What is rmerge crystallography

D69, As the title indicates, this paper discusses at what resolution the data should be cut. One important finding is that a perfect model gives an R value of This tells us that a model that gives significantly lower R free in the current high resolution shell may benefit from including higher resolution data. Diederichs and P. Karplus Improved R-factors for diffraction data analysis in macromolecular crystallography. Nature Struct. Weiss and R. Hilgenfeld On the use of the merging R-factor as a quality indicator for X-ray data.

Global indicators of X-ray data quality. Diederichs Some aspects of quantitative analysis and correction of radiation damage. Acta Cryst D62, [4]. Cookies help us deliver our services. By using our services, you agree to our use of cookies. An electron-density map is, in a sense, the end-product of crystallographic structure determination.

Simply put, the map is an image of the electron clouds surrounding the molecule. In a process called map interpretation, the crystallographer builds a model to fit this image. NMR structure determination entails building models that comply with structural restraints obtained by analysis of J or NOE couplings. Half a dozen to several dozen models are built in order to see the full variety of models that fit all restraints.

The resulting set of models is called an ensemble see figure below. A single model is usually derived by averaging atom positions and then minimizing the energy of the resulting model. Both the ensemble coordinates and the averaged model coordinates are usually available from the Protein Data Bank. See Which model to use.

The products of "structure determination" by diffraction methods primarily single-crystal X-ray crystallography and NMR spectroscopy are referred to as experimental models , in contrast with theoretical models , which include homology models and those obtained by simulation of folding or molecular dynamics.

See Model versus structure. First, see R-factor. R-factors are measures of the extent to which a crystallographic model accounts for the original experimental data -- specifically, the measured intensities of reflections in the diffraction pattern.

As such, R-factors are important indicators of progress in refining models, and the final values of R-factors are important criteria of model quality. The free R-factor, R free , is computed in the same manner as R , but using only a small set of randomly chosen intensities the "test set" which are set aside from the beginning and not used during refinement.

They are used only in the cross-validation or quality control process of assessing the agreement between calculated from the model and observed data. At any stage in refinement, R free measures how well the current atomic model predicts a subset of the measured reflection intensities that were not included in the refinement, whereas R measures how well the current model predicts the entire data set that produced the model.

Many crystallographers believe that R free gives a better and less-biased measure of refinement progress. In many test calculations, R free correlates very well with phase accuracy of the atomic model. In general, during intermediate stages of refinement, R free values are higher than R, but in the final stages, the two often become more similar.

Because incompleteness of data can make structure determination more difficult and perhaps because the lower values of R are somewhat seductive during stages where some encouragement is welcome , some crystallographers at first resisted using R free.

But many now use both Rs to guide them in refinement, looking for refinement procedures that improve both, and proceeding with great caution when the two criteria appear to be in conflict.

The symmetry of functional macromolecular complexes in solution is sometimes important to understanding their functions, as in the binding of regulatory proteins having twofold rotational symmetry to palindromic DNA sequences. Users of models should be careful to distinguish the crystallographic asymmetric unit from the functional unit , which the Protein Data Bank has dubbed the "biologically functional molecule.

We say that hemoglobin functions as an a 2 b 2 tetramer. In some hemoglobin crystals, the twofold rotational symmetry axis of the tetramer corresponds to a unit-cell symmetry axis, and the asymmetric unit is a single ab dimer.

In other cases, the crystallographic asymmetric unit may contain more than one biological unit. A means of estimating the overall or average precision of atom locations in a refined crystallographic model. At best, the Luzzati plot allows an estimate of the upper limit of error in atomic coordinates. The figure below shows four theoretical curves on a Luzzati plot.

The numbers to the right of each smooth curve are theoretical estimates of the average uncertainty in the positions of atoms in the refined model more precisely, the rms errors in atom positions. The average uncertainty has been shown to depend upon R-factors derived from the final model in various resolution ranges.

