Information Theory Optimization of Signals from Small Angle Scattering Measurements

IF 3.2 3区 生物学 Q2 BIOPHYSICS
Robert P. Rambo, John A. Tainer
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Abstract

Small angle X-ray scattering (SAXS) of particles in solution informs on the conformational states and assemblies of biological macromolecules (bioSAXS) outside of cryo- and solid-state conditions. In bioSAXS, the SAXS measurement under dilute conditions, is resolution-limited and through an inverse Fourier transform, the measured SAXS intensities directly relates to the physical space occupied by the particles via the P(r)-distribution. Yet, this inverse transform of SAXS data has been historically cast as an ill-posed, ill-conditioned problem requiring an indirect approach. Here, we show that through the applications of matrix and information theories, the inverse transform of SAXS intensity data is a well-conditioned problem. The so-called ill-conditioning of the inverse problem is directly related to the Shannon number. By exploiting the oversampling enabled by modern detectors, a direct inverse Fourier transform of the SAXS data is possible provided the recovered information does not exceed the Shannon number. The Shannon limit corresponds to the maximum number of significant singular values that can be recovered in a SAXS experiment suggesting this relationship is a fundamental property of band-limited inverse integral transform problems. This correspondence reduces the complexity of the inverse problem to the Shannon limit and maximum dimension. We propose a hybrid scoring function using an information theory framework that assesses both the quality of the model-data fit as well as the quality of the recovered P(r)-distribution. The hybrid score utilizes the Akaike Information Criteria and Durbin-Watson (DW) statistic that considers parameter-model complexity, i.e., degrees-of-freedom, and randomness of the model-data residuals. The described tests and findings extend the boundaries for bioSAXS by completing the information theory formalism initiated by Peter B. Moore to enable a quantitative measure of resolution in SAXS, robustly determine maximum dimension, and more precisely define the best paramater-model appropriately representing the observed scattering data.
小角散射测量信号的信息论优化
溶液中粒子的小角x射线散射(SAXS)反映了生物大分子(bioSAXS)在低温和固态条件下的构象状态和组装。在bioSAXS中,在稀释条件下的SAXS测量是分辨率有限的,并且通过傅里叶反变换,测量的SAXS强度通过P(r)分布与粒子占用的物理空间直接相关。然而,SAXS数据的这种逆变换一直被认为是一个病态的、病态的问题,需要间接的方法。本文通过矩阵理论和信息论的应用,证明了SAXS强度数据的逆变换是一个良条件问题。所谓逆问题的病态性与香农数直接相关。通过利用现代探测器的过采样功能,只要恢复的信息不超过香农数,就可以对SAXS数据进行直接的傅立叶反变换。香农极限对应于在SAXS实验中可以恢复的显著奇异值的最大数量,表明这种关系是带限逆积分变换问题的基本性质。这种对应关系将反问题的复杂性降低到香农极限和最大维数。我们提出了一个混合评分函数,使用信息理论框架来评估模型数据拟合的质量以及恢复的P(r)分布的质量。混合评分采用了Akaike信息标准和Durbin-Watson (DW)统计,考虑了参数模型的复杂性,即自由度和模型数据残差的随机性。所描述的测试和发现扩展了bioSAXS的边界,完成了Peter B. Moore发起的信息论形式,使SAXS能够定量测量分辨率,稳健地确定最大维度,并更精确地定义最佳参数模型,适当地表示观测到的散射数据。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Biophysical journal
Biophysical journal 生物-生物物理
CiteScore
6.10
自引率
5.90%
发文量
3090
审稿时长
2 months
期刊介绍: BJ publishes original articles, letters, and perspectives on important problems in modern biophysics. The papers should be written so as to be of interest to a broad community of biophysicists. BJ welcomes experimental studies that employ quantitative physical approaches for the study of biological systems, including or spanning scales from molecule to whole organism. Experimental studies of a purely descriptive or phenomenological nature, with no theoretical or mechanistic underpinning, are not appropriate for publication in BJ. Theoretical studies should offer new insights into the understanding ofexperimental results or suggest new experimentally testable hypotheses. Articles reporting significant methodological or technological advances, which have potential to open new areas of biophysical investigation, are also suitable for publication in BJ. Papers describing improvements in accuracy or speed of existing methods or extra detail within methods described previously are not suitable for BJ.
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