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Paramagnetism-based Constraints
Lucia Banci CERM University of Florence
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What are paramagnetic molecules?
molecules containing unpaired electron(s)
T1N, T2N ? 1 s
tS10-7-10-13 s
µs 658 µp
Bertini, Luchinat, Parigi, Solution NMR of
Paramagnetic Molecules, Elsevier (2001)
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Paramagnetic metalloproteins
Iron proteins Copper proteins Manganese
proteins Lanthanide substituted Calcium
proteins Cobalt substituted zinc proteins
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NMR of paramagnetic molecules
The presence of unpaired electrons has profound
effects on the NMR spectra
- chemical shifts can have sizeable
contributions (hyperfine shift) -
relaxation rates are enhanced
Couplings between nuclear and electron
spins (hyperfine coupling)
contact (through bonds)
M
E ?Ac?Sz?
?
S(S1)/3kT
dipolar (through space)
N
E ??I?S (3cos2?-1) /rMN3
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The hyperfine coupling
It comprises contact and dipolar interactions
H
m2
m1
through bonds
through space
B0
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The hyperfine shift
- contact
?cont ?Ac?Sz?
M
- pseudocontact
d (ppm)
A
N
d (ppm)
20
25
15
60
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The origin of contact shifts
Contact shift contribution to the chemical
shift due to the unpaired electron spin density
on the resonating nucleus
A contact hyperfine coupling proportional to the
spin density of the resonating nucleus
S number of unpaired electrons
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The origin of pseudocontact shifts

