Data quality and model parameterisation Martyn Winn CCP4, Daresbury Laboratory, U.K. Prague, April 2009

Model Parameters E.g. asymmetric unit contains n copies of a protein of N atoms Coordinates 3 x N x n xyz co-ordinates or... 6 x M x n if each protein modelled as M rigid bodies or... ~ 0.5 x N x n torsion angles Displacement parameters 1 x N x n B factors or... 6 x N x n anisotropic U factors or x M x n if each protein has M TLS groups

Model Parameters (2) Occupancies Usually fixed at 1.0 for protein... except for alternative conformations (usually sum to 1.0) Water/ligand occupancies Scaling parameters etc. k overall, B overall, k Babinet, B Babinet, k solvent, B solvent twin fraction Ultra-high resolution Multipolar expansion coefficients Interatomic scatterers

Reflection Data Number of independent reflections, dependent on: – spacegroup – resolution – completeness For each reflection, one has at least F/sigF. Might also have reliable experimental phases φ or F(+)/F(-) How many reflections to include? What I/σI is acceptable for refinement? Answer: Include ALL reflections no matter how weak... unless systematic errors... different answer for phasing... quoted resolution may be lower

Data / parameter ratio Refinement means minimise -log(likelihood): Nonlinear function of model parameters. Global minimum and many local minima. Need good data/parameter ratio. Strong dependence on resolution. No strong dependence on protein size. Generally not enough data.... Reduce number of parameters - constraints Add data - restraints

Restraints Expected geometry of the protein  treated as additional data bond lengths bond angles torsions / dihedral (but not φ,ψ) chirality (e.g. chiral volume) planarity non-bonded (VdW, H-bonds, etc.) B factors (between bonded atoms) U factor restraints (similarity, sphericity, rigid bond) NCS (position or conformation)

Data / parameter ratio Not really true... assumes all data independent bond lengths and angles and planar restraints in ring system bond length restraint vs. high resolution diffraction data Estimate as: no. reflections + no. restraints no. parameters Restraints may be more necessary in poorly determined parts of the structure. Restraints have associated weights: Overall w.r.t. reflection data Individual weights e.g. W B

calmodulin at 1.8 Å (1clm) 1132 protein atoms, 4 Ca atoms, 71 waters  4828 x, y, z, B factors No. of unique reflections (deposited 1993  no test set!)  data/parameter = 2.2 Bond restraints: 1144 Angle restraints: 1536 Torsion restraints: 429 Chiral restraints: 170 Planar restraints: 874 Non-bonded restraints: 1391 B factor restraints: 2680 (no NCS) total restraints = 8224  data/parameter = 3.9

calmodulin at 1.0 Å (1exr) 1467 protein atoms (inc. alt. conf.), 5 Ca atoms, 178 waters  4950 x, y, z anisotropic U factors occupancy parameters  total parameter count = No. of unique reflections No. in test set 7782 (10%) Data for refinement No. of restraints (PDB header)  data/parameter = 4.6  data/parameter = 6.1

GCPII at 1.75 Å (3d7g) 5724 protein atoms (inc. alt. conf.), 211 ligand atoms, 617 waters  x, y, z, B factors anisotropic U factors (S, Zn, Ca, Cl only) occupancy parameters  total parameter count = No. of unique reflections No. in test set 1550 (1.5%) Data for refinement No. of restraints (PDB header)  data/parameter = 3.9  data/parameter = 5.6

Thioredoxin reductase at 3.0Å (1h6v) protein atoms, 552 ligand atoms, 9 waters  x, y, z, residual B factors 6 TLS groups  120 TLS parameters No. of unique reflections No. in test set 3441 (5%) Data for refinement No. of restraints (inc NCS restraints)  data/parameter = 0.7  data/parameter = 3.0

Getting a good R-factor The old way: 1.Refine parameters so that F calc (from model) agrees with F obs for all reflections 2.Calculate: R =  |F obs | - s | F calc | /  |F obs | (Note: precise value may depend on scaling used) 3.Add parameters until R is sufficiently low What’s wrong with that ? ?

Avoiding overfitting: Rfree What's wrong?: Can add any old parameters to improve R-factor, when low data/parameter ratio May not be physically correct – "overfitting" Solution: Calculate R-factor on a set of reflections not used in refinement = "Rfree" If changes to model improve Rfree as well as R, then they are good. Note: Rfree is global number - useful for refinement strategies, not useful for assessing changes to a few atoms

Choosing your free reflections Usually a randomly chosen subset. Typically 5-10% (CCP4 default is 5%) If you have enough reflections, impose maximum number (2000 in phenix.refine ) Free set also used in maximum likelihood to estimate σ A parameters

Rfree and NCS NCS operators map different regions of reciprocal asymmetric unit onto each other. Reflections in these regions are correlated. gaps = free set working reflections free reflections

Rfree and NCS Solution: choose free set from thin shells in reciprocal space Pros: NCS operators link regions of same resolution which should be both in a shell or outside it Cons: Large number of shells  thin shells  most free reflections close to edge and correlated to non-free reflections Small number of shells  significant gaps in resolution range, poor determination of σ A SFTOOLS: RFREE 0.05 SHELL rd argument = width of shells in Å -1 Also DATAMAN.

Width shells Width shells (default) 1xmp (1.8 Å) Width shells Width shells (default) XXX (3.8 Å)

Can increase size of free set to mitigate edge effects Or use NCS-related free set islands Reflections also correlated to immediate neighbours in reciprocal space - can exclude these from working and free sets Fabiola, Korostelev & Chapman, Acta Cryst D62, 227, (2006) Rapidly run out of working reflections! Be aware that correlations can artificially reduce your Rfree Rfree and NCS

Rfree and twinning Twinning operator might relate e.g. reflection (1,2,3) to (2,1,-3) These two reflections should both be in the working set or the free set. 1.Select free set in thin shells (as NCS) 2.Select free reflections in higher lattice symmetry

Transferring free R sets Use the same free set for: additional datasets for same protein datasets from isomorphous proteins (derivatives, complexes, etc.) (how isomorphous is not clear, but play safe...) Otherwise initial R & Rfree will be similar and low for second structure - it has been refined against most of your free reflections Further refinement may lead to divergence of R & Rfree, masking the bias. Harder to detect over-fitting. Although may eventually reset Rfree. How: Use "CAD" / "Merge MTZ files (CAD)" in CCP4.

Useful resources - CCP4 Wiki - CCP4 community wiki Proceedings of Study Weekend 2004 (Acta Cryst D, Dec 2004)