Profile Comparer: a program for scoring and aligning profile hidden Markov models

Summary: Profile Comparer (PRC) is a stand-alone program for scoring and aligning profile hidden Markov models (HMMs) of protein families. PRC can read models produced by SAM and HMMER, two popular profile HMM packages, as well as PSI-BLAST checkpoint files. This application note provides a brief description of the profile–profile algorithm used by PRC

Accurate statistical model of comparison between multiple sequence alignments

Comparison of multiple protein sequence alignments (MSA) reveals unexpected evolutionary relations between protein families and leads to exciting predictions of spatial structure and function. The power of MSA comparison critically depends on the quality of statistical model used to rank the similarities found in a database search, so that biologically relevant relationships are discriminated from spurious connections. Here, we develop an accurate statistical description of MSA comparison that does not originate from conventional models of single sequence comparison and captures essential features of protein families. As a final result, we compute E-values for the similarity between any two MSA using a mathematical function that depends on MSA lengths and sequence diversity. To develop these estimates of statistical significance, we first establish a procedure for generating realistic alignment decoys that reproduce natural patterns of sequence conservation dictated by protein secondary structure. Second, since similarity scores between these alignments do not follow the classic Gumbel extreme value distribution, we propose a novel distribution that yields statistically perfect agreement with the data. Third, we apply this random model to database searches and show that it surpasses conventional models in the accuracy of detecting remote protein similarities

Beyond the E-value: stratified statistics for protein domain prediction

E-values have been the dominant statistic for protein sequence analysis for the past two decades: from identifying statistically significant local sequence alignments to evaluating matches to hidden Markov models describing protein domain families. Here we formally show that for "stratified" multiple hypothesis testing problems, controlling the local False Discovery Rate (lFDR) per stratum, or partition, yields the most predictions across the data at any given threshold on the FDR or E-value over all strata combined. For the important problem of protein domain prediction, a key step in characterizing protein structure, function and evolution, we show that stratifying statistical tests by domain family yields excellent results. We develop the first FDR-estimating algorithms for domain prediction, and evaluate how well thresholds based on q-values, E-values and lFDRs perform in domain prediction using five complementary approaches for estimating empirical FDRs in this context. We show that stratified q-value thresholds substantially outperform E-values. Contradicting our theoretical results, q-values also outperform lFDRs; however, our tests reveal a small but coherent subset of domain families, biased towards models for specific repetitive patterns, for which FDRs are greatly underestimated due to weaknesses in random sequence models. Usage of lFDR thresholds outperform q-values for the remaining families, which have as-expected noise, suggesting that further improvements in domain predictions can be achieved with improved modeling of random sequences. Overall, our theoretical and empirical findings suggest that the use of stratified q-values and lFDRs could result in improvements in a host of structured multiple hypothesis testing problems arising in bioinformatics, including genome-wide association studies, orthology prediction, motif scanning, and multi-microarray analyses.Comment: 31 pages, 8 figures, does not include supplementary file

Error statistics of hidden Markov model and hidden Boltzmann model results

<p>Abstract</p> <p>Background</p> <p>Hidden Markov models and hidden Boltzmann models are employed in computational biology and a variety of other scientific fields for a variety of analyses of sequential data. Whether the associated algorithms are used to compute an actual probability or, more generally, an odds ratio or some other score, a frequent requirement is that the error statistics of a given score be known. What is the chance that random data would achieve that score or better? What is the chance that a real signal would achieve a given score threshold?</p> <p>Results</p> <p>Here we present a novel general approach to estimating these false positive and true positive rates that is significantly more efficient than are existing general approaches. We validate the technique via an implementation within the HMMER 3.0 package, which scans DNA or protein sequence databases for patterns of interest, using a profile-HMM.</p> <p>Conclusion</p> <p>The new approach is faster than general naïve sampling approaches, and more general than other current approaches. It provides an efficient mechanism by which to estimate error statistics for hidden Markov model and hidden Boltzmann model results.</p

HARMONY: a server for the assessment of protein structures

Protein structure validation is an important step in computational modeling and structure determination. Stereochemical assessment of protein structures examine internal parameters such as bond lengths and Ramachandran (φ,ψ) angles. Gross structure prediction methods such as inverse folding procedure and structure determination especially at low resolution can sometimes give rise to models that are incorrect due to assignment of misfolds or mistracing of electron density maps. Such errors are not reflected as strain in internal parameters. HARMONY is a procedure that examines the compatibility between the sequence and the structure of a protein by assigning scores to individual residues and their amino acid exchange patterns after considering their local environments. Local environments are described by the backbone conformation, solvent accessibility and hydrogen bonding patterns. We are now providing HARMONY through a web server such that users can submit their protein structure files and, if required, the alignment of homologous sequences. Scores are mapped on the structure for subsequent examination that is useful to also recognize regions of possible local errors in protein structures. HARMONY server is located a

