130106 solid-state nmr of paramagnetic...
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SolidSolid--state NMR of state NMR of Paramagnetic SystemsParamagnetic SystemsParamagnetic SystemsParamagnetic Systems
Yoshitaka IshiiDepartment of Chemistry,Department of Chemistry,
University of Illinois at Chicago
1
OutlineOutlineOutlineOutline
1 Background and Motivation1. Background and Motivation2. Basic Theory 3 E l & A li ti3. Examples & Applications4. Some Practical Aspects
Goal: Theoretical background to understand recentGoal: Theoretical background to understand recent applications of paramagnetic interactions (PRE etc) for biological SSNMR
2
for biological SSNMR
Sec 1 Background & MotivationSec 1 Background & MotivationSec. 1 Background & MotivationSec. 1 Background & Motivation
1 1 Motivation of the Study?1.1 Motivation of the Study?1.2 Overview & Recent Applications
S ll P ti S t Small Paramagnetic Systems Paramagnetic Proteins &
Non-paramagnetic Proteins1.3 The Problems in Paramagnetic g
Solid-state NMR
3
The Periodic Table for The Periodic Table for Bi l l NMR S dBi l l NMR S dBiomolecular NMR StudentsBiomolecular NMR Students
1 2H HeH He3 4 5 13 15 16 19 10Li Be B C N O F Ne11 12 13 14 31 16 17 18Na Mg Al Si P S Cl Ar19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 5437 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe55 56 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86Cs Ba Lu Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn
4
More than 1/3 of the Elements More than 1/3 of the Elements Sh Sh P tiP tiShow Show ParamagnetismParamagnetismin Periodic Table!in Periodic Table!1 2
HH He3 4 5 6 7 8 9 10Li Be B C N O F Ne11 12 13 14 15 16 17 18Na Mg Al Si P S Cl ArNa Mg Al Si P S Cl Ar19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr
37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe55 56 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86Cs Ba Lu Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn
57 58 59 60 61 62 63 64 65 66 67 68 69 70La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm YbLa Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb
Paramagnetic Anti-Ferromagnetic
5
Diamagnetic FerromagneticModified from http://www.aacg.bham.ac.uk/magnetic_materials/type.htm
Market Analysis of HighMarket Analysis of High--Resolution Resolution SolidSolid state NMR (SSNMR)state NMR (SSNMR)SolidSolid--state NMR (SSNMR)state NMR (SSNMR)
In 2002Diamagnetic
SystemParamagnetic
System
Spin = 1/2 ~30 Articles over
Spin 1
30 YearsCP, MAS, Decoupling Recoupling
Spin 1DAS, DOR,MQMAS, STMAS
7
Market Analysis of HighMarket Analysis of High--Resolution Resolution SolidSolid state NMR (SSNMR)state NMR (SSNMR)SolidSolid--state NMR (SSNMR)state NMR (SSNMR)
In 2013Diamagnetic
SystemParamagnetic
System
Spin = 1/2 Very Fast MAS Approach
Spin 1
CP, MAS, Decoupling Recoupling
Approach
Spin 1DAS, DOR,MQMAS, STMAS
9
MotivationMotivationM P t ti l A li ti f P S tMany Potential Applications for Paramag Systems More than 1/3 of Elements in the Periodic Table Show
Paramagnetism Nanoscience (Self-assembled structures) Molecular Electronics Drugs Drugs Metal-Protein Complex
Generally, NMR analysis was difficult!
Still Underdeveloped Spectroscopy
y, y
Structural Information Assignment Sensitivity
10
y Resolution
1.2 Overview & Recent Application1.2 Overview & Recent ApplicationMAS SSNMR for Small Compounds13C for Cu(DL-Ala)2 1H for Mn(acac)3
(a) 24 kHz( )2 H for Mn(acac)3
(a) 10 kHz
(c) 5 kHz
11 Sensitivity under VFMAS is comparable to that of diamagnetic SSNMR
IdealIdeal Structural Measurements for Structural Measurements for Biomolecules by SolidBiomolecules by Solid--state NMR?state NMR?Biomolecules by SolidBiomolecules by Solid state NMR?state NMR?
• No extra cross peaks for resolution Paramagnetic Interactions?
