"mopro" : a free software for electron density analysis. of small
TRANSCRIPT
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Laboratoire de Cristallographie & Résonance Magnétique
& Modélisations (CRM2)
Christian Jelsch
"MoPro" : a free software for electron density analysis.
of small compounds and biological macromolecules.
1
Christian Jelsch
CNRS Nancy Université France
ANGD Reciprocs 14 sept. 2011 Aussois
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* Charge density refinement with MoPro
* VMoPro visualisation tool of properties
* Database Transfer
2
* Application to proteins
* Electrostatic Interaction Energy
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Spherical Atom Model : approximation
Fourier Residual Map Fobs – Fcal
3
Dimethyl Stilbene
Temperature 16 KResolution 0.65 Å
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Proteins X Y Zd ≈ 2 Å Thermal B factor isotropic
RESOLUTION & X-Ray CRISTALLOGRAPHY
Molecular Structure
4
ATOMIC Thermal B anisotropic d ≈≈≈≈ 1 Å Hydrogen
SUB-ATOMIC Deformation Electron Densityd ≈≈≈≈ 0.5 Å Atomic Charges
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ρ(r) = ρc(r) + Pval κ3 ρ(κ) + Σ κ‘3 R(κ’r) Σ Plm ylm
Multipolar Atom Model
ValencePopulation
Atom coreMultipolePopulations
5
Hansen & Coppens
(1978) Acta Cryst. A34, 909
κ κ’ expansion / contraction
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3 dipoles 5 quadripolesZ
XY
7 octupoles
6xyz(x2-y2)z
x[4z 2-(x 2+y 2)]y[4z 2-(x 2+y 2)]x(x 2-3y 2) y(y 2- 3x 2)
2z3 -3z(x2+y2)
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Deformationof ElectronDensity +/- 0.05 e/A3
7
∆ρ(r) = ρmolecule - ∑ ρ atoms_spherical_neutral
= ( Nval – Pval ) κ3 ρ(κ) + Σ κ’3 R(κ’r) Σ Plm ylm
MultipolarAtomModel
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High Order Refinement
Scattering factor of a carbon atom
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HighresolutionRefine vs. Reflections at
Deconvolution of thermal motion & deformation density
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Diffraction Power & Temperature Factor
Log F 2
100 K
9
Carbonatom
Low temperature
Small molecules
T = 100
B ~ 1 Å2
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Subatomic Resolution Structure & Electron Density
~0.5Å
Atomic Resolution Structure with Hydrogen Atoms
MOPRO Crystallographic Refinement Software
10
0.7 – 1.5 Å Transfer Databank Electron Density
Guillot et al., J. Appl. Cryst. (2001) 34, 214-223Jelsch et al., J. Appl. Cryst. (2005) . 38, 38-54
Small Compounds & Macromolecules
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* MoProGUI.jar
* Import2MoPro
* MoPro : crystallographic refinement
& structure analysis
The main programs
MoProSuite : the main programs
11
& structure analysis
* VMoPro :
visualisation maps, molecular properties
* MoProViewer
molecule viewer & GUI
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Import2MoPro.exe
Formats :
pdb
Cif
res / ins
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Xyz
Molly
Mopro
XD
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MoProGUI - MoPro : Main Menus.
File declarations Graphical User Interface
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Refinement of Variables
MoProGUIMoProGUIMoProGUI
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MoPro input commands file ’’mopro.inp’’
Example of script
RESO 0.4 0.7
SELE XYZ UIJ NOH
REFI LS 1
Can be
generated
by
15
RESO 0.4 99.
SELE KP1 + KP2 NOH
REFI LS 1 DAMP 0.5
CONS DIST
WRIT DIST
by
MoProGUI
(hydrogen H-X)
Print distances
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Example of loop in « mopro.inp »
LOOP lp1 5
RESO 0.4 0.7
SELE XYZ UIJ NOH
REFI LS 1
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RESO 0.4 99.