The resulting curve should roughly fit one of the theoretical curves on the Luzzati plot. From the theoretical curve closest to the experimental R-factor curve, we learn the average uncertainty in the atom positions of the final model. It has been claimed that Luzzati plots with the free R-factor give even better estimates of uncertainty in coordinates.

Some scientists argue for using the term structure to refer to the results of experimental methods, like X-ray crystallography and NMR spectroscopy, and the term model to refer to theoretical models, including homology models and those derived from simulations of folding, dynamics, and ligand binding.

Other scientists, pointing out that molecular structure is not open to our direct view, are more comfortable with the term model for all results of attempts to know molecular structure. In this view, models, experimental or theoretical an imprecise distinction itself , represent the best we can do in our diverse efforts to know molecular structure.

All of us sometimes refer loosely to a model as a structure, and to the process of constructing and refining models as structure determination. But in the end, no matter what the method, we are trying to construct models that agree with, and explain, what we know from experiments that are quite different from actually looking at structure.

One of several parameters included in refinement. The occupancy n j of atom j is a measure of the fraction of molecules in the crystal in which atom j actually occupies the position specified in the model. If all molecules in the crystal are precisely identical, then occupancies for all atoms are 1.

Occupancy is included among refinement parameters because occasionally two or more distinct conformations are observed for a small region like a surface side chain. The model might refine better if atoms in this region are assigned occupancies equal to the fraction of side chains in each conformation. For example, if the two conformations occur with equal frequency, then atoms involved receive occupancies of 0. By including occupancies among the refinement parameters, we obtain estimates of the frequency of alternative conformations, giving some additional information about the dynamics of the protein molecule.

We also make the model more accurate, which contributes to progress in the refinement. In crystallography, unlike microscopy, the term resolution simply refers to the amount of data ultimately used in structure determination. In contrast, the precision of atom positions depends in part upon the resolution limits of the data, but also depends critically upon the quality of the data, as reflected by the R-factor. Good data can yield atom positions that are precise to within one-fifth to one-tenth of the stated resolution.

One means of estimating the average or overall precision of atomic positions is the Luzzati plot. Also see temperature factor. See Rms deviations rmsd from average ensemble coordinate positions. A measure of agreement between the crystallographic model and the original X-ray diffraction data. The crystallographer calculates from the model the expected intensity of each reflection in the diffraction pattern, and then compares these calculated "data" with the experimental data, which consist of measured positions and intensities.

The R-factor is used to assess the progress of structure refinement , and the final R-factor is one measure of model quality. In this expression, each F obs is derived from the measured intensity of a reflection in the diffraction pattern, and each F calc is the intensity of the same reflection calculated from the current model. Values of R range from zero perfect agreement of calculated and observed intensities to about 0.

An R-factor greater than 0. An early model with R near 0. A desirable target R-factor for a protein model refined with data to 2. When R approaches about 0. See Free R-factor.

Measure of the similarity between an electron-density map calculated directly from the model and one calculated from experimental data. This measure is often provided in the form of a graph of RSR values versus residue number, showing clearly which residues give best and worst agreement with the experimental electron-density map. RSR is an excellent model-validation tool, and is calculated as follows rho's are electron density values at grid points that cover the residue in question.

The latter does not require that the two densities be scaled against each other, but for the model user, the difference is not important. A measure of agreement among multiple measurements of the same not symmetry-related -- see R symm reflections, with the different measurements being in different frames of data or different data sets. Often, separate values of R merge are given for a all the data and b data from the last or highest-resolution shell.

The latter allows the model user to evaluate the reliability of data at the highest resolution used. A measure of agreement among the independent measurements of symmetry-related reflections in a crystallographic data set.

Symmetry-related reflections should have identical intensities. If they do not, it suggests some type of measurement error. R symm is calculated as follows I and I with bar on top represent intensities of two symmetry-related reflections :. A common reason for high R symm is strong absorption of X-rays by the crystal. If the lengths of the X-ray paths through such a crystal is very different for two symmetry-related reflections, then absorption will be different for the two measurements.

