Paramagnetic Constraints in Structure Determination

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Contents

Introduction

The collection of paramagnetic constraint data and the use of those data as a part of a structure determination is fairly straight forward.  RDCs can be collected using either the J-modulation or HSQC-TROSY methods described in the RDC section.  Paramagnetic relaxation enhancements (PREs) are collected based on attenuation of signal intensity in HSQC or TROSY spectra.  When Curie contributions from paramagnetic metals dominate it will be convenient to make measurements at multiple field strengths as the effects are field squared dependent and field variation provides a useful way to probe different distance ranges.  We have access to spectrometers operating from 600 to 900 MHz.  Pseudocontact shifts (PCSs) are measured by comparison of HSQC (or TROSY) cross-peak positions in diamagnetic (La3+) and paramagnetic complexes (Dy3+ or Tb3+).  Pairing of shifted and non-shifted peaks is facilitated by the fact that shifts in in both 1H and 15N dimensions are nearly equal on the ppm scale and are therefore connected by diagonal lines.  Paramagnetic relaxation interferences (PRIs) produce differential effects on the α and β cross peaks of coupled HSQC spectra and the cross-correlation effects can be measured using experiments that we have developed for the measurement of correlation times from CSA/DD interference [1].  Integration of these data into structure characterization protocols in the NESG is accomplished using programs such as XPLOR-NIH [2,3] or REDCAT [4].  CYANA can also accommodate pseudocontact shifts.  


Protocols

Generation of MTSL-cysteine pseudo-residue

Editing the Xplor/CNS topology library

Apply the following lines to protein-allhdg.top:

residue CYSM
  group
    atom N   type=NH1 charge=-0.36 end
    atom HN  type=H   charge= 0.26 end
    atom CA  type=CH1E  charge= 0.00 end
    atom HA  type=HA  charge= 0.10 end
    atom CB  type=CH2E  charge=-0.20 end
    atom HB1 type=HA  charge= 0.10 end
    atom HB2 type=HA  charge= 0.10 end
    atom SG  type=SH1E   charge=-0.05 end
!    atom HG  type=H   charge= 0.05 end
    atom C   type=C   charge= 0.48 end
    atom O   type=O   charge=-0.48 end
  ATOM CAE  TYPE= CMAE CHARGE= 0.016 END
  ATOM CAL  TYPE= CMAL CHARGE= 0.097 END
  ATOM CAF  TYPE= CMAF CHARGE= 0.016 END
  ATOM NAI  TYPE= NMAI CHARGE=-0.164 END
  ATOM OAB  TYPE= OMAB CHARGE=-0.114 END
!  ATOM HAA  TYPE= MMAA CHARGE= 0.029 END
  ATOM CAK  TYPE= CMAK CHARGE= 0.097 END
  ATOM CAC  TYPE= CMAC CHARGE= 0.016 END
  ATOM CAD  TYPE= CMAD CHARGE= 0.016 END
  ATOM CAG  TYPE= CMAG CHARGE=-0.042 END
  ATOM CAJ  TYPE= CMAJ CHARGE=-0.011 END
  ATOM CAH  TYPE= CMAH CHARGE= 0.038 END
  ATOM SAA  TYPE= SMAA CHARGE= 0.041 END

  ATOM HAG  TYPE = MMA  charge= 0.14 end !yizhou
  ATOM HAH1 type=MMA charge= 0.10 end
  ATOM HAH2 type=MMA charge= 0.10 end
   ATOM HAE1 type=MMA charge= 0.10 end
   ATOM HAE2 type=MMA charge= 0.10 end
   ATOM HAE3 type=MMA charge= 0.10 end
   ATOM HAF1 type=MMA charge= 0.10 end
   ATOM HAF2 type=MMA charge= 0.10 end
   ATOM HAF3 type=MMA charge= 0.10 end
   ATOM HAD1 type=MMA charge= 0.10 end
   ATOM HAD2 type=MMA charge= 0.10 end
   ATOM HAD3 type=MMA charge= 0.10 end
   ATOM HAC1 type=MMA charge= 0.10 end
   ATOM HAC2 type=MMA charge= 0.10 end
   ATOM HAC3 type=MMA charge= 0.10 end
  bond N  HN
  bond N  CA     bond CA HA
  bond CA CB     bond CB HB1     bond CB HB2
  bond CB SG    ! bond SG HG
  bond CA C
  bond C  O
  bond SG SAA !yizhou
  bond CAG HAG !yizhou
  bond CAH HAH1
  bond CAH HAH2
  bond CAE HAE1
  bond CAE HAE2
  bond CAE HAE3
  bond CAF HAF1
  bond CAF HAF2
  bond CAF HAF3
  bond CAC HAC1
  bond CAC HAC2
  bond CAC HAC3
  bond CAD HAD1
  bond CAD HAD2
  bond CAD HAD3

  BOND CAE  CAL
  BOND CAL  CAF
  BOND CAL  NAI
  BOND CAL  CAJ
  BOND NAI  OAB
  BOND NAI  CAK
! BOND OAB  HAA

  BOND CAK  CAC
  BOND CAK  CAD
  BOND CAK  CAG
  BOND CAG  CAJ
  BOND CAJ  CAH
  BOND CAH  SAA

  ANGLE CAE  CAL  CAF
  ANGLE CAE  CAL  NAI
  ANGLE CAE  CAL  CAJ
  ANGLE CAF  CAL  NAI
  ANGLE CAF  CAL  CAJ
  ANGLE NAI  CAL  CAJ
  ANGLE CAL  NAI  OAB
  ANGLE CAL  NAI  CAK
  ANGLE OAB  NAI  CAK
!  ANGLE NAI  OAB  HAA
  ANGLE NAI  CAK  CAC
  ANGLE NAI  CAK  CAD
  ANGLE NAI  CAK  CAG
  ANGLE CAC  CAK  CAD
  ANGLE CAC  CAK  CAG
  ANGLE CAD  CAK  CAG
  ANGLE CAK  CAG  CAJ
  ANGLE CAL  CAJ  CAG
  ANGLE CAL  CAJ  CAH
  ANGLE CAG  CAJ  CAH
  ANGLE CAJ  CAH  SAA
  ANGLE CAH  SAA  SG