SELE SCA PLM VAL
REFI LS 1
ADDR lp1
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Scattering Factor
core / valence / multipolar f( s2)
High order
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Carbon atom Pval = 4 e
Biso = 4 Å 2
multipolar part averaged
High order
refinement:
XUZ UIJ
non hydrogen atoms
⇒ Deconvolution
Uij & ∆ρ
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Charge Density Refinement Strategy
HIGH ORDER : RESOLUTION d < 0.7 ÅXYZ UIJ non-hydrogen
WHOLE RESOLUTIONSUCCESSIVE INTRODUCTION OF VARIABLES
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* SCALE FACTOR
* XYZ Uiso Hydrogen
* Valence populations
* Multipoles
* Kappa (spherical)
* Kappa’ (multipoles)
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* MoPro automatic charge density refinement small molecules
- Preparation of restraints & constraints
- High order refinement XYZ UIJ NOH
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- High order refinement XYZ UIJ NOH
- Iterative & progressive refinement of VAL PLM KP1 KP2
- Progressive release of constraints
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* MoPro automatic refinement
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CRYSTALLOGRAPHIC REFINEMENT
LEAST SQUARES MINIMIZATION
ΣΣΣΣH ( ΙΙΙΙH calc - ΙΙΙΙH obs )2 / σσσσΙΙΙΙ2
21
+ ΣΣΣΣr ( Rcalc - Rtarget )2 /σσσσr2
H reflections (h,k,l) IH Intensity
R restraints (stereochemistry: distances, angles,
thermal motion, charge density similarity, targets for κ & κ’ …)
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Least Squares Minimisation
1 refinement cycle : solve
A dP = V normal equations
22q
Ip
Iw
calccalc
∂∂
∂∂Σ= HH
HH A pqNormal
Matrix
pI
IIwcalc
calcH
obsH ∂
∂−Σ= HHH )( Vp
gradient
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Solve normal equations
A dP = b
matrix inversion dP = A -1 b
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conjugate gradients iterative method
dP0 → dP1 → … → dPn
► Useful for Large systems (sparse matrix)
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Normal Matrix INVERSION
)( )VAR( . 2pp ppZB σ==
dP = A -1 V
B = A -1 matrix of (variance , covariance)
24
pp
Binary correlation coefficient parameters p & q
2/1, )(
qqpp
pqqp BB
B=ρ
),( )( )( ),COV( pq qpppqpZB ρσσ==
Z = ΣH WH( Iobs - Icalc ) 2/( Nobs - Nvar )]½ goodness of fit
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RESTRAINTS
distance, angles, planarity
Thermal motion URATIO ISOTRO UIJRES UIJRAT
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SIMDIS SIMANG SIMVAL SIMPLM SIMKAP …
RSYPLM multipoles symmetryKAPVAL KP1 & Pval correlated
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RESTRAINTS
Thermal Displacement Parameters
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Rigid Bond Uijproj ~ Uij
proj'
Uiso proportional
Uij ~ k . Uij’
Limited Anisotropy
Uiso ~ k . Ueq
Uij proportional
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Stereochemical CONSTRAINTS
Angles AXYZH AXYHH AXHHH
Distances d ( Atom,Hydrogen)
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AXYH AXHH
AXH AHH
Exemple for C-CH3
CONANG AXHHH C1 C2 H11 H12 H13
Automatic preparation of constraints
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Restraints / Constraints on the charge density in software MoPro
SYMPLM – symmetry of multipoles
CONPVM – valence and multipole populations
CONPLM – multipole populations
CONVAL – valence population s
Equivalence of atoms
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OW has two mirrors
H1 & H2 equivalent
bZX
CONVAL – valence population s
CONKAP –kappas expansion/contraction
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Symmetry C ONSTRAINTS / RESTRAINTS
on the Charge Density
mx 1 mirror plane ⊥ x
mymz 2 mirrors
3m 3m axis
Symmetry on Multipoles
aromatic C
CH3, NH 3+
29
i inversion centre
….
