Sequence comparison and protein structure prediction

Sequence comparison is a major step in the prediction of protein structure from existing templates in the Protein Data Bank. The identification of potentially remote homologues to be used as templates for modeling target sequences of unknown structure and their accurate alignment remain challenges, despite many years of study. The most recent advances have been in combining as many sources of information as possible--including amino acid variation in the form of profiles or hidden Markov models for both the target and template families, known and predicted secondary structures of the template and target, respectively, the combination of structure alignment for distant homologues and sequence alignment for close homologues to build better profiles, and the anchoring of certain regions of the alignment based on existing biological data. Newer technologies have been applied to the problem, including the use of support vector machines to tackle the fold classification problem for a target sequence and the alignment of hidden Markov models. Finally, using the consensus of many fold recognition methods, whether based on profile-profile alignments, threading or other approaches, continues to be one of the most successful strategies for both recognition and alignment of remote homologues. Although there is still room for improvement in identification and alignment methods, additional progress may come from model building and refinement methods that can compensate for large structural changes between remotely related targets and templates, as well as for regions of misalignment.     

A novel approach to remote homology detection: jumping alignments.

We describe a new algorithm for protein classification and the detection of remote homologs. The rationale is to exploit both vertical and horizontal information of a multiple alignment in a well-balanced manner. This is in contrast to established methods such as profiles and profile hidden Markov models which focus on vertical information as they model the columns of the alignment independently and to family pairwise search which focuses on horizontal information as it treats given sequences separately. In our setting, we want to select from a given database of "candidate sequences" those proteins that belong to a given superfamily. In order to do so, each candidate sequence is separately tested against a multiple alignment of the known members of the superfamily by means of a new jumping alignment algorithm. This algorithm is an extension of the Smith-Waterman algorithm and computes a local alignment of a single sequence and a multiple alignment. In contrast to traditional methods, however, this alignment is not based on a summary of the individual columns of the multiple alignment. Rather, the candidate sequence is at each position aligned to one sequence of the multiple alignment, called the "reference sequence." In addition, the reference sequence may change within the alignment, while each such jump is penalized. To evaluate the discriminative quality of the jumping alignment algorithm, we compare it to profiles, profile hidden Markov models, and family pairwise search on a subset of the SCOP database of protein domains. The discriminative quality is assessed by median false positive counts (med-FP-counts). For moderate med-FP-counts, the number of successful searches with our method is considerably higher than with the competing methods.     

Stylized chromosome images

Stylized chromosome images 1) serve as a format to test effects of preprocessing algorithms used in automated karyotyping; 2) enhance the ability of humans to perform quantitative analysis of chromosomal aberrations; 3) provide an alternative format for karyotype hard copies produced by automated systems. Stylized chromosomes are two-dimensional computer-generated images based on information extracted from one-dimensional width and density profiles. These profiles correspond to what cytogeneticists observe through the microscope as the shape and banding patterns of stained chromosomes. Stylized presentation sharpens chromosome band boundaries and perimeters, reduces "noise," and enhances gray level variations, which are difficult to distinguish by humans on photographic or computer generated karyotypes. Karyotyping accuracy using stylized images was used to detect difficult areas for automated chromosome identification. Landmark bands sufficient to classify chromosomes were identified; shapes of chromosomes reflected in width profiles were said to aid classification. A two-step automated karyotyping strategy proposed is: 1) classify chromosomes by landmarks, minimum information needed for identification; 2) subsequently employ the full banding pattern with maximum resolution to detect aberrations. Stylized images of abnormal chromosomes have potential for testing hypothesis regarding breakpoints and quantitative analysis, but improvements are needed in homologue normalization and definition of termini of chromosomes.     

Use of runs statistics for pattern recognition in genomic DNA sequences.

In this article, the use of the finite Markov chain imbedding (FMCI) technique to study patterns in DNA under a hidden Markov model (HMM) is introduced. With a vision of studying multiple runs-related statistics simultaneously under an HMM through the FMCI technique, this work establishes an investigation of a bivariate runs statistic under a binary HMM for DNA pattern recognition. An FMCI-based recursive algorithm is derived and implemented for the determination of the exact distribution of this bivariate runs statistic under an independent identically distributed (IID) framework, a Markov chain (MC) framework, and a binary HMM framework. With this algorithm, we have studied the distributions of the bivariate runs statistic under different binary HMM parameter sets; probabilistic profiles of runs are created and shown to be useful for trapping HMM maximum likelihood estimates (MLEs). This MLE-trapping scheme offers good initial estimates to jump-start the expectation-maximization (EM) algorithm in HMM parameter estimation and helps prevent the EM estimates from landing on a local maximum or a saddle point. Applications of the bivariate runs statistic and the probabilistic profiles in conjunction with binary HMMs for pattern recognition in genomic DNA sequences are illustrated via case studies on DNA bendability signals using human DNA data.     

