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A polynomial-time nuclear vector replacement algorithm for automated NMR resonance assignments.

High-throughput NMR structural biology can play an important role in structural genomics. We report an automated procedure for high-throughput NMR resonance assignment for a protein of known structure, or of a homologous structure. These assignments are a prerequisite for probing protein-protein interactions, protein-ligand binding, and dynamics by NMR. Assignments are also the starting point for structure determination and refinement. A new algorithm, called Nuclear Vector Replacement (NVR) is introduced to compute assignments that optimally correlate experimentally measured NH residual dipolar couplings (RDCs) to a given a priori whole-protein 3D structural model. The algorithm requires only uniform( 15)N-labeling of the protein and processes unassigned H(N)-(15)N HSQC spectra, H(N)-(15)N RDCs, and sparse H(N)-H(N) NOE's (d(NN)s), all of which can be acquired in a fraction of the time needed to record the traditional suite of experiments used to perform resonance assignments. NVR runs in minutes and efficiently assigns the (H(N),(15)N) backbone resonances as well as the d(NN)s of the 3D (15)N-NOESY spectrum, in O(n(3)) time. The algorithm is demonstrated on NMR data from a 76-residue protein, human ubiquitin, matched to four structures, including one mutant (homolog), determined either by x-ray crystallography or by different NMR experiments (without RDCs). NVR achieves an assignment accuracy of 92-100%. We further demonstrate the feasibility of our algorithm for different and larger proteins, using NMR data for hen lysozyme (129 residues, 97-100% accuracy) and streptococcal protein G (56 residues, 100% accuracy), matched to a variety of 3D structural models. Finally, we extend NVR to a second application, 3D structural homology detection, and demonstrate that NVR is able to identify structural homologies between proteins with remote amino acid sequences using a database of structural models.

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Efficient algorithms for protein sequence design and the analysis of certain evolutionary fitness landscapes.

Protein sequence design is a natural inverse problem to protein structure prediction: given a target structure in three dimensions, we wish to design an amino acid sequence that is likely fold to it. A model of Sun, Brem, Chan, and Dill casts this problem as an optimization on a space of sequences of hydrophobic (H) and polar (P) monomers; the goal is to find a sequence that achieves a dense hydrophobic core with few solvent-exposed hydrophobic residues. Sun et al. developed a heuristic method to search the space of sequences, without a guarantee of optimality or near-optimality; Hart subsequently raised the computational tractability of constructing an optimal sequence in this model as an open question. Here we resolve this question by providing an efficient algorithm to construct optimal sequences; our algorithm has a polynomial running time, and performs very efficiently in practice. We illustrate the implementation of our method on structures drawn from the Protein Data Bank. We also consider extensions of the model to larger amino acid alphabets, as a way to overcome the limitations of the binary H/P alphabet. We show that for a natural class of arbitrarily large alphabets, it remains possible to design optimal sequences efficiently. Finally, we analyze some of the consequences of this sequence design model for the study of evolutionary fitness landscapes. A given target structure may have many sequences that are optimal in the model of Sun et al.; following a notion raised by the work of J. Maynard Smith, we can ask whether these optimal sequences are "connected" by successive point mutations. We provide a polynomial-time algorithm to decide this connectedness property, relative to a given target structure. We develop the algorithm by first solving an analogous problem expressed in terms of submodular functions, a fundamental object of study in combinatorial optimization.

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An exponential example for a partial digest mapping algorithm.

The partial digest problem for small-scale DNA physical mapping is known is known in computer science as the turnpike reconstruction problem. Although no polynomial algorithm for this problem is known, a simple backtracking algorithm of Skiena et al. works well in practice. Weiss raises the question whether an exponential example exists for this algorithm. This paper presents such an exponential example for this backtracking algorithm.

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Hunting for trees in binary character sets: efficient algorithms for extraction, enumeration, and optimization.

