Yuanxin Gu

A method of electron diffraction intensity correction in combination with high-resolution electron microscopy

A robust algorithm and computer program have been developed for the parameterization of elastic and absorptive electron atomic scattering factors. The algorithm is based on a combined modified simulated-annealing and least-squares method, and the computer program works well for fitting both elastic and absorptive atomic scattering factors with five Gaussians. As an application of this program, the elastic electron atomic scattering factors have been parameterized for all neutral atoms and for s up to 6 Angstrom(-1). Error analysis shows that the present results are considerably more accurate than the previous analytical fits in terms of the mean square value of the deviation between the numerical and fitted scattering factors. Parameterization for absorptive atomic scattering factors has been made for 17 important materials with the zinc blende structure over the temperature range 1 to 1000 K, where appropriate, and for temperature ranges for which accurate Debye-Waller factors are available. For other materials, the parameterization of the absorptive electron atomic scattering factors can be made using the program by supplying the atomic number of the element, the Debye-Waller factor and the acceleration voltage. For ions or when more accurate numerical results for neutral atoms are available, the program can read in the numerical values of the elastic scattering factors and return the parameters for both the elastic and absorptive scattering factors. The computer routines developed have been tested both on computer workstations and desktop PC computers, and will be made freely available via electronic mail or on floppy disk upon request.

SAD phasing by combination of direct methods with the Solve/Resolve procedure

In the initial stage of SAD phasing, the essential point is to break the intrinsic phase ambiguity. The presence of two kinds of phase information enables the discrimination of phase doublets from SAD data prior to density modification. One is from the heavy atoms (anomalous scatterers), while the other is from the direct-methods phase relationships. The former can be expressed by the Sim distribution, while the latter can be expressed by the Cochran distribution. Typically, only the Sim distribution has been used to yield initial phases for subsequent density modification. However, it has been demonstrated that using direct-methods phases based on the product of the Sim and Cochran distributions can lead to improved initial phases. In this paper, the direct-methods phasing procedure OASIS has been improved and combined with the SOLVE/RESOLVE procedure. Experimental SAD data from three known proteins with expected Bijvoet ratios / in the range 1.4-7.0% were used as test cases. In all cases, the phases obtained using the program RESOLVE beginning with initial phases based on experimental phases plus Sim and direct-methods information were more accurate than those based on experimental plus Sim phase information alone.

Comparison of phasing methods for sulfur-SAD using in-house chromium radiation: case studies for standard proteins and a 69 kDa protein

Phasing of the crystal structures of four standard proteins (lysozyme, trypsin, glucose isomerase and thaumatin) and a novel 69 kDa protein from Thermus thermophilus, TT0570, was performed using the single-wavelength anomalous diffraction of S atoms intrinsically present within the native protein molecules. To utilize the sulfur anomalous diffraction, the data sets were collected using the loopless data-collection method with chromium Kalpha X-rays of wavelength 2.29 A. Three phasing methods, MLPHARE, SHARP and OASIS-2004, were tested in combination with the DM or SOLOMON density-modification method. The results showed that the solvent contents are still an important factor for phasing with the S-SAD method, even when longer wavelength Cr Kalpha radiation is used. Of the three procedures, the improved direct phasing of OASIS-2004 with its implemented fragment feedback to the direct-method probability calculation gave the best results in determining the initial phases. For all five proteins, almost the entire models could be built automatically.

SAD phasing by OASIS-2004 : case studies of dual-space fragment extension

The principle of dual-space phasing is used in dealing with protein SAD data. Four programs are involved in iterative dual-space fragment extension to improve automatic model building. OASIS-2004 is used to break the phase ambiguity intrinsic in the SAD experiment. In the initial cycle, discrimination of SAD phase doublets is performed by the direct method incorporating the known anomalous-scattering substructure. In subsequent cycles, discrimination is performed by the direct method incorporating both the known anomalous-scattering substructure and the partial protein structure obtained from model building in the preceding cycle. DM is used to improve direct-method phases via density modification. RESOLVE is used for initial model building and ARP/wARP is used to complete the structure. Case studies with three sets of difficult SAD data showed that the procedure is beneficial to high-throughput protein-structure determination and all of the four programs involved make their unique contribution to the process.

Direct-method SAD phasing with partial-structure iteration: towards automation.