                                           
angle SAA SG CB   !yizhou
 angle HAG CAG CAK !yizhou
 angle HAG CAG CAJ !yizhou


!  IMPROPER CAJ  CAL  CAG  CAH
!  IMPROPER CAL  CAE  CAF  NAI
!  IMPROPER CAK  NAI  CAD  CAC
  IMPROPER NAI  CAL  OAB  CAK

IMPROPER HAH1 HAH2 SAA CAJ
IMPROPER HAE1 HAE2 CAL HAE3
IMPROPER HAF1 HAF2 CAL HAF3
IMPROPER HAC1 HAC2 CAK HAC3
IMPROPER HAD1 HAD2 CAK HAD3

!  DIHEDRAL CAE  CAL  NAI  CAK
!  DIHEDRAL CAE  CAL  CAJ  CAH
!  DIHEDRAL CAL  NAI  OAB  HAA

!  DIHEDRAL CAG  CAK  NAI  CAL
!  DIHEDRAL NAI  CAK  CAG  CAJ
!  DIHEDRAL CAK  CAG  CAJ  CAH
  DIHEDRAL CAL  CAJ  CAH  SAA

!  DIHEDRAL SG  SAA  CAH  CAJ
!  dihedral OAB NAI CAL CAJ

  dihedral HAG CAG CAJ CAL !yizhou

  improper HA N C CB   !chirality CA
  improper HB1 HB2 CA SG  !stereo CB

  dihedral SG  CB  CA  N

end

residue C2M
  group
    atom N   type=NH1 charge=-0.36 end
    atom HN  type=H   charge= 0.26 end
    atom CA  type=CH1E  charge= 0.00 end
    atom HA  type=HA  charge= 0.10 end
    atom CB  type=CH2E  charge=-0.20 end
    atom HB1 type=HA  charge= 0.10 end
    atom HB2 type=HA  charge= 0.10 end
    atom SG  type=SH1E   charge=-0.05 end
!    atom HG  type=H   charge= 0.05 end
    atom C   type=C   charge= 0.48 end
    atom O   type=O   charge=-0.48 end
  ATOM CAE  TYPE= CMAE CHARGE= 0.016 END
  ATOM CAL  TYPE= CMAL CHARGE= 0.097 END
  ATOM CAF  TYPE= CMAF CHARGE= 0.016 END
  ATOM NAI  TYPE= NMAI CHARGE=-0.164 END
  ATOM OAB  TYPE= OMAB CHARGE=-0.114 END
!  ATOM HAA  TYPE= MMAA CHARGE= 0.029 END
  ATOM CAK  TYPE= CMAK CHARGE= 0.097 END
  ATOM CAC  TYPE= CMAC CHARGE= 0.016 END
  ATOM CAD  TYPE= CMAD CHARGE= 0.016 END
  ATOM CAG  TYPE= CMAG CHARGE=-0.042 END
  ATOM CAJ  TYPE= CMAJ CHARGE=-0.011 END
  ATOM CAH  TYPE= CMAH CHARGE= 0.038 END
  ATOM SAA  TYPE= SMAA CHARGE= 0.041 END

  ATOM CBE  TYPE= CMAE CHARGE= 0.016 END
  ATOM CBL  TYPE= CMAL CHARGE= 0.097 END
  ATOM CBF  TYPE= CMAF CHARGE= 0.016 END
  ATOM NBI  TYPE= NMAI CHARGE=-0.164 END
  ATOM OBB  TYPE= OMAB CHARGE=-0.114 END
  ATOM CBK  TYPE= CMAK CHARGE= 0.097 END
  ATOM CBC  TYPE= CMAC CHARGE= 0.016 END
  ATOM CBD  TYPE= CMAD CHARGE= 0.016 END
  ATOM CBG  TYPE= CMAG CHARGE=-0.042 END
  ATOM CBJ  TYPE= CMAJ CHARGE=-0.011 END
  ATOM CBH  TYPE= CMAH CHARGE= 0.038 END
  ATOM SBA  TYPE= SMAA CHARGE= 0.041 END
!  ATOM SBG   type=SM1E   charge=-0.05 end


  ATOM HAG  TYPE = MMA  charge= 0.14 end !yizhou
  ATOM HAH1 type=MMA charge= 0.10 end
  ATOM HAH2 type=MMA charge= 0.10 end
   ATOM HAE1 type=MMA charge= 0.10 end
   ATOM HAE2 type=MMA charge= 0.10 end
   ATOM HAE3 type=MMA charge= 0.10 end
   ATOM HAF1 type=MMA charge= 0.10 end
   ATOM HAF2 type=MMA charge= 0.10 end
   ATOM HAF3 type=MMA charge= 0.10 end
   ATOM HAD1 type=MMA charge= 0.10 end
   ATOM HAD2 type=MMA charge= 0.10 end
   ATOM HAD3 type=MMA charge= 0.10 end
   ATOM HAC1 type=MMA charge= 0.10 end
   ATOM HAC2 type=MMA charge= 0.10 end
   ATOM HAC3 type=MMA charge= 0.10 end

  ATOM HBG  TYPE = MMA  charge= 0.14 end !yizhou
  ATOM HBH1 type=MMA charge= 0.10 end
  ATOM HBH2 type=MMA charge= 0.10 end
   ATOM HBE1 type=MMA charge= 0.10 end
   ATOM HBE2 type=MMA charge= 0.10 end
   ATOM HBE3 type=MMA charge= 0.10 end
   ATOM HBF1 type=MMA charge= 0.10 end
   ATOM HBF2 type=MMA charge= 0.10 end
   ATOM HBF3 type=MMA charge= 0.10 end
   ATOM HBD1 type=MMA charge= 0.10 end
   ATOM HBD2 type=MMA charge= 0.10 end
   ATOM HBD3 type=MMA charge= 0.10 end
   ATOM HBC1 type=MMA charge= 0.10 end
   ATOM HBC2 type=MMA charge= 0.10 end
   ATOM HBC3 type=MMA charge= 0.10 end

  bond N  HN
  bond N  CA     bond CA HA
  bond CA CB     bond CB HB1     bond CB HB2
  bond CB SG    ! bond SG HG
  bond CA C
  bond C  O
  bond SG SAA !yizhou
  bond CAG HAG !yizhou
  bond CAH HAH1
  bond CAH HAH2
  bond CAE HAE1
  bond CAE HAE2
  bond CAE HAE3
  bond CAF HAF1
  bond CAF HAF2
  bond CAF HAF3
  bond CAC HAC1
  bond CAC HAC2
  bond CAC HAC3
  bond CAD HAD1
  bond CAD HAD2
  bond CAD HAD3

