The Statistics of Repeats

在马尔可夫加性过程(MAP)中，不精确的简单重复(包括无间隔和有间隔)可以被量化为局部和。局部和的最大值具有渐近的Gumbel分布，其参数由一般映射公式确定。这些公式通常在计算上很困难，但在无间隔重复的情况下进行必要的简化，就可以进行可行的计算。Spouge博士对无间隔重复序列的分析结果比G.Achaz等人的模拟结果更详细。(2006)“从大DNA序列中检索近似重复序列的工具RepSeek”。我们使用解析公式来提供洞察力和数字检验，同时确定相应的间隔重复的统计参数。希特林博士实施了公开可用的程序RepWords，用于寻找有间隙的串联重复序列并计算其统计数据。此外，Spouge博士、Sheetlin博士和Mario-Ramrez博士通过一个简单的笔划，将重要的线性时间Ruzzo-Tompa算法推广到寻找不寻常组成的无间隔子序列，以找到不寻常组成的间隔子序列。该推广包括了我们的重复发现算法作为特例。Park博士、Sheetlin博士和Spouge博士目前正在开发公开分发的程序，以计算统计上显著重复的阈值分数，并在生物序列中寻找重复。由此产生的程序将解释疟疾等重要病原体的扭曲基因组的组成，其中重复序列帮助病原体逃避免疫系统。

Inexact simple repeats (both ungapped and gapped) can be quantified as local sums in a Markov additive process (MAP). The maximum of the local sums has an asymptotic Gumbel distribution, with parameters determined by general MAP formulas. The formulas are usually computationally intractable, but an essential simplification in the case of ungapped repeats permits feasible computations. Dr. Spouge's analytic results for ungapped repeats are more detailed than results derived by simulation in G. Achaz et al. (2006) "Repseek, a tool to retrieve approximate repeats from large DNA sequences". We have used the analytic formulas to provide insight and numerical checks while determining the corresponding statistical parameters for gapped repeats. Dr. Sheetlin implemented the publicly available program RepWords for finding gapped tandem repeats and calculating their statistics. In addition, with a single simple stroke, Drs. Spouge, Sheetlin, and Mario-Ramrez generalized the important linear-time Ruzzo-Tompa algorithm for finding ungapped subsequences of unusual composition to finding gapped subsequences of unusual composition. The generalization includes our repeat-finding algorithms as a special case. Drs. Park, Sheetlin, and Spouge are presently developing programs for public distribution, to calculate threshold scores for statistically significant repeats and to find repeats in biological sequences. The resulting programs will account for composition of skewed genomes of important pathogens like malaria, where repeats aid the pathogen in evading the immune system.