Walczak Michał, Grubmüller Helmut
Department of Theoretical and Computational Biophysics, Max Planck Institute for Biophysical Chemistry, 37077 Göttingen, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Aug;90(2):022714. doi: 10.1103/PhysRevE.90.022714. Epub 2014 Aug 20.
We developed a Bayesian method to extract macromolecular structure information from sparse single-molecule x-ray free-electron laser diffraction images. The method addresses two possible scenarios. First, using a "seed" structural model, the molecular orientation is determined for each of the provided diffraction images, which are then averaged in three-dimensional reciprocal space. Subsequently, the real space electron density is determined using a relaxed averaged alternating reflections algorithm. In the second approach, the probability that the "seed" model fits to the given set of diffraction images as a whole is determined and used to distinguish between proposed structures. We show that for a given x-ray intensity, unexpectedly, the achievable resolution increases with molecular mass such that structure determination should be more challenging for small molecules than for larger ones. For a sufficiently large number of recorded photons (>200) per diffraction image an M^{1/6} scaling is seen. Using synthetic diffraction data for a small glutathione molecule as a challenging test case, successful determination of electron density was demonstrated for 20000 diffraction patterns with random orientations and an average of 82 elastically scattered and recorded photons per image, also in the presence of up to 50% background noise. The second scenario is exemplified and assessed for three biomolecules of different sizes. In all cases, determining the probability of a structure given set of diffraction patterns allowed successful discrimination between different conformations of the test molecules. A structure model of the glutathione tripeptide was refined in a Monte Carlo simulation from a random starting conformation. Further, effective distinguishing between three differently arranged immunoglobulin domains of a titin molecule and also different states of a ribosome in a tRNA translocation process was demonstrated. These results show that the proposed method is robust and enables structure determination from sparse and noisy x-ray diffraction images of single molecules spanning a wide range of molecular masses.
我们开发了一种贝叶斯方法，用于从稀疏的单分子X射线自由电子激光衍射图像中提取大分子结构信息。该方法适用于两种可能的情况。第一种情况是，使用“种子”结构模型确定每个提供的衍射图像的分子取向，然后在三维倒易空间中对这些取向进行平均。随后，使用松弛平均交替反射算法确定实空间电子密度。在第二种方法中，确定“种子”模型整体上与给定衍射图像集的拟合概率，并用于区分所提出的结构。我们发现，对于给定的X射线强度，出乎意料的是，可实现的分辨率随分子质量增加，因此小分子的结构测定应该比大分子更具挑战性。对于每个衍射图像有足够多记录光子（>200）的情况，可以看到M^{1/6}缩放关系。以小谷胱甘肽分子的合成衍射数据作为具有挑战性的测试案例，在存在高达50%背景噪声的情况下，对于20000个具有随机取向且每个图像平均有82个弹性散射并记录的光子的衍射图案，成功展示了电子密度的测定。第二种情况以三种不同大小的生物分子为例进行了说明和评估。在所有情况下，确定给定衍射图案集下结构的概率能够成功区分测试分子的不同构象。谷胱甘肽三肽的结构模型在蒙特卡罗模拟中从随机起始构象进行了优化。此外，还展示了在肌联蛋白分子的三个不同排列的免疫球蛋白结构域之间以及在tRNA转位过程中核糖体的不同状态之间的有效区分。这些结果表明，所提出的方法具有鲁棒性，能够从跨越广泛分子质量范围的单分子稀疏且有噪声的X射线衍射图像中确定结构。
