中国物理B ›› 2010, Vol. 19 ›› Issue (8): 86102-086102.doi: 10.1088/1674-1056/19/8/086102

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New expression of bimodal phase distributions in direct-method phasing of protein single-wavelength anomalous diffraction data

古元新1, 郑朝德1, 范海福1, 张涛2   

  1. (1)Beijing National Laboratory for Condensed Matter Physics and Key Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China; (2)Research Institute of Magnetic Materials, School of Physical Sciences and Technology, Lanzhou University, Lanzhou 730000, China; Beijing National Laboratory for Condensed Matter Physics and Key Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
  • 收稿日期:2010-04-21 修回日期:2010-04-29 出版日期:2010-08-15 发布日期:2010-08-15
  • 基金资助:
    Project supported by the Innovation Foundation of the Chinese Academy of Sciences and by the National Basic Research Program of China (Grant No. 2002CB713801).

New expression of bimodal phase distributions in direct-method phasing of protein single-wavelength anomalous diffraction data

Zhang Tao (张涛)ab, Gu Yuan-Xin (古元新)b, Zheng Chao-De (郑朝德)b, Fan Hai-Fu (范海福)b   

  1. a Research Institute of Magnetic Materials, School of Physical Sciences and Technology, Lanzhou University, Lanzhou 730000, China; b Beijing National Laboratory for Condensed Matter Physics and Key Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
  • Received:2010-04-21 Revised:2010-04-29 Online:2010-08-15 Published:2010-08-15
  • Supported by:
    Project supported by the Innovation Foundation of the Chinese Academy of Sciences and by the National Basic Research Program of China (Grant No. 2002CB713801).

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摘要： One of the essential points of the direct-method single-wavelength anomalous diffraction (SAD) phasing for proteins is to express the bimodal SAD phase distribution by the sum of two Gaussian functions peaked respectively at φ"h + |Δφh| and φ"h - |Δφh|. The probability for Δφh being positive (P+) can be derived based on the Cochran distribution in direct methods. Hence the SAD phase ambiguity can be resolved by multiplying the Gaussian function peaked at φ"h + |Δφh| with P+ and multiplying the Gaussian function peaked at φ"h - |Δφh| with P- (=1-P+).The direct-method SAD phasing has been proved powerful in breaking SAD phase ambiguities, in particular when anomalous-scattering signals are weak.However, the approximation of bimodal phase distributions by the sum of two Gaussian functions introduces considerable errors. In this paper we show that a much better approximation can be achieved by replacing the two Gaussian functions with two von Mises distributions. Test results showed that this leads to significant improvement on the efficiency of direct-method SAD-phasing.

Abstract: One of the essential points of the direct-method single-wavelength anomalous diffraction (SAD) phasing for proteins is to express the bimodal SAD phase distribution by the sum of two Gaussian functions peaked respectively at $\varphi''_h+|\Delta\varphi_h|$ and $\varphi''_h-|\Delta\varphi_h|$. The probability for $\Delta\varphi$ being positive (P+) can be derived based on the Cochran distribution in direct methods. Hence the SAD phase ambiguity can be resolved by multiplying the Gaussian function peaked at $\varphi''_h+|\Delta\varphi_h|$  with P+ and multiplying the Gaussian function peaked at $\varphi''_h-|\Delta\varphi_h|$  with P- (=1-P+).The direct-method SAD phasing has been proved powerful in breaking SAD phase ambiguities, in particular when anomalous-scattering signals are weak.However, the approximation of bimodal phase distributions by the sum of two Gaussian functions introduces considerable errors. In this paper we show that a much better approximation can be achieved by replacing the two Gaussian functions with two von Mises distributions. Test results showed that this leads to significant improvement on the efficiency of direct-method SAD-phasing.

Key words: direct methods, single-wavelength anomalous diffraction, OASIS program, proteins

中图分类号:  (Scattering of visible, uv, and infrared radiation)

  • 87.64.Cc
02.50.Ng (Distribution theory and Monte Carlo studies) 87.14.E- (Proteins) 87.15.B- (Structure of biomolecules)