Regression Analysis of Multiple Protein Structures

title: Minimal-Risk Scoring Matrices for Sequence Analysis
abstract: We introduce a minimal-risk method for estimating the frequencies of amino acids at conserved positions in a protein family. Our method, called minimal-risk estimation, finds the optimal weighting between a set of observed amino acid counts and a set of pseudofrequencies, which represent prior information about the frequencies. We compute the optimal weighting by minimizing the expected distance between the estimated frequencies and the true population frequencies, measured by either a squared-error or a relative-entropy metric. Our method accounts for the source of the pseudofrequencies, which arise either from the background distribution of amino acids or from applying a substitution matrix to the observed data. Our frequency estimates therefore depend on the size and composition of the observed data as well as the source of the pseudofrequencies. We convert our frequency estimates into minimal-risk scoring matrices for sequence analysis. A large-scale cross-validation study, involving 48 variants of seven methods, shows that the best performing method is minimal-risk estimation using the squared-error metric. Our method is implemented in the package EMATRIX, which is available on the Internet at http://motif.stanford.edu/ematrix.

title: Discovering Empirically Conserved Amino Acid Substitution Groups in Databases of Protein Families
abstract: This paper introduces a method for identifying empirically conserved amino acid substitution groups. In contrast with existing approaches that view amino acid substitution as a pairwise phenomenon, the method presented here identifies conserved groups of amino acids using a data structure called a conditional distribution matrix. The conditional distribution matrix extends the concept of a pairwise substitution matrix by changing the context of substitution from a single amino acid to a group of amino acids. The matrix tabulates information from a database of protein families that contains numerous aligned positions. Each row in the matrix contains the distribution of amino acids in those aligned positions that contain a given conditioning group of amino acids. The method converts a database of protein families into a conditional distribution matrix and then examines each possible substitution group for evidence of conservation. The algorithm is applied to the BLOCKS and HSSP databases. Twenty amino acid substitution groups are found to be conserved empirically in both databases. These groups provide insight into biochemical properties that are conserved in protein evolution.

title: Regression analysis of multiple protein structures
abstract: A general framework is presented for analyzing multiple protein structures using statistical regression methods. The regression approach can superimpose protein structures rigidly or with shear. Also, this approach can superimpose multiple structures explicitly, without resorting to pairwise superpositions. The algorithm alternates between matching corresponding landmarks among the protein structures and superimposing these landmarks. Matching is performed using a robust dynamic programming technique that uses gap penalties that adapt to the given data. Superposition is performed using either orthogonal transformations, which impose the rigid-body assumption, or affine transformations, which allow shear. The resulting regression model of a protein family measures the amount of structural variability at each landmark. A variation of our algorithm permits a separate weight for each landmark, thereby allowing one to emphasize particular segments of a protein structure or to compensate for variances that differ at various positions in a structure. In addition, a method is introduced for finding an initial correspondence, by measuring the discrete curvature along each protein backbone. Discrete curvature also characterizes the secondary structure of a protein backbone, distinguishing among helical, strand, and loop regions. An example is presented involving a set of seven globin structures. Regression analysis, using both affine and orthogonal transformations, reveals that globins are most strongly conserved structurally in helical regions, particularly in the mid-regions of the E, F, and G helices.

title: Fast probabilistic analysis of sequence function using scoring matrices
abstract: We present techniques for increasing the speed of sequence analysis using scoring matrices. Our techniques are based on calculating, for a given scoring matrix, the quantile function, which assigns a probability, or p, value to each segmental score. Our techniques also permit the user to specify a p threshold to indicate the desired trade-off between sensitivity and speed for a particular sequence analysis. The resulting increase in speed should allow scoring matrices to be used more widely in large-scale sequencing and annotation projects.



We develop three techniques for increasing the speed of sequence analysis: probability filtering, lookahead scoring, and permuted lookahead scoring. In probability filtering, we compute the score threshold that corresponds to the user-specified p threshold. We use the score threshold to limit the number of segments that are retained in the search process. In lookahead scoring, we test intermediate scores to determine whether they will possibly exceed the score threshold. In permuted lookahead scoring, we score each segment in a particular order designed to maximize the likelihood of early termination. Our two lookahead scoring techniques reduce substantially the number of residues that must be examined. The fraction of residues examined ranges from 62 to 6%, depending on the p threshold chosen by the user. These techniques permit sequence analysis with scoring matrices at speeds that are several times faster than existing programs. On a database of 12 177 alignment blocks, our techniques permit sequence analysis at a speed of 225 residues/s for a p threshold of 10-6, and 541 residues/s for a p threshold of 10-20. In order to compute the quantile function, we may use either an independence assumption or a Markov assumption. We measure the effect of first- and second-order Markov assumptions and find that they tend to raise the p value of segments, when compared with the independence assumption, by average ratios of 1.30 and 1.69, respectively. We also compare our technique with the empirical 99. 5th percentile scores compiled in the BLOCKSPLUS database, and find that they correspond on average to a p value of 1.5 x 10-5.


AVAILABILITY
The techniques described above are implemented in a software package called EMATRIX. This package is available from the authors for free academic use or for licensed commercial use. The EMATRIX set of programs is also available on the Internet at http://motif.stanford.edu/ematrix.

title: Efficient mobile content delivery by exploiting user interest correlation
abstract: Accelerating multimedia content delivery to mobile devices is challenging because we must not only address long and unpredictable latency created by the error-prone air interface, but also meet mobility-specific requirements such as efficient terminal power consumption. In this paper, we present a novel architecture for content delivery in the mobile environment (ACME) that significantly accelerates interactive mobile services such as Web browsing. ACME exploits the key concept of user interest correlation (the interest in the same content among different users) to push content to mobile users efficiently. Trace-driven simulations show that ACME achieves 50% effectiveness of content broadcasting by, on average, pushing content to only 0.7% to 6% of all users, thus substantially reducing mobile terminal power consumption. Furthermore, ACME has superior scalability as the push group size increases by only 62% when the total number of users increases by 16 times