  BOND CAE  CAL
  BOND CAL  CAF
  BOND CAL  NAI
  BOND CAL  CAJ
  BOND NAI  OAB
  BOND NAI  CAK
! BOND OAB  HAA

  BOND CAK  CAC
  BOND CAK  CAD
  BOND CAK  CAG
  BOND CAG  CAJ
  BOND CAJ  CAH
  BOND CAH  SAA

!  bond CB SG    ! bond SG HG
!  bond SG SBA !yizhou
        bond SG SBA
  bond CBG HBG !yizhou
  bond CBH HBH1
  bond CBH HBH2
  bond CBE HBE1
  bond CBE HBE2
  bond CBE HBE3
  bond CBF HBF1
  bond CBF HBF2
  bond CBF HBF3
  bond CBC HBC1
  bond CBC HBC2
  bond CBC HBC3
  bond CBD HBD1
  bond CBD HBD2
  bond CBD HBD3

  BOND CBE  CBL
  BOND CBL  CBF
  BOND CBL  NBI
  BOND CBL  CBJ
  BOND NBI  OBB
  BOND NBI  CBK
! BOND OBB  HBA

  BOND CBK  CBC
  BOND CBK  CBD
  BOND CBK  CBG
  BOND CBG  CBJ
  BOND CBJ  CBH
  BOND CBH  SBA


  ANGLE CAE  CAL  CAF
  ANGLE CAE  CAL  NAI
  ANGLE CAE  CAL  CAJ
  ANGLE CAF  CAL  NAI
  ANGLE CAF  CAL  CAJ
  ANGLE NAI  CAL  CAJ
  ANGLE CAL  NAI  OAB
  ANGLE CAL  NAI  CAK
  ANGLE OAB  NAI  CAK
!  ANGLE NAI  OAB  HAA
  ANGLE NAI  CAK  CAC
  ANGLE NAI  CAK  CAD
  ANGLE NAI  CAK  CAG
  ANGLE CAC  CAK  CAD
  ANGLE CAC  CAK  CAG
  ANGLE CAD  CAK  CAG
  ANGLE CAK  CAG  CAJ
  ANGLE CAL  CAJ  CAG
  ANGLE CAL  CAJ  CAH
  ANGLE CAG  CAJ  CAH
  ANGLE CAJ  CAH  SAA
  ANGLE CAH  SAA  SG

 angle SAA SG CB   !yizhou
 angle HAG CAG CAK !yizhou
 angle HAG CAG CAJ !yizhou

  ANGLE CBE  CBL  CBF
  ANGLE CBE  CBL  NBI
  ANGLE CBE  CBL  CBJ
  ANGLE CBF  CBL  NBI
  ANGLE CBF  CBL  CBJ
  ANGLE NBI  CBL  CBJ
  ANGLE CBL  NBI  OBB
  ANGLE CBL  NBI  CBK
  ANGLE OBB  NBI  CBK
!  ANGLE NBI  OBB  HBA
  ANGLE NBI  CBK  CBC
  ANGLE NBI  CBK  CBD
  ANGLE NBI  CBK  CBG
  ANGLE CBC  CBK  CBD
  ANGLE CBC  CBK  CBG
  ANGLE CBD  CBK  CBG
  ANGLE CBK  CBG  CBJ
  ANGLE CBL  CBJ  CBG
  ANGLE CBL  CBJ  CBH
  ANGLE CBG  CBJ  CBH
  ANGLE CBJ  CBH  SBA
  ANGLE CBH  SBA  SG

 angle SBA SG CB   !yizhou
 angle HBG CBG CBK !yizhou
 angle HBG CBG CBJ !yizhou

!  IMPROPER CAJ  CAL  CAG  CAH
!  IMPROPER CAL  CAE  CAF  NAI
!  IMPROPER CAK  NAI  CAD  CAC


IMPROPER NAI  CAL  OAB  CAK
IMPROPER NBI  CBL  OBB  CBK


IMPROPER HAH1 HAH2 SAA CAJ
IMPROPER HAE1 HAE2 CAL HAE3
IMPROPER HAF1 HAF2 CAL HAF3
IMPROPER HAC1 HAC2 CAK HAC3
IMPROPER HAD1 HAD2 CAK HAD3

IMPROPER HBH1 HBH2 SBA CBJ
IMPROPER HBE1 HBE2 CBL HBE3
IMPROPER HBF1 HBF2 CBL HBF3
IMPROPER HBC1 HBC2 CBK HBC3
IMPROPER HBD1 HBD2 CBK HBD3


!  DIHEDRAL CAE  CAL  NAI  CAK
!  DIHEDRAL CAE  CAL  CAJ  CAH
!  DIHEDRAL CAL  NAI  OAB  HAA

!  DIHEDRAL CAG  CAK  NAI  CAL
!  DIHEDRAL NAI  CAK  CAG  CAJ
!  DIHEDRAL CAK  CAG  CAJ  CAH
  DIHEDRAL CAL  CAJ  CAH  SAA

!  DIHEDRAL SG  SAA  CAH  CAJ
!  dihedral OAB NAI CAL CAJ

  dihedral HAG CAG CAJ CAL !yizhou
   dihedral HBG CBG CBJ CBL !yizhou

  improper HA N C CB   !chirality CA
  improper HB1 HB2 CA SG  !stereo CB

  dihedral SG  CB  CA  N

end


residue C3M
  group
    atom N   type=NH1 charge=-0.36 end
    atom HN  type=H   charge= 0.26 end
    atom CA  type=CH1E  charge= 0.00 end
    atom HA  type=HA  charge= 0.10 end
    atom CB  type=CH2E  charge=-0.20 end
    atom HB1 type=HA  charge= 0.10 end
    atom HB2 type=HA  charge= 0.10 end
    atom SG  type=SH1E   charge=-0.05 end
!    atom HG  type=H   charge= 0.05 end
    atom C   type=C   charge= 0.48 end
    atom O   type=O   charge=-0.48 end
  ATOM CAE  TYPE= CMAE CHARGE= 0.016 END
  ATOM CAL  TYPE= CMAL CHARGE= 0.097 END
  ATOM CAF  TYPE= CMAF CHARGE= 0.016 END
  ATOM NAI  TYPE= NMAI CHARGE=-0.164 END
  ATOM OAB  TYPE= OMAB CHARGE=-0.114 END
!  ATOM HAA  TYPE= MMAA CHARGE= 0.029 END
  ATOM CAK  TYPE= CMAK CHARGE= 0.097 END
  ATOM CAC  TYPE= CMAC CHARGE= 0.016 END
  ATOM CAD  TYPE= CMAD CHARGE= 0.016 END
  ATOM CAG  TYPE= CMAG CHARGE=-0.042 END
  ATOM CAJ  TYPE= CMAJ CHARGE=-0.011 END
  ATOM CAH  TYPE= CMAH CHARGE= 0.038 END
  ATOM SAA  TYPE= SMAA CHARGE= 0.041 END