Capturing protein sequence–structure specificity using computational sequence design

It is well known that protein fold recognition can be greatly improved if models for the underlying evolution history of the folds are taken into account. The improvement, however, exists only if such evolutionary information is available. To circumvent this limitation for protein families that only have a small number of representatives in current sequence databases, we follow an alternate approach in which the benefits of including evolutionary information can be recreated by using sequences generated by computational protein design algorithms. We explore this strategy on a large database of protein templates with 1747 members from different protein families. An automated method is used to design sequences for these templates. We use the backbones from the experimental structures as fixed templates, thread sequences on these backbones using a self‐consistent mean field approach, and score the fitness of the corresponding models using a semi‐empirical physical potential. Sequences designed for one template are translated into a hidden Markov model‐based profile. We describe the implementation of this method, the optimization of its parameters, and its performance. When the native sequences of the protein templates were tested against the library of these profiles, the class, fold, and family memberships of a large majority (>90%) of these sequences were correctly recognized for an E‐value threshold of 1. In contrast, when homologous sequences were tested against the same library, a much smaller fraction (35%) of sequences were recognized; The structural classification of protein families corresponding to these sequences, however, are correctly recognized (with an accuracy of >88%). Proteins 2013; © 2013 Wiley Periodicals, Inc.     

Hidden Markov models that use predicted secondary structures for fold recognition.

There are many proteins that share the same fold but have no clear sequence similarity. To predict the structure of these proteins, so called "protein fold recognition methods" have been developed. During the last few years, improvements of protein fold recognition methods have been achieved through the use of predicted secondary structures (Rice and Eisenberg, J Mol Biol 1997;267:1026-1038), as well as by using multiple sequence alignments in the form of hidden Markov models (HMM) (Karplus et al., Proteins Suppl 1997;1:134-139). To test the performance of different fold recognition methods, we have developed a rigorous benchmark where representatives for all proteins of known structure are matched against each other. Using this benchmark, we have compared the performance of automatically-created hidden Markov models with standard-sequence-search methods. Further, we combine the use of predicted secondary structures and multiple sequence alignments into a combined method that performs better than methods that do not use this combination of information. Using only single sequences, the correct fold of a protein was detected for 10% of the test cases in our benchmark. Including multiple sequence information increased this number to 16%, and when predicted secondary structure information was included as well, the fold was correctly identified in 20% of the cases. Moreover, if the correct secondary structure was used, 27% of the proteins could be correctly matched to a fold. For comparison, blast2, fasta, and ssearch identifies the fold correctly in 13-17% of the cases. Thus, standard pairwise sequence search methods perform almost as well as hidden Markov models in our benchmark. This is probably because the automatically-created multiple sequence alignments used in this study do not contain enough diversity and because the current generation of hidden Markov models do not perform very well when built from a few sequences.     

DNA进化马尔可夫过程模型的评价与推广

本文对ＤＮＡ序列进化过程中核苷酸替代的随机模型进行了评价,对替代速率在时间和空间上不恒定的情形进行了考察和推广。Ｌａｎａｖｅ等（１９８４）曾提出一个模型,宣称对替代的模式未做任何假定,但事实上我们证明它假定替代过程是可逆的。运用２－ｐ、４－ｐ和６－ｐ模型进行的计算表明替代速度在位点间的差异会造成估计的替代数严重偏低,并且替代数越大,偏差也越大。替代模式在位点间的差异也会造成估计值偏低,但偏差不严重     

Statistical analysis of nucleotide sequences.

In order to scan nucleic acid databases for potentially relevant but as yet unknown signals, we have developed an improved statistical model for pattern analysis of nucleic acid sequences by modifying previous methods based on Markov chains. We demonstrate the importance of selecting the appropriate parameters in order for the method to function at all. The model allows the simultaneous analysis of several short sequences with unequal base frequencies and Markov order k not equal to 0 as is usually the case in databases. As a test of these modifications, we show that in E. coli sequences there is a bias against palindromic hexamers which correspond to known restriction enzyme recognition sites.     

