Jean Richelle

SFCHECK: a unified set of procedures for evaluating the quality of macromolecular structure-factor data and their agreement with the atomic model

In this paper we present SFCHECK, a stand-alone software package that features a unified set of procedures for evaluating the structure-factor data obtained from X-ray diffraction experiments and for assessing the agreement of the atomic coordinates with these data. The evaluation is performed completely automatically, and produces a concise PostScript pictorial output similar to that of PROCHECK [Laskowski, MacArthur, Moss & Thornton (1993). J. Appl. Cryst. 26, 283-291], greatly facilitating visual inspection of the results. The required inputs are the structure-factor amplitudes and the atomic coordinates. Having those, the program summarizes relevant information on the deposited structure factors and evaluates their quality using criteria such as data completeness, structure-factor uncertainty and the optical resolution computed from the Patterson origin peak. The dependence of various parameters on the nominal resolution (d spacing) is also given. To evaluate the global agreement of the atomic model with the experimental data, the program recomputes the R factor, the correlation coefficient between observed and calculated structure-factor amplitudes and Rfree (when appropriate). In addition, it gives several estimates of the average error in the atomic coordinates. The local agreement between the model and the electron-density map is evaluated on a per-residue basis, considering separately the macromolecule backbone and side-chain atoms, as well as solvent atoms and heterogroups. Among the criteria are the normalized average atomic displacement, the local density correlation coefficient and the polymer chain connectivity. The possibility of computing these criteria using the omit-map procedure is also provided. The described software should be a valuable tool in monitoring the refinement procedure and in assessing structures deposited in databases.

The aMAZE LightBench: a web interface to a relational database of cellular processes

The aMAZE LightBench (http://www.amaze.ulb. ac.be/) is a web interface to the aMAZE relational database, which contains information on gene expression, catalysed chemical reactions, regulatory interactions, protein assembly, as well as metabolic and signal transduction pathways. It allows the user to browse the information in an intuitive way, which also reflects the underlying data model. Moreover links are provided to literature references, and whenever appropriate, to external databases.

Determination of sensory bristles and pattern formation in Drosophila. I. A model

A model is presented to explain the formation of the pattern of sensory bristles in Drosophila. The model is based on the idea that precision and reproducibility in pattern formation can be achieved by averaging out of many moderately accurate responses to positional cues. According to this model, the determination of bristles in imaginal discs occurs in two steps. First, large numbers of imaginal cells synthesize a freely diffusible inducer, the chaetogen. Second, cells in which the concentration of this chaetogen reaches a threshold are induced to differentiate into a bristle apparatus. Induced cells prevent neighboring cells from being induced too. The synthesis of chaetogen is supposed to be a probabilistic response of cells to positional cues, so that a cell located in one region of the disc is more likely to have its chaetogen gene turned on than a cell located in another region. Various probability distributions are shown to generate the various bristle patterns observed in the adult: precisely located bristles (e.g., thoracic macrochaetes), evenly spaced bristles (e.g., tergal microchaetes), and rows of bristles (e.g., thoracic microchaetes). In the particular case of the precisely located bristles, we show that (i) the distribution of chaetogen concentration in the tissue presents a unique maximum even when a large number of contiguous cells are all engaged in the synthesis of chaetogen; (ii) the position of the maximum is largely unaffected by statistical fluctuations in the decision of each cell to synthesize or not to synthesize the chaetogen; (iii) different maxima can be reproducibly generated even when the corresponding populations of chaetogen-producing cells overlap.

Determination of sensory bristles and pattern formation in Drosophila: II. The achaete-scute locus

In the first paper of this series, we developed a model of bristle determination in which a key role is played by a freely diffusible inducer, the chaetogen. In this paper we show that the complex properties of the achaete-scute locus of Drosophila, including the generalized effect of deficiencies, the peculiar phenotypes of some alleles, the existence of bristle-overproducing variants, and the local nonautonomy, correspond exactly to the properties expected for the locus that controls the synthesis of chaetogen. The correspondence between expectations derived from the model and observations made on a genetic locus of the fly is taken as experimental support for the model.

Macromolecular structure information and databases

The current status and future outlook of macromolecular structure databases and information handling, with particular reference to European databases, are reviewed, Issues concerning the efficiency with which data are represented, validated, archived and accessed are discussed in view of the fast growing body of information on structures of biological macromolecules.

