Direct Use of Phase Information in Refmac Abingdon, University of Leiden P. Skubák

SAD EXPERIMENT PHASING and DENSITY MODIFICATION REFINEMENT and MODEL BUILDING  |F||F| |F + |, |F - | |F| = ( |F + | + |F - | ) ‏ REFINEMENT WITHOUT PRIOR PHASE INFORMATION

SAD EXPERIMENT PHASING and DENSITY MODIFICATION REFINEMENT and MODEL BUILDING  , P e (  ) ‏ |F||F| |F + |, |F - | REFINEMENT WITH INDIRECT PRIOR PHASE INFORMATION P e (  ) = e A cos(  ) + B sin(  ) + C cos(2.  ) + D sin(2.  )‏ |F| = ( |F + | + |F - | ) ‏

SAD EXPERIMENT PHASING and DENSITY MODIFICATION REFINEMENT and MODEL BUILDING , heavy atom model |F + |, |F - | REFINEMENT WITH DIRECT PRIOR PHASE INFORMATION |F + |, |F - | |F| = ( |F + | + |F - | ) ‏

Rice refinement target P( |F o |,  o, |F c |,  c )‏ integration over all  o P( |F o |, |F c |,  c )‏ P( |F o | ; |F c |,  c )‏ division by P( |F c |,  c )‏  conditional probability distribution P( |F o | ; |F c |,  c )‏  maximum likelihood refinement target with no prior phase information

MLHL refinement target P( |F o |,  o, |F c |,  c )‏ weighted integration over all  o P( |F o |, |F c |,  c )‏ P( |F o | ; |F c |,  c )‏ division by P( |F c |,  c )‏  conditional probability distribution P( |F o | ; |F c |,  c )‏  maximum likelihood refinement target indirectly incorporating prior phase information

P(|F o - |, |F o + | ; |F c - |,  c -, |F c + |,  c + )‏ P(|F o - |, |F o + |, |F c - |,  c -, |F c + |,  c + )‏ SAD refinement target P(|F o - |,  o -, |F o + |,  o +, |F c - |,  c -, |F c + |,  c + )‏ integration over all  o -,  o + division by P( |F c - |,  c -, |F c + |,  c + )‏  maximum likelihood refinement target directly incorporating prior phase information  conditional probability distribution P( |F o - |, |F o + | ; |F c - |,  c -, |F c + |,  c + )‏

SAD distribution P( |F o + |, |F o - | ; A c, B c, A Hc, B Hc ) ‏ (strong prior phase information) ‏ Rice distribution P( |F o | ; A c, B c ) ‏ (no prior phase information) ‏

SAD distribution (weak prior phase information) ‏

SAD REFINEMENT TARGET USE IN REFMAC  iterated automated model building with SAD function refinement  substructure refinement and scaling  refinement of models in the final stages

 iterated automated model building with SAD function refinement  substructure refinement and scaling  refinement of models in the final stages SAD REFINEMENT TARGET USE IN REFMAC

 automated model building programs do not support SAD target (yet), workarounds needed in order to test:  the heavy atoms parameters file inputed to model building program separately by a script which also calls Refmac with the extra keywords needed for SAD refinement  this workaround used in CRANK for ARP/wARP+Refmac_sad implementation  better integration of ARP/wARP with Refmac SAD is on the way MODEL BUILDING WITH SAD REFINEMENT

Fraction of ARP/wARP built residues to total number of residues resolution lower than 2.4 Åresolution higher than 2.4 Å

 iterated automated model building with SAD function refinement  substructure refinement and scaling  refinement of models in the final stages SAD REFINEMENT TARGET USE IN REFMAC

SAD SUBSTRUCTURE REFINEMENT & SCALING IN REFMAC (VERY PRELIMINARY RESULTS) ‏  being tested on ~ 200 JSCG datasets using CRANK package with pipeline: Refmac5_sad for scaling, Solomon for DM and Refmac5_sad for model building  average phase error after refmac phasing 75.4 deg  70 runs finished, of which 22 with successful model building  similar results ( 67 runs finished of which 25 with successful model building ) achieved with the same pipeline using BP3 instead of Refmac5_sad for phasing

 iterated automated model building with SAD function refinement  substructure refinement and scaling  refinement of models in the final stages SAD REFINEMENT TARGET USE IN REFMAC

