Optimisation of NMR dynamic models I. Minimisation algorithms and their performance within the model-free and Brownian rotational diffusion spaces.
Optimisation of NMR dynamic models I. Minimisation algorithms and their performance within the model-free and Brownian rotational diffusion spaces.
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DOI：
10.1007/s10858-007-9214-2
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发表时间：
2008-02
影响因子：
2.7
通讯作者：
Gooley PR
中科院分区：
文献类型：
--
作者：
d'Auvergne EJ;Gooley PR
获得大分子动力学的无模型描述的关键是使用收集的R1，R2和稳态NOE弛豫数据优化无模型和布朗旋转扩散参数。优化卡方值的问题通常被认为是微不足道的，然而，其计算所需的依赖关系的长链使无模型卡方空间变得复杂。卷积是由洛伦兹形式的谱密度函数，某些谱密度值的线性重组，以获得松弛率，NOE的计算使用这些速率的两个比率，最后卡方方程本身的二次形式引起的。无模型空间的两个主要拓扑特征使优化复杂化。第一个是一个长而浅的谷，它开始于无限的相关时间，并逐渐接近最小值。最严重的卷积发生在两个时间尺度上的运动中，其中最小值通常位于穿过空间的长、深、弯曲的隧道或多维谷的末端。大量的优化算法将进行调查和他们的性能比较，以确定哪些技术是适合用于无模型分析。局部优化算法将被证明是足够的最小化，不仅在模型的自由空间，但也最小化的布朗旋转扩散张量。此外，还对Modelfree和Dasha程序的性能进行了研究。确定了一些无模型优化失败：无法沿沿着限制滑动，Levenberg-Marquardt最小化算法的奇异矩阵失败，两个程序的精度低，以及Modelfree中的错误。值得注意的是，奇异矩阵失效的Levenberg-Marquardt算法发生时，内部相关时间是不确定的，并大大放大了无模型分析的网格搜索和约束算法。程序relax（http：www.nmr-relax.com）也作为一个新的软件包介绍，该软件包设计用于通过使用NMR弛豫数据来分析大分子动力学，并且该软件包阐明了无模型分析中固有的所有问题。本文的在线版本（doi：10.1007/s10858-007-9214-2）包含补充材料，可供授权用户使用。
The key to obtaining the model-free description of the dynamics of a macromolecule is the optimisation of the model-free and Brownian rotational diffusion parameters using the collected R1, R2 and steady-state NOE relaxation data. The problem of optimising the chi-squared value is often assumed to be trivial, however, the long chain of dependencies required for its calculation complicates the model-free chi-squared space. Convolutions are induced by the Lorentzian form of the spectral density functions, the linear recombinations of certain spectral density values to obtain the relaxation rates, the calculation of the NOE using the ratio of two of these rates, and finally the quadratic form of the chi-squared equation itself. Two major topological features of the model-free space complicate optimisation. The first is a long, shallow valley which commences at infinite correlation times and gradually approaches the minimum. The most severe convolution occurs for motions on two timescales in which the minimum is often located at the end of a long, deep, curved tunnel or multidimensional valley through the space. A large number of optimisation algorithms will be investigated and their performance compared to determine which techniques are suitable for use in model-free analysis. Local optimisation algorithms will be shown to be sufficient for minimisation not only within the model-free space but also for the minimisation of the Brownian rotational diffusion tensor. In addition the performance of the programs Modelfree and Dasha are investigated. A number of model-free optimisation failures were identified: the inability to slide along the limits, the singular matrix failure of the Levenberg–Marquardt minimisation algorithm, the low precision of both programs, and a bug in Modelfree. Significantly, the singular matrix failure of the Levenberg–Marquardt algorithm occurs when internal correlation times are undefined and is greatly amplified in model-free analysis by both the grid search and constraint algorithms. The program relax (http://www.nmr-relax.com) is also presented as a new software package designed for the analysis of macromolecular dynamics through the use of NMR relaxation data and which alleviates all of the problems inherent within model-free analysis. The online version of this article (doi:10.1007/s10858-007-9214-2) contains supplementary material, which is available to authorized users.
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