SHARP Output Guide

Contents

• Introduction
  • Preparation of data
  • ML Refinement
  • Residual maps
  • Electron-density maps
• Reading the input parameter file
  • Cell information
  • Symmetry information
  • Atomic scattering information
• Preparation of data
  • Changing the resolution bins
  • Accepted reflexions
  • Initial outlier rejection
  • Computing statistics
  • Estimation of the absolute scale
  • Estimation of the relative scale
  • Estimation of lack of isomorphism
• Maximum-Likelihood refinement
  • Outlier rejection using likelihood histograms
  • List of refined parameters
  • Auxiliary Cycle Information
  • Weeding
  • Refinement step in parameter space
  • Step length
  • Lack of isomorphism
  • Other statistics
• Residual maps
  • Type of residual map
  • What to look for in a residual map
• Electron-density map
  • Statistics
  • Displaying an electron-density map
  • Solvent flattening (density modification)

Introduction 

• Preparation of data

  This section is present in all types of calculations. The crystallographic data are read, undergo statistical information gathering and filtering and (optional) robust estimation of scale.

• ML Refinement

  All parameters that have been marked for refinement in the input will be allowed to vary in order to maximise the log-likelihood function. This refinement is done following a Newton method with full second-order derivative information. The Hessian matrix (normal matrix of the maximisation) is filtered of its positive eigenvalues, so that the refinement only proceeds in the parameter subspace where the function is convex. The Hessian matrix is also used to calculate standard deviations for all parameters. This in turn provides a way to objectively measure the distance of each step (parameter update) in parameter space, in units of standard deviations. Convergence is achieved when this step becomes small enough.

• Residual maps

  Once convergence is achieved for the parameters of the current model, it is possible to detect unaccounted-for substitution features using the various kinds of residual maps provided. The Fourier coefficients for these maps are the components of the gradient of the log-likelihood function. This means that after a Fourier Synthesis positive peaks will appear where the data "expects" more heavy-atom density and negative peaks where the data "wants" less heavy-atom density.

• Electron-density maps

  Once the substitution model is satisfactory (no significant peaks left in the residual maps), it is time to inspect the electron-density maps, post-process them using density modification algorithms and try to interpret them in terms of molecular structure. Fourier coefficients calculated by SHARP are an extension of the "best phases" in the sense of Blow and Crick (Blow & Crick, 1959): instead of being one-dimensional phase centroids they are two-dimensional centroids of the probability distribution of the complex native structure factor.

  Note : The phase information output by SHARP is not limited to the centroid structure factor that is used to calculate the electron-density map. A complete summary of the phase probability distribution is available via Hendrickson-Lattman (HL) coefficients. In many cases, the quality of phasing that SHARP provides may not be noticeable at the level of centroid maps, but only after the HL coefficients have been used in a density modification procedure.

Reading the input parameter file

Cell information

• reciprocal cell parameters
• the volume of the unit cell
• the Brookhaven matrix (which, multiplied by a vector of fractional coordinates, returns the vector of coordinates in Å), and the inverse Brookhaven matrix (which performs the inverse operation).

Symmetry information

Atomic scattering information

what SHARP understood of the input parameter file

Preparation of data

Changing the resolution bins

Advanced users can specify the exact number of bins during preparation of the SHARP input file. A maximum of 20 bins is possible.

Accepted reflexions

Initial outlier rejection

Computing statistics

• the mean squared amplitudes for each batch
• the mean squared isomorphous differences for each batch
• the mean squared anomalous differences for each batch
• the mean squared native amplitudes

Note 1 : The statistics of mean squared isomorphous - or in the case of MAD dispersive - and anomalous differences as a function of resolution (as plotted in this section in a log-graph) are a very good indicator of the quality of your derivative. The plot should more or less follow a straight line. It has repeatedly happened that high-resolution data deemed worthless by other criteria have been very useful for phasing. As a general rule DO NOT DISCARD DATA WITH LOW PHASING POWER. These data are extremely useful for refining scale factors, heavy-atom temperature factors and other parameters. In addition, their full potential is only expressed in the density modification step, where high-resolution reflexions with FOM of 0.1 of 0.2 on average are crucial to obtain the best possible map as an outcome. You are strongly advised to judge for yourself in the tutorials.

