# Presentation: 642178

## Exploring Symmetry, Outlier Detection & Twinning update

- Peter Zwart

## Overview

- Exploring metric symmetry
- iotbx.explore_metric_symmetry
- Outlier detection
- mmtbx.remove_outliers
- Twinning
- mmtbx.twin_map_utils
- Actually:
- cctbx.python $MMTBX_DIST/mmtbx/twinning/twin_map_utils.py

## Exploring metric symmetry

- Protein crystals grown under various conditions can sometimes exhibit drastic changes in symmetry and unit cell dimensions
- Sometimes, the crystal symmetries are related
- The relation is not always obvious
- Finding the relation between two unit cells can be not so straightforward
- Knowing the relations between the different crystal forms can be helpful during structure solution

## Exploring metric symmetry

- How to find relations between unit cells?
- A sub-lattice formalism allows one to generate a family of related lattices from a given lattice
- The number of unique unit cells that are N times larger than the original unit cell is quite small
- 	Rutherford*, Acta Cryst.* (2006). A**62**, 93-97
- Unit cells of approximate equal volume can be compared to each other by checking a large number of uni-modular transforms
- Ralfs work

## Exploring metric symmetry

- Sub lattice?
- Given all lattice points, ignore some of them while ensuring that the remaining lattice points form a regular lattice

## Exploring metric symmetry

- Examples
- 	Native : *P212121*
**	****61.8 97.7 148.9 90 90 90**
- 	SeMet1 : *P21 *
**	****115.5 149.0 115.6 90 115 90**
- 	SeMet2 : C2221
**	****123.6 195.4 148.9 90 90 90 **
- Poulsen, *et al*, (2001). *Acta Cryst.* **D57**, 1251-1259.

## Exploring metric symmetry

- Future
- Provide reindexing methods between related unit cells.
- Would make molecular replacement of related structures easier
- Useful for multi crystal averaging
- Obtain non-merohedral twin laws from this analyses

## Outlier detection

- Outliers can have a detrimental effect on the progress of structure solution and refinement
- Read, *Acta Cryst.* (1999). D**55**, 1759-1764
- The detection of outliers should be performed on the basis of all information available.
- Use model info if you can
- One would like to have the flexibility of correcting for mistakes made earlier
- Those reflection with E-values larger then 5 could have been valid observations!

## Outlier detection

- What is an outlier?
- A data point that does not fit a model because of an abnormal situation such as an erroneous measurement.
- How to spot them?
- If  Fobs is not reconcilable with Fcalc, Fobs might be an outlier
- Reconcilable?
- Fobs should be explainable from Fcalc and the current quality of the model (A)

## Outlier detection

- Model based outlier detection is done in a similar way to the method described by Read (*Acta Cryst.* (1999). D**55**, 1759-1764)
- Fobs and Fcalc are normalized to get Eobs & Ecalc
- A is estimated for each reflection
- Combining standard likelihood techniques with kernel methods to obtain smooth varying estimates
- Find :
- Compute :

## Outlier detection

- Q  is approximately 2 distributed
- Acceptable values of Q are determined by the size of the dataset
- If the dataset is large, large deviations are expected
- A p-value is computed for each reflection
- The p-value is the probability that if this particular Q-value was the largest in the dataset, a Q value of equal or larger value is observed by chance.
- Observations for which the p-value is smaller than 5% are considered outliers.

## Outlier detection

- Example: 1ty3
- Wilson statistics indicate 1 outlier
- 	(25,6,-43)
- 	Eobs = 3.938
- 	centric = True
- 	p-wilson = 1.83E-07
- 	p-extreme = 9.0E-03
- Model based outlier detection indicate that the (25,6,-43) is a valid observation

## Outlier Detection

- The outlier detection algorithm is embedded in a class that caches the original observed data.
- This will allow one to perform outlier detection during different macro-cycles/rebuilding states and update
- Will be incorporated in *phenix.refine* at the appropriate juncture
- Command line tool available

## Twinning progress report

- Routines available
- Least squares target functions
- Both intensity and amplitude
- Target values and first derivatives
- Detwinning
- Standard and a la Sheldrick
- R-values
- Map coefficients
- 2mFo-DFc & gradient maps
- Bulk solvent scaling
- Estimation of twin fraction, ksol Bsol, U* and overall scale on twinned data
- Using global optimizer (differential evolution) for the moment

## Twinning progress report

- Bulk solvent scaling and detwinned map generation available as a command line tool *mmtbx.twin_map_utils*
- Results similar to CNS
*mmtbx.twin_map_utils *should be seen as the first step to full integration of twin utilities in *phenix.refine*

## Twinning progress report

- mmtbx.twin_map_utils

- CNS

## Twinning progress report

- Twinning not taken into account

- 1eyx: twin fraction = 0.47; difference maps at 2.5 sigma
- Ligands and waters deleted (10% of total model)

- Twinning taken into account

## Twinning progress report

- Twinning not taken into account

- Difference in 2mFO-DFC density is less striking

- Twinning taken into account

## Twinning progress report

- Future plans
- Likelihood based map coefficients
- in collaboration with Randy Read
- Incorporation of least squares targets in *phenix.refine*
- Likelihood based targets
- in collaboration with Randy Read

## Ackowledgements

- Paul Adams
**Ralf Grosse-Kunstleve**
- Pavel Afonine
- Nigel Moriarty
- Nick Sauter
- Michael Hohn

**Cambridge**
- 	Randy Read
- 	Airlie McCoy
**Los Alamos**
- 	Tom Terwilliger
- 	Li Wei Hung
**Texas A&M Univeristy**
- 	Jim Sacchettini
- 	Tom Ioerger
- 	Eric McKee
**Duke University**
- 	Jane Richardson
- 	David Richardson
**Phenix industrial Consortium**
- 	Robert Nolte
- 	Eric Vogan

## Kernel methods

- Discrete binning of X-ray data introduces discontinuous jumps of properties that are continuously varying properties
- Mean intensity (normalisation)
- The estimation of A
- Possible remedies:
- Spline functions
- Used extensively by K. Cowtan

## Kernel methods

- Discreet binning assumes a constant value in a certain range

## Kernel methods

- With Kernel methods, the estimate at each position is based on a full dataset.
- The amount that each datum contributes is determined by a weighting function (usually depending on the squared distance)

## Kernel methods

- Kernel method available for normalisation
- Used by xtriage in intensity statistics
- Kernel method available for of A estimation
- Used in the outlier detection

## Kernel methods

- Determination of alpha from A estimated using kernel methods results in values similar as those obtained by what is available in phenix.refine
- Similar results for beta