We describe a useful and efficient tree building technique that is closely related to the maximum compatible subset method. Given a set of binary characters C and a degree bound d, the algorithm we describe counts the number of trees T that satisfy (1) the edges of T correspond to characters contained in C, and (2) the vertices of T have degree bounded by d. If the characters are weighted then we can efficiently determine which of these trees have maximum summed edge weight, where the weight of an edge equals the weight of the corresponding binary character in C. The complexity of the algorithms equals O(nk + ndK(d-1), where n is the number of taxa, k is the number of characters, and K is the number of distinct characters. A number of new tree consensus methods based on the algorithm are introduced, including one that uses edge weighted trees. As well, we illustrate the applicability of the algorithm for large sequence data sets by analyzing sequences from the "Out of Africa" mtDNA data set.

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An iterative algorithm for correcting sequencing errors in DNA coding regions.

Insertion and deletion (indel) sequencing errors in DNA coding regions disrupt DNA-to-protein translation frames, and hence make most frame-sensitive coding recognition approaches fail. This paper extends the authors' previous work on indel detection and "correction" algorithms, and presents a more effective algorithm for localizing indels that appear in DNA coding regions and "correcting" the located indels by inserting or deleting DNA bases. The algorithm localizes indels by discovering changes of the preferred translation frames within presumed coding regions, and then "corrects" them to restore a consistent translation frame within each coding region. An iterative strategy is exploited to repeatedly localize and "correct" indels until no more indels can be found. Test results have shown that this improved algorithm can detect and "correct" more indels while not worsening the rate of introduction of false indels when compared to the authors' previous work.

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A segment-based dynamic programming algorithm for predicting gene structure.

An algorithm called segment-based dynamic programming is described for predicting gene structure from a sequence of genomic DNA. The algorithm explores the space of gene structures that satisfy junctional and frame constraints and finds the gene structure that optimizes the sum of junctional and segmental scoring functions. Junctional constraints specify acceptable sites of initiation, termination, and splicing, whereas frame constraints ensure that the total exon length is a multiple of three and that no in-frame stop codons occur within exons or at exon-exon junctions. By computing over segments, segment-based dynamic programming maintains reading frame and phase information for each segment, it can assemble exons in-frame as well as score them in-frame. The algorithm is used to quantify the computational power of constraints. Experimental results show that frame constraints reduce the size of the search space by several orders of magnitude and that cardinality constraints place an asymptotic limit on the size of the search space. The algorithm is also used to compare the accuracy of different methods for assembly and scoring. A scoring scheme based on fifth-order Markov hexamer frequencies is presented and used in three objective functions, corresponding to in-frame, frame-independent, and frame-maximal scoring strategies. Experimental results show that in-frame assembly improves specificity only slightly over frame-independent assembly, whereas in-frame scoring improves specificity substantially over frame-independent and frame-maximal scoring.

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Las Vegas algorithms for gene recognition: suboptimal and error-tolerant spliced alignment.

Recently, Gelfand, Mironov and Pevzner (1996) proposed a spliced alignment approach to gene recognition that provides 99% accurate recognition of human genes if a related mammalian protein is available. However, even 99% accurate gene predictions are insufficient for automated sequence annotation in large-scale sequencing projects and therefore have to be complemented by experimental gene verification. One hundred percent accurate gene predictions would lead to a substantial reduction of experimental work on gene identification. Our goal is to develop an algorithm that either predicts an exon assembly with accuracy sufficient for sequence annotation or warns a biologist that the accuracy of a prediction is insufficient and further experimental work is required. We study suboptimal and error-tolerant spliced alignment problems as the first steps towards such an algorithm, and report an algorithm which provides 100% accurate recognition of human genes in 37% of cases (if a related mammalian protein is available). In 52% of genes, the algorithm predicts at least one exon with 100% accuracy.

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A pairwise alignment algorithm which favors clusters of blocks.

Pairwise sequence alignments aim to decide whether two sequences are related and, if so, to exhibit their related domains. Recent works have pointed out that a significant number of true homologous sequences are missed when using classical comparison algorithms. This is the case when two homologous sequences share several little blocks of homology, too small to lead to a significant score. On the other hand, classical alignment algorithms, when detecting homologies, may fail to recognize all the significant biological signals. The aim of the paper is to give a solution to these two problems. We propose a new scoring method which tends to increase the score of an alignment when "blocks" are detected. This so-called Block-Scoring algorithm, which makes use of dynamic programming, is worth being used as a complementary tool to classical exact alignments methods. We validate our approach by applying it on a large set of biological data. Finally, we give a limit theorem for the score statistics of the algorithm.

