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Sorting Cancer Karyotypes by Elementary Operations

机译：通过基本操作对癌症核型进行分类

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Since the discovery of the "Philadelphia chromosome" in chronic myelogenous leukemia in 1960, there is an ongoing intensive research of chromosomal aberrations in cancer. These aberrations, which result in abnormally structured genomes, became a hallmark of cancer.Many studies give evidence to the connection between chromosomal alterations and aberrant genes involved in the carcinogenesis process. An important problem in the analysis of cancer genomes, is inferring the history of events leading to the observed aberrations. Cancer genomes are usually described in form of karyotypes, which present the global changes in the genomes' structure. In this study, we propose a mathematical framework for analyzing chromosomal aberrations in cancer karyotypes.We introduce the problem of sorting karyotypes by elementary operations, which seeks for a shortest sequence of elementary chromosomal events transforming a normal karyotype into a given (abnormal) cancerous karyotype. Under certain assumptions, we prove a lower bound for the elementary distance, and present a polynomial-time 3-approximation algorithm. We applied our algorithm to karyotypes from the Mitelman database, which records cancer karyotypes reported in the scientific literature. Approximately 94% of the karyotypes in the database, totalling 57,252 karyotypes, supported our assumptions, and each of them was subjected to our algorithm. Remarkably, even though the algorithm is only guaranteed to generate a 3-approximation, it produced a sequence whose length matches the lower bound (and hence optimal) in 99.9% of the tested karyotypes.
机译：自从1960年在慢性粒细胞性白血病中发现“费城染色体”以来，正在进行有关癌症染色体畸变的深入研究。这些畸变导致基因组结构异常，成为癌症的标志。许多研究为染色体改变与致癌过程中涉及的异常基因之间的联系提供了证据。癌症基因组分析中的一个重要问题是推断导致观察到的像差的事件的历史。癌症基因组通常以核型的形式描述，其呈现出基因组结构的整体变化。在这项研究中，我们提出了一个用于分析癌症核型中染色体畸变的数学框架。我们介绍了通过基本操作对核型进行分类的问题，该问题寻求最短的基本染色体事件序列，将正常核型转化为给定的（异常）癌性核型。 。在某些假设下，我们证明了基本距离的下界，并提出了多项式时间3逼近算法。我们将算法应用于Mitelman数据库中的核型，该数据库记录了科学文献中报道的癌症核型。数据库中大约94％的核型，总计57,252个核型，支持我们的假设，并且每种假设都接受了我们的算法。值得注意的是，即使仅保证算法生成3个近似值，它仍会生成一个序列，其长度与99.9％的受试核型中的下限匹配（因此为最佳）。

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