The joint distribution of patterns in random sequences with application to the RC-measure for expressivity

A method previously developed for computation of pattern probabilitiesin random sequences under Markov chain models. We extend thismethod to the calculation of the joint distribution for twopatterns. An application yields the distribution of the rightchoice measure for expressivity and how significance boundsdepend on sequence length. These bounds are used to show thatthe choice of pyrimidine in codon position 3 of Escherichiacoli genes deviates considerably from a general Markov processmodel for coding regions. We also derive some statistical evidencethat this significant deviation is limited to codon position3.     

Identification of related proteins on family, superfamily and fold level

Proteins might have considerable structural similarities even when no evolutionary relationship of their sequences can be detected. This property is often referred to as the proteins sharing only a "fold". Of course, there are also sequences of common origin in each fold, called a "superfamily", and in them groups of sequences with clear similarities, designated "family". Developing algorithms to reliably identify proteins related at any level is one of the most important challenges in the fast growing field of bioinformatics today. However, it is not at all certain that a method proficient at finding sequence similarities performs well at the other levels, or vice versa.Here, we have compared the performance of various search methods on these different levels of similarity. As expected, we show that it becomes much harder to detect proteins as their sequences diverge. For family related sequences the best method gets 75% of the top hits correct. When the sequences differ but the proteins belong to the same superfamily this drops to 29%, and in the case of proteins with only fold similarity it is as low as 15%. We have made a more complete analysis of the performance of different algorithms than earlier studies, also including threading methods in the comparison. Using this method a more detailed picture emerges, showing multiple sequence information to improve detection on the two closer levels of relationship. We have also compared the different methods of including this information in prediction algorithms.For lower specificities, the best scheme to use is a linking method connecting proteins through an intermediate hit. For higher specificities, better performance is obtained by PSI-BLAST and some procedures using hidden Markov models. We also show that a threading method, THREADER, performs significantly better than any other method at fold recognition.     

Rye cytology,cytogenetics and genetics — current status

Summary Progress in rye karyology is reviewed with respect to chromosome structure, recognition and chromosome nomenclature. Considerable contributions have been brought about by molecular techniques which have even revealed nucleotide sequences of some of the ribosomal DNA. DNA sequence organization correlates with the distribution of major Giemsa C-band regions as well as with N-bands and the binding sites of fluorescent dyes. The several banding patterns permit the classification of rye chromosomes. The increased data and widespread application of banding analysis require a consistent system of chromosome and/or band designation. Therefore, a standard band nomenclature is proposed with reference to the recommendations of the Paris Conference on Standardization in Human Cytogenetics. In addition, advances in genetics are summarized and discussed. Based on the original accepted standard karyogram and banding patterns of the rye chromosomes, meanwhile, 120 genes determining several characters have been associated with individual chromosomes and/or chromosome arms, including linkage studies for about 19 arrangements. Most results were obtained using wheat-rye addition lines as well as test crosses with defined translocations. Moreover, genetical studies based on appropriate trisomic and telotrisomic material resulted in the localization of 19 genes, including their linkage relationships.     

Prophase chromosome unique band sequences: definition and utilization

Extensive experience with the analysis of human prophase chromosomes and studies into the complexity of prophase banding patterns have suggested that at least some prophase chromosomal segments can be accurately identified and characterized independently of the morphology of the chromosome as a whole. The feasibility of identifying and analyzing specified prophase chromosome segments was thus investigated as an alternative approach to prophase chromosome analysis based on whole-chromosome recognition. Through the use of prophase idiograms at the 850-band stage (Francke, 1981) and a systematic comparison system, we have demonstrated that it is possible to divide the 24 human prophase idiograms into a set of 94 unique band sequences, each of which has a banding pattern that is recognizable and distinct from any other nonhomologous chromosome portion. The use of a unique band sequence approach in prophase chromosome analysis is expected to increase efficiency and sensitivity through more effective use of available banding information.     

A random effects branch-site model for detecting episodic diversifying selection

Adaptive evolution frequently occurs in episodic bursts, localized to a few sites in a gene, and to a small number of lineages in a phylogenetic tree. A popular class of "branch-site" evolutionary models provides a statistical framework to search for evidence of such episodic selection. For computational tractability, current branch-site models unrealistically assume that all branches in the tree can be partitioned a priori into two rigid classes--"foreground" branches that are allowed to undergo diversifying selective bursts and "background" branches that are negatively selected or neutral. We demonstrate that this assumption leads to unacceptably high rates of false positives or false negatives when the evolutionary process along background branches strongly deviates from modeling assumptions. To address this problem, we extend Felsenstein's pruning algorithm to allow efficient likelihood computations for models in which variation over branches (and not just sites) is described in the random effects likelihood framework. This enables us to model the process at every branch-site combination as a mixture of three Markov substitution models--our model treats the selective class of every branch at a particular site as an unobserved state that is chosen independently of that at any other branch. When benchmarked on a previously published set of simulated sequences, our method consistently matched or outperformed existing branch-site tests in terms of power and error rates. Using three empirical data sets, previously analyzed for episodic selection, we discuss how modeling assumptions can influence inference in practical situations.     