  ATOM CBE  TYPE= CMAE CHARGE= 0.016 END
  ATOM CBL  TYPE= CMAL CHARGE= 0.097 END
  ATOM CBF  TYPE= CMAF CHARGE= 0.016 END
  ATOM NBI  TYPE= NMAI CHARGE=-0.164 END
  ATOM OBB  TYPE= OMAB CHARGE=-0.114 END
  ATOM CBK  TYPE= CMAK CHARGE= 0.097 END
  ATOM CBC  TYPE= CMAC CHARGE= 0.016 END
  ATOM CBD  TYPE= CMAD CHARGE= 0.016 END
  ATOM CBG  TYPE= CMAG CHARGE=-0.042 END
  ATOM CBJ  TYPE= CMAJ CHARGE=-0.011 END
  ATOM CBH  TYPE= CMAH CHARGE= 0.038 END
  ATOM SBA  TYPE= SMAA CHARGE= 0.041 END
!  ATOM SBG   type=SM1E   charge=-0.05 end

  ATOM CCE  TYPE= CMAE CHARGE= 0.016 END
  ATOM CCL  TYPE= CMAL CHARGE= 0.097 END
  ATOM CCF  TYPE= CMAF CHARGE= 0.016 END
  ATOM NCI  TYPE= NMAI CHARGE=-0.164 END
  ATOM OCB  TYPE= OMAB CHARGE=-0.114 END
  ATOM CCK  TYPE= CMAK CHARGE= 0.097 END
  ATOM CCC  TYPE= CMAC CHARGE= 0.016 END
  ATOM CCD  TYPE= CMAD CHARGE= 0.016 END
  ATOM CCG  TYPE= CMAG CHARGE=-0.042 END
  ATOM CCJ  TYPE= CMAJ CHARGE=-0.011 END
  ATOM CCH  TYPE= CMAH CHARGE= 0.038 END
  ATOM SCA  TYPE= SMAA CHARGE= 0.041 END
!  ATOM SCG   type=SM1E   charge=-0.05 end

  ATOM HAG  TYPE = MMA  charge= 0.14 end !yizhou
  ATOM HAH1 type=MMA charge= 0.10 end
  ATOM HAH2 type=MMA charge= 0.10 end
   ATOM HAE1 type=MMA charge= 0.10 end
   ATOM HAE2 type=MMA charge= 0.10 end
   ATOM HAE3 type=MMA charge= 0.10 end
   ATOM HAF1 type=MMA charge= 0.10 end
   ATOM HAF2 type=MMA charge= 0.10 end
   ATOM HAF3 type=MMA charge= 0.10 end
   ATOM HAD1 type=MMA charge= 0.10 end
   ATOM HAD2 type=MMA charge= 0.10 end
   ATOM HAD3 type=MMA charge= 0.10 end
   ATOM HAC1 type=MMA charge= 0.10 end
   ATOM HAC2 type=MMA charge= 0.10 end
   ATOM HAC3 type=MMA charge= 0.10 end

  ATOM HBG  TYPE = MMA  charge= 0.14 end !yizhou
  ATOM HBH1 type=MMA charge= 0.10 end
  ATOM HBH2 type=MMA charge= 0.10 end
   ATOM HBE1 type=MMA charge= 0.10 end
   ATOM HBE2 type=MMA charge= 0.10 end
   ATOM HBE3 type=MMA charge= 0.10 end
   ATOM HBF1 type=MMA charge= 0.10 end
   ATOM HBF2 type=MMA charge= 0.10 end
   ATOM HBF3 type=MMA charge= 0.10 end
   ATOM HBD1 type=MMA charge= 0.10 end
   ATOM HBD2 type=MMA charge= 0.10 end
   ATOM HBD3 type=MMA charge= 0.10 end
   ATOM HBC1 type=MMA charge= 0.10 end
   ATOM HBC2 type=MMA charge= 0.10 end
   ATOM HBC3 type=MMA charge= 0.10 end

  ATOM HCG  TYPE = MMA  charge= 0.14 end !yizhou
  ATOM HCH1 type=MMA charge= 0.10 end
  ATOM HCH2 type=MMA charge= 0.10 end
   ATOM HCE1 type=MMA charge= 0.10 end
   ATOM HCE2 type=MMA charge= 0.10 end
   ATOM HCE3 type=MMA charge= 0.10 end
   ATOM HCF1 type=MMA charge= 0.10 end
   ATOM HCF2 type=MMA charge= 0.10 end
   ATOM HCF3 type=MMA charge= 0.10 end
   ATOM HCD1 type=MMA charge= 0.10 end
   ATOM HCD2 type=MMA charge= 0.10 end
   ATOM HCD3 type=MMA charge= 0.10 end
   ATOM HCC1 type=MMA charge= 0.10 end
   ATOM HCC2 type=MMA charge= 0.10 end
   ATOM HCC3 type=MMA charge= 0.10 end


  bond N  HN
  bond N  CA     bond CA HA
  bond CA CB     bond CB HB1     bond CB HB2
  bond CB SG    ! bond SG HG
  bond CA C
  bond C  O
  bond SG SAA !yizhou
  bond CAG HAG !yizhou
  bond CAH HAH1
  bond CAH HAH2
  bond CAE HAE1
  bond CAE HAE2
  bond CAE HAE3
  bond CAF HAF1
  bond CAF HAF2
  bond CAF HAF3
  bond CAC HAC1
  bond CAC HAC2
  bond CAC HAC3
  bond CAD HAD1
  bond CAD HAD2
  bond CAD HAD3

