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PubMed2004

Phylogeny of protein-folding trajectories reveals a unique pathway to native structure.

To scrutinize how a protein folds at atomic resolution, we performed 200 molecular dynamics simulations (each of 50 ns) of the miniprotein Trp-cage on the computational grid. Within the trajectories, 58 folding and 31 unfolding events were identified and subjected to extensive comparison and classification. Based on an analogy with biological sequences, the folding and unfolding trajectories (arrays of sequential snapshots of structures) were aligned by dynamic programming allowing gaps. A phylogenetic tree derived from the alignments revealed four distinct groups of the trajectories, characterized by the Trp side-chain motions and the main-chain motions. It was found that only one group attained the native structure and that the other three led to pseudonative structures having the correct main-chain trace but different nonnative Trp side-chain rotamers, indicating that those four folded structures were each attained through a unique folding pathway.

Computational Biology↗
PubMed2004

A versatile statistical analysis algorithm to detect genome copy number variation.

We have developed a versatile statistical analysis algorithm for the detection of genomic aberrations in human cancer cell lines. The algorithm analyzes genomic data obtained from a variety of array technologies, such as oligonucleotide array, bacterial artificial chromosome array, or array-based comparative genomic hybridization, that operate by hybridizing with genomic material obtained from cancer and normal cells and allow detection of regions of the genome with altered copy number. The number of probes (i.e., resolution), the amount of uncharacterized noise per probe, and the severity of chromosomal aberrations per chromosomal region may vary with the underlying technology, biological sample, and sample preparation. Constrained by these uncertainties, our algorithm aims at robustness by using a priorless maximum a posteriori estimator and at efficiency by a dynamic programming implementation. We illustrate these characteristics of our algorithm by applying it to data obtained from representational oligonucleotide microarray analysis and array-based comparative genomic hybridization technology as well as to synthetic data obtained from an artificial model whose properties can be varied computationally. The algorithm can combine data from multiple sources and thus facilitate the discovery of genes and markers important in cancer, as well as the discovery of loci important in inherited genetic disease.

Algorithms↗
PubMed2005

An algorithm for progressive multiple alignment of sequences with insertions.

Dynamic programming algorithms guarantee to find the optimal alignment between two sequences. For more than a few sequences, exact algorithms become computationally impractical, and progressive algorithms iterating pairwise alignments are widely used. These heuristic methods have a serious drawback because pairwise algorithms do not differentiate insertions from deletions and end up penalizing single insertion events multiple times. Such an unrealistically high penalty for insertions typically results in overmatching of sequences and an underestimation of the number of insertion events. We describe a modification of the traditional alignment algorithm that can distinguish insertion from deletion and avoid repeated penalization of insertions and illustrate this method with a pair hidden Markov model that uses an evolutionary scoring function. In comparison with a traditional progressive alignment method, our algorithm infers a greater number of insertion events and creates gaps that are phylogenetically consistent but spatially less concentrated. Our results suggest that some insertion/deletion "hot spots" may actually be artifacts of traditional alignment algorithms.

Algorithms↗
PubMed1971

Stochastic speculative price.

Because a commodity like wheat can be carried forward from one period to the next, speculative arbitrage serves to link its prices at different points of time. Since, however, the size of the harvest depends on complicated probability processes impossible to forecast with certainty, the minimal model for understanding market behavior must involve stochastic processes. The present study, on the basis of the axiom that it is the expected rather than the known-for-certain prices which enter into all arbitrage relations and carryover decisions, determines the behavior of price as the solution to a stochastic-dynamic-programming problem. The resulting stationary time series possesses an ergodic state and normative properties like those often observed for real-world bourses.

Journal Article↗
PubMed1987

Profile analysis: detection of distantly related proteins.

Profile analysis is a method for detecting distantly related proteins by sequence comparison. The basis for comparison is not only the customary Dayhoff mutational-distance matrix but also the results of structural studies and information implicit in the alignments of the sequences of families of similar proteins. This information is expressed in a position-specific scoring table (profile), which is created from a group of sequences previously aligned by structural or sequence similarity. The similarity of any other sequence (target) to the group of aligned sequences (probe) can be tested by comparing the target to the profile using dynamic programming algorithms. The profile method differs in two major respects from methods of sequence comparison in common use: (i) Any number of known sequences can be used to construct the profile, allowing more information to be used in the testing of the target than is possible with pairwise alignment methods. (ii) The profile includes the penalties for insertion or deletion at each position, which allow one to include the probe secondary structure in the testing scheme. Tests with globin and immunoglobulin sequences show that profile analysis can distinguish all members of these families from all other sequences in a database containing 3800 protein sequences.

Amino Acid Sequence↗
PubMed1990

Automatic generation of primary sequence patterns from sets of related protein sequences.

