Direct-space methods in phase extension and phase determination. I. Low-density elimination

Towards the automatic crystal structure solution of nucleic acids: automated model building using the new CAB program

CAB, a recently described automated model-building (AMB) program, has been modified to work effectively with nucleic acids. To this end, several new algorithms have been introduced and the libraries have been updated. To reduce the input average phase error, ligand heavy atoms are now located before starting the CAB interpretation of the electron-density maps. Furthermore, alternative approaches are used depending on whether the ligands belong to the target or to the model chain used in the molecular-replacement step. Robust criteria are then applied to decide whether the AMB model is acceptable or whether it must be modified to fit prior information on the target structure. In the latter case, the model chains are rearranged to fit prior information on the target chains. Here, the performance of the new AMB program CAB applied to various nucleic acid structures is discussed. Other well documented programs such as Nautilus, ARP/wARP and phenix.autobuild were also applied and the experimental results are described.

A new density-modification procedure extending the application of the recent |ρ|-based phasing algorithm to larger crystal structures

The incorporation of the new peakness-enhancing fast Fourier transform compatible ipp procedure (ipp = inner-pixel preservation) into the recently published S_M algorithm based on |ρ| [Rius (2020). Acta Cryst A76, 489-493] improves its phasing efficiency for larger crystal structures with atomic resolution data. Its effectiveness is clearly demonstrated via a collection of test crystal structures (taken from the Protein Data Bank) either starting from random phase values or by using the randomly shifted modulus function (a Patterson-type synthesis) as initial ρ estimate. It has been found that in the presence of medium scatterers (e.g. S or Cl atoms) crystal structures with 1500 × c atoms in the unit cell (c = number of centerings) can be routinely solved. In the presence of strong scatterers like Fe, Cu or Zn atoms this number increases to around 5000 × c atoms. The implementation of this strengthened S_M algorithm is simple, since it only includes a few easy-to-adjust parameters.

Insight into the structure of decagonite - the extraterrestrial decagonal quasicrystal

A set of X-ray data collected on a fragment of decagonite, Al71Ni24Fe5, the only known natural decagonal quasicrystal found in a meteorite formed at the beginning of the Solar System, allowed us to determine the first structural model for a natural quasicrystal. It is a two-layer structure with decagonal columnar clusters arranged according to the pentagonal Penrose tiling. The structural model showed peculiarities and slight differences with respect to those obtained for other synthetic decagonal quasicrystals. Interestingly, decagonite is found to exhibit low linear phason strain and a high degree of perfection despite the fact it was formed under conditions very far from those used in the laboratory.

ARCIMBOLDO on coiled coils

ARCIMBOLDO solves the phase problem by combining the location of small model fragments using Phaser with density modification and autotracing using SHELXE. Mainly helical structures constitute favourable cases, which can be solved using polyalanine helical fragments as search models. Nevertheless, the solution of coiled-coil structures is often complicated by their anisotropic diffraction and apparent translational noncrystallographic symmetry. Long, straight helices have internal translational symmetry and their alignment in preferential directions gives rise to systematic overlap of Patterson vectors. This situation has to be differentiated from the translational symmetry relating different monomers. ARCIMBOLDO_LITE has been run on single workstations on a test pool of 150 coiled-coil structures with 15-635 amino acids per asymmetric unit and with diffraction data resolutions of between 0.9 and 3.0 Å. The results have been used to identify and address specific issues when solving this class of structures using ARCIMBOLDO. Features from Phaser v.2.7 onwards are essential to correct anisotropy and produce translation solutions that will pass the packing filters. As the resolution becomes worse than 2.3 Å, the helix direction may be reversed in the placed fragments. Differentiation between true solutions and pseudo-solutions, in which helix fragments were correctly positioned but in a reverse orientation, was found to be problematic at resolutions worse than 2.3 Å. Therefore, after every new fragment-placement round, complete or sparse combinations of helices in alternative directions are generated and evaluated. The final solution is once again probed by helix reversal, refinement and extension. To conclude, density modification and SHELXE autotracing incorporating helical constraints is also exploited to extend the resolution limit in the case of coiled coils and to enhance the identification of correct solutions. This study resulted in a specialized mode within ARCIMBOLDO for the solution of coiled-coil structures, which overrides the resolution limit and can be invoked from the command line (keyword coiled_coil) or ARCIMBOLDO_LITE task interface in CCP4i.

