Pathological rate matrices: from primates to pathogens.
Pathological rate matrices: from primates to pathogens.
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DOI：
10.1186/1471-2105-9-550
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发表时间：
2008-12-19
影响因子：
3
通讯作者：
Huttley GA
中科院分区：
文献类型：
--
作者：
Schranz HW;Yap VB;Easteal S;Knight R;Huttley GA
连续时间马尔可夫模型允许对序列分歧进行灵活、参数化的简洁描述。这些模型的不可逆形式在生物学上更加现实，但开发起来具有挑战性。为这些模型定义的瞬时速率矩阵通常使用采用特征分解的矩阵求幂算法转换为替换概率矩阵，但该算法具有特征漏洞，当速率矩阵具有某些“病态”属性时，会导致严重错误。在这里，我们测试了自然界中是否存在病理率矩阵，并考虑了不同算法对其计算的适用性。我们使用来自微生物基因组、灵长类基因组的串联蛋白质编码基因比对和来自灵长类基因组的独立内含子比对。将泰勒级数展开和特征分解矩阵求幂算法与应用较少但更稳健的 Padé 算法进行比较，Padé 具有用于核苷酸、二核苷酸、密码子和三核苷酸率矩阵的缩放和平方算法。微生物数据集中存在明显的病理性二核苷酸和三核苷酸矩阵，分别影响特征分解和泰勒算法。即使使用矩阵误差的保守估计（出现无效概率），泰勒算法和特征分解算法都表现出相当大的错误率：约 100% 的所有外显子三核苷酸矩阵对于泰勒算法来说是病理性的，而约 10% 的密码子位置 1 和 2 二核苷酸矩阵和内含子三核苷酸矩阵以及约 30% 的密码子矩阵对于特征分解来说是病理性的。大多数泰勒算法错误源自多个未观察到的状态的出现。三核苷酸矩阵上的 Padé 算法检测到少量负概率，这归因于机器精度。尽管 Padé 算法不利于缓存中间结果，但它比相同矩阵上的特征分解快 3 倍。开发用于计算不可逆二核苷酸、密码子和更高进化模型的强大软件需要使用缩放和平方算法来实现 Padé。
Continuous-time Markov models allow flexible, parametrically succinct descriptions of sequence divergence. Non-reversible forms of these models are more biologically realistic but are challenging to develop. The instantaneous rate matrices defined for these models are typically transformed into substitution probability matrices using a matrix exponentiation algorithm that employs eigendecomposition, but this algorithm has characteristic vulnerabilities that lead to significant errors when a rate matrix possesses certain 'pathological' properties. Here we tested whether pathological rate matrices exist in nature, and consider the suitability of different algorithms to their computation. We used concatenated protein coding gene alignments from microbial genomes, primate genomes and independent intron alignments from primate genomes. The Taylor series expansion and eigendecomposition matrix exponentiation algorithms were compared to the less widely employed, but more robust, Padé with scaling and squaring algorithm for nucleotide, dinucleotide, codon and trinucleotide rate matrices. Pathological dinucleotide and trinucleotide matrices were evident in the microbial data set, affecting the eigendecomposition and Taylor algorithms respectively. Even using a conservative estimate of matrix error (occurrence of an invalid probability), both Taylor and eigendecomposition algorithms exhibited substantial error rates: ~100% of all exonic trinucleotide matrices were pathological to the Taylor algorithm while ~10% of codon positions 1 and 2 dinucleotide matrices and intronic trinucleotide matrices, and ~30% of codon matrices were pathological to eigendecomposition. The majority of Taylor algorithm errors derived from occurrence of multiple unobserved states. A small number of negative probabilities were detected from the Padé algorithm on trinucleotide matrices that were attributable to machine precision. Although the Padé algorithm does not facilitate caching of intermediate results, it was up to 3× faster than eigendecomposition on the same matrices. Development of robust software for computing non-reversible dinucleotide, codon and higher evolutionary models requires implementation of the Padé with scaling and squaring algorithm.
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影响因子：
3
作者：
Butterfield A;Vedagiri V;Lang E;Lawrence C;Wakefield MJ;Isaev A;Huttley GA
通讯作者：
Huttley GA
影响因子：
12.3
作者：
Knight R;Maxwell P;Birmingham A;Carnes J;Caporaso JG;Easton BC;Eaton M;Hamady M;Lindsay H;Liu Z;Lozupone C;McDonald D;Robeson M;Sammut R;Smit S;Wakefield MJ;Widmann J;Wikman S;Wilson S;Ying H;Huttley GA
通讯作者：
Huttley GA
影响因子：
3.9
作者：
Lawrence, JG;Ochman, H
通讯作者：
Ochman, H
影响因子：
2.1
作者：
DEMMEL, JW
通讯作者：
DEMMEL, JW
影响因子：
56.9
作者：
Gibbs, Richard A.;Rogers, Jeffrey;Zwieg, Ann S.
通讯作者：
Zwieg, Ann S.