We have developed a computer algorithm that can extract the pattern of conserved primary sequence elements common to all members of a homologous protein family. The method involves clustering the pairwise similarity scores among a set of related sequences to generate a binary dendrogram (tree). The tree is then reduced in a stepwise manner by progressively replacing the node connecting the two most similar termini by one common pattern until only a single common "root" pattern remains. A pattern is generated at a node by (i) performing a local optimal alignment on the sequence/pattern pair connected by the node with the use of an extended dynamic programming algorithm and then (ii) constructing a single common pattern from this alignment with a nested hierarchy of amino acid classes to identify the minimal inclusive amino acid class covering each paired set of elements in the alignment. Gaps within an alignment are created and/or extended using a "pay once" gap penalty rule, and gapped positions are converted into gap characters that function as 0 or 1 amino acid of any type during subsequent alignment. This method has been used to generate a library of covering patterns for homologous families in the National Biomedical Research Foundation/Protein Identification Resource protein sequence data base. We show that a covering pattern can be more diagnostic for sequence family membership than any of the individual sequences used to construct the pattern.

Amino Acid Sequence↗
PubMed1992

Parametric sequence comparisons.

Current algorithms can find optimal alignments of two nucleic acid or protein sequences, often by using dynamic programming. While the choice of algorithm penalty parameters greatly influences the quality of the resulting alignments, this choice has been done in an ad hoc manner. In this work, we present an algorithm to efficiently find the optimal alignments for all choices of the penalty parameters. It is then possible to systematically explore these alignments for those with the most biological or statistical interest. Several examples illustrate the method.

Algorithms↗
PubMed1999

A theoretical search for folding/unfolding nuclei in three-dimensional protein structures.

When a protein folds or unfolds, it has to pass through many half-folded microstates. Only a few of them can be seen experimentally. In a two-state transition proceeding with no accumulation of metastable intermediates [Fersht, A. R. (1995) Curr. Opin. Struct. Biol. 5, 79-84], only the semifolded microstates corresponding to the transition state can be outlined; they influence the folding/unfolding kinetics. Our aim is to calculate them, provided the three-dimensional protein structure is given. The presented approach follows from the capillarity theory of protein folding and unfolding [Wolynes, P. G. (1997) Proc. Natl. Acad. Sci. USA 94, 6170-6175]. The approach is based on a search for free-energy saddle point(s) on a network of protein unfolding pathways. Under some approximations, this search is rapidly performed by dynamic programming and, despite its relative simplicity, gives a good correlation with experiment. The computed folding nuclei look like ensembles of those compact and closely packed parts of the three-dimensional native folds that contain a small number of disordered protruding loops. Their estimated free energy is consistent with the rapid (within seconds) folding and unfolding of small proteins at the point of thermodynamic equilibrium between the native fold and the coil.

Protein Conformation↗
PubMed2005

Classification of cancer cell lines using an automated two-dimensional liquid mapping method with hierarchical clustering techniques.

A two-dimensional liquid mapping method was used to map the protein expression of eight ovarian serous carcinoma cell lines and three immortalized ovarian surface epithelial cell lines. Maps were produced using pI as the separation parameter in the first dimension and hydrophobicity based upon reversed-phase HPLC separation in the second dimension. The method can be reproducibly used to produce protein expression maps over a pH range from 4.0 to 8.5. A dynamic programming method was used to correct for minor shifts in peaks during the HPLC gradient between sample runs. The resulting corrected maps can then be compared using hierarchical clustering to produce dendrograms indicating the relationship between different cell lines. It was found that several of the ovarian surface epithelial cell lines clustered together, whereas specific groups of serous carcinoma cell lines clustered with each other. Although there is limited information on the current biology of these cell lines, it was shown that the protein expression of certain cell lines is closely related to each other. Other cell lines, including one ovarian clear cell carcinoma cell line, two endometrioid carcinoma cell lines, and three breast epithelial cell lines, were also mapped for comparison to show that their protein profiles cluster differently than the serous samples and to study how they cluster relative to each other. In addition, comparisons can be made between proteins differentially expressed between cell lines that may serve as markers of ovarian serous carcinomas. The automation of the method allows reproducible comparison of many samples, and the use of differential analysis limits the number of proteins that might require further analysis by mass spectrometry techniques.

Adenocarcinoma, Clear Cell↗
PubMedDate not supplied

Automatic contour tracking in ultrasound images.