  BOND CAE  CAL
  BOND CAL  CAF
  BOND CAL  NAI
  BOND CAL  CAJ
  BOND NAI  OAB
  BOND NAI  CAK
! BOND OAB  HAA

  BOND CAK  CAC
  BOND CAK  CAD
  BOND CAK  CAG
  BOND CAG  CAJ
  BOND CAJ  CAH
  BOND CAH  SAA

!  bond CB SG    ! bond SG HG
!  bond SG SBA !yizhou
  bond SG SBA
  bond CBG HBG !yizhou
  bond CBH HBH1
  bond CBH HBH2
  bond CBE HBE1
  bond CBE HBE2
  bond CBE HBE3
  bond CBF HBF1
  bond CBF HBF2
  bond CBF HBF3
  bond CBC HBC1
  bond CBC HBC2
  bond CBC HBC3
  bond CBD HBD1
  bond CBD HBD2
  bond CBD HBD3

  BOND CBE  CBL
  BOND CBL  CBF
  BOND CBL  NBI
  BOND CBL  CBJ
  BOND NBI  OBB
  BOND NBI  CBK
! BOND OBB  HBA

  BOND CBK  CBC
  BOND CBK  CBD
  BOND CBK  CBG
  BOND CBG  CBJ
  BOND CBJ  CBH
  BOND CBH  SBA

  bond SG SCA
  bond CCG HCG !yizhou
  bond CCH HCH1
  bond CCH HCH2
  bond CCE HCE1
  bond CCE HCE2
  bond CCE HCE3
  bond CCF HCF1
  bond CCF HCF2
  bond CCF HCF3
  bond CCC HCC1
  bond CCC HCC2
  bond CCC HCC3
  bond CCD HCD1
  bond CCD HCD2
  bond CCD HCD3

  BOND CCE  CCL
  BOND CCL  CCF
  BOND CCL  NCI
  BOND CCL  CCJ
  BOND NCI  OCB
  BOND NCI  CCK
! BOND OCB  HCA

  BOND CCK  CCC
  BOND CCK  CCD
  BOND CCK  CCG
  BOND CCG  CCJ
  BOND CCJ  CCH
  BOND CCH  SCA

  ANGLE CAE  CAL  CAF
  ANGLE CAE  CAL  NAI
  ANGLE CAE  CAL  CAJ
  ANGLE CAF  CAL  NAI
  ANGLE CAF  CAL  CAJ
  ANGLE NAI  CAL  CAJ
  ANGLE CAL  NAI  OAB
  ANGLE CAL  NAI  CAK
  ANGLE OAB  NAI  CAK
!  ANGLE NAI  OAB  HAA
  ANGLE NAI  CAK  CAC
  ANGLE NAI  CAK  CAD
  ANGLE NAI  CAK  CAG
  ANGLE CAC  CAK  CAD
  ANGLE CAC  CAK  CAG
  ANGLE CAD  CAK  CAG
  ANGLE CAK  CAG  CAJ
  ANGLE CAL  CAJ  CAG
  ANGLE CAL  CAJ  CAH
  ANGLE CAG  CAJ  CAH
  ANGLE CAJ  CAH  SAA
  ANGLE CAH  SAA  SG

 angle SAA SG CB   !yizhou
 angle HAG CAG CAK !yizhou
 angle HAG CAG CAJ !yizhou


  BOND CCK  CCC
  BOND CCK  CCD
  BOND CCK  CCG
  BOND CCG  CCJ
  BOND CCJ  CCH
  BOND CCH  SCA

  ANGLE CAE  CAL  CAF
  ANGLE CAE  CAL  NAI
  ANGLE CAE  CAL  CAJ
  ANGLE CAF  CAL  NAI
  ANGLE CAF  CAL  CAJ
  ANGLE NAI  CAL  CAJ
  ANGLE CAL  NAI  OAB
  ANGLE CAL  NAI  CAK
  ANGLE OAB  NAI  CAK
!  ANGLE NAI  OAB  HAA
  ANGLE NAI  CAK  CAC
  ANGLE NAI  CAK  CAD
  ANGLE NAI  CAK  CAG
  ANGLE CAC  CAK  CAD
  ANGLE CAC  CAK  CAG
  ANGLE CAD  CAK  CAG
  ANGLE CAK  CAG  CAJ
  ANGLE CAL  CAJ  CAG
  ANGLE CAL  CAJ  CAH
  ANGLE CAG  CAJ  CAH
  ANGLE CAJ  CAH  SAA
  ANGLE CAH  SAA  SG

 angle SAA SG CB   !yizhou
 angle HAG CAG CAK !yizhou
 angle HAG CAG CAJ !yizhou


angle SAA SG SBA
angle SAA SG SCA
angle SBA SG SCA

!  IMPROPER CAJ  CAL  CAG  CAH
!  IMPROPER CAL  CAE  CAF  NAI
!  IMPROPER CAK  NAI  CAD  CAC


IMPROPER NAI  CAL  OAB  CAK
IMPROPER NBI  CBL  OBB  CBK
IMPROPER NCI  CCL  OCB  CCK

IMPROPER HAH1 HAH2 SAA CAJ
IMPROPER HAE1 HAE2 CAL HAE3
IMPROPER HAF1 HAF2 CAL HAF3
IMPROPER HAC1 HAC2 CAK HAC3
IMPROPER HAD1 HAD2 CAK HAD3

IMPROPER HBH1 HBH2 SBA CBJ
IMPROPER HBE1 HBE2 CBL HBE3
IMPROPER HBF1 HBF2 CBL HBF3
IMPROPER HBC1 HBC2 CBK HBC3
IMPROPER HBD1 HBD2 CBK HBD3

IMPROPER HCH1 HCH2 SCA CCJ
IMPROPER HCE1 HCE2 CCL HCE3
IMPROPER HCF1 HCF2 CCL HCF3
IMPROPER HCC1 HCC2 CCK HCC3
IMPROPER HCD1 HCD2 CCK HCD3

!  DIHEDRAL CAE  CAL  NAI  CAK
!  DIHEDRAL CAE  CAL  CAJ  CAH
!  DIHEDRAL CAL  NAI  OAB  HAA

!  DIHEDRAL CAG  CAK  NAI  CAL
!  DIHEDRAL NAI  CAK  CAG  CAJ
!  DIHEDRAL CAK  CAG  CAJ  CAH
  DIHEDRAL CAL  CAJ  CAH  SAA

