Probability and Statistics and Related Biomolecular Sequence Analysis

本研究的重点是开发与生物分子序列分析相关的新的概率和统计工具，特别强调：(i)在多个相关序列中使用标记阵列的扫描统计分析。具体来说，为了找到几个随机模型的极值r扫描长度的渐近分布，通过容纳依赖和/或转换数据扩展了研究人员早期的工作。然后，这些渐近性作为解释各种生物相关多序列数据的基准，通过提供沿一个或多个序列的聚类或过度分散标记的概率估计。（ii）提供一个灵活和通用的框架，用于表征蛋白质3D结构中不寻常成分的残基簇和统计显著性，以及评估两个或多个此类结构之间强局部相似性的统计显著性的方法。所提出的框架是基于对加权标记图随机模型的研究，因此它推广了以前在蛋白质序列比较中使用的基于一般分数的方法的概率基础上的工作。自1995年以来，几个原核生物基因组和一个真核生物基因组已经被报道，许多即将到来。这些基因组为描述基因组的不同质性、检测重要的序列模式以及进行进化比较提供了机会，同时也提出了挑战。全基因组和大量DNA和蛋白质序列的可用性开启了生物信息学研究的新时代。上述(i)和（ii）的进展可以为生物分子数据分析以及蛋白质序列和相应三维结构的比较提供急需的工具。软件方法通常用于发现新发现的序列与现有数据库之间的关系。检测到的相似性可用于预测新结构的生物特征，为进一步的实验研究指明方向，并指出可能的医学应用。然而，由于数据库的加速增长，随机相关性可能一开始看起来很重要，从而掩盖了数据中存在的真实生物信息。本研究旨在将生物分子数据分析程序建立在坚实的数学基础上，同时减少随机相关的掩蔽效应。

9704552 Karlin This research centers on developing new probabilistic and statistical tools of relevance to biomolecular sequence analysis with particular emphasis on: (i) The use of scan statistical analysis of marker arrays in multiple correlated sequences. Specifically, to find asymptotic distributions of extremal r-scan lengths for several stochastic models, extending earlier work of the investigators by accommodating dependent and/or transformed data. These asymptotics then serve as benchmarks for interpreting various biological correlated multiple sequence data by providing estimates of probabilities of clustering or over-dispersion of markers along one or more sequences. (ii) To provide a flexible and general framework for characterizing residue clusters and statistical significance of unusual compositions in protein 3D structures as well as the means of assessing statistical significance of strong local similarities among two or more such structures. The proposed framework is based on the study of random models for weighted labeled graphs and as such it generalizes previous work on the probabilistic foundation of general score based methods for use in protein sequence comparison. Since 1995, several prokaryotic genomes and one eukaryotic genome have been reported, and many are forthcoming. These genomes provide opportunities and pose challenges for characterizing genomic inhomogeneities, for detecting significant sequence patterns, and for evolutionary comparisons. Availability of complete genomes and massive amounts of DNA and protein sequences opens a new era in bioinformatics research. Advances in (i) and (ii) above can provide much needed tools for biomolecular data analysis and for comparison of protein sequences and corresponding three-dimensional structures. Software approaches are often used to find relationships between newly discovered sequences and the existing data banks. Similarities detected can be used to predict biologi cal characteristics of new structures, suggest directions for further experimental study, and point to possible medical applications. However, due to the accelerating growth of the data banks, random correlations might at first appear significant and thus mask the true biological information existing in the data. This research aims at putting biomolecular data analysis procedures on a firm mathematical foundation, and concomitantly reducing the masking effect of random correlations.