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Parallel hash-based EST clustering algorithm for gene sequencing.

EST clustering is a simple, yet effective method to discover all the genes present in a variety of species. Although using ESTs is a cost-effective approach in gene discovery, the amount of data, and hence the computational resources required, make it a very challenging problem. Time and storage requirements for EST clustering problems are prohibitively expensive. Existing tools have quadratic time complexity resulting from all against all sequence comparisons. With the rapid growth of EST data we need better and faster clustering tools. In this paper, we present HECT (Hash based EST Clustering Tool), a novel time- and memory-efficient algorithm for EST clustering. We report that HECT can cluster a 10,000 Human EST dataset (which is also used in benchmarking d2_cluster), in 207 minutes on a 1 GHz Pentium III processor which is 36 times faster than the original d2_cluster algorithm. A parallel version of HECT (PECT) is also developed and used to cluster 269,035 soybean EST sequences on IA-32 Linux cluster at National Center for Supercomputing Applications at UIUC. The parallel algorithm exhibited excellent speedup over its sequential counterpart and its memory requirements are almost negligible making it suitable to run virtually on any data size. The performance of the proposed clustering algorithms is compared against other known clustering techniques and results are reported in the paper.

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Comparison of SWAN and WISE menopausal status classification algorithms.

BACKGROUND: Classification of menopausal status is important for epidemiological and clinical studies as well as for clinicians treating midlife women. Most epidemiological studies, including the Study of Women's Health Across the Nation (SWAN), classify women based on self-reported bleeding history. METHODS: The Women's Ischemia Syndrome Evaluation (WISE) study developed an algorithm using menstrual and reproductive history and serum hormone levels to reproduce the menopausal status classifications assigned by the WISE hormone committee. We applied that algorithm to women participating in SWAN and examined characteristics of women with concordant and discordant SWAN and WISE classifications. RESULTS: Of the 3215 SWAN women with complete information at baseline (1995-1997), 2466 (76.7%) received concordant classifications (kappa = 0.52); at the fifth annual follow-up visit, of the 1623 women with complete information, 1154 (72.7%) received concordant classifications (kappa = 0.57). At each time point, we identified subgroups of women with discordant SWAN and WISE classifications. These subgroups, ordered by chronological age, showed increasing trends for menopausal symptoms and follicle-stimulating hormone (FSH) and a decreasing trend for estrogen (p < 0.001). CONCLUSIONS: The WISE algorithm is a useful tool for studies that have access to blood samples for hormone data unrelated to menstrual cycle phase, with or without an intact uterus, and no resources for adjudication. Future studies may want to combine aspects of the SWAN and WISE algorithms by adding hormonal measures to the series of bleeding questions in order to determine more precisely where women are in the perimenopausal continuum.

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Creation of clinical research databases in the 21st century: a practical algorithm for HIPAA Compliance.

BACKGROUND: Enforcement of the Health Insurance Portability and Accountability Act (HIPAA) began in April, 2003. Designed as a law mandating health insurance availability when coverage was lost, HIPAA imposed sweeping and broad-reaching protections of patient privacy. These changes dramatically altered clinical research by placing sizeable regulatory burdens upon investigators with threat of severe and costly federal and civil penalties. This report describes development of an algorithmic approach to clinical research database design based upon a central key-shared data (CK-SD) model allowing researchers to easily analyze, distribute, and publish clinical research without disclosure of HIPAA Protected Health Information (PHI). METHODS: Three clinical database formats (small clinical trial, operating room performance, and genetic microchip array datasets) were modeled using standard structured query language (SQL)-compliant databases. The CK database was created to contain PHI data, whereas a shareable SD database was generated in real-time containing relevant clinical outcome information while protecting PHI items. Small (< 100 records), medium (< 50,000 records), and large (> 10(8) records) model databases were created, and the resultant data models were evaluated in consultation with an HIPAA compliance officer. RESULTS: The SD database models complied fully with HIPAA regulations, and resulting "shared" data could be distributed freely. Unique patient identifiers were not required for treatment or outcome analysis. Age data were resolved to single-integer years, grouping patients aged > 89 years. Admission, discharge, treatment, and follow-up dates were replaced with enrollment year, and follow-up/outcome intervals calculated eliminating original data. Two additional data fields identified as PHI (treating physician and facility) were replaced with integer values, and the original data corresponding to these values were stored in the CK database. Use of the algorithm at the time of database design did not increase cost or design effort. CONCLUSIONS: The CK-SD model for clinical database design provides an algorithm for investigators to create, maintain, and share clinical research data compliant with HIPAA regulations. This model is applicable to new projects and large institutional datasets, and should decrease regulatory efforts required for conduct of clinical research. Application of the design algorithm early in the clinical research enterprise does not increase cost or the effort of data collection.