!  DIHEDRAL SG  SAA  CAH  CAJ
!  dihedral OAB NAI CAL CAJ

  dihedral HAG CAG CAJ CAL !yizhou
   dihedral HBG CBG CBJ CBL !yizhou
 dihedral HCG CCG CCJ CCL !yizhou
  improper HA N C CB   !chirality CA
  improper HB1 HB2 CA SG  !stereo CB

  dihedral SG  CB  CA  N

end

Apply the following lines to protein-allhdg.param

! param for MTSL
evaluate ($pd_x = 1.0)

eval ($pd_v=$pd_x* 16000.0) BOND  CMAE  CMAL $pd_v  {sd=     0.001}   1.530
eval ($pd_v=$pd_x* 16000.0) BOND  CMAL  CMAF $pd_v  {sd=     0.001}   1.530
eval ($pd_v=$pd_x* 18000.0) BOND  CMAL  NMAI $pd_v  {sd=     0.001} 1.468
eval ($pd_v=$pd_x* 16000.0) BOND  CMAL  CMAJ $pd_v  {sd=     0.001}  1.516
eval ($pd_v=$pd_x* 12000.0) BOND  NMAI  OMAB $pd_v  {sd=     0.001}  1.318
eval ($pd_v=$pd_x* 18000.0) BOND  NMAI  CMAK $pd_v  {sd=     0.001}  1.463
eval ($pd_v=$pd_x* 15000.0) BOND  OMAB  MMAA $pd_v  {sd=     0.001}  1.000
eval ($pd_v=$pd_x* 16000.0) BOND  CMAK  CMAC $pd_v  {sd=     0.001}  1.530
eval ($pd_v=$pd_x* 16000.0) BOND  CMAK  CMAD $pd_v  {sd=     0.001}  1.530
eval ($pd_v=$pd_x* 16000.0) BOND  CMAK  CMAG $pd_v  {sd=     0.001}  1.506
eval ($pd_v=$pd_x* 16000.0) BOND  CMAG  CMAJ $pd_v  {sd=     0.001}  1.338
eval ($pd_v=$pd_x* 16000.0) BOND  CMAJ  CMAH $pd_v  {sd=     0.001}  1.530
eval ($pd_v=$pd_x* 18000.0) BOND  CMAH  SMAA $pd_v  {sd=     0.001}  1.830
eval ($pd_v=$pd_x* 15000.0) BOND  SMAA  SH1E $pd_v  {sd=     0.001}  2.030
eval ($pd_v=$pd_x* 15000.0) BOND  CMAG  MMA $pd_v  {sd=     0.001}  1.000
 BOND  CMAH MMA      1000.000 {sd=     0.001}      1.080
 BOND  CMAC MMA      1000.000 {sd=     0.001}      1.080
 BOND  CMAD MMA      1000.000 {sd=     0.001}      1.080
 BOND  CMAE MMA      1000.000 {sd=     0.001}      1.080
 BOND  CMAF MMA      1000.000 {sd=     0.001}      1.080
 
! BOND  CH2E SH1E    1000.000 {sd=     0.001}      1.808


eval ($pd_v=$pd_x*   880.0) ANGLE  CMAE  CMAL  CMAF $pd_v  {sd=     0.031} 109.130
eval ($pd_v=$pd_x*   880.0) ANGLE  CMAE  CMAL  NMAI $pd_v {sd=     0.031} 108.044
eval ($pd_v=$pd_x*   760.0) ANGLE  CMAE  CMAL  CMAJ $pd_v {sd=     0.031} 111.354
eval ($pd_v=$pd_x*   880.0) ANGLE  CMAF  CMAL  NMAI $pd_v {sd=     0.031} 113.418
eval ($pd_v=$pd_x*   760.0) ANGLE  CMAF  CMAL  CMAJ $pd_v {sd=     0.031} 109.251
eval ($pd_v=$pd_x*   880.0) ANGLE  NMAI  CMAL  CMAJ $pd_v {sd=     0.031} 105.635
eval ($pd_v=$pd_x*   720.0) ANGLE  CMAL  NMAI  OMAB $pd_v {sd=     0.031} 115.650
eval ($pd_v=$pd_x*   880.0) ANGLE  CMAL  NMAI  CMAK $pd_v {sd=     0.031} 104.000
eval ($pd_v=$pd_x*   720.0) ANGLE  OMAB  NMAI  CMAK $pd_v {sd=     0.031} 106.714
eval ($pd_v=$pd_x*   760.0) ANGLE  NMAI  OMAB  MMAA $pd_v {sd=     0.031} 109.500
eval ($pd_v=$pd_x*   880.0) ANGLE  NMAI  CMAK  CMAC $pd_v {sd=     0.031} 113.839
eval ($pd_v=$pd_x*   880.0) ANGLE  NMAI  CMAK  CMAD $pd_v {sd=     0.031} 109.317
eval ($pd_v=$pd_x*   880.0) ANGLE  NMAI  CMAK  CMAG $pd_v {sd=     0.031} 105.283
eval ($pd_v=$pd_x*   880.0) ANGLE  CMAC  CMAK  CMAD $pd_v {sd=     0.031} 109.700
eval ($pd_v=$pd_x*   760.0) ANGLE  CMAC  CMAK  CMAG $pd_v {sd=     0.031} 108.346
eval ($pd_v=$pd_x*   760.0) ANGLE  CMAD  CMAK  CMAG $pd_v {sd=     0.031} 110.253
eval ($pd_v=$pd_x*   800.0) ANGLE  CMAK  CMAG  CMAJ $pd_v {sd=     0.031} 110.468
eval ($pd_v=$pd_x*   800.0) ANGLE  CMAL  CMAJ  CMAG $pd_v {sd=     0.031} 108.765
eval ($pd_v=$pd_x*   800.0) ANGLE  CMAL  CMAJ  CMAH $pd_v {sd=     0.031} 120.000
eval ($pd_v=$pd_x*   800.0) ANGLE  CMAG  CMAJ  CMAH $pd_v {sd=     0.031} 126.000
eval ($pd_v=$pd_x*   880.0) ANGLE  CMAJ  CMAH  SMAA $pd_v {sd=     0.031} 111.000
eval ($pd_v=$pd_x*   760.0) ANGLE  CMAH  SMAA  SH1E $pd_v {sd=     0.031} 103.8
eval ($pd_v=$pd_x*   760.0) ANGLE  SMAA  SH1E  CH2E $pd_v {sd=     0.031} 103.8 !yizhou
eval ($pd_v=$pd_x*   800.0) ANGLE  MMA  CMAG  CMAK $pd_v {sd=     0.031} 126.8575 !yizhou
eval ($pd_v=$pd_x*   800.0) ANGLE  MMA  CMAG  CMAJ $pd_v {sd=     0.031} 122.675 !yizhou
! ANGLE  SM1E  CH2E  SM1E 0.0 {sd=     0.031} 0.000
ANGLE  SMAA  SH1E  SMAA 0.0 {sd=     0.031} 110.000