Exemple
SYMPLM 3m ALA CB
SYMPLM mymz PHE CD1
CH3, NH 3+
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MoProGUI stereochemical analysis by MoPro
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MoProGUI write ouput files
molecular structure & hkl reflections
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* Charge density refinement with MoPro
* VMoPro visualisation tool of properties
* Database Transfer
32
* Application to proteins
* Electrostatic Interaction Energy
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VMoProSTAT : STATic (deformation) electron density
ELEC : ELECtrostatic potential map
FOUR : FOURier m*Fo-n*Fc electron density
LAPL : LAPLacian of total electron density
GRAD : GRADient NORM of electron density or electrostatic potential
CRIT : CRITical points search of density, laplacian or electrostatic potential
Properties computation & visualization
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CRIT : CRITical points search of density, laplacian or electrostatic potential
ENER : ENERgy computations
INTE : INTEgration : topology
SELE : define atoms SELEction for property calculationPARA : read new MoPro molecular parameters filePLOT : create & PLOT postscript image from 2D gridGRID : GRIDs handling ( + - x mask statistics)CONT : set Gradient / Basin / CONTour lines options
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Static total electron density
Log scale
Regularcontours
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SquareRootscale
Gradient lines
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Basin Lines in 2D
Bader Theory : Atoms In Molecules
Grad (ρ) = 0.
Total Electron Density
Fidarestat
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VMoPro Laplacian
cp critical points:
grad ρ = 0
∇2ρ = ∂2ρ/ ∂x2 + ∂2ρ/∂y2 + ∂2ρ/∂z2
red ∇2ρ < 0
electron accumulation
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grad ρ = 0
Analysis of CP
Covalent bonds
Hydrogen bonds
Ionic interactions
ρρρρ = total electron density
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Surface of Zero Laplacien ∇2ρ = 0
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VMoPro VisualisationReactivity Surface
Open surface:
sites for nucleophiles
thymidine
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VMoPro FOUR m * Fo – n * Fc
Fourier Residual map m = n = 1
Fhkl � grid rho(x,y,z)
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FFT Fast Fourier Transform
Available for 3D maps of unit cell
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Dynamic deformation
electron density
Aldose reductase &
Idd594 inhibitor.
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Idd594 inhibitor.
Fourier transform of
|Fobs|exp(iΦmult) - |Fcalc,sph|exp(iΦsph)
Difference of 2 Fourier files
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VMoPro ELECElectrostatic potential and gradient lines
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Gradient linesContour +/- 0.05 e/A
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MoProViewer : a graphical layer for MoPro( Benoît Guillot )
- Reads MoPro (and other) file formats- Easy and graphically aided 2D / 3D VMoPro maps generation- Classical functionalities of molecular viewer :
- lines, sticks, ball & sticks representations - stereochemistry computation
- Maps representations :- iso-surfaces- gradient lines - 2D slices
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- 2D slices
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Some other examples of MoProViewer capabilities :
Carboxyphenylammonium stacking with C-C interactions bond paths and their (3,-1) critical points shown as green spheres
AlaMet molecule with a plane showing a slice of the electrostatic potential in the COO plane (left), and its corresponding 2D contour map (right).
42AlaMet molecule with 50% probability thermal ellipsoids, and orthogonal atomic axis systems represented for the COO atoms AlaMet electron density isosurface of 0.01 e/Å3 colored
according to the molecular electrostatic potential values
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* Charge density refinement with MoPro
* VMoPro visualisation tool of properties
* Database Transfer
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* Application to proteins
* Electrostatic Interaction Energy
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Database of Experimental
Multipolar Parameters
Average { P ; P ; κκκκ } TRANSFER
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Charge Density
Peptide Crystals
Average { Pval ; Plm ; κκκκ }
equivalent atoms
PROTEIN
or SMALL COMPOUND
at lower Resolution
TRANSFER
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Protein or Small Compound
TRANSFER
Experimental LibraryExperimental LibraryMultipolar Atom Model Multipolar Atom Model
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at Lower Resolution
Crystal Structure More Precise- Thermal Motion, - Hydrogen Positions- lower RF & RF-free factors
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Electron Density Databases
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Volkov, Abramov & Coppens
Acta Cryst (2001). A57, 272
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relation between expansion/contraction of valence shell (κ)
& net atomic charge (q) for carbon, nitrogen & oxygen atoms ( multipole refinements of crystal B3LYP/ 6-31G** structure factors )
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Experimental LibraryExperimental Library
Multipolar Atom ModelMultipolar Atom Model
Zarychta, B., Pichon-Pesme, V., Guillot, B., Lecomte, C.
ELMAM proteins
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Zarychta, B., Pichon-Pesme, V., Guillot, B., Lecomte, C.