In this paper, a new automatic contour tracking system, EdgeTrak, for the ultrasound image sequences of human tongue is presented. The images are produced by a head and transducer support system (HATS). The noise and unrelated high-contrast edges in ultrasound images make it very difficult to automatically detect the correct tongue surfaces. In our tracking system, a novel active contour model is developed. Unlike the classical active contour models which only use gradient of the image as the image force, the proposed model incorporates the edge gradient and intensity information in local regions around each snake element. Different from other active contour models that use homogeneity of intensity in a region as the constraint and thus are only applied to closed contours, the proposed model applies local region information to open contours and can be used to track partial tongue surfaces in ultrasound images. The contour orientation is also taken into account so that any unnecessary edges in ultrasound images will be discarded. Dynamic programming is used as the optimisation method in our implementation. The proposed active contour model has been applied to human tongue tracking and its robustness and accuracy have been verified by quantitative comparison analysis to the tracking by speech scientists.

Algorithms↗
PubMedDate not supplied

Tongue motion averaging from contour sequences.

In this paper, a method to get the best representation of a speech motion from several repetitions is presented. Each repetition is a representation of the same speech captured at different times by sequence of ultrasound images and is composed of a set of 2D spatio-temporal contours. These 2D contours in different repetitions are time aligned first by a shape based Dynamic Programming (DP) method. The best representation of the speech motion is then obtained by averaging the time aligned contours from different repetitions. Procrustes analysis is used to measure the contour similarity in the time alignment process and to get the averaged best representation. To get the point correspondence for Procrustes analysis, a nonrigid point correspondence recovery method based on a local stretching model and a global constraint is developed. Synthetic validations and experiments on real tongue motion are also presented in this paper.

Algorithms↗
PubMed2002

Haplotype block structure and its applications to association studies: power and study designs.

Recent studies have shown that the human genome has a haplotype block structure, such that it can be divided into discrete blocks of limited haplotype diversity. In each block, a small fraction of single-nucleotide polymorphisms (SNPs), referred to as "tag SNPs," can be used to distinguish a large fraction of the haplotypes. These tag SNPs can potentially be extremely useful for association studies, in that it may not be necessary to genotype all SNPs; however, this depends on how much power is lost. Here we develop a simulation study to quantitatively assess the power loss for a variety of study designs, including case-control designs and case-parental control designs. First, a number of data sets containing case-parental or case-control samples are generated on the basis of a disease model. Second, a small fraction of case and control individuals in each data set are genotyped at all the loci, and a dynamic programming algorithm is used to determine the haplotype blocks and the tag SNPs based on the genotypes of the sampled individuals. Third, the statistical power of tests was evaluated on the basis of three kinds of data: (1) all of the SNPs and the corresponding haplotypes, (2) the tag SNPs and the corresponding haplotypes, and (3) the same number of randomly chosen SNPs as the number of tag SNPs and the corresponding haplotypes. We study the power of different association tests with a variety of disease models and block-partitioning criteria. Our study indicates that the genotyping efforts can be significantly reduced by the tag SNPs, without much loss of power. Depending on the specific haplotype block-partitioning algorithm and the disease model, when the identified tag SNPs are only 25% of all the SNPs, the power is reduced by only 4%, on average, compared with a power loss of approximately 12% when the same number of randomly chosen SNPs is used in a two-locus haplotype analysis. When the identified tag SNPs are approximately 14% of all the SNPs, the power is reduced by approximately 9%, compared with a power loss of approximately 21% when the same number of randomly chosen SNPs is used in a two-locus haplotype analysis. Our study also indicates that haplotype-based analysis can be much more powerful than marker-by-marker analysis.

Algorithms↗
PubMed2002

Sensitive and efficient detection of RB1 gene mutations enhances care for families with retinoblastoma.

Timely molecular diagnosis of RB1 mutations enables earlier treatment, lower risk, and better health outcomes for patients with retinoblastoma; empowers families to make informed family-planning decisions; and costs less than conventional surveillance. However, complexity has hindered clinical implementation of molecular diagnosis. The majority of RB1 mutations are unique and distributed throughout the RB1 gene, with no real hot spots. We devised a sensitive and efficient strategy to identify RB1 mutations that combines quantitative multiplex polymerase chain reaction (QM-PCR), double-exon sequencing, and promoter-targeted methylation-sensitive PCR. Optimization of test order by stochastic dynamic programming and the development of allele-specific PCR for four recurrent point mutations decreased the estimated turnaround time to <3 wk and decreased direct costs by one-third. The multistep method reported here detected 89% (199/224) of mutations in bilaterally affected probands and both mutant alleles in 84% (112/134) of tumors from unilaterally affected probands. For 23 of 27 exons and the promoter region, QM-PCR was a highly accurate measure of deletions and insertions (accuracy 95%). By revealing those family members who did not carry the mutation found in the related proband, molecular analysis enabled 97 at-risk children from 20 representative families to avoid 313 surveillance examinations under anesthetic and 852 clinic visits. The average savings in direct costs from clinical examinations avoided by children in these families substantially exceeded the cost of molecular testing. Moreover, health care savings continue to accrue, as children in succeeding generations avoid unnecessary repeated anaesthetics and examinations.