Substructure determination using phase-retrieval techniques

Thus far, the application of phase-retrieval methods in crystallography has mainly been aimed at variants of charge flipping or structure-factor flipping. In this work, the relaxed averaged alternating reflections (RAAR) algorithm is applied to determine anomalously scattering substructures from single-wavelength anomalous diffraction (SAD) data of macromolecules. The algorithm has been implemented in a new program, PRASA, and has been shown to significantly outperform charge flipping in determining anomalously scattering substructures on a test sample of 169 SAD data sets with resolutions up to 3.88 Å.

Synergy among phase-refinement techniques in macromolecular crystallography

Ab initio and non-ab initio phasing methods are often unable to provide phases of sufficient quality to allow the molecular interpretation of the resulting electron-density maps. Phase extension and refinement is therefore a necessary step: its success or failure can make the difference between solution and nonsolution of the crystal structure. Today phase refinement is trusted to electron-density modification (EDM) techniques, and in practice to dual-space methods which try, via suitable constraints in direct and in reciprocal space, to generate higher quality electron-density maps. The most popular EDM approaches, denoted here as mainstream methods, are usually part of packages which assist crystallographers in all of the structure-solution steps from initial phasing to the point where the molecular model perfectly fits the known features of protein chemistry. Other phase-refinement approaches that are based on different sources of information, denoted here as out-of-mainstream methods, are not frequently employed. This paper aims to show that mainstream and out-of-mainstream methods may be combined and may lead to dramatic advances in the present state of the art. The statement is confirmed by experimental tests using molecular-replacement, SAD-MAD and ab initio techniques.

Asymmetric band flipping for time-of-flight neutron diffraction data

Charge flipping with powder diffraction data is known to produce a result more reliably with high-resolution data, i.e. visible reflections at small d spacings. Such data are readily accessible with the neutron time-of-flight technique but the assumption that negative scattering density is nonphysical is no longer valid where elements with negative scattering lengths are present. The concept of band flipping was introduced in the literature, where a negative threshold is used in addition to a positive threshold during the flipping. However, it was not tested with experimental data at the time. Band flipping has been implemented in TOPAS together with the band modification of low-density elimination and tested with experimental powder and Laue single-crystal neutron data.

Volumic omit maps in ab initio dual-space phasing

Alternating-projection-type dual-space algorithms have a clear construction, but are susceptible to stagnation and, thus, inefficient for solving the phase problem ab initio. To improve this behaviour new omit maps are introduced, which are real-space perturbations applied periodically during the iteration process. The omit maps are called volumic, because they delete some predetermined subvolume of the unit cell without searching for atomic regions or analysing the electron density in any other way. The basic algorithms of positivity, histogram matching and low-density elimination are tested by their solution statistics. It is concluded that, while all these algorithms based on weak constraints are practically useless in their pure forms, appropriate volumic omit maps can transform them to practically useful methods. In addition, the efficiency of the already useful reflector-type charge-flipping algorithm can be further improved. It is important that these results are obtained by using non-sharpened structure factors and without any weighting scheme or reciprocal-space perturbation. The mathematical background of volumic omit maps and their expected applications are also discussed.

Atomic structure and phason modes of the Sc-Zn icosahedral quasicrystal

The detailed atomic structure of the binary icosahedral (i) ScZn7.33 quasicrystal has been investigated by means of high-resolution synchrotron single-crystal X-ray diffraction and absolute scale measurements of diffuse scattering. The average atomic structure has been solved using the measured Bragg intensity data based on a six-dimensional model that is isostructural to the i-YbCd5.7 one. The structure is described with a quasiperiodic packing of large Tsai-type rhombic triacontahedron clusters and double Friauf polyhedra (DFP), both resulting from a close-packing of a large (Sc) and a small (Zn) atom. The difference in chemical composition between i-ScZn7.33 and i-YbCd5.7 was found to lie in the icosahedron shell and the DFP where in i-ScZn7.33 chemical disorder occurs on the large atom sites, which induces a significant distortion to the structure units. The intensity in reciprocal space displays a substantial amount of diffuse scattering with anisotropic distribution, located around the strong Bragg peaks, that can be fully interpreted as resulting from phason fluctuations, with a ratio of the phason elastic constants K 2/K 1 = -0.53, i.e. close to a threefold instability limit. This induces a relatively large perpendicular (or phason) Debye-Waller factor, which explains the vanishing of 'high-Q perp' reflections.

ARCIMBOLDO_LITE: single-workstation implementation and use

ARCIMBOLDO solves the phase problem at resolutions of around 2 Å or better through massive combination of small fragments and density modification. For complex structures, this imposes a need for a powerful grid where calculations can be distributed, but for structures with up to 200 amino acids in the asymmetric unit a single workstation may suffice. The use and performance of the single-workstation implementation, ARCIMBOLDO_LITE, on a pool of test structures with 40-120 amino acids and resolutions between 0.54 and 2.2 Å is described. Inbuilt polyalanine helices and iron cofactors are used as search fragments. ARCIMBOLDO_BORGES can also run on a single workstation to solve structures in this test set using precomputed libraries of local folds. The results of this study have been incorporated into an automated, resolution- and hardware-dependent parameterization. ARCIMBOLDO has been thoroughly rewritten and three binaries are now available: ARCIMBOLDO_LITE, ARCIMBOLDO_SHREDDER and ARCIMBOLDO_BORGES. The programs and libraries can be downloaded from http://chango.ibmb.csic.es/ARCIMBOLDO_LITE.

Macromolecular Crystallography for Synthetic Abiological Molecules: Combining xMDFF and PHENIX for Structure Determination of Cyanostar Macrocycles

Crystal structure determination has long provided insight into structure and bonding of small molecules. When those same small molecules are designed to come together in multimolecular assemblies, such as in coordination cages, supramolecular architectures and organic-based frameworks, their crystallographic characteristics closely resemble biological macromolecules. This resemblance suggests that biomacromolecular refinement approaches be used for structure determination of abiological molecular complexes that arise in an aggregate state. Following this suggestion we investigated the crystal structure of a pentagonal macrocycle, cyanostar, by means of biological structure analysis methods and compared results to traditional small molecule methods. Cyanostar presents difficulties seen in supramolecular crystallography including whole molecule disorder and highly flexible solvent molecules sitting in macrocyclic and intermolecule void spaces. We used the force-field assisted refinement method, molecular dynamics flexible fitting algorithm for X-ray crystallography (xMDFF), along with tools from the macromolecular structure determination suite PHENIX. We found that a standard implementation of PHENIX, namely one without xMDFF, either fails to produce a solution by molecular replacement alone or produces an inaccurate structure when using generic geometry restraints, even at a very high diffraction data resolution of 0.84 Å. The problems disappear when taking advantage of xMDFF, which applies an optimized force field to realign molecular models during phasing by providing accurate restraints. The structure determination for this model system shows excellent agreement with the small-molecule methods. Therefore, the joint xMDFF-PHENIX refinement protocol provides a new strategy that uses macromolecule methods for structure determination of small molecules and their assemblies.

Crystal structure determination and refinementviaSIR2014

SIR2014is the latest program of theSIRsuite for crystal structure solution of small, medium and large structures. A variety of phasing algorithms have been implemented, bothab initio(standard or modern direct methods, Patterson techniques,Vive la Différence) and non-ab initio(simulated annealing, molecular replacement). The program contains tools for crystal structure refinement and for the study of three-dimensional electron-density mapsviasuitable viewers.

SHELXT - integrated space-group and crystal-structure determination

The new computer program SHELXT employs a novel dual-space algorithm to solve the phase problem for single-crystal reflection data expanded to the space group P1. Missing data are taken into account and the resolution extended if necessary. All space groups in the specified Laue group are tested to find which are consistent with the P1 phases. After applying the resulting origin shifts and space-group symmetry, the solutions are subject to further dual-space recycling followed by a peak search and summation of the electron density around each peak. Elements are assigned to give the best fit to the integrated peak densities and if necessary additional elements are considered. An isotropic refinement is followed for non-centrosymmetric space groups by the calculation of a Flack parameter and, if appropriate, inversion of the structure. The structure is assembled to maximize its connectivity and centred optimally in the unit cell. SHELXT has already solved many thousand structures with a high success rate, and is optimized for multiprocessor computers. It is, however, unsuitable for severely disordered and twinned structures because it is based on the assumption that the structure consists of atoms.

Structure of decagonal Al-Ni-Rh

The crystal structure of the decagonal phase in the system Al-Ni-Rh (d-Al-Ni-Rh) was analyzed in the five-dimensional embedding approach based on single-crystal synchrotron X-ray diffraction data. The structure can be described as a quasiperiodic packing of partially overlapping decagonal and pentagonal columnar clusters with ∼ 21 Å diameter and ∼ 4 Å period along the tenfold axis.

The quasiperiodic average structure of highly disordered decagonal Zn-Mg-Dy and its temperature dependence

A single-crystal X-ray diffraction structure analysis of decagonal Zn-Mg-Dy, a Frank-Kasper-type quasicrystal, was performed using the higher-dimensional approach. For this first Frank-Kasper (F-K) decagonal quasicrystal studied so far, significant differences to the decagonal Al-TM-based (TM: transition metal) phases were found. A new type of twofold occupation domain is located on certain edge centers of the five-dimensional unit cell. The structure can be described in terms of a two-cluster model based on a decagonal cluster (∼ 23 Å diameter) arranged on the vertices of a pentagon-Penrose tiling (PPT) and a star-like cluster covering the remaining space. This model is used for the five-dimensional refinements, which converged to an R value of 0.126. The arrangement of clusters is significantly disordered as indicated by high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM). In order to check the structure and stability at higher temperatures, in-situ high-temperature (HT) single-crystal X-ray diffraction experiments were conducted at 598 and 648 K (i.e. slightly below the decomposition temperature). The structure does not change significantly, however, the best quasiperiodic order is found at 598 K. The implication of these results on the stabilization mechanism of quasicrystals is discussed.

WinCSD: software package for crystallographic calculations (Version 4)

The fourth version of the program packageWinCSDis multi-purpose computer software for crystallographic calculations using single-crystal and powder X-ray and neutron diffraction data. The software environment and the graphical user interface are built using the platform of the Microsoft .NET Framework, which grants independence from changing Windows operating systems and allows for transferring to other operating systems. Graphic applications use the three-dimensional OpenGL graphics language.WinCSDcovers the complete spectrum of crystallographic calculations, including powder diffraction pattern deconvolution, crystal structure solution and refinement in 3 + dspace, refinement of the multipole model and electron density studies from diffraction data, and graphical representation of crystallographic information.

A robust tangent procedure

Third-generation direct methods programs are based on a phasing algorithm (e.g.the tangent or the parameter shift method) and on dual space refinement techniques. The two spaces may be alternated during the phasing procedure or used in a sequential way: for example, first phase and after extend and refine. The tangent approach inSIR2011belongs to the second category: phases are first estimated by the tangent formula, then their extension and refinement is performed in direct spaceviaelectron density modification techniques. In this article a number of new algorithms are described, with the aim of improving theSIR2011tangent step and allowing more efficient phase extension and refinement. New criteria were chosen for defining the number of reflections to phase, for modifying the tangent weighting scheme, and for fixing the active use of the psi-0 triplets and of the quartet invariants. Each tangent trial may now be submitted to the RELAX procedure, a tool for moving to the correct position a well oriented but misplaced structural model. The resulting procedure shows surprising efficiency, testified by a wide set of applications. The experimental results have been compared with the tangent and VLD (vive la différence) approaches implemented inSIR2011.

Lensless coherent imaging of proteins and supramolecular assemblies: Efficient phase retrieval by the charge flipping algorithm

Diffractive imaging using the intense and coherent beam of X-ray free-electron lasers opens new perspectives for structural studies of single nanoparticles and biomolecules. Simulations were carried out to generate 3D oversampled diffraction patterns of non-crystalline biological samples, ranging from peptides and proteins to megadalton complex assemblies, and to recover their molecular structure from nanometer to near-atomic resolutions. Using these simulated data, we show here that iterative reconstruction methods based on standard and variant forms of the charge flipping algorithm, can efficiently solve the phase retrieval problem and extract a unique and reliable molecular structure. Contrary to the case of conventional algorithms, where the estimation and the use of a compact support is imposed, our approach does not require any prior information about the molecular assembly, and is amenable to a wide range of biological assemblies. Importantly, the robustness of this ab initio approach is illustrated by the fact that it tolerates experimental noise and incompleteness of the intensity data at the center of the speckle pattern.

Estimation of the variance in any point of an electron-density map for any space group

In a recent paper [Giacovazzo & Mazzone (2011). Acta Cryst. A67, 210-218] a mathematical expression of the variance at any point of the unit cell has been described. The formulas were derived in P1 for any type of Fourier synthesis (observed, difference and hybrid) under the following hypothesis: the current phases are distributed on the trigonometric circle about the correct values according to von Mises distributions. This general hypothesis allows the variance expressions to be valid at any stage of the phasing process. In this paper the method has been extended to any space group, no matter whether centric or acentric. The properties of the variance generated by space-group symmetry are described; in particular it is shown that the variance is strictly connected with the implication transformations, which are basic for Patterson deconvolution. General formulas simultaneously taking into account phase uncertainty and measurement errors have been obtained, valid no matter what the quality of the model.

Maximum entropy method and charge flipping, a powerful combination to visualize the true nature of structural disorder from in situ X-ray powder diffraction data

In a systematic approach, the ability of the Maximum Entropy Method (MEM) to reconstruct the most probable electron density of highly disordered crystal structures from X-ray powder diffraction data was evaluated. As a case study, the ambient temperature crystal structures of disordered alpha-Rb(2)[C(2)O(4)] and alpha-Rb(2)[CO(3)] and ordered delta-K(2)[C(2)O(4)] were investigated in detail with the aim of revealing the ;true' nature of the apparent disorder. Different combinations of F (based on phased structure factors) and G constraints (based on structure-factor amplitudes) from different sources were applied in MEM calculations. In particular, a new combination of the MEM with the recently developed charge-flipping algorithm with histogram matching for powder diffraction data (pCF) was successfully introduced to avoid the inevitable bias of the phases of the structure-factor amplitudes by the Rietveld model. Completely ab initio electron-density distributions have been obtained with the MEM applied to a combination of structure-factor amplitudes from Le Bail fits with phases derived from pCF. All features of the crystal structures, in particular the disorder of the oxalate and carbonate anions, and the displacements of the cations, are clearly obtained. This approach bears the potential of a fast method of electron-density determination, even for highly disordered materials. All the MEM maps obtained in this work were compared with the MEM map derived from the best Rietveld refined model. In general, the phased observed structure factors obtained from Rietveld refinement (applying F and G constraints) were found to give the closest description of the experimental data and thus lead to the most accurate image of the actual disorder.

Ab initiostructure solution by iterative phase-retrieval methods: performance tests on charge flipping and low-density elimination

Comprehensive tests on the density-modification methods charge flipping [Oszlányi & Sütő (2004).Acta Cryst.A60, 134–141] and low-density elimination [Shiono & Woolfson (1992).Acta Cryst.A48, 451–456] for solving crystal structures are performed on simulated diffraction data of periodic structures and quasicrystals. A novel model-independent figure of merit, which characterizes the reliability of the retrieved phase of each reflection, is introduced and tested. The results of the performance tests show that the quality of the phase retrieval highly depends on the presence or absence of an inversion center and on the algorithm used for solving the structure. Charge flipping has a higher success rate for solving structures, while low-density elimination leads to a higher accuracy in phase retrieval. The best results can be obtained by combining the two methods,i.e.by solving a structure with charge flipping followed by a few cycles of low-density elimination. It is shown that these additional cycles dramatically improve the phases not only of the weak reflections but also of the strong ones. The results can be improved further by averaging the results of several runs and by applying a correction term that compensates for a reduction of the structure-factor amplitudes by averaging of inconsistently observed reflections. It is further shown that in most cases the retrieved phases converge to the best solution obtainable with a given method.

The Co–Ni distribution in decagonal Al69.7(4)Co10.0(4)Ni20.3(4)

The Co—Ni distribution in d-Al69.7(4)Co10.0(4)Ni20.3(4) was investigated based on X-ray and neutron diffraction data. The structure was modelled in higher dimensional space using the ‘charge-flipping’ and ‘low-density elimination’ methods and it was quantitatively refined in three-dimensional space employing a pseudo-approximant approach. In higher-dimensional description, the Co atoms are found at the centre of one of the two symmetry independent occupation domains, enclosed by regions mainly occupied by Ni. The other occupation domain is mostly occupied by Al. In physical space Co atoms are located in the centres of small Al pentagons and form pentagonal units, which are arranged in decagonal rings. On these sites Co is partly substituted by Ni, while all other transition metal sites are occupied by Ni and to a minor degree by Al. The fraction of Co found on transition metal sites decreases with decreasing Co–Co distances, whereby Co is replaced by Ni.

Macromolecular phasing with SHELXE

SHELXE was designed to provide a simple, fast and robust route from substructure sites found by the program SHELXD to an initial electron density map, if possible with an indication as to which heavy-atom enantiomorph is correct. This should be understood as a small contribution to high-throughput structural genomics. The new sphere of influence algorithm combined with a fuzzy solvent boundary enables some chemical knowledge to be incorporated into the density modification in a general and effective manner. In the special cases of high solvent content (greater than 0.6) or very high resolution data (better than 1.5 Å) high quality maps can be produced. This raises the possibility of a new paradigm for atomic resolution structure refinement: instead of alternating atom parameter refinement with weighted electron density maps calculated with the phases of the current model, which inevitably leads to some model bias, all model building should be based on the model free experimental density map!

Structure of commelinin, a blue complex pigment from the blue flowers of Commelina communis

The X-ray crystal structure of natural commelinin is investigated. The results demonstrate that commelinin is a tetranuclear (4 Mg(2+)) metal complex, in which two Mg(2+) ions chelate to six anthocyanin molecules, while the other two Mg(2+) ions bind to six flavone molecules, stabilizing the commelinin complex, a new type of supramolecular complex.

The charge flipping algorithm

This paper summarizes the current state of charge flipping, a recently developed algorithm ofab initiostructure determination. Its operation is based on the perturbation of large plateaus of low electron density but not directly on atomicity. Such a working principle radically differs from that of classical direct methods and offers complementary applications. The list of successful structure-solution cases includes periodic and aperiodic crystals using single-crystal and powder diffraction data measured with X-ray and neutron radiation. Apart from counting applications, the paper mainly deals with algorithmic issues: it describes and compares new variants of the iteration scheme, helps to identify and improve solutions, discusses the required data and the use of known information. Finally, it tries to foretell the future of such an alternative among well established direct methods.

Ab initio structure determination of cytochrome c6 by combined reciprocal space-real space approach

The direct method program SAYTAN has been applied successfully to redetermine the structure of cytochrome c6, a heme-containing redox protein with 89 amino acids, a Fe atom and 151 solvent water molecules in the asymmetric unit and data to 1.1 Å resolution. The crystal system is rhombohedral with space group R3, cell parameters a = b = c = 40.43(10) Å, α = β = γ = 80.25(5)°. Starting with initially random phases, useful phase sets could be obtained from multiple trials of direct methods based on reciprocal space. The E-map corresponding to the phase set with the lowest mean phase error, 45.4°, showed a distorted octahedral coordination around the Fe site. The phase estimates from the metal atom and a few neighbouring atoms in the initial E-map have been improved by density modification procedure (PERP) operating in direct space. The resulting electron density map can be interpreted readily by an automated procedure to build up the protein structure.

Ab initio structure determination of icosahedral Zn-Mg-Ho quasicrystals by density modification method

A novel density modification method is applied for the first time to phase reconstruction of x-ray single crystal data of quasicrystals. The structure of icosahedral Zn-Mg-Ho quasicrystals has been determined by means of this ab initio structure determination within a framework of a 6D description. The location, size, and shape of the occupation domains are deduced. The suggested Ho sites in the 3D structure are consistent with the results of magnetic diffuse scattering [T. J. Sato et al., Phys. Rev. Lett. 81, 2364 (1998)].

Density modification for macromolecular phase improvement

Density modification provides a simple and largely automatic tool for improving phase estimates for observed structure factors. The phase information arises from a combination of the known structure factor magnitudes, the current phase estimates, and stereochemical information. The magnitudes, the current phase estimates, and stereochemical information. The addition of these phase information derived from theoretical sources renders new structures amenable to solution, and reduces the effort required to solve other structures. A diverse array of techniques which have been applied to the phase improvement problem are reviewed.

Structure determination of racemic trichogin A IV using centrosymmetric crystals

Direct methods of crystal structure solution are greatly facilitated in centrosymmetric space groups where the complexity of the phase-problem is reduced. For most peptides and proteins, crystallization in a centrosymmetric arrangement is precluded by an intrinsic dissymmetry due to the constituent chiral amino acid residues. The synthetic accessibility of peptide sequences containing amino acids of either chirality offers the possibility for co-crystallization of racemic crystals. We report here the first use of such an approach for the de novo structure determination of a medium-sized molecule, trichogin A IV, which is a constituent of a fungal lipopeptaibol mixture possessing membrane-modifying properties of biological interest.

Computational challenges for macromolecular structure determination by X-ray crystallography and solution NMR-spectroscopy

Macromolecular structure determination by X-ray crystallography and solution NMR spectroscopy has experienced unprecedented growth during the past decade.