Exploiting mid-range DNA patterns for sequence classification: binary abstraction Markov models

Messenger RNA sequences possess specific nucleotide patterns distinguishing them from non-coding genomic sequences. In this study, we explore the utilization of modified Markov models to analyze sequences up to 44 bp, far beyond the 8-bp limit of conventional Markov models, for exon/intron discrimination. In order to analyze nucleotide sequences of this length, their information content is first reduced by conversion into shorter binary patterns via the application of numerous abstraction schemes. After the conversion of genomic sequences to binary strings, homogenous Markov models trained on the binary sequences are used to discriminate between exons and introns. We term this approach the Binary Abstraction Markov Model (BAMM). High-quality abstraction schemes for exon/intron discrimination are selected using optimization algorithms on supercomputers. The best MM classifiers are then combined using support vector machines into a single classifier. With this approach, over 95% classification accuracy is achieved without taking reading frame into account. With further development, the BAMM approach can be applied to sequences lacking the genetic code such as ncRNAs and 5'-untranslated regions.     

MLR-OOD: A Markov Chain Based Likelihood Ratio Method for Out-Of-Distribution Detection of Genomic Sequences

Machine learning or deep learning models have been widely used for taxonomic classification of metagenomic sequences and many studies reported high classification accuracy. Such models are usually trained based on sequences in several training classes in hope of accurately classifying unknown sequences into these classes. However, when deploying the classification models on real testing data sets, sequences that do not belong to any of the training classes may be present and are falsely assigned to one of the training classes with high confidence. Such sequences are referred to as out-of-distribution (OOD) sequences and are ubiquitous in metagenomic studies. To address this problem, we develop a deep generative model-based method, MLR-OOD, that measures the probability of a testing sequencing belonging to OOD by the likelihood ratio of the maximum of the in-distribution (ID) class conditional likelihoods and the Markov chain likelihood of the testing sequence measuring the sequence complexity. We compose three different microbial data sets consisting of bacterial, viral, and plasmid sequences for comprehensively benchmarking OOD detection methods. We show that MLR-OOD achieves the state-of-the-art performance demonstrating the generality of MLR-OOD to various types of microbial data sets. It is also shown that MLR-OOD is robust to the GC content, which is a major confounding effect for OOD detection of genomic sequences. In conclusion, MLR-OOD will greatly reduce false positives caused by OOD sequences in metagenomic sequence classification.     

On the representability of complete genomes by multiple competing finite-context (Markov) models

A finite-context (Markov) model of order k yields the probability distribution of the next symbol in a sequence of symbols, given the recent past up to depth k. Markov modeling has long been applied to DNA sequences, for example to find gene-coding regions. With the first studies came the discovery that DNA sequences are non-stationary: distinct regions require distinct model orders. Since then, Markov and hidden Markov models have been extensively used to describe the gene structure of prokaryotes and eukaryotes. However, to our knowledge, a comprehensive study about the potential of Markov models to describe complete genomes is still lacking. We address this gap in this paper. Our approach relies on (i) multiple competing Markov models of different orders (ii) careful programming techniques that allow orders as large as sixteen (iii) adequate inverted repeat handling (iv) probability estimates suited to the wide range of context depths used. To measure how well a model fits the data at a particular position in the sequence we use the negative logarithm of the probability estimate at that position. The measure yields information profiles of the sequence, which are of independent interest. The average over the entire sequence, which amounts to the average number of bits per base needed to describe the sequence, is used as a global performance measure. Our main conclusion is that, from the probabilistic or information theoretic point of view and according to this performance measure, multiple competing Markov models explain entire genomes almost as well or even better than state-of-the-art DNA compression methods, such as XM, which rely on very different statistical models. This is surprising, because Markov models are local (short-range), contrasting with the statistical models underlying other methods, where the extensive data repetitions in DNA sequences is explored, and therefore have a non-local character.