Checking nucleic acid crystal structures

The program SFCHECK [Vaguine et al. (1999), Acta Cryst. D55, 191-205] is used to survey the quality of the structure-factor data and the agreement of those data with the atomic coordinates in 105 nucleic acid crystal structures for which structure-factor amplitudes have been deposited in the Nucleic Acid Database [NDB; Berman et al. (1992), Biophys. J. 63, 751-759]. Nucleic acid structures present a particular challenge for structure-quality evaluations. The majority of these structures, and DNA molecules in particular, have been solved by molecular replacement of the double-helical motif, whose high degree of symmetry can lead to problems in positioning the molecule in the unit cell. In this paper, the overall quality of each structure was evaluated using parameters such as the R factor, the correlation coefficient and various atomic error estimates. In addition, each structure is characterized by the average values of several local quality indicators, which include the atomic displacement, the density correlation, the B factor and the density index. The latter parameter measures the relative electron-density level at the atomic position. In order to assess the quality of the model in specific regions, the same local quality indicators are also surveyed for individual groups of atoms in each structure. Several of the global quality indicators are found to vary linearly with resolution and less than a dozen structures are found to exhibit values significantly different from the mean for these indicators, showing that the quality of the nucleic acid structures tends to be rather uniform. Analysis of the mutual dependence of the values of different local quality indicators, computed for individual residues and atom groups, reveals that these indicators essentially complement each other and are not redundant with the B factor. Using several of these indicators, it was found that the atomic coordinates of the nucleic acid bases tend to be better defined than those of the backbone. One of the local indicators, the density index, is particularly useful in spotting regions of the model that fit poorly in the electron density. Using this parameter, the quality of crystallographic water positions in the analyzed structures was surveyed and it was found that a sizable fraction of these positions have poorly defined electron density and may therefore not be reliable. The possibility that cases of poorly positioned water molecules are symptomatic of more widespread problems with the structure as a whole is also raised.

POSITIVE LOOPS AND DIFFERENTIATION

This paper focuses on the relation between the presence of positive feedback loops and the occurrence of multiple states of gene expression. After a short recall on single feedback loops and their properties, we discuss more extensively the properties of positive loops. This discussion includes a theorem (demonstrated elsewhere) which states that the presence of positive loop(s) is a necessary condition for multistationarity. We also discuss some general principles for pattern formation, in terms of involvement of different types of positive feedback loops. Finally, we briefly mention recent experimental results involving positive loops in crucial differentiative processes.

Positive feedback loops and multistationarity

Abstract This paper aims to draw the attention of mathematicians to a class of problems whose resolution has recently become possible from the practical viewpoint but still badly lacks a firm mathematical basis. These problems arise in biological systems which involve multiple interacting feedback loops. Such systems may be described in terms of differential equations. However, the non-linear character of most of these equations precludes an analytic treatment, and it is often very difficult to obtain a global idea of their complex dynamics. Logical methods (briefly summarised in this paper) have been developed (Thomas [13–15]). In spite of the somewhat caricatural character inherent to logical descriptions, these methods grasp the essential qualitative features of the dynamics of the systems, and, for complex systems, they greatly help in clarifying the continuous description. Graphs are involved at two distinct levels; first, the logical structure of a system can be described by a graph of interactions , and at a later stage of the analysis one obtains a graph of the logical sequences of states . Although algorithms permit the second type of graph to be derived from the first, there is so far no general mathematical analysis of their relation. The paper gives, as an illustration of this type of problem, the relation between positive loops (in the graph of interactions) and multiple steady states (which are found as the final states in the graph of the sequences of states). In short, a system comprising n positive loops may have up to 3 n steady states (2 n attractors); interactions between the loops reduce these numbers in a predictable way.

Advanced pairwise structure alignments of proteins and analysis of conformational changes.

MOTIVATION Comparing the 3D structures of two proteins or analyzing the structural changes undergone by a protein upon ligand binding or when it crystallizes under different conditions, can be both tricky and tedious, especially when the two proteins are distantly related, or when the structural changes are complex. Readily accessible tools for performing these tasks automatically and reliably should therefore be welcome. RESULTS We describe a web interface to several automatic procedures for performing pairwise structure superposition in a flexible manner, for detailed analyses of conformational changes and for displaying the results in a pictorial fashion. AVAILABILITY This interface can be accessed at the Brussels and Cuba Web sites, respectively: http://www.ucmb.ulb.ac.be/SCMBB/Tools.htmland http://bio.cigb.edu.cu.

Assessing the quality of macromolecular structures

In this chapter, an overview is presented of the different types of validation procedures applied to proteins and nucleic acids. An approach to model validation based on atomic volumes embodied in the program PROVE is illustrated in some detail and the package SFCHECK, which combines a set of criteria for evaluating the quality of the experimental data and the agreement of the model with the data, is described.