Scaling symmetry, renormalization, and time series modeling

We present and discuss a stochastic model of financial assets dynamics based on the idea of an inverse renormalization group strategy. With this strategy we construct the multivariate distributions of elementary returns based on the scaling with time of the probability density of their aggregates. In its simplest version the model is the product of an endogenous auto-regressive component and a random rescaling factor designed to embody also exogenous influences. Mathematical properties like increments' stationarity and ergodicity can be proven. Thanks to the relatively low number of parameters, model calibration can be conveniently based on a method of moments, as exemplified in the case of historical data of the S&P500 index. The calibrated model accounts very well for many stylized facts, like volatility clustering, power law decay of the volatility autocorrelation function, and multiscaling with time of the aggregated return distribution. In agreement with empirical evidence in finance, the dynamics is not invariant under time reversal and, with suitable generalizations, skewness of the return distribution and leverage effects can be included. The analytical tractability of the model opens interesting perspectives for applications, for instance in terms of obtaining closed formulas for derivative pricing. Further important features are: The possibility of making contact, in certain limits, with auto-regressive models widely used in finance; The possibility of partially resolving the long-memory and short-memory components of the volatility, with consistent results when applied to historical series.Comment: Main text (17 pages, 13 figures) plus Supplementary Material (16 pages, 5 figures

Inference of the genetic network regulating lateral root initiation in Arabidopsis thaliana

Regulation of gene expression is crucial for organism growth, and it is one of the challenges in Systems Biology to reconstruct the underlying regulatory biological networks from transcriptomic data. The formation of lateral roots in Arabidopsis thaliana is stimulated by a cascade of regulators of which only the interactions of its initial elements have been identified. Using simulated gene expression data with known network topology, we compare the performance of inference algorithms, based on different approaches, for which ready-to-use software is available. We show that their performance improves with the network size and the inclusion of mutants. We then analyse two sets of genes, whose activity is likely to be relevant to lateral root initiation in Arabidopsis, by integrating sequence analysis with the intersection of the results of the best performing methods on time series and mutants to infer their regulatory network. The methods applied capture known interactions between genes that are candidate regulators at early stages of development. The network inferred from genes significantly expressed during lateral root formation exhibits distinct scale-free, small world and hierarchical properties and the nodes with a high out-degree may warrant further investigation

Predicting conserved protein motifs with Sub-HMMs

BackgroundProfile HMMs (hidden Markov models) provide effective methods for modeling the conserved regions of protein families. A limitation of the resulting domain models is the difficulty to pinpoint their much shorter functional sub-features, such as catalytically relevant sequence motifs in enzymes or ligand binding signatures of receptor proteins.ResultsTo identify these conserved motifs efficiently, we propose a method for extracting the most information-rich regions in protein families from their profile HMMs. The method was used here to predict a comprehensive set of sub-HMMs from the Pfam domain database. Cross-validations with the PROSITE and CSA databases confirmed the efficiency of the method in predicting most of the known functionally relevant motifs and residues. At the same time, 46,768 novel conserved regions could be predicted. The data set also allowed us to link at least 461 Pfam domains of known and unknown function by their common sub-HMMs. Finally, the sub-HMM method showed very promising results as an alternative search method for identifying proteins that share only short sequence similarities.ConclusionsSub-HMMs extend the application spectrum of profile HMMs to motif discovery. Their most interesting utility is the identification of the functionally relevant residues in proteins of known and unknown function. Additionally, sub-HMMs can be used for highly localized sequence similarity searches that focus on shorter conserved features rather than entire domains or global similarities. The motif data generated by this study is a valuable knowledge resource for characterizing protein functions in the future

Genomic scale sub-family assignment of protein domains

Many classification schemes for proteins and domains are either hierarchical or semi-hierarchical yet most databases, especially those offering genome-wide analysis, only provide assignments to sequences at one level of their hierarchy. Given an established hierarchy, the problem of assigning new sequences to lower levels of that existing hierarchy is less hard (but no less important) than the initial top level assignment which requires the detection of the most distant relationships. A solution to this problem is described here in the form of a new procedure which can be thought of as a hybrid between pairwise and profile methods. The hybrid method is a general procedure that can be applied to any pre-defined hierarchy, at any level, including in principle multiple sub-levels. It has been tested on the SCOP classification via the SUPERFAMILY database and performs significantly better than either pairwise or profile methods alone. Perhaps the greatest advantage of the hybrid method over other possible approaches to the problem is that within the framework of an existing profile library, the assignments are fully automatic and come at almost no additional computational cost. Hence it has already been applied at the SCOP family level to all genomes in the SUPERFAMILY database, providing a wealth of new data to the biological and bioinformatics communities