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An algorithmic approach to thyroid function testing in a managed care setting. 3-year experience.

An algorithm (directed thyrotropin [TSH], directed thyroid testing algorithm [DRTSH]) for the initial evaluation and monitoring of thyroid function was established in our institution in 1990. The algorithm begins with measurement of TSH by a sensitive immunoassay. If TSH is either < 0.4 mU/L or > 5.5 mU/L, a free thyroid index (T4 x Resin Uptake Ratio (RU)) is automatically performed on the same sample on the same day. In the setting of a large, predominately outpatient, prepaid health care population, the algorithm reduces unnecessary testing and focuses resources on the patients who need it. Three years after its introduction, physician acceptance of this approach is high ( > 90%), test utilization is reduced, test turnaround time is reduced, and significant cost-savings can be demonstrated.

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Comparing a mass-balance algorithm with a Bayesian regression analysis computer program for predicting serum phenytoin concentrations.

The ability of a mass-balance algorithm to predict non-steady-state phenytoin concentrations in neurosurgery patients was compared with that of Phenda, a computerized Bayesian regression analysis program. Fifty neurosurgery patients who had had two or more initial phenytoin serum concentrations measured at least 60 hours apart and at least 1 hour after any i.v. doses, with the second concentration being not more than twice and not less than half of the first, and who had had a third or final phenytoin measurement (for use in a prediction analysis) were evaluated. The patients' maximum rates of metabolism were calculated by using the two initial phenytoin concentrations and a mass-balance algorithm, and the third phenytoin concentration was predicted. The patients' demographics and phenytoin dosages and concentrations were entered into Phenda, which was used to predict the third phenytoin concentration. The ability of the two methods to predict the third concentration was evaluated by the method of Sheiner and Beal. Fifty observations from 48 patients were evaluated. The mass-balance algorithm had a positive prediction bias of 2.52 mg/L and a precision error of 5.08 mg/L, compared with 2.30 and 5.30, respectively, for Phenda. The difference in the results between the two methods was not significant. There was no significant difference between the mass-balance algorithm and Phenda in the ability to predict phenytoin concentrations.

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Data bank homology search algorithm with linear computation complexity.

A new algorithm for data bank homology search is proposed. The principal advantages of the new algorithm are: (i) linear computation complexity; (ii) low memory requirements; and (iii) high sensitivity to the presence of local region homology. The algorithm first calculates indicative matrices of k-tuple 'realization' in the query sequence and then searches for an appropriate number of matching k-tuples within a narrow range in database sequences. It does not require k-tuple coordinates tabulation and in-memory placement for database sequences. The algorithm is implemented in a program for execution on PC-compatible computers and tested on PIR and GenBank databases with good results. A few modifications designed to improve the selectivity are also discussed. As an application example, the search for homology of the mouse homeotic protein HOX 3.1 is given.

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A probabilistic algorithm for interactive huge genome comparison.