No extra cross peaks for resolution • Detectable by shifts or relaxation
L di t (10 Ǻ l )• Long-range distances (10 Ǻ or longer)
~10 Ǻ
Amyloid Fibrils
12
Amyloid Intermediate &for A(1-40)Ishii et al. Nat Struct Biol (20
PG-1 -barrel in membrane
Hong et al. PNAS (2006)
for A(1-40)
Tycko et al. PNAS (2002)Biochemistry (2006)
SSNMR of Paramagnetic SSNMR of Paramagnetic MetalloMetallo--proteinsproteinsSt t l I f ti f P d t t ShiftStructural Information from Pseudo-contact Shifts
Application to selectively 13CO-Leu, 15N-Phe, Gly labeled P450 BM-3 protein Application to uniformly
13C-labeled Co(II)-MMP
McDermott et al. JACS 127, 13816 (2005) Bertini et al .13816 (2005) Bertini et al .
JACS 129, 2219 (2007)
13 Distance Info (10-20 Ǻ)
Applications to Applications to NonNon--paramagneticparamagnetic ProteinsProteinsParamagnetic-tag for
SSNMR of ProteinsParamagnetic Doping & Condensed Data Collection (PACC)
I hii t l J M R 184 250 (2007) Jaroniec et al. JACS 129 7502(2007)
Nat. Chem 4 410 (2012)
Ishii et al. J. Mag. Reson. 184 250 (2007) Ishii et al. Nat. Methods (2009)
150 ms/scan
Long-range distance
[email protected] s/scan
Cu2+-EDTA@8
14 Sensitivity enhancement& Structural Info
Challenges in Solid-state NMR for Paramagnetic SystemsParamagnetic Systems
Range of the Shifts Large
1H MAS NMR of Mn(acac)3
(a)Range of the Shifts Large
Limited Resolution 13C MAS NMR of Mn(acac)
(b)
Assignment
Requirement of Labeling
MAS 10 kHz 1H Dec 100 kHz13C MAS NMR of Mn(acac)3
Requirement of Labeling
Structural Information 2D MAS NMR of 2D-label Cu(DL-Ala)2
McDermott et al.
How can we solve these problems? CD3
JACS (1995)
15
these problems? CD3
Sec 2 Theory & BackgroundSec 2 Theory & BackgroundSec. 2 Theory & BackgroundSec. 2 Theory & Background2.0 Definition of Paramagnetism2 1 Th l A i f El t l2.1 Thermal Averaging of Electron-nuclear
Interactions Contact Coupling e-/n Dipolar Coupling g tensor Contact Coupling, e-/n Dipolar Coupling, g-tensor Thermal Averaging of Electron Spin States Electron Spin Correlation Time Electron Spin Correlation Time Contact & Dipolar (Pseudo-contact) Chemical Shifts
2.2 Relaxation Propertiese a at o ope t es Relaxation Mechanisms Electron Spin-correlation-time Dependence
162.3 Short Problem Solving Session
“Rough” Definition of “Rough” Definition of ParamagnetismParamagnetismfor NMR for NMR SpectroscopistsSpectroscopistsp pp p
Diamagnetic Paramagnetic
No unpaired electron spinsNo unpaired electron spins in molecules No bulk spin magnetic
Unpaired electron spins orientrandomly without B0
No bulk spin magnetic momentmoment without B0
No bulk spin magnetic moment without B0
When B0 is applied,M = H0 = B0/0
M = B0/0 > 0 & Small
17
Magnetic susceptibility: < 0 & ~ 0 (usually ~ ppm)
0 & S a ~ C/T
Atomic Magnetic Moment Atomic Magnetic Moment Atomic Magnetic Moment There are two components in electronic magnetic moment in an atom or ion:
– Spin componentp ps = SS = -gSBS, [2.1]
– Orbital component L = LL = -gLBL, [2.2]
where S and L are spin and orbital angular momentum, respectively. The net atomic magnetic moment isThe net atomic magnetic moment is
= -gSBS - gLBL = -B(gSS + gLL), [2.3] B denotes Bohr magneton (e/2m). B is used as a “unit” to measure the
electron magnetic moment. g-factor For electrons, g-factor g is defined by
18
, g g ygB = -, [2.4]
where gS for a free electron spin is ge ~ 2.00 (S ~ -2BS).
