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Curie-Dipole Dipole Cross Correlation
B0
M
q
time averaged electron magnetic moment ltmgt
N
H
E2Edip2ECurie22EdipECurie
Bertini, Luchinat, Tarchi, Chem. Phys. Lett.,
1993 Bertini, Luchinat, Piccioli, Tarchi Concept
Magn. Reson., 1994
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Magnetic susceptibility
A magnetic field B0 orients the electron magnetic
moments ltmgt is the average
induced magnetic moment per particle
B
0
ltmgt0
ltmgt¹0
Field off
Field on
in lanthanides
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Magnetic susceptibility
?r rotational correlation time
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Curie-Dipole Dipole Cross Correlation
Effect of reducing J in an antiphase doublet
having equal / unequal linewidths
True and false COSY cross peaks
Bertini, Luchinat, Tarchi Chem. Phys. Lett., 1993
Bertini, Luchinat, Piccioli, Tarchi Concept
Magn. Reson., 1994
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Curie-Dipole Dipole Cross Correlation
Real part of the spectral density
(proposed by Marion et al. as structural
constraints) Boisbouvier, Gans, Blackledge,
Brutscher, Marion, J.Am.Chem.Soc., 1999
Imaginary part of the spectral density
Ghose, Prestegard, J. Magn. Reson., 1997
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Manifestation of Curie-DD Cross Correlation
Desvaux, Gochin, Mol. Phys., 1999 We now
assume that the g tensor is isotropic but a large
ZFS is present () During the calculation of
cross-correlation functions, one takes the
average of the products of the Wigner matrices.
Since they are of different ranks, all products
vanish, and thus the cross-correlation rates. ?
Lanthanides should have no CCR!
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Complete theory for CCR outside spin Hamiltonian
formalism
The angles qXAK, qYAK and qZAK specify the
directions of the principal axes X, Y and Z of
the shift tensor of nucleus A with respect to the
AK axis. The principal axes for the shift tensor
are obtained by first calculating the tensor in
the principal frame of the susceptibility tensor
and then diagonalising the symmetric part
Bertini, Kowalewski, Luchinat, Parigi J. Magn.
Reson. 2001, in press
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Isotropic versus Anisotropic Curie-DD Cross
Correlation
Following Vega and Fiat, the dipolar shift
Hamiltonian is H gA IA?s?B0
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Isotropic versus Anisotropic Curie-DD Cross
Correlation
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Isotropic versus Anisotropic Curie-DD Cross
Correlation
A
B
C
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Curie-DD CCR measured on lanthanide-substituted
calbindin
Bleaney, 1972
cisoBleaney cisofit Ce 4.6 4.4 10-32
m3 Yb 14.4 16.6 10-32 m3
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Calbindin
Obs vs calc
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• CCR
• depend on r-3
• depend on the angles between the NH vectors and
  the direction metal ion - protons.
• depend mainly on the size of the magnetic
  susceptibility, rather than on its anisotropy

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Structure of Ce substituted Calbindin D9k
Ca2
Ce3
site II
site I
C-terminal
N-terminal
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Ca2 binding proteins

• Substitution of Ca2 with Ln3
• Full assignment with standard techniques
• Direct detection 13C experiments

Identification of ligands to obtain new
structural constraints
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1H, 15N e 13C full assignment using 2D and 3D
techniques 13C direct detection
1D-Weft-like 13C and 13C13C COSY spectra
Bertini, Lee, Luchinat, Piccioli, Poggi,
ChemBioChem 2001
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Observed Hyperfine Shift
Pseudocontact shift The program FANTASIAN1 can
predict pseudocontact shifts
Contact shifts Values of about 10 ppm for
backbone 13CO coordinating Ce are expected
Identification of backbone CO coordinating the
metal
1L. Banci, I. Bertini, K.L. Bren, M.A. Cremonini,
H.B. Gray, C. Luchinat, P. Turano, JBIC 1996
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Calbindin structure refinement with paramagnetic
constraints
Diamagnetic constraints

• 1793 NOEs
• 57 phi values
• 46 psi values
• 30 Hbonds
• 13 1D-NOE (RMSD0.69Å)

• Paramagnetic constraints
• 1164 pcs from 11 lanthanides
• 26 T1 values
• 64 rdc from Ce (RMSD0.26 Å)

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Structure of Ce3 substituted Calbindin D9k
With paramagnetic constraints
With diamgnetic constraints only
RMSD 0.26 Å
RMSD 0.69 Å
Bertini, Donaire, Jiménez, Luchinat, Parigi,
Piccioli, Poggi, in press
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Structure of Ce3 substituted Calbindin D9k
Bertini, Donaire, Jiménez, Luchinat, Parigi,
Piccioli, Poggi, in press
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Towards structure without NOEs
Bertini, Donaire, Jiménez, Luchinat, Parigi,
Piccioli, Poggi, J. Biomol. NMR, in press
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Turning disadvantages into advantages
Contact shifts may provide dihedral angle
constraints Pseudocontact shifts provide the
coordinates of the metal ion and new structural
constraints Nuclear relaxation provides
metal-nucleus distances Cross-correlation
provides distances and angles Self-Orientation
provides relative orientations of inernuclear
vectors
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Dihedral angle dependence of hyperfine shifts of
H? nuclei of iron-coordinated cysteines
a 10.3 b -2.2 c 3.9
Fe2.5
Bertini, Capozzi, Luchinat, Piccioli, Vila, JACS
1994
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Nuclear relaxation due to the electron-nucleus
dipolar coupling Solomons equations
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Constraint surfaces
A
B