a 0
B0


E ?Iz ?(?) (3cos2? -1)
N
If ?(?) is isotropic
a
???
a 90
N
1
?
(3cos2? -1) dcos? 0
?
-1
If ? (?) is anisotropic
? ? ???/B0
1
?
?(?)(3cos2? -1) dcos? ? 0
-1
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Pseudocontact shifts
?zz
z
X
?
y
r
M
?yy
?xx
?
y
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Nuclear relaxation
R1,2 ? E2f(?c, ?)
- Contact relaxation
? Ac2 f(?s, ?)
- Dipolar relaxation
? (1/rNM6 )f(?c, ?)
- Curie relaxation
? (?Sz?2/rNM6 )f(?r, ?)
S 2(S1)2B02 /rNM6
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Dynamic Information from Relaxation
Logo of the Chianti Workshops on Nuclear and
Electron Relaxation
Relaxation is the process by which an ensemble of
spins, brought into an non-equilibrium state by
an external perturbation, regains the thermal
equilibrium
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Dipolar interaction
Molecular tumbling generates fluctuating magnetic
fields at the nucleus which provide a relaxation
mechanism
Bo
J
q
q
r
I
I
r
J
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Nuclear relaxation due to the electron-nucleus
dipolar coupling
4?c
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Curie relaxation
Electronic Zeeman
1H
Curie Paramagnetism
Curie relaxation upon rotation
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Curie relaxation
R2M
R1M
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Contact relaxation
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Electron relaxation and nuclear relaxation
?
?
?
?
?
?
?
Proton relaxation rates due to Solomon and Curie
contributions, 5 Å, 800 MHz, no contact
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Electron Relaxation and Linewidths in
Macromolecules
ts (ps) R2(Hz) Cu(II) 300 3000-20000 VO(I
V) 500 15000 Ti(III) 40 100-500 Mn(II) 350
0 200000 Fe(III) 90 8000-50000 Fe(II) 1 40
00 Cr(III) 400 10000-60000 Co(II) 5 1000-200
0 Ni(II) 5 400 Gd(III) 120 100000-400000 Ln(
III) 0.1-1 3-80000(Curie)
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Structural Constraints
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Paramagnetic constraints turning disadvantages
into advantages
? R1, R2 Contact shifts PCS
RDC CC Curie-DD
R1, R2 Robust, reliable, correspond to long range
metal-nucleus NOEs
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R1, R2 constraints
M
R1,R2 from metal
NOEs among nuclei
The constraints have the same spherical symmetry
as NOEs (1/r6) They are applied as M-N NOE
constraints
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A Fe4S4 domain of the 2?Fe4S4?2 ferredoxin from
C. pasteurianum
Without R1 constraints
With R1 constraints
Bertini I., Donaire A., Luchinat C., Rosato A.,
Proteins 1997
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Paramagnetic constraints
R1, R2 Contact shifts ? PCS RDC
CC Curie-DD
Pseudocontact shifts
?zz
z
X
?
y
r
M
?yy
?xx
?
y
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Pseudocontact shifts in cytochrome b5
Arnesano, Banci, Bertini, Felli, Biochemistry
1998
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Structure calculations with pseudocontact shifts
NOEs, 3J couplings, pseudocontact shift
The position of the metal is determined without
any assumption
Banci L., Bertini I., Gori Savellini G., Luchinat
C., Wüthrich K., Güntert P., J. Biomol. NMR 1998
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Structure calculations with pseudocontact shifts
Starting from random coil structures, molecular
dynamics aimed at structure calculation is
performed at decreasing temperatures as driven by
the pseudopotential constituted by all structural
constraints
PSEUDYANA - A module of DYANA
XDIPO_PCS - A module of Xplor-NIH
ti tolerance wi weight
The magnetic susceptibility tensor parameters are
fitted during the structure calculations no
assumption is needed
Banci L., Bertini I., Gori Savellini G., Luchinat
C., Wüthrich K., Güntert P., J. Biomol. NMR 1998
Banci L., Bertini I., Cavallaro G., Giachetti,
A., Luchinat C., Parigi, G., submitted
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Protocols for using pseudocontact shifts for
solution structure determination
PSEUDODYANA (Banci, Bertini, Cremonini, Gori
Savellini, Luchinat, Wüthrich, Güntert, J.
Biomol. NMR 1998) module for the torsion angle
dynamic program DYANA HOW TO GET
IT http//www.mol.biol.ethz.ch/wuthrich/software/
dyana
PCSHIFT (Banci, Bertini, Gori Savellini,
Romagnoli, Turano, Cremonini, Luchinat, Gray,
Proteins Struct., Funct., Genet.,
1997) Integrated module of the SANDER module of
the AMBER package HOW TO GET IT http//www.amber
.ucfs.edu/amber/ amber.htmlobtain
PARArestraints For Xplor-NIH (Banci, Bertini,
Cavallaro, Giachetti, Luchinat, Parigi,
submitted) Integrated package for the structure