Interactions of Electron Spins 1Interactions of Electron Spins 1Interactions of Electron Spins 1Interactions of Electron Spins 1• Electron Zeeman Interaction
H = B t • = B t • (g L+ g S) [2 5]HEZ = - B0t • = B0
t • B(gLL+ geS) [2.5]In general, handling the orbital contribution L is
complicated. One simple way to include the orbital effect is to define the g tensor g as
HEZ = - B0t • = B B0
t [g ] S, [2.6],where g is a 3-by-3 matrix (or tensor) that is defined by
= [g] S gLL+ geS [2.7a](g)nm = (S)n(gLL + geS)m/{S(S+1)} [2.7b]
Eq. [2.6] does not include L apparently.Th t i t d lli id
gzz
19
The g-tensor is represented as an ellipsoid, as CSA tensor. When gL = 0, g = ge (isotropic!).
gxxgyy
Electron Spin Magnetic Electron Spin Magnetic MMMomentMoment
• electron spin = g • Selectron spin g S=
Y
X
YY
XX
SS
Rgg
R 10000
Z
Y
ZZ
YY
Sgg00
XXX Sg 00
HEZ = -B0• g • S=
Z
Y
X
ZZ
YY
XX
SSR
gg
gRB 1
0
000000
gZZ
gYY
gXX
gZZgYY gXX
20
gZZ
Interactions of Electron Spins 2Interactions of Electron Spins 2Interactions of Electron Spins 2Interactions of Electron Spins 2Fermi Contact CouplingThe Hamiltonian for Fermi contact coupling with nuclear p g
spin I is given by HCON = AS • I, [2.8a]
withwithA = 20Lge B . [2.9] = ||2 - ||2 [2.10] || || , [2.10]
where k denotes the MO wave function (for the electron S) at Spin I when S takes the spin state k (k = , ).
Q. What kind of properties are needed for the MO k for the system to have non-zero A? S IMetal
21
S IMetal
Interactions of Electron Spins 3Interactions of Electron Spins 3Pseudo Contact Coupling (Dipolar Coupling)Like nuclear dipolar coupling the Hamiltonian for electron-Like nuclear dipolar coupling, the Hamiltonian for electron
nuclear (e-n) dipolar coupling is given by
HPC = S • D • I. [2.11]If we can assume that the electron delocalizes at the atom
or ion, in the high field approximation, eq. [2.11] yields H = (d/r3)(1 3cos2 )I S [2 12]HPC = (d/r3)(1-3cos2 )IZ SZ. [2.12]
What are r and ?What are r and ?When the g anisotropy is not negligible,
HPC = (/g ) • D • I [2 11b]22
HPC (/ge) D I. [2.11b]
Thermal AveragingThermal AveragingElectron Zeeman (for S =1/2)
1/2
mS
~10 cm-1 << 200 cm-1 = kT(B0 at 10 T) (T = 300 K)
-1/2 & Electron spin relaxation isusually fast
So ms = ½ will be thermally mixed. 1/21/2The next question:
What is the thermal effect on contact coupling for NMR?
kex ~ 1/C
23-1/2
contact coupling for NMR?How quickly can the averaging happen?
Thermal Averaging of Contact CouplingThermal Averaging of Contact Coupling(Case 1) NMR spectrum of I with slow thermal averaging
-1/2 1/2A (~ MHz)
1/C << A
(Case 2) NMR spectrum of I with moderate thermal averaging
1/ A1/C ~ A
CA2/8
(Case 3) NMR spectrum of I with fast thermal averaging
Q. Where do you expect the lines? 1/C >> A
24
C
Thermal Averaging of Contact Coupling(Case 1) NMR spectrum of I with slow thermal averaging
-1/2 1/2A (~ MHz)
1/C << A
(Case 2) NMR spectrum of I with moderate thermal averaging
1/ A1/C ~ A
(Case 3) NMR spectrum of I with fast thermal averaging
1/C >> AcontactContact shift!
25
C
<ASZ > = (P – P)A/2contact =
Calculation of Thermally Averaged Calculation of Thermally Averaged Contact Contact Shift & Dipolar Shift Shift & Dipolar Shift Contact Contact Shift & Dipolar Shift Shift & Dipolar Shift
General High field Isotropic g• HCON =A<S>·I ~ A<Sz>Iz ~ A<Sz> Iz
[2.13]
• HPC ={<>/ge}·D·I ~ {(<>/ge)·D}zIz ~ D<Sz> Iz[2 14][2.14]
L t’ bt i & S fi t26
Let’s obtain <> & <S> first.