In some cases, data can be improved by correcting for crystal absorption. A plot showing the main-chain conformational angles in a polypeptide. This diagram is used to find problems in models during structure refinement. The pair of angles phi and psi of a single residue is greatly restricted by steric repulsion. The allowed pairs of values are depicted on a Ramachandran diagram as irregular polygons that enclose backbone conformational angles that do not give steric repulsion yellow, inner polygons or give only modest repulsion blue, outer polygons.

Every point phi, psi on the diagram represents the conformational angles phi and psi on either side of the alpha carbon of one residue. Each residue in the protein is represented with a dot or other mark on the plot.

During the final stages of map fitting and crystallographic refinement, Ramachandran diagrams are a great aid in finding conformationally unrealistic regions of the model. Structure publications often include the diagram, with an explanation of any residues that lie in high-energy "forbidden" areas.

Glycines, because they lack a side chain, usually account for most of the residues that lie outside allowed regions. If nonglycine residues exhibit forbidden conformational angles, there should be some explanation, such as structural constraints that overcome the energetic cost of an unusual backbone conformation.

If a homology model appears to be correct not harboring impossibilities such as clashing atoms and accurate fitting its templates well , we can also ask if it is reasonable , or in keeping with expectations for similar proteins.

Researchers have developed several assessments of reasonableness that can sometimes signal problems with a model or specific regions of a model. One is to sum up the probabilities that each residue should occur in the environment in which it is found in the model. For all Protein Data Bank models, each of the 20 amino acids has a certain probability of belonging to one of the following classes: solvent-accessible surface, buried polar, exposed nonpolar, helix, sheet, or turn.

Regions of a model that do not fit expectations based on these probabilities are suspect. Another criterion of reasonableness is to look at how often pairs of residues interact with each other in the model in comparison to the same pairwise interactions in templates or proteins in general.

The sum of pairwise potentials for the model, usually expressed as an "energy" smaller is better should be similar to that for the templates. One form of this criterion is called threading energy. Such criteria ask, in a sense, whether a particular stretch of residues is "happy" in its three-dimensional setting. If a fragment is "unhappy" by these criteria, then that part of the model may be in error.

To be meaningful, all assessments of reasonableness of the model must be compared with the same properties of the templates. After all, the templates themselves, even if they are high-quality experimental structures, may be unusual in comparison to the average protein. The calculation gives the average number of independent measurements of each reflection in a crystallographic data set. Two factors, symmetry and overlap, contribute to redundancy in a crystallographic data set. As a result of these two factors, a data set contains several independent measurements of each reflection.

To improve accuracy in measuring reflection intensities, data collection strategies are intentionally designed to take advantage of symmetry and overlap to give redundancy of measurement. Such statistical parameters as standard deviation are used to measure agreement among the repeated measurements. The iterative process of improving agreement between the molecular model and the crystallographic data. An important element in refinement is a computationally massive least-squares adjustment of 1 the atomic positions in the model, 2 occupancies , and 3 temperature factors in order to improve their agreement with 1 the data reflection intensities , and 2 criteria of chemical reasonableness structural parameters such as bond lengths and angles.

The crystallographer might impose certain constraints and restraints on the model during refinement, often relaxing these restrictions as the refinement proceeds. Energy minimization may also be included in refinement. In the latter stages of structure determination, the crystallographer alternates between refinement and interpretation of the electron-density map.

Signs of progress and ultimate success of refinement include 1 decreasing R-factor , 2 disappearance of residues from unfavorable regions of the Ramachandran plot , and 3 diminishing average deviation from ideal structural parameters.

The iterative process of improving agreement between the molecular model and NMR data. Protein structure determination by NMR ends with building a model of the protein that fits distance restraints from multidimensional NMR spectra. This is no trivial task. One general procedure entails starting from a model of the protein having the known sequence of residues, and having standard bond lengths and angles but random conformational angles.