Algorithms↗
PubMed2003

Haplotype block partition with limited resources and applications to human chromosome 21 haplotype data.

Recent studies have shown that the human genome has a haplotype block structure such that it can be decomposed into large blocks with high linkage disequilibrium (LD) and relatively limited haplotype diversity, separated by short regions of low LD. One of the practical implications of this observation is that only a small fraction of all the single-nucleotide polymorphisms (SNPs) (referred as "tag SNPs") can be chosen for mapping genes responsible for human complex diseases, which can significantly reduce genotyping effort, without much loss of power. Algorithms have been developed to partition haplotypes into blocks with the minimum number of tag SNPs for an entire chromosome. In practice, investigators may have limited resources, and only a certain number of SNPs can be genotyped. In the present article, we first formulate this problem as finding a block partition with a fixed number of tag SNPs that can cover the maximal percentage of the whole genome, and we then develop two dynamic programming algorithms to solve this problem. The algorithms are sufficiently flexible to permit knowledge of functional polymorphisms to be considered. We apply the algorithms to a data set of SNPs on human chromosome 21, combining the information of coding and noncoding regions. We study the density of SNPs in intergenic regions, introns, and exons, and we find that the SNP density in intergenic regions is similar to that in introns and is higher than that in exons, results that are consistent with previous studies. We also calculate the distribution of block break points in intergenic regions, genes, exons, and coding regions and do not find any significant differences.

Chromosomes, Human, Pair 21↗
PubMed2003

Minimum description length block finder, a method to identify haplotype blocks and to compare the strength of block boundaries.

We describe a new probabilistic method for finding haplotype blocks that is based on the use of the minimum description length (MDL) principle. We give a rigorous definition of the quality of a segmentation of a genomic region into blocks and describe a dynamic programming algorithm for finding the optimal segmentation with respect to this measure. We also describe a method for finding the probability of a block boundary for each pair of adjacent markers: this gives a tool for evaluating the significance of each block boundary. We have applied the method to the published data of Daly and colleagues. The results expose some problems that exist in the current methods for the evaluation of the significance of predicted block boundaries. Our method, MDL block finder, can be used to compare block borders in different sample sets, and we demonstrate this by applying the MDL-based method to define the block structure in chromosomes from population isolates.

Haplotypes↗
PubMedDate not supplied

DNA segmentation through the Bayesian approach.

We present a new approach to DNA segmentation into compositionally homogeneous blocks. The Bayesian estimator, which is applicable for both short and long segments, is used to obtain the measure of homogeneity. An exact optimal segmentation is found via the dynamic programming technique. After completion of the segmentation procedure, the sequence composition on different scales can be analyzed with filtration of boundaries via the partition function approach.

Algorithms↗
PubMedDate not supplied

Bayesian segmentation of protein secondary structure.

We present a novel method for predicting the secondary structure of a protein from its amino acid sequence. Most existing methods predict each position in turn based on a local window of residues, sliding this window along the length of the sequence. In contrast, we develop a probabilistic model of protein sequence/structure relationships in terms of structural segments, and formulate secondary structure prediction as a general Bayesian inference problem. A distinctive feature of our approach is the ability to develop explicit probabilistic models for alpha-helices, beta-strands, and other classes of secondary structure, incorporating experimentally and empirically observed aspects of protein structure such as helical capping signals, side chain correlations, and segment length distributions. Our model is Markovian in the segments, permitting efficient exact calculation of the posterior probability distribution over all possible segmentations of the sequence using dynamic programming. The optimal segmentation is computed and compared to a predictor based on marginal posterior modes, and the latter is shown to provide significant improvement in predictive accuracy. The marginalization procedure provides exact secondary structure probabilities at each sequence position, which are shown to be reliable estimates of prediction uncertainty. We apply this model to a database of 452 nonhomologous structures, achieving accuracies as high as the best currently available methods. We conclude by discussing an extension of this framework to model nonlocal interactions in protein structures, providing a possible direction for future improvements in secondary structure prediction accuracy.

Algorithms↗
PubMed2001

A sequence alignment algorithm with an arbitrary gap penalty function.

An algorithm for aligning biological sequences is presented that is an adaptation of the sequence generating function approach used in the statistical mechanics of biopolymers. This algorithm uses recursion relationships developed from a partition function formalism of alignment probabilities. It is implemented within a dynamic programming format that closely resembles the forward algorithm used in hidden Markov models (HMM). The algorithm aligns sequences or structures according to the statistically dominant alignment path and will be referred to as the SDP algorithm. An advantage of this method over previous ones is that it allows more complicated and physically realistic gap penalty functions to be incorporated into the algorithm in a facile manner. The performance of this algorithm in a case study of aligning the heavy and light chain from the variable region of an immunoglobulin is investigated.

Algorithms↗