The putative assignment of disulfide bonds was confirmed by ISD and PSD fragmentation of the corresponding protonated molecules

Two-Stage Method for Protein−Ligand Docking

A two-stage method for the computational prediction of the structure of protein−ligand complexes is proposed. Given an experimentally determined structure of the protein, in the first stage a large number of plausible ligand conformations is generated using the fast docking algorithm FlexX. In the second stage these conformations are minimized and reranked using a method based on a classical force field. The two-stage method is tested for 10 different protein−ligand complexes. For 9 of them experimentally determined structures are known. It turns out that the two-stage method strongly improves the predictive power as compared to that of the fast docking stage alone. The tenth case is a bona fide prediction of a complex of thrombin with a new inhibitor for which no experimentally determined structure is available so far