SAD REFINEMENT – CLOSE TO FINAL MODEL

SIRAS EXPERIMENT DIRECT USE OF PRIOR PHASES SIRAS X-RAY EXPERIMENT PHASING and DENSITY MODIFICATION REFINEMENT and MODEL BUILDING  substructure model |F N |, |F D + |,|F D - |  P( |F oN |,|F oD - |, |F oD + | ; |F cN |,  cN,|F cD - |,  cD -, |F cD + |,  cD + )‏

SIRAS IMPLEMENTATION REQUIREMENTS AND TODO  numerical approximations to the 3-dimensional SIRAS integral – done for the function and first derivatives evaluation  second derivatives of SIRAS function should be calculated and used in minimisation too  modelling of non-isomorphism:  more models in Refmac with restraints between them and their parts

SIRAS VERY PRELIMINARY RESULTS –number of protein residues correctly built : –results from Refmac5D - not modeling non-isomorphism (sharing protein part for native and derivative model), heavy atom refinement outside of Refmac, only first derivatives etc

Plans for the coming months  run and analyze massive JCSG tests on both Refmac SAD substructure refinement and scaling and protein model building with iterative Refmac SAD refinement  analyze the SAD target improvements for close to final models  better integration of SAD with model building programs  anisotropic ATP's refinement for SAD target  simultaneous refinement of occupancies and ATP's for all targets  more models in Refmac (input, output, refinement etc) ‏  geometry restraints between more models  SIRAS target implementation and testing for substructure refinement and scaling and protein model building  target for joint refinement of protein and ligand P( |F oP |,|F oPL |; |F cP |,  cP,|F cPL |,  cPL )‏

I. Original Refmac5 code files II. Modified Refmac5 code files III. Bridge code files – layer between Refmac5 and SAD function itself IV. SAD function code files Refmac5 code organisation fortran C/C++

SAD/SIRAS function implementation  standalone C++ template class with double or single precision  general likelihood function for 1 or 2 observed structure factors and N model structure factors (includes a.o. SAD, SIR or Rice functions for both centric and acentric cases) ‏  possibility to define arbitrary covariance matrices for different experiments/situations, with real or complex terms  calculation of functional value, 1. and 2. derivatives with regards to calculated structure factors and Luzzati D parameters  Gaussian integration over unknown observed phases  use of tabulated Sin, Cos, Exp and modified Bessel I 0, I 1 functions to increase the evaluation speed  use of LAPACK package for calculation of eigenvalues of covariance matrices

I. Original Refmac5 code files II. Modified Refmac5 code files III. Bridge code files – layer between Refmac5 and SAD function itself IV. SAD function code files Refmac5 code organisation fortran C/C++

Tasks performed by bridge layer  passing the calls and parameters between Refmac5 part and likelihood function part in both directions  place of instantiation and “life” of likelihood class  transformation of derivatives with regards to structure factors amplitudes and phases (polar coordinates) to derivates with regards to real and imaginary structure factore part (as used by Refmac5) ‏  role in read/write of substructure files  checks of reasonability and/or correctness of some input and output likelihood function parameters

I. Original Refmac5 code files II. Modified Refmac5 code files III. Bridge code files – layer between Refmac5 and SAD function itself IV. SAD function code files Refmac5 code organisation fortran C/C++

Tasks performed by modified Refmac5 files  input, output and availability in code of observed |F + |, |F - | columns (via standard CCP4 libraries to read and write mtz files) ‏  input, output and availability in code of substructure parameters (standard pdb file format and new internally used refmac5 format for both input and output) ‏  gathering and precomputation of all information required as input by SAD function  calling of SAD function passing all required input information(via bridge functions) ‏  replacement and/or modification of all original Refmac5 subroutines requiring different treatment with SAD function  harvesting of input keywords specific for SAD refinement  all original tasks performed by these files