Magnetic Moment under Thermal Averaging Magnetic Moment under Thermal Averaging Case 1: For the isotropic g tensor
<S> = )}/{exp(/)}/exp({ kTHTrkTHTr EZEZ S
}{/)}({ BSgTBSgT ZeBZeB 00 11 Sexp(-A)~ 1-A
Case 1: For the isotropic g-tensor
~ }{/)}({kT
SgTrkT
SgTr ZeBZeB 00 11 S
H/kT
)}()/{(|))((| 10 TrkTBgSS BeZjkl
jj
e
<S> =jkl
)}()/{(|| 10 TrkTSSBg BZjejkl
j
e
where ej is an unit vector along the axis j (j =x, y, z) and |> denotes a basis ket.
[2.15]
jkl
)/()}({ kTSSBg BeZjkl
310 e
)/()}({ kTSSg 31 B )/()}({ kTSSg Be 310 B
In the high field approximation for the parameterized g tensor, <> is given by
< > g <S> C: Curie factor27
[2.16]TCgkTSSg eBe //)}({ 0
220
2 31 BB <> = Bge<S> C: Curie factor
Magnetic Moment under Averaging 2Magnetic Moment under Averaging 2
<S> = )}/{exp(/)}/exp({ kTHTrkTHTr S exp(-A)~ 1-A
Case 2: A more general case
~)}{ p()}p({
}{/)}({kT
TrkT
Tr BB 00 11 BgSBgSS
=H/kT}{)/(|))((| 1TkTBSS
p( )
<S> =
}{)/(|))((| 10 TrkTBgSS Blklkjkl
jj
e
}{)/(|| 1TrkTSSBg e
where ej is an unit vector along the axis j (j =x, y, z) and |> denotes a basis ket.
}{)/(|| 10 TrkTSSBg Bkjlkljkl
j
e
)/(}/)({ kTSSBg Bjklkljjkl
310 e
[2.17]
jkl
)/(}/)({ kTSS B310 BgIn the high field approximation for the parameterized g tensor <> is given by
28[2.18]
In the high field approximation for the parameterized g tensor, <> is given by
)/()}({ kTSS B 31 20 Bgg<> = Bg·<S>
Susceptibility TensorSusceptibility TensorThe susceptibility tensor is defined by
<> = ·B0/0. [2.19]From [2.18,19], we obtain
[2.20]Thus, the frame that diagonalizes g-tensor also
gg )}/()({ 02 31 kTSS B
, g gdiagonalizes . The principal values of the tensors and g are related as g
kk = gkk2 [2.21]
= (C/T )g 2)}/()({ 0
2 31 kTSS B
29
= (C/T0)gkk ,where kk and gkk denote principal values for and g .
Calculation of Thermally Averaged Calculation of Thermally Averaged Contact Contact Shift & Dipolar Shift Shift & Dipolar Shift Contact Contact Shift & Dipolar Shift Shift & Dipolar Shift
Case 1: g-anitoropy neglected
• CON =A<SZ> )/()}({ kTSSBAg Be 310
Isotropic shift [2.22]
• =D()<S > )/()}({)( kTSSBgRD 31
p NOT Removable by MAS
• PC =D()<SZ> )/()}({),( kTSSBgRD Be 310
Anisotropic shift [2.23]Anisotropic shift
D(, R) = (1-3cos2)/R3
30 Removable by MAS
Anisotropic Shift for Paramagnetic Anisotropic Shift for Paramagnetic S t i S t i 11H VFH VF MAS NMRMAS NMRSystems in Systems in 11H VFH VF--MAS NMRMAS NMR
Cu(II)(DL-Ala)2 Mn(III)(acac)3
S = 1/2 S = 2
31dipolar S(S+1)/R3 Q. What is R?1/2(1+1/2) = 3/4 2(1+2) = 6
Thermally Averaged Hyperfine ShiftsThermally Averaged Hyperfine ShiftsC 2 it NOT l t dCase 2: g-anitoropy NOT neglected
CON = A<Sz>Iz=
}coscossincossin{ 222220 gggCAB
ZBZ ITCA )}/()({ 0Bg This is actually anisotropic
PCS = (<>/g ·D) I
}coscossincossin{ zzyyxx
B
gggT
(,, ) denote Euler angles that
[2.24]PCS = (<>/ge D)zIz
= ZZe ITgC ))(/( DggB 0
(,, ) denote Euler angles that define the g-tensor orientation withrespect to the Lab frame
[2 25]The tensor is NOT traceless (g