calculation program Xplor-NIH HOW TO GET
IT Just wait
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The impact of pseudocontact shifts on solution
structure determination
Without pseudocontact shifts
With pseudocontact shifts
Banci et al., Horse heart cyt c, Biochemistry,
1997
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Solution structure of Cu(I)-CopC
Through EXAFS the Cu(I) binding site is
defined. It is formed by 3 Met and 1 His
Conserved residues in the Cu(I) binding site
Cu(I) binding site
Tyr 79
Met 40
C
Met 43
Met 51
N
Cu(II) binding site
His 48
Met 46
Arnesano, Banci, Bertini, Mangani, Thompsett,
PNAS, 2003
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Some NMR properties of Copper
Type II Cu (II) ts 10-8- 10-9 s NMR
prohibitive Type I Cu (II) ts 10-10 s
NMR almost prohibitive Cu (I)
diamagnetic 63,65 Cu insensitive
for NMR
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Electron and Nuclear relaxation times of Cu2 ions
Type 2 copper is a much harder challenge
transverse
longitudinal
ts (s)
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Cu(II)-CopC
About 20 residues are lost due to paramagnetic
type II copper(II)
NMR signal disappearance
Chemical shift changes and/or line broadening
C
N
r 11Å
The position of the potential Cu(II) binding site
coincides with the center of the sphere
Arnesano, Banci, Bertini, Thompsett, Structure
2002
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Direct 13C and 15N detection
13C and 15N are less sensitive than
proton ...but relaxation rate enhancements
due to the presence of a paramagnetic center are
much smaller
1H 1 13C 1.59 x 10-2 15N 1.04 x 10-3
gI 1H 2.67 x 108 13C 6.73 x
107 15N -2.71 x 107
R1I, R2I ? gI2 gS2 f(tc)
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Heteronuclear experiments
JCaCO 55 Hz JCaCb 35 Hz JNCO 15 Hz
C-C correlations CT-COSY COCAMQ NOESY
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13C13C CT-COSY spectrum of Cu(II)-CopC
R2 ? g213C 1/16(g21H)
Ca-Cb cross-peaks of Ser
Apo Cu(II)
Machonkin TE, Westler WM, Markley JL., JACS 2002
Bertini I, Lee YM, Luchinat C, Piccioli M, Poggi
L., ChemBioChem 2001
Arnesano, Banci, Bertini, Felli, Luchinat,
Thompsett, JACS 2003
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Cu(II)-CopC
About 15 out of 20 residues are recovered
Ser 26
1H NMR signals disappear
Ser 88
Chemical shift changes and/or line broadening
C
r 6Å
N
The structure in the vicinity of Cu(II) binding
site was calculated using using 83 1H and 18 13C
pseudocontact shifts and 23 paramagnetic
relaxation rates as structural constraints
Assignment 1H detection 13C,15N detection
13C 76 85 15N 83 95
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Solution structure of Cu(II)-CopC
EXAFS ? Metal-ligand constraints are added and
interaction of the metal ion with water molecules
EPR ? tetragonal type 2 copper with N/O as donor
atoms
NMRD ? Interaction of the metal ion with water
molecules
Conserved residues in the Cu(II) binding site
C
Glu 27
Lys 3
N
Met-rich region
His 1
Asp 89
Arnesano, Banci, Bertini, Felli, Luchinat,
Thompsett, JACS 2003
His 91
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Paramagnetic constraints
R1, R2 ? Contact shifts PCS RDC
CC Curie-DD
Contact shifts Robust, reliable, correspond to 3J
values involving the metal ion
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e-
M
H
? ? cos2 ?
?
D
C
e-
M
H
? ? sin2 ?
?
D
C
? M-D-C-H
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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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1st solution structure of a paramagnetic
protein Reduced HiPIP I from E. halophila
Cofactor Fe4S42 (shortest T1min ?
2ms) AA 73 1D NOE 40 2D NOESY
1233 (945) Fe-H dipolar 58 constraints Refine
ment procedure REMV, RMDV
RMSD (Å) BB - 0.45?0.09 HA - 1.09?0.17 Metal
cluster 26 links Dihedral angle constraints ?
45 (3JHNH?, 3JHNC) ?1 26 (3J?NH?,
3JH?N) Fe-S-C-H 4
Banci L., Bertini I., Eltis L.D., Felli
I.C.,Kastrau D.H.W., Luchinat C.,Piccioli M.,
Pierattelli R., Smith M., Eur. J. Biochem.
1994 Bertini I., Donaire A., Eltis L.D., Felli
I.C., Luchinat C., Rosato A., Eur. J. Biochem.
1996
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Calculated vs. observed shifts of methyl protons
in bis-histidine cytochromes
? 1-CH3, ? 3-CH3, ? 5-CH3, ? 8-CH3
I. Bertini, C. Luchinat, G. Parigi, F.A. Walker,
JBIC 1999
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The case of oxidized cytochrome b5
Banci, Bertini, Cavallaro, Luchinat JBIC, 2002
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Inclusion of histidine planes orientation in
structure calculations
Banci, Bertini, Cavallaro, Luchinat JBIC
2002
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Paramagnetic constraints