 ANGLe  MMA   CMAH MMA       500.00 {sd=     0.031}    109.4074
 ANGLe  MMA   CMAC MMA       500.00 {sd=     0.031}    109.4703
 ANGLe  MMA   CMAD MMA       500.00 {sd=     0.031}    109.4703
 ANGLe  MMA   CMAE MMA       500.00 {sd=     0.031}    109.4703
 ANGLe  MMA   CMAF MMA       500.00 {sd=     0.031}    109.4703
 ANGLe  CMAJ CMAH MMA       500.00 {sd=     0.031}    108.7236
 ANGLe  MMA   CMAH SMAA        500.00 {sd=     0.031}    107.9228
 ANGLe  CMAL CMAE MMA       500.00 {sd=     0.031}    109.4726
 ANGLe  CMAL CMAF MMA       500.00 {sd=     0.031}    109.4726
 ANGLe  CMAK CMAC MMA       500.00 {sd=     0.031}    109.4726
 ANGLe  CMAK CMAD MMA       500.00 {sd=     0.031}    109.4726
! ANGLe  HA   CH2E SM1E     500.00 {sd=     0.031}    107.9185
! ANGLe  CH1E CH2E SM1E     500.00 {sd=     0.031}    114.3558

eval ($pd_v=$pd_x*   800.0) IMPR  CMAJ  CMAL  CMAG  CMAH $pd_v 0   0.000
eval ($pd_v=$pd_x*   400.0) IMPR  CMAL  CMAE  CMAF  NMAI $pd_v 0  35.264
eval ($pd_v=$pd_x*   400.0) IMPR  NMAI  CMAL  OMAB  CMAK $pd_v {sd=     2.0} 0  -35.264
eval ($pd_v=$pd_x*   400.0) IMPR  CMAK  NMAI  CMAC  CMAD $pd_v {sd=     0.031} 0  35.264

IMPR MMA MMA SMAA CMAJ 500.00 {sd=     0.031}    0    -70.7825
IMPR MMA MMA CMAL MMA  500.00 {sd=     0.031}    0    -66.5692
IMPR MMA MMA CMAK MMA  500.00 {sd=     0.031}    0    -66.5692
! IMPRoper  HA   HA   CH1E SM1E      500.00 {sd=     0.031}    0    -72.0234

eval ($pd_v=$pd_x*     0) DIHE  CMAE  CMAL  NMAI  CMAK $pd_v 3   0.000
eval ($pd_v=$pd_x*     0) DIHE  CMAE  CMAL  CMAJ  CMAH $pd_v 6   0.000
!eval ($pd_v=$pd_x*     0.9) DIHE  CMAL  NMAI  OMAB  MMAA $pd_v 3   0.000
eval ($pd_v=$pd_x*     8.1) DIHE  CMAG  CMAK  NMAI  CMAL $pd_v 3   0.000
eval ($pd_v=$pd_x*     0.1) DIHE  NMAI  CMAK  CMAG  CMAJ $pd_v 6   0.000
eval ($pd_v=$pd_x*    19.6) DIHE  CMAK  CMAG  CMAJ  CMAH $pd_v 2 180.000
eval ($pd_v=$pd_x*     0) DIHE  CMAL  CMAJ  CMAH  SMAA $pd_v 6   0.000
!eval ($pd_v=$pd_x*     4.9) DIHE  SM1E  SMAA  CMAH  CMAJ $pd_v 3   0.000
eval ($pd_v=$pd_x*    19.6) DIHE MMA CMAG CMAJ CMAL $pd_v 2 180.000 !yizhou

eval ($pd_v=$pd_x*    19.6) DIHE OMAB NMAI CMAL CMAJ $pd_v {sd=     0.031} 2 -146.7663 !yizhou
! DIHEdral  NH1  CH1E CH2E SM1E   0.00 {sd=     0.031}    3  0.0000

!NBONds
!  TOLERANCE=0.5 NBXMOD=5 WMIN=1.5
!  REPEL=1.0 REXPONENT=4 IREXPONENT=1 RCONST=16.0
!  CTONNB=5.5 CTOFNB=6.0 CUTNB=7.0
!END

NONBONDED  CMAE  0.10000 3.29633 0.10000 3.02906
NONBONDED  CMAL  0.10000 3.29633 0.10000 3.02906
NONBONDED  CMAF  0.10000 3.29633 0.10000 3.02906
NONBONDED  NMAI  0.10000 2.67270 0.10000 2.40543
NONBONDED  OMAB  0.10000 2.58361 0.10000 2.31634
NONBONDED  MMAA  0.10000 1.42544 0.10000 1.15817
NONBONDED  CMAK  0.10000 3.29633 0.10000 3.02906
NONBONDED  CMAC  0.10000 3.29633 0.10000 3.02906
NONBONDED  CMAD  0.10000 3.29633 0.10000 3.02906
NONBONDED  CMAG  0.10000 3.29633 0.10000 3.02906
NONBONDED  CMAJ  0.10000 3.29633 0.10000 3.02906
NONBONDED  CMAH  0.10000 3.29633 0.10000 3.02906
NONBONDED  SMAA  0.10000 3.20724 0.10000 2.93997
NONBONDED  MMA  0.10000 1.42544 0.10000 1.15817
!NONBONDED  SM1E  0.10000 3.20724 0.10000 2.93997

Invoking pseudo-residues

In the protein sequence file, use “CYSM” to represent a cysteine residue conjugated to a MTSL molecule. If MTSL chain mobility is considered for ensemble averaging, use “C2M” or “C3M”, which allows averaging for 2 or 3 MTSL conformers.

Generate psf/mtf file and an extended pdb structure from the primary sequence, and examine the pseudo-residue structure by your favorite PDB viewer.

