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首页> 外文期刊>Proceedings of the National Academy of Sciences of the United States of America >Singular value decomposition of genome-scale mRNA lengths distribution reveals asymmetry in RNA gel electrophoresis band broadening
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Singular value decomposition of genome-scale mRNA lengths distribution reveals asymmetry in RNA gel electrophoresis band broadening

机译：基因组尺度mRNA长度分布的奇异值分解揭示了RNA凝胶电泳谱带展宽的不对称性

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摘要

We describe the singular value decomposition (SVD) of yeast genome-scale mRNA lengths distribution data measured by DNA microarrays. SVD uncovers in the mRNA abundance levels data matrix of genes x arrays, i.e., electrophoretic gel migration lengths or mRNA lengths, mathematically unique decorrelated and decoupled "eigengenes." The eigengenes are the eigenvectors of the arrays x arrays correlation matrix, with the corresponding series of eigenvalues proportional to the series of the "fractions of eigen abundance." Each fraction of eigen abundance indicates the significance of the corresponding eigengene relative to all others. We show that the eigengenes fit "asymmetric Hermite functions," a generalization of the eigenfunctions of the quantum harmonic oscillator and the integral transform which kernel is a generalized coherent state. The fractions of eigen abundance fit a geometric series as do the eigenvalues of the integral transform which kernel is a generalized coherent state. The "asymmetric generalized coherent state" models the measured data, where the profiles of mRNA abundance levels of most genes as well as the distribution of the peaks of these profiles fit asymmetric Gaussians. We hypothesize that the asymmetry in the distribution of the peaks of the profiles is due to two competing evolutionary forces. We show that the asymmetry in the profiles of the genes might be due to a previously unknown asymmetry in the gel electrophoresis thermal broadening of a moving, rather than a stationary, band of RNA molecules.
机译：我们描述了通过DNA芯片测量的酵母基因组规模mRNA长度分布数据的奇异值分解（SVD）。 SVD在基因x阵列的mRNA丰度水平数据矩阵中发现，即电泳凝胶迁移长度或mRNA长度，数学上独特的去相关和解耦的“本征基因”。特征基因是数组x数组相关矩阵的特征向量，对应的特征值系列与“特征丰度分数”系列成比例。本征丰度的每个部分都表明相应本征基因相对于所有其他特征的重要性。我们表明，本征基因适合“非对称Hermite函数”，即量子谐波振荡器的本征函数的一般化和内核为广义相干态的积分变换。本征丰度的分数与积分变换的特征值拟合，该积分变换的特征值的核是广义相干态。 “非对称广义相干态”对测量的数据进行建模，其中大多数基因的mRNA丰度水平分布图以及这些分布图的峰分布适合非对称高斯分布。我们假设轮廓峰分布的不对称是由于两个相互竞争的进化力所致。我们表明，基因图谱中的不对称性可能是由于先前未知的凝胶电泳中移动的而不是固定的RNA分子带的热扩宽所致。

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