• R1, R2
• Contact shifts
• PCS
• RDC
• CC Curie-DD

Residual dipolar couplings
Partial orientation at high magnetic fields
Magnetic anisotropy (in paramagnetic molecules
can be very high)
Orienting agents
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Paramagnetism based RDC
Drdcmol - Drdcdia Drdcpara
D?para
shiftpara - shiftdia pcs
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Magnetic susceptibility tensors in cytochrome b5
??axmol 2.20 ? 10-32 m3 ??rhmol -1.34 ?
10-32 m3
??axpara 2.8 ? 10-32 m3 ??rhpara -1.1 ?
10-32 m3
Total magnetic susceptibility metal
diamagnetic contributions
??axmol (calc) 2.1 ? 10-32 m3 ??rhmol
(calc) -1.0 ? 10-32 m3
??axdia -0.8 ? 10-32 m3 ??rhdia 0.1 ?
10-32 m3

Banci, Bertini, Huber, Luchinat, Rosato JACS 1998
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Partial molecular orientation at high magnetic
fields
??axpara 2.8 ? 10-32 m3 ??rhpara -1.1 ?
10-32 m3
Banci, Bertini, Huber, Luchinat, Rosato JACS 1998
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NH vectors in the protein frame of Fe(III) cyt
b562
Arnesano, Banci, Bertini, Van der Wetering,
Czich, Kaptein, J. Biomol. NMR, 2000
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Magnetic susceptibility tensors in cyt b562
Metal contribution
Calculated
diamagnetic metal contributions molecular
magnetic susceptibility
Experimental
Diamagnetic contribution
Arnesano, Banci, Bertini, Van der Wetering,
Czich, Kaptein, J. Biomol. NMR, 2000
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NH and CH Drdcs
CH and NH
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Quick structure determination backbone
constraints only
NOE3JPCS
NH,CH Drdc
CSI
a3
a4
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Structure of Ce substituted Calbindin D9k
Ca2
Ce3
site II
site I
C-terminal
N-terminal
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Drdcmol - Drdcdia Drdcpara
D?para
shiftpara - shiftdia pcs
Availability of independent sets of rdc data
(e.g. through substitution of calcium with 2 or
more different lanthanide ions)
Simultaneous fitting provides the values of ?
and ?, which define the orientation of the
internuclear vector in an arbitrary reference
system
The case of Ca Ln Calbindin (Ln Ce Tb Dy Ho Er
Tm Yb)
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RDCDYANA-ANGLES and XANGLES
A new module of the programs PARAMAGNETIC-DYANA
and Xplor-NIH
FIXED REF. FRAME
H
Efficient implementation of rdc-derived ? and
? angles as constraints in solution structure
calculations
q
N
f
A two-minima (or single minimum) potential is
used for each N-H vector
Dramatic improvement in convergence with
respect to simulated annealing protocols which
use straightforwardly rdcs as constraints
RDCDYANA-ANGLES available at www.postgenomicnmr.
net
Bertini, Barbieri, Cavallaro, Lee, Luchinat
Rosato, JACS 2002
Banci, Bertini, Cavallaro, Giachetti, Luchinat
Parigi, submitted
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RDCDYANA-ANGLES
Ce Tb Dy Ho Er Tm Yb
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? and ? constraints
0.280.06 Å
Calbindin D9k
Backbone RMSD
Bertini, Barbieri, Cavallaro, Lee, Luchinat
Rosato, JACS 2002
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Paramagnetic constraints
R1, R2 Contact shifts PCS
RDC ? CC Curie-DD
Cross correlation between Curie Relaxation and
Dipole-Dipole relaxation provides information on
the relative position between the metal and a
dipolarly coupled atom pair
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CCR between Curie and DD relaxation
Electronic Zeeman
1H
Curie Paramagnetism (Ds)
Curie relaxation
1H
15N
The proton magnetic moment induces 15N
relaxation (DD relaxation)
Both with correlation time ?r
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Curie-Dipole Dipole Cross Relaxation for
isotropic systems
H(A)
re
N(K)
?
M(S)
? 1H
Boisbouvier, Gans, Blackledge, Brutscher, Marion
J.Am.Chem.Soc., 1999
The two components in the proton dimension have
unequal linewidths
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Calbindin structure refinement with paramagnetic
constraints
Diamagnetic constraints

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

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

Bertini, Donaire, Jiménez, Luchinat, Parigi,
Piccioli, Poggi, ChemBioChem. (2002)
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Towards structure without NOEs
At least 2 lanthanide ions are needed Bertini,
Longinetti, Luchinat, Parigi, Sgheri, J. Biomol.
NMR (2002) in press
Structure can be obtained with PCS, RDC, CCR and
less than 10 NOEs
Bertini, Donaire, Jiménez, Luchinat, Parigi,
Piccioli, Poggi, J. Biomol. NMR, 2001
62
Magnetic coupling and NMR
dipolar coupling
magnetic coupling
N
M1
M2


Slow relaxing metal ion
Fast relaxing metal ion

H J S1 S2
e.g. M1 Cu2 tsM1(0)10-9 s M2 Co2
tsM2(0)10-12 s
I. Bertini and C. Luchinat, Coordination
Chemistry Reviews 1996
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The miracle of Cu2Co2SOD
ts(s) Cu Co uncoupled
210-9 10-11 coupled 10-11
510-12 decrease 200
2 factor
Cu
B
His 44
His 118
N
M
H
C
J,F
His 69
G
His 46
O
R
P
I,J
K
J,I
D
L
A
His 61
Q


His 118
His 46
His 44

Co

E
His 78
F,J
Banci, Bertini, Luchinat, Piccioli, Scozzafava,
Turano, Inorganic Chemistry 1989
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Marie Curie Training Site NMR in Inorganic
Structural Biology
CERM, University of Florence
Topics NMR spectroscopy Structural
biology Protein expression Drug
discovery Bioinformatics Functional genomics
Training in a Large Scale Research Infrastructure
Conditions Being an Europen PhD student
http\\www.cerm.unifi.it cerm_at_cerm.unifi.it
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