Ensemble averaging of PRE

Basics


                          Image:PRE_Eq1.png                                                                                     (1)

Where Ne is the number of ensemble states, i.e. the number of conformers the protein has, Nm is the number of MTSL conformers used to represent chain mobility, e.g. Nm =3 if C3M is used, rij is the distance between the unpaired electron (approximated by MTSL oxygen OAB/OBB/OCB) and a proton for the i-th protein conformer and the j-th MTSL conformer.

To relate <r-6> to PRE, use Solomon-Bloembergen (SB) equation for delta R2:

                        Image:PRE_Eq2.png                                   (2)

Where,

                          Image:PRE_Eq3.png                                                                                         (3)

Range of validity: Eq(3) is a good approximation when the amplitude of internal motions, including the motion among the protein and MTSL conformers, is small or when the time-scale of these motions is significantly longer than that of the global tumbling. For motions of both large amplitude and short time-scale, a more accurate description is by the SBMF equation [5]. It should be noted that the error from Eq(3) in the latter case is in the relaxation space, i.e., in <r-6>. The propagated error in the distance space r, which is of more interest to us for structure purpose, is usually quite small.

Implementation in Xplor-nih

Dealing with averaging

Xplor-nih-python provides a nice interface for using ensemble averaged potential energy.
To create such an instance,

from ensembleSimulation import EnsembleSimulation
esim = EnsembleSimulation("ensemble",ensembleSize)

ensembleSize is an integer number which specifies the number of alternative protein conformers, i.e., Ne in Eq (1).

To add an energy term to the potential list, such as PRE, do the following
(Read the inline comments on certain commands):

potList = PotList()   !initiate the potential list for esim. This needs to be done only once

import prePot
pre1=prePot.PREPot("PRE_CT_1",open("pre_CT_1.tbl").read(),"normal")
pre2=prePot.PREPot("PRE_CT_2",open("pre_CT_2.tbl").read(),"normal")
pre3=prePot.PREPot("PRE_NT_1",open("pre_NT_1.tbl").read(),"normal")
pre4=prePot.PREPot("PRE_NT_2",open("pre_NT_2.tbl").read(),"normal")
! There are 4 pre input files. Read them into 4 pre pot terms, pre1, pre2, pre3, and pre4.
! You can combine them into one, but keeping separate is easier to manage.
allpre = (pre1,pre2,pre3,pre4)

tauc=30 ! tauc is 30ns. Tauc can be measured or estimated based on protein size.
for pre in allpre: !Define equation and parameters for PRE back-calcualtion
        pre.setEquType("sb") !Use Solomon-Bloembergen equation
        pre.setAveType("r-6") ! Averaging type for ambiguous PRE assignment
        pre.setSclType("obsig")
        pre.setRlxType("r2dd")
        pre.setGammaI(26.752196)
        pre.setSqn(0.5)
        pre.setGfac(2.0)
        pre.setTcType("fix")
        pre.setTauC(tauc)
        print " setting for ", pre.instanceName()
        potList.add(pre)    ! Add pre into potlist for ensemble averaging.
        pass

Note that so far we only specified averaging of protein conformers, but we haven’t done so for MTSL conformers. To do this, we can use ambiguous assignment in the pre input file, such as “pre_CT_1.tbl”

assign (resid 149 and name HN) (resid 117 and (name OAB or name OBB or name OCB)) 106.2 6.1

Where, resid 117 is a C3M residue. The 106.2 ± 6.1 s-1 PRE on HN of resid 149 is <r-6> averaged by the 3 MTSL conformers with electron position represented by OAB, OBB, and OCB respectively. This averaging type is specified by “pre.setAveType("r-6")” in the pre setup loop.

Remove van der waals interaction among MTSL conformers

Note that the MTSL conformers are used to simulate motions, so they must not interfere with each other. Meanwhile, multiple MTSL labels are not simultaneously on the protein, therefore they shouldn’t interfere either. However, MTSL clash with native residues on the protein should be avoided. To express this in xplor language:

command(“””  
vector identity ( store1 ) (chemical MM* or chemical CM* or chemical OM* or chemical NM* or chemical SM*)
vector identity ( store2 ) (known and not (store1 or (resname ANI)))
        constraints
           interaction (store1) (store1) weights * 1 vdw 0 end
           interaction (store2) (known and not (resname ANI)) weights * 1 angl %f impr %f
        end
“””)

Semi-Rigid-body dynamics

PRE is frequently used to dock two proteins of known structures. In this case, both proteins can be treated as rigid bodies during simulated annealing while the MTSL chains are variable. To realize this:

command("""
vector identity (store8) (name N or name HN or name CA or name HA or name C or name O)
""")
dyn.group( select('resid 17:178 and ((store8) or not (resid 176 or resid 117 or resid 83 or resid 55 or resid 59)) '))

In the example above, there are 5 C3M residues, 176, 117, 83, 55, and 59. Their side-chains are mobile. All other residues are grouped and therefore rigid.

To ensemble or not to ensemble

Some potential terms are not intended for ensemble averaging. Most of these are generic Xplor potentials, such as bond and angle energies. To signify this, use the “AvePot” command before adding them to the potential list.

potList.append( AvePot(XplorPot,"BOND") )

As a second example, NOEs may be treated as averaged between different protein conformers, or simply treated as related to each member individually, depending on how you want to treat them. For the former case,

enoe = create_NOEPot('enoe','noe.tbl')
potList.append( enoe )

For the latter case,

potList.append( AvePot(XplorPot,"NOE") )


References

1.   Liu, Y.Z., and Prestegard, J.H. (2008) Direct measurement of dipole-dipole/CSA cross-correlated relaxation by a constant-time experiment. J. Magn. Reson. 193, 23-31.

2.   Schwieters, C.D., Kuszewski, J.J., and Clore, G.M. (2006). Using Xplor-NIH for NMR molecular structure determination. Prog. NMR Spect. 48, 47-62.

3.   Banci, L., Bertini, I., Cavallaro, G., Giachetti, A., Luchinat, C., and Parigi, G. (2004) Paramagnetism-based restraints for Xplor-NIH. J. Biomol. NMR 28, 249-261.

4.   Valafar, H., and Prestegard, J.H. (2004) REDCAT: a residual dipolar coupling analysis tool. J. Magn. Reson. 167, 228-241.

5.   Iwahara, J., Schwieters, C.D., and Clore, G.M. (2004) Ensemble approach for NMR structure refinement against (1)H paramagnetic relaxation enhancement data arising from a flexible paramagnetic group attached to a macromolecule.  J Am Chem Soc. 126, 5879-96.

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