This starting structure will, of course, be inconsistent with most of the distance and conformational restraints derived from NMR. The amount of inconsistency can be expressed as a numerical parameter that should decline in value as the model improves, in somewhat the same fashion as the R-factor decreases as a crystallographic model's agreement with diffraction data improves during crystallographic refinement.

Starting from a random conformation, simulated annealing or some form of molecular dynamics is used to fold the model under the influence of simulated forces that maintain correct bond lengths and angles, provide weak versions of van der Waals repulsions, and draw the model toward allowed conformations, as well as toward satisfying the restraints derived from NMR. Electrostatic interactions and hydrogen-bonding are usually not simulated, in order to give larger weight to restraints based on experimental data; after all, we want to discover these interactions in the end, not build them into the model before the data have had their say.

The resulting model is examined for serious van der Waals collisions, and for large deviations from even one distance or conformational restraint.

Models that suffer from one or more such problems are judged not to have converged to a satisfactory final conformation. They are discarded. The entire simulated folding process is carried out repeatedly, each time from a different random starting conformation, until a number of models an ensemble are found that are chemically realistic and consistent with all NMR-derived restraints. When the group of models appears to contain the full range of structures that satisfy all restraints, this phase of structure determination is complete.

The number of measured reflections in a crystallographic data set, neglecting all repeated measurements of the same reflection or symmetry-related reflections.

Repeated measurements of a reflection arise for reasons described under Redundancy. See Reflections, number of. The total number of measured reflections in a crystallographic data set, including all repeated measurements of the same reflection or symmetry-equivalent reflections.

See Reflections, unique and Redundancy. More closely spaced planes of atoms give rise to reflections farther from the center of the diffraction pattern. Presumably, data farther out than the stated resolution is unobtainable or too weak to be reliable. The main constraint is that we know we can fit the map with groups of atoms -- amino-acid residues -- having known connectivities, bond lengths, bond angles, and stereochemistry.

A subsidiary condition imposed on parameters during crystallographic refinement , such as the condition that all bond lengths and bond angles be within a specified range of values. See crystallographic constraint. Atomic distances and conformational angles determined from NMR couplings or correlations. In NMR structure determination, the construction of a model complies with these restraints, resulting in a model that fits what NMR spectra say about which pairs of atoms are near each other through bonds or through space.

An example of the effect of a restraint is shown in the figure below. The final model complies with this restraint, as shown by the dotted line between the two atoms. The total number of distance and conformational restraints for an NMR model, divided by the number of residues in the model. How much structural information must we obtain from NMR in order to derive reliable models? As summarized in the PDB file header for thioredoxin PDB 3trx , the ensemble of 33 human thioredoxin models were determined from interproton distance restraints derived from NOE couplings, and 52 hydrogen-bonding distance restraints defining 26 hydrogen bonds.

Finally, there were 98 phi and 71 psi backbone dihedral-angle restraints, and 72 CB-CG side-chain dihedral-angle restraints, derived from NOE and J coupling. Thus the conformation of each of the 33 final thioredoxin models is defined by a total of restraints. Thioredoxin contains residues, so these models are based on about 22 restraints per residue.

Very roughly speaking , an NMR model with over 20 restraints per residue is comparable to a 2. A measure of how much the position of each atom in a model varies throughout the ensemble. The rmsd for an atom is the square root of the sum of squares of distances between that atom in all models in an NMR ensemble and the average position for that atom in the ensemble.

The best quality models exhibit main-chain deviations no greater than 0. For emphasis: such coloring DOES NOT reflect the distances of averaged-model atoms from the average, but instead the amount of variation in atom positions in the ensemble. A measure of how well the final crystallographic model conforms to expected values of bond lengths and bond angles. Expected values are derived from measurements of the same parameters in high-resolution models of small molecules.

A high quality crystallographic model has rmsd values lower than 0. These values are restrained or constrained during parts of crystallographic refinement, so they are not as useful as quality indicators than parameters that are allowed to refine freely.