Note 2 : When there is no native dataset (eg in MAD), the mean squared native amplitudes will be approximated as those of the reference dataset until big cycle 3. After that they are more accurately estimated by subtracting the heavy-atom contribution to the statistics of the reference dataset. This estimation will be done again at the start of each new big cycle, because their accuracy depends on the exactness of the substitution model.

Estimation of the absolute scale

Estimation of the relative scale

The Wilson-plot is there to show you how well the logarithm of the relative scale fits a straight line (as a function of resolution). Any significant departure from the line is an alarming symptom and that dataset should be revisited. If all Wilson-plots show a comparable pattern of misbehaviour, the reference dataset may need questionable.

Estimation of lack of isomorphism

Details

• incomplete heavy-atom model, characterised by values above the line at low resolution
• non-crystallographic symmetry, characterised by a hump at medium resolution
• questionable data quality, characterised by marked wiggles around the line

Always have a look at the table printed in the main SHARP log-file for all estimated parameters: any comment after one parameter should be taken as a warning and investigated further. If your refinement starts with very large values of non-isomorphism it might not recover from these starting values during the refinement.

Note 2 : by default the estimation of non-isomorphism parameters is switched off in the interface.

Maximum-Likelihood refinement

Outlier rejection using likelihood histograms

This likelihood filtering procedure is applied again to all reflexions (including those which were previously rejected by that procedure) at the beginning of each new big cycle. The number of rejected reflexions based on this filter should in general decrease during the refinement.

List of refined parameters

Therefore, the list of parameters that are being refined may vary during a run of SHARP. You will be given a link to the current list at the beginning of the ML refinement. Every time the list gets modified it will be presented too. The tree-like representation on the left side mirrors the hierarchical organisation of parameters within SHARP.

Auxiliary Cycle Information

For each small cycle SHARP computes the likelihood, the gradient (1st order derivatives )and Hessian (2nd order derivatives) at the current set of parameters. From this information a trial point is determined and the likelihood value at that point is computed. If this value has increased, the trial step becomes the 'new' current step and SHARP continues with another small cycle. If the value has decreased, a new trial point is determined using a smaller radius of the trust region.

What you'll see in the file depends on your user level'.

• STANDARD and ADVANCED:

  A line per trial step with the value of the trust region radius is printed.

• EXPERT:

  There are links to files with the gradient and (diagonal elements) of the Hessian of the likelihood at the current set of parameters as well as a link to a file with the eigenvalues of the Hessian.

  If you add the keyword PRINT_HESS to the general section of the SIN file, the Hessian file will contain all elements and there will also be a link to a file with the eigenvectors. The latter is useful to detect problems due to over-parametrisation.

  Also, at each trial point, additional information is printed which can help if you report problems to the SHARP developers.

Weeding

When weeding has been requested the file contains a list of G-Sites for which the refinement of coordinates and (optionally) B-factor(s) has been stopped for this BIG cycle. If the user level is EXPERT, more details are given.

Refinement step in parameter space

Details

Two hyper-links point to the first and second-order derivatives of the log-likelihood function with respect to the refined parameters. This is used to check if a value connected to a particular parameter is surprising (for instance, positive values for second-order derivatives are not healthy).

The next analysis is performed on the normal matrix and consists in an eigenvalue decomposition of that matrix. This algorithm looks for 'principal directions' in parameter space, and tells you which combinations of parameters are badly conditioned (coordinates of filtered eigenvalue(s)).

For each parameter the shift is tested if it would lead to an invalid parameter (Allowed range analysis).

The rest of the page consists of technical comments about the fastest way to maximise the function.

Note on eigenvalues : If the refinement is well-conditioned, all eigenvalues should be negative (meaning that the log-likelihood function is convex at that point in parameter space). In practise, it happens quite often that a few eigenvalues are filtered during the first cycles of a new refinement, meaning that the starting point is far from the maximum of the log-likelihood function. If the number of filtered eigenvalues does not decrease rapidly - and is not zero at convergence - this is a strong diagnostic of a pathology in the description of the heavy-atom substitution.

Remedies : You should then find out what combinations of parameters are associated with the most unfavourable (i.e. strongly positive) eigenvalues, and figure out where the problem comes from.