We designed a new probabilistic algorithm, named PAGEC (probabilistic algorithm for genome comparison), which allowed a highly interactive study of long genomic strings. The comparison between two nucleic acid sequences is based on the creation of multiple index tables, which drastically reduces processing time for huge genomes, e.g. 13 min for a 4 Mb/4 Mb comparison. PAGEC lowered the need for memory when compared with other types of algorithm and took into account the low resolution of the final representation (paper or computer screen). Considering that standard printers permit a 300 d.p.i. resolution, the loss of computed information due to the probabilistic conception of the algorithm was not usually noticeable in the present study, mainly due to increased genomic sizes. Refinement was possible through an interactive zooming system, which enabled the visualization of the lexical base sequences of a considered part of both of the studied genomes. Biological examples of computation based on yeast and animal nucleic acid sequences presented in this paper reveal the flexibility of the PAGEC program, which is a valuable tool for genetic studies as it offers a solution to an important problem that will become even more important as time passes.

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Introduction of a distance cut-off into structural alignment by the double dynamic programming algorithm.

Two approximations were introduced into the double dynamic programming algorithm, in order to reduce the computational time for structural alignment. One of them was the so-called distance cut-off, which approximately describes the structural environment of each residue by its local environment. In the approximation, a sphere with a given radius is placed at the center of the side chain of each residue. The local environment of a residue is constituted only by the residues with side chain centers that are present within the sphere, which is expressed by a set of center-to-center distances from the side chain of the residue to those of all the other constituent residues. The residues outside the sphere are neglected from the local environment. Another approximation is associated with the distance cut-off, which is referred to here as the delta N cut-off. If two local environments are similar to each other, the numbers of residues constituting the environments are expected to be similar. The delta N cut-off was introduced based on the idea. If the difference between the numbers of the constituent residues of two local environments is greater than a given threshold value, delta N, the evaluation of the similarity between the local environments is skipped. The introduction of the two approximations dramatically reduced the computational time for structural alignment by the double dynamic programming algorithm. However, the approximations also decreased the accuracy of the alignment. To improve the accuracy with the approximations, a program with a two-step alignment algorithm was constructed. At first, an alignment was roughly constructed with the approximations. Then, the epsilon-suboptimal region for the alignment was determined. Finally, the double dynamic programming algorithm with full structural environments was applied to the residue pairs within the epsilon-suboptimal region to produce an improved alignment.

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A fast, stochastic threading algorithm for proteins.

MOTIVATION: Sequences for new proteins are being determined at a rapid rate, as a result of the Human Genome Project, and related genome research. The ability to predict the three-dimensional structure of proteins from sequence alone would be useful in discovering and understanding their function. Threading, or fold recognition, aims to predict the tertiary structure of a protein by aligning its amino acid sequence with a large number of structures, and finding the best fit. This approach depends on obtaining good performance from both the scoring function, which simulates the free energy for given trial alignments, and the threading algorithm, which searches for the lowest-score alignment. It appears that current scoring functions and threading algorithms need improvement. RESULTS: This paper presents a new threading algorithm. Numerical tests demonstrate that it is more powerful than two popular approximate algorithms, and much faster than exact methods.

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Sequence search algorithm assessment and testing toolkit (SAT).

MOTIVATION: The Sequence Search Algorithm Assessment and Testing Toolkit (SAT) aims to be a complete package for the comparison of different protein homology search algorithms. The structural classification of proteins can provide us with a clear criterion for judgment in homology detection. There have been several assessments based on structural sequences with classifications but a good deal of similar work is now being repeated with locally developed procedures and programs. The SAT will provide developers with a complete package which will save time and produce more comparable performance assessments for search algorithms. The package is complete in the sense that it provides a non-redundant large sequence resource database, a well-characterized query database of proteins domains, all the parsers and some previous results from PSI-BLAST and a hidden markov model algorithm. RESULTS: An analysis on two different data sets was carried out using the SAT package. It compared the performance of a full protein sequence database (RSDB100) with a non-redundant representative sequence database derived from it (RSDB50). The performance measurement indicated that the full database is sub-optimal for a homology search. This result justifies the use of much smaller and faster RSDB50 than RSDB100 for the SAT. AVAILABILITY: A web site is up. The whole packa ge is accessible via www and ftp. ftp://ftp.ebi.ac.uk/pub/contrib/jong/SAT http://cyrah.ebi.ac.uk:1111/Proj/Bio/SAT http://www.mrc-lmb.cam.ac.uk/genomes/SAT In the package, some previous assessment results produced by the package can also be found for reference. CONTACT: jong@ebi.ac.uk

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