M
A
C
B
C
D
NOE
T1
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Residual Dipolar Coupling
Pseudocontact shift
Residual Dipolar Coupling
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PCS RDC CCR
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positive
Pseudocontact shifts
negative

Axial Totally Rhombic
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Pseudocontact shifts
 
A

A
M1, M2, M3
M
C
B
3 atoms, the same metal ion
Three metal ions, the same atom
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RDC
3 NH, the same metal ion
Two metal ions, the same NH
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Tensor 1
Tensor 2
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Quick structure
Hyperfine based structural constraints
- Pseudocontact shifts
- Residual dipolar couplings
- Cross correlation
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Quick structure (program LOOPS)
Structure of Calbindin D9k
M
site II
site I
M
CSI
X 4
N
C
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Quick structure (program LOOPS)
Structure of cytochrome b562
M
CSI
X 4
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First step
?
? n





jth helix
jth helix-tensor structure
RDC and PCS values are fit to obtain the metal
tensor 23 orientations 4 have correct
chirality Repeat n times
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Second step
j n
j 2

?
? 4n-1

j 2
j 1
j n
j 1
Match the tensor positions 1 tricks to remove
degeneracy
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2. Strategy to remove degeneracy use of a second
metal
2nd metal
1st metal

?
? n
Degeneracy is removed!
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Results Cytochrome b562
modeled helices
real helices (NMR)
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Results Calbindin D9k
modeled helices
real helices (X-ray)
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NMR structure calculation with DYANA

• Simulated annealing by molecular dynamics in
  torsion angle space ( covalent structure
  parameters are kept fixed! )

• The TARGET FUNCTION has the role of the potential
  energy to be minimized

• Violated experimental constraints and steric
  overlap contribute to the target function

Few minutes!!
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Experimental constraints
Traditional
from CERM!

• Pseudocontact shifts
• Residual dipolar couplings
• Heme methyl chemical shifts
• Cross-correlations

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Integration of the equations of motion

• On the basis of the torsional positions,
  calculate the potential energy function (target
  function) and its gradient ??pot
• Determine the time-step
• Adapt the temperature by scaling of the torsional
  velocities
• Calculate the torsional accelerations
• Calculate the new velocities
• Calculate the new torsional positions

• The general form of the target function is

V ? ?t wt ?c wc (c c0)2
Where tconstraint type and cconstraint
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R1M and R2M constraints - proportional to r-6,
- they all refer to the same nucleus, thus
relating all atoms to one center and not many
atoms among them The dependence on r-6 makes
this class of constraints accurate to determine
the distance of protons close to the paramagnetic
center with respect to it, and important to have
an upper distance limit of protons far from the
paramagnetic center. They are robust, reliable
constraints, corresponding to long range NOEs,
all related to one nucleus, the metal ion.
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B0
?kk
?zz
 
?xx
?yy
? metal-nucleus vector - B0 angle
in case B0 is parallel to the molecular ?zz
direction
Edip depends on the field direction with respect
to the
tensor
? Self- orientation
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Self-orientation Versus orientation induced by
external agents

• Advantages
• No perturbations due to the interactions with
  the orienting material
• Disadvantages
• linebroadening due to the presence of the
  paramagnetic ion. However, linebroadening is ?
  r-6
• ? no disadvantages far from the
  paramagnetic ion

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• PCS
• proportional to r-3 (instead of r-6 as R1
  constraints)
• ? the effect is propagated to atoms farther from
  the paramagnetic center
• their amplitude is not simply related to a
  distance
• strong covariance between the angular
  dependence parameters and the distance of the
  atom from the paramagnetic center
• angular dependence provided by quadratic
  trigonometric functions eight positions for any
  rigid sub-structure are possible, provided by the
  symmetries of the reference frame axes. Four of
  these solutions are excluded as they lead to
  build aminoacids with wrong chirality.
• ? they are difficult to be used efficiently as
  constraints in torsion angle dynamics programs
  like PSEUDYANA or X-PLOR

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RDC - provide the NH / CaHa / CbCa vector
orientation - do not depend on any distance with
respect to the metal ion - are not related to a
particular position of a specific atom, as they
are independent on the position of the metal ion
but depend only on the direction of the NH, CaHa
or CbCa pairs. Therefore, values of the same
order of magnitude can be obtained for all the NH
of the protein - they all refer to the same
reference system, and thus relate all the
internuclear vectors to the same frame (and not
the internuclear vectors to one another).