The probability formula of direct-method SAD (single-wavelength anomalous diffraction) phasing proposed by Fan & Gu (1985, Acta Cryst. A41, 280-284) contains partial-structure information in the form of a Sim-weighting term. Previously, only the substructure of anomalous scatterers has been included in this term. In the case that the subsequent density modification and model building yields only structure fragments, which do not straightforwardly lead to the complete solution, the partial structure can be fed back into the Sim-weighting term of the probability formula in order to strengthen its phasing power and to benefit the subsequent automatic model building. The procedure has been tested with experimental SAD data from two known proteins with copper and sulfur as the anomalous scatterers.

Direct-method SAD phasing of proteins enhanced by the use of intrinsic bimodal phase distributions in the subsequent phase-improvement process

A modified SAD (single-wavelength anomalous diffraction) phasing algorithm has been introduced in the latest version of the program OASIS. In addition to direct-method phases and figures of merit, Hendrickson-Lattman coefficients that correspond to the original unresolved bimodal phase distributions are also output and used in subsequent phase-improvement procedures in combination with the improved phases. This provides the possibility of rebreaking the SAD phase ambiguity using the ever-improving phases resulting from the phase-improvement process. Tests using experimental SAD data from six known proteins showed that in all cases the new treatment produced significant improved results.

Optimizing the error term in direct-method SAD phasing.

The probability formula of the direct-method SAD (single-wavelength anomalous diffraction) phasing proposed by Fan & Gu (1985, Acta Cryst. A41, 280-284) contains an error term which is related to the lack-of-closure error. This error term is used as a weighting function in the phase derivation and in the subsequent calculation of electron-density maps. Previously, there has been a constant in the error term that has had to be determined empirically for each particular case. It has been found that improper choice of the constant often leads to failure of the direct-method SAD phasing. The problem is resolved by introducing a modified error term and a method of automatically tuning the associated scaling factor.

Solving crystal structures from two-wavelength X-ray powder diffraction data – breaking the phase ambiguity in the noncentrosymmetric case

Direct methods of breaking phase ambiguities in protein crystallography have been introduced in powder diffraction analysis. This is aiming at ab initio solution of noncentrosymmetric structures using two-wavelength anomalous powder diffraction data. The known structure of the hydrogen bromide salt of leotidine (C(14)H(20)O(2)N(2).HBr) in space group P2(1)2(1)2(1) was used for simulating two-wavelength anomalous powder diffraction with the Br atom as anomalous scatterer. X-ray wavelengths are selected at lambda(1) = 0.920 and lambda(2) = 1.500 A. Unique reflections from the diffraction pattern of lambda(2) were able to locate the Br atom accurately. All overlapping diffraction peaks were uniformly partitioned to decompose into single reflections. Structure-factor amplitudes were then extracted. With these and the substructure of Br atoms, unique phases for centric reflections (hk0, h0l and 0kl) and phase doublets for noncentric reflections were obtained. The direct method was used to break the phase ambiguity leading to an interpretable electron-density map, from which five cycles of Fourier iteration yielded the complete structure.

Use of single isomorphous replacement data of proteins - resolving the phase ambiguity and a new procedure for phase extension.

A procedure combining direct methods and solvent flattening to break the phase ambiguity intrinsic to the single isomorphous replacement (SIR) technique has been tested with the experimental SIR data of the known protein RNase Sa at 2.5 A resolution. The use of direct methods provided better initial phases for the solvent-flattening procedure, while the solvent-flattening procedure greatly improved direct-method phases leading to a traceable Fourier map. A small subset of known phases at low resolution makes direct phasing of SIR data much easier. Accordingly a method for extending low-resolution phases to high-resolution ones is proposed making use of additional SIR information. This reduces the problem of finding a value in the range of 0-2pi for each unknown phase to that of just making a choice between two possible values. Tests with the known protein RNase Sa showed that the method is able to extend phases from a resolution of 6 to 2.5 A leading to an easily traceable Fourier map. The solvent-flattening technique and the combination of which with direct methods were used for the phase extension. Either procedure yielded reasonably good results, but on the whole, the result from the combination of direct methods with solvent flattening is better. Results of the latter procedure were further compared with that from direct phasing of the 2.5 A SIR data and with that from phase extension by solvent flattening without SIR information. An improvement gained by the use of SIR information is evident.

SFX analysis of non-biological polycrystalline samples

A serial femtosecond crystallography based method has been proposed, which enables simultaneous X-ray phase identification and structure solution for multiphase polycrystalline samples. Test results from simulating calculations are encouraging.