& Jelsch, C. (2007). Acta Cryst. A63, 108-125
ELMAM2 common chemical groupsoptimal local axes for multipoles symmetry
Domagala S, Munshi P, Ahmed M, Guillot B & Jelsch C.
Acta Cryst. (2011). B67. 1-16.
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Experimental Experimental MultipolarMultipolar Database Database
for Proteinsfor Proteins
Ca- Ha
+octapolesΚ κ’
49Atom Type N
Ca- Ha/
H- N\
C=O/
Ca
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ELMAM2 Database : Optimal local axes systems for multipoles
bZXXY 3Zb
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3ZX
3bZ
Domagala & Jelsch (2008) J. Applied Cryst. 41, 1140–1149
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L-Seryl-L-valine
Effect of Database Transfer
Moen et al., 2004,
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0.73 Å resolution
Moen et al., 2004, Acta Cryst. C60,
o564–o565
Univ.Buffalo
Same number of variables & restraints
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EFFECT of TRANSFER on B-FACTORS
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Acta Cryst(1998) D54 1306Helical octapeptde
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3
4
5
6
7
8
sph
mul
wR2(F) (%)
Small Compound & Spherical or Multipolar At om
(E)-2,2’-dimethylstilbene (Ogawa et al. 1992)
54
0
1
2
16 K 7O K 116 K 175 K 234 K
Transfer Library Multipoles & Refinement Maximal Constraints: atom equivalencies & local symmetries
=> Improved Thermal Displacement Parameters
Dynamical Analysis ( Pr Bürgi Bern )
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Peanut representation
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quercetin
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• Electron Density Transfer & Refinement of small molecules
• increasing precision of the refined Flack parameter (Dittrich, Strumpel et al., 2006)
• used as a starting point in refinement of the constrained multipolar parameters of Proteins (Jelsch et al., 2000; Guillot et al., 2008)
Main applications of the databases published so far
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parameters of Proteins (Jelsch et al., 2000; Guillot et al., 2008)
• calculation of the electrostatic interaction energy (Li et al., 2006; Dominiak et al., 2007; Dominiak et al., 2009; Fournier et al., 2009)
• modelling of ED of disordered groups & detecting disorder (Dittrich et al., 2007; Bąk et al., 2009; Dittrich, Warren et al., 2009)
• calculation of electrostatic potential of macromolecules (Muzet et al., 2003; Liebschner et al., 2009; Dittrich, Weber et al., 2009; Dittrich et al., 2010
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* Charge density refinement with MoPro
* VMoPro visualisation tool of properties
* Database Transfer
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* Database Application to Proteins
* Electrostatic Interaction Energy
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average polypeptide
Electron Density
Spherical Residual & Static Deformation
Peptide ab initio calculation Hartree-Fock self-consistent fieldtriplezeta-plus-(C,N,O-d and H-p)-polarization-function Gaussian basis set.
Protein Crambin
0.54 Å resolution
Database Transfer & Refinement
60
+/- 0.05 e-/Å3
Corr = 88% |∆ρ| = 0.18 & 0.20 e/A3
Jelsch et al., P.N.A.S. 2000, 97.
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Database
Transfer
& Refinement
Multipolar
Crambin Residual Electron Density
Spherical Atom Model
61+/- 0.02 e-/Å3 Average 34 peptides
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Spherical Atom Model
Residual electron density
Human Aldose ReductaseRésolution 0.65 Å
Collab. Podjarny et al.
IGBMC Strasbourg
Complications Diabetis
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Involved in Diabetes complications
� Normal conditions : glycolysis (hexokinase adds phosphate)
� Hyperglycemic conditions : the polyol pathway
The Human Aldose Reductase
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INHIBITIOND-glucose
SORBITOL
Retinopathy Nephropathy
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Enzyme & NADP+ & Inhibiteur
Aldose Réductase Humaine
Ligand IDD - Protéine
64Muzet et al. P.N.A.S. 2003
Complementarity
Electrostatic Potential
& Deformation Density
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Thermal ellipsoids h. Aldose Reductase
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(Blue) 2.41 < Beq < 51 Å2 (Red)
50% probability level
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Residual electron density Aldose Reductase
spherical atomstandard high order refinement refinement.
66+0.5 e/Å3-0.5 e/Å3
tyr48
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Residual electron density following transfer
A: standard spherical refinement. B: high order refinement.
AB
Lys262
67
+0.45 e/Å3-0.45 e/Å3
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HO
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Main Chain Constrained Multipolar Refinement
Protein Human Aldose Reductase
DATABANKDATABANK
TRANSFER +
∆ρρρρ contour
+/- 0.05 e/Å3
REFINEMENT
0.66 Å resolution
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TRANSFERTRANSFER +
REFINEMENTfrom ∆ρρρρ = 0
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Multipolar refinement
Main Chain Valence Electron populations
Transfer Trf + Ref Ref
Cαααα 4.12 4.06(2) 4.02(2)
Aldose Reductase
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C 3.89 3.92(2) 3.97(2)
O 6.31 6.30(2) 6.15(2)
N 5.32 5.24(2) 5.09(2)
Hαααα 0.81 0.89(3) 0.92(3)
H0 0.69 0.76(3) 0.85(3)
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Electrostatic potentials : Inhibitor binding
DFT Experimental
Active site Bromine anchor pointAldose reductase
72
0.05 e.Å-1
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Electrostatic potentials : Inhibitor binding
inhibitor : Bromine BR …. Og(THR)
Complex Active site DFT calculation
73+/-0.05 e.Å-1
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Theoretical Deformation Electron Density DFT
Br…OG1-Thr113 inhibitor aldose reductase NADP+
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Inhibitor alone
+/ - 0.05 e-/Å3
SIESTA software
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ELUCIDATION OF PHOSPHATE HPO 42-
BINDING to PfluDING PROTEIN
phosphate ion
Low barrior H-bond
75
PfluDING is a bacterial protein isolated from Pseudomonas fluorescens.
The three-dimensional structure was obtained at sub-Ångstrom resolution
(0.88Å and 0.98Å) at two different pH (4.5 and 8.5).
H atomsVisible in binding site
Low barrior H-bond
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ELUCIDATION of PHOSPHATE HPO 42-
BINDING to PfluDING PROTEIN
Contrary to previous theories on
phosphate binding proteins,
ELMAM multipolar database
electrostatic potential calculations show
that the binding cleft has a positive
76Liebschner et al., JACS, 2009
electrostatic potential
The PfluDING structures
reveal that the protein is specific for the
dibasic form of phosphate
(notably HPO42- vs. SO4
2-). Electrostatic potential
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* Charge density refinement with MoPro
* VMoPro visualisation tool of properties
* Database Transfer
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* Application to proteins
* Electrostatic Interaction Energy
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Integration Eelectrostatic = ∭∭∭∭V ρρρρ1 . Φ2 . dv
Electrostatic Interaction Energy
ρρρρ * refinement vs. Xray diffraction data
78
ρρρρelectron densityfrom :
* refinement vs. Xray diffraction data
* refinement vs. theoretical data
* experimental databank transfer
* theoretical databank transfer
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Electrostatic Interaction Energy
E total, electrostatic = ∑grid wi . ρA(ri) . VB(ri)
* High Order Numerical Grid Integration (Taylor formulas 5th order)
* Zooming on regions with large variations
VMoPro
SP : spherical integration
BU : spherical integration / Buckingham summation
(1)
(2)
(3)
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Protein: molecule B
Electrostatic potential VB (r) Charge density ρρρρA(r)
Ligand: molecule A
(3)
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Fidarestat Inhibitor / Human Aldose Reductase
Experimental deformationelectron densityresolution = 0.50 Å
Protein / LigandElectrostatic interaction energy.
fidarestat
80
ElectrostaticPotential on van der Waals surface
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Electrostatic Interaction Energy
between dimers
in the crystal packing
Paracetamol
81Closest atoms
Bouhmaida et al.
Acta Cryst B 2009
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Tutorial MoPro
1) Database transfer & structure refinement
molecule with diffraction data at usual resolution
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2) Charge density refinement
data at ultra high resolution (0.5 Å)
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Angélique Lagoutte
Sophie Alexandre
Bertrand Fournier
Dorothee Liebschner
Acknowledgements to MoPro developpers
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Dorothee Liebschner
Slawomir Domagala
Ignasi Mata
Benoît Guillot
& students programming MoProGUI
Thanks to the organizers Claude Lecomte & Fernando J. Lahoz
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