• In MIR, it may happen that lack-of-isomorphism parameters are estimated at a high value because the starting parameters are very far from optimal. If the refinement converges too rapidly thereafter, it sometimes happens that lack-of-isomorphism parameters remain "stuck" at high values and cannot refine because the function is not convex at that point. In this case, the coordinates of that filtered eigenvalue are almost 0 everywhere and almost 1 for that parameter. You should set that parameter back to zero (or half its value). Keep the refined value of all other parameters and start refining again.
• In MAD, it is sometimes the case that a false maximum is found - with filtered eigenvalues. This usually arises from a wrong starting combination of f' and f'' parameters. You should try refinement again from the start, with a different (more realistic) set of f' and f'' values - ideally from a good fluorescence measurement.

Step length

To provide a simple image of this, let us consider the case when only one parameter is being refined. Its standard deviation is then best approximated by the square root of the inverse of the second-order derivative of the log-likelihood function with respect to this parameter. The "natural" measure of distance is then given as a number of standard deviations, also called CHI SQUARE.

This simple picture can be generalised in the multi-dimensional parameter space : the reduced CHI SQUARE distance is then the distance in the metric of the Hessian matrix. It still can be understood intuitively as a "generalised number of standard deviations".

Lack of isomorphism

Near the bottom of the page the same information is available as a plot. This way you can check if the current model for lack of isomorphism fits the noise in the data properly on average. According to our experience, the model for "isomorphous" lack of isomorphism is valid - except when there are several NCS-related molecules in the asymmetric unit. The "anomalous" lack of isomorphism often displays a bad fit to the lack of closure analysis. But it is usually smaller than the measurement noise anyhow.

Other statistics

The definitions of these statistical quantities are :

Rcullis = <phase-integrated lack of closure> / < | Fph - Fp | >

Rkraut = <phase-integrated lack of closure> / < | Fph | >

Ppower = < [ | Fh(calc) | / phase-integrated lack of closure ] >

Residual maps

Type of residual map

• In SIRAS or MIRAS, it is important to compare the isomorphous and anomalous maps for each batch. These have different degrees of clarity and may offer different kinds of information.

  Example : if the heavy-atom substituent in the crystal is PtCl2, the Platinum will appear in both isomorphous and anomalous residual maps in all batches of this compound. But the two Chlorines will only be seen (if the resolution and the quality of the data are good enough) in the isomorphous residual map.

• In MAD, the best information is found in the anomalous map of the wavelength where f" is maximal.
• In MAD, if a specific anomalous residual map shows peaks exactly on all (or most) of the heavy atom positions, it probably indicates an error in f''. These values could be refined or better starting values supplied.

What to look for in a residual map

A good rule of thumb for determining if a peak is significant, is as follows :

• A peak above 6 sigma levels is signal
• A peak under 5 sigma levels is noise

• A positive peak far from any known site is a minor site
• One or more positive peaks close to a known site - without negative peaks in the vicinity - are light-atom ligands of the heavy-atom
• A anti-symmetrical arrangement of positive and negative peaks close to a known site is characteristic for anisotropic thermal motion of that site
• At high resolution, a lone negative peak close to a known site is 'something' (usually a water molecule) that has been pushed away by the substituent

Electron-density map

Statistics

Note : These figures are a figure of merit for the quality of the centroid structure factor and not of the phase distributions. For instance, in a SIR case, very sharp bimodal phase distributions will yield a poor average figure of merit. Thus, the statistical quality of the phasing is better appreciated when consulting the phasing power statistics at convergence.

Displaying an electron-density map

Why take the centroid ? Blow & Crick (1959) have demonstrated the power of taking centroids as Fourier coefficients to plot an electron-density map. They have applied it to the one-dimensional case, namely when the modulus |Fp| is assumed to be perfectly known. SHARP frees itself from this assumption, so we have to work in the whole complex plane of the Harker diagram, thus fully exploiting the optimality of the centroid.

At this level you can choose what you want to see in the electron density map:

• protein/DNA/RNA alone (i.e. the part of the structure which is common to all datasets without any heavy atoms). This will mean that in Se-MAD the Met side-chain has a hole in it!
  
  
• density of reference: this will contain any heavy atoms that were defined for the reference. So in Se-MAD it will have proper Se-Met side-chains.
  
  
• density with average heavy atom contribution: contains protein/DNA/RNA and an average of all heavy atoms declared in SHARP.
  
  

Solvent flattening (density modification)