The partial structure with errors: a probabilistic treatment

About difference electron densities and their properties

Difference electron densities do not play a central role in modern phase refinement approaches, essentially because of the explosive success of the EDM (electron-density modification) techniques, mainly based on observed electron-density syntheses. Difference densities however have been recently rediscovered in connection with theVLD(Vive la Difference) approach, because they are a strong support for strengthening EDM approaches and forab initiocrystal structure solution. In this paper the properties of the most documented difference electron densities, here denoted asF−Fp,mF−FpandmF−DFpsyntheses, are studied. In addition, a fourth new difference synthesis, here denoted as {\overline F_q} synthesis, is proposed. It comes from the study of the same joint probability distribution function from which theVLDapproach arose. The properties of the {\overline F_q} syntheses are studied and compared with those of the other three syntheses. The results suggest that the {\overline F_q} difference may be a useful tool for making modern phase refinement procedures more efficient.

Solving proteins at non-atomic resolution by direct methods: update

Direct methods can be used to solve proteins of great structural complexity even when diffraction data are at non-atomic resolution. However, one of the main obstacles to the wider application of direct methods is that they reliably phase only a small fraction of the observed reflections, those with a sufficiently large value of the normalized structure factor amplitude. The subsequent phase expansion and refinement required for full structure solution are difficult. Here a new phase refinement procedure is described, which combines (1–2) difference Fourier synthesis with electron density modification techniques and thevive la differenceand Free Lunch algorithms. This procedure is able to solve data resistant to other direct space refinement procedures.

The phantom derivative method when a structure model is available: about its theoretical basis

This study clarifies why, in the phantom derivative (PhD) approach, randomly created structures can help in refining phases obtained by other methods. For this purpose the joint probability distribution of target, model, ancil and phantom derivative structure factors and its conditional distributions have been studied. Since PhD may usenphantom derivatives, withn≥ 1, a more general distribution taking into account all the ancil and derivative structure factors has been considered, from which the conditional distribution of the target phase has been derived. The corresponding conclusive formula contains two components. The first is the classical Srinivasan & Ramachandran term, relating the phases of the target structure with the model phases. The second arises from the combination of two correlations: that between model and derivative (the first is a component of the second) and that between derivative and target. The second component mathematically codifies the information on the target phase arising from model and derivative electron-density maps. The result is new, and explains why a random structure, uncorrelated with the target structure, adds useful information on the target phases, provided a model structure is known. Some experimental tests aimed at checking if the second component really provides information on φ (the target phase) were performed; the favourable results confirm the correctness of the theoretical calculations and of the corresponding analysis.

Phase improvementviathePhantom Derivativetechnique: ancils that are related to the target structure

Density modification is a general standard technique which may be used to improve electron density derived from experimental phasing and also to refine densities obtained byab initioapproaches. Here, a novel method to expand density modification is presented, termed thePhantom derivativetechnique, which is based on non-existent structure factors and is of particular interest in molecular replacement. ThePhantom derivativeapproach uses randomly generated ancil structures with the same unit cell as the target structure to create non-existent derivatives of the target structure, called phantom derivatives, which may be used forab initiophasing or for refining the available target structure model. In this paper, it is supposed that a model electron density is available: it is shown that ancil structures related to the target obtained by shifting the target by origin-permissible translations may be employed to refine model phases. The method enlarges the concept of the ancil, is as efficient as the canonical approach using random ancils and significantly reduces the CPU refinement time. The results from many real test cases show that the proposed methods can substantially improve the quality of electron-density maps from molecular-replacement-based phases.

Advances in molecular-replacement procedures: theREVANpipeline

TheREVANpipeline aiming at the solution of protein structuresviamolecular replacement (MR) has been assembled. It is the successor toREVA, a pipeline that is particularly efficient when the sequence identity (SI) between the target and the model is greater than 0.30. TheREVANandREVAprocedures coincide when the SI is >0.30, but differ substantially in worse conditions. To treat these cases,REVANcombines a variety of programs and algorithms (REMO09,REFMAC,DM,DSR,VLD,free lunch,Coot,Buccaneerandphenix.autobuild). The MR model, suitably rotated and positioned, is first refined by a standardREFMACrefinement procedure, and the corresponding electron density is then submitted to cycles ofDM–VLD–REFMAC. The nextREFMACapplications exploit the better electron densities obtained at the end of theVLD–EDM sections (a procedure called vector refinement). In order to make the model more similar to the target, the model is submitted to mutations, in whichCootplays a basic role, and it is then cyclically resubmitted toREFMAC–EDM–VLDcycles. The phases thus obtained are submitted tofree lunchand allow most of the test structures studied by DiMaioet al.[(2011),Nature (London),473, 540–543] to be solved without using energy-guided programs.

Refining a model electron-density mapviathePhantom Derivativemethod

ThePhantom Derivative(PhD) method [Giacovazzo (2015),Acta Cryst.A71, 483–512] has recently been described forab initioand non-ab initiophasing. It is based on the random generation of structures with the same unit cell and the same space group as the target structure (called ancil structures), which are used to create derivatives devoid of experimental diffraction amplitudes. In this paper, the non-ab initiovariant of the method was checked using phase sets obtained by molecular-replacement techniques as a starting point for phase extension and refinement. It has been shown that application ofPhDis able to extend and refine phases in a way that is competitive with other electron-density modification techniques.

About the hybrid Fourier syntheses: a probabilistic approach

The difference electron density has recently been revisited via the method of joint probability distribution functions [Burla et al. (2010). Acta Cryst. A 66, 347-361]. New Fourier coefficients were devised which were the basis of a new ab initio method for the solution of the phase problem (i.e. VLD, vive la difference). In this paper we study the joint probability distribution functions P(F, F(p), F(Q)), where F(Q) is the structure factor corresponding to the ideal hybrid Fourier synthesis ρ(Q) = τρ - ωρ(p) and τ and ω are any pair of real numbers. New Fourier coefficients for the calculations of any hybrid synthesis are obtained, and the properties of the corresponding electron-density maps are discussed. The first applications show the correctness of our theoretical approach and suggest possible applications in phasing procedures.

From a random to the correct structure: the VLD algorithm

A recent probabilistic reformulation of the difference electron-density Fourier synthesis [Burla, Caliandro, Giacovazzo & Polidori (2010).Acta Cryst.A66, 347–361] suggested that the most suitable Fourier coefficients are the sum of the classical difference term (mF−DFp) with a flipping term, depending on the model and on its quality. The flipping term is dominant when the model is poor and is negligible when the model is a good representation of the target structure. In the case of a random model the Fourier coefficient does not vanish and therefore could allow the recovery of the target structure from a random model. This paper describes a new phasing algorithm which does not require use of the concept of structure invariants or semi-invariants: it is based only on the properties of the new difference electron density and of the observed Fourier synthesis. The algorithm is cyclic and very easy to implement. It has been applied to a large set of small-molecule structures to verify the suitability of the approach.

The cross-correlation function: main properties and first applications

When a model structure, and more generally a model electron density ρM(r), is available, its cross-correlation functionC(u) with the unknown true structure ρ(r) cannot be exactly calculated. A useful approximation ofC(u) is obtained by replacing exp[i(φh − φMh)] by its expected value. In this caseC′(u), a potentially useful approximation of the functionC(u), is obtained. In this paper the main crystallographic properties of the functionsC(u) andC′(u) are established. It is also shown that such functions may be useful for the success of the phasing process.

A novel type of monoheme cytochrome c: biochemical and structural characterization at 1.23 A resolution of rhodothermus marinus cytochrome c

Monoheme cytochromes of the C-type are involved in a large number of electron transfer processes, which play an essential role in multiple pathways, such as respiratory chains, either aerobic or anaerobic, and the photosynthetic electron transport chains. This study reports the biochemical characterization and the crystallographic structure, at 1.23 A resolution, of a monoheme cytochrome c from the thermohalophilic bacterium Rhodothermus marinus. In addition to an alpha-helical core folded around the heme, common for this type of cytochrome, the X-ray structure reveals one unusual alpha-helix and a unique N-terminal extension, which wraps around the back of the molecule. Based on a thorough structural and amino acid sequence comparison, we propose R. marinus cytochrome c as the first characterized member of a new class of C-type cytochromes.

Fourier transform infrared characterization of a CuB-nitrosyl complex in cytochrome ba3 from Thermus thermophilus: relevance to NO reductase activity in heme-copper terminal oxidases

The two heme-copper terminal oxidases of Thermus thermophilus have been shown to catalyze the two-electron reduction of nitric oxide (NO) to nitrous oxide (N2O) [Giuffre, A.; Stubauer, G.; Sarti, P.; Brunori, M.; Zumft, W. G.; Buse, G.; Soulimane, T. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 14718-14723]. While it is well-established that NO binds to the reduced heme a3 to form a low-spin heme {FeNO}7 species, the role CuB plays in the binding of the second NO remains unclear. Here we present low-temperature FTIR photolysis experiments carried out on the NO complex formed by addition of NO to fully reduced cytochrome ba3. Low-temperature UV-vis, EPR, and RR spectroscopies confirm the binding of NO to the heme a3 and the efficiency of the photolysis at 30 K. The nu(NO) modes from the light-induced FTIR difference spectra are isolated from other perturbed vibrations using 15NO and 15N18O. The nu(N-O)a3 is observed at 1622 cm-1, and upon photolysis, it is replaced by a new nu(N-O) at 1589 cm-1 assigned to a CuB-nitrosyl complex. This N-O stretching frequency is more than 100 cm-1 lower than those reported for Cu-NO models with three N-ligands and for CuB+-NO in bovine aa3. Because the UV-vis and RR data do not support a bridging configuration between CuB and heme a3 for the photolyzed NO, we assign the exceptionally low nu(NO) to an O-bound (eta1-O) or a side-on (eta2-NO) CuB-nitrosyl complex. From this study, we propose that, after binding of a first NO molecule to the heme a3 of fully reduced Tt ba3, the formation of an N-bound {CuNO}11 is prevented, and the addition of a second NO produces an O-bond CuB-hyponitrite species bridging CuB and Fea3. In contrast, bovine cytochrome c oxidase is believed to form an N-bound CuB-NO species; the [{FeNO}7{CuNO}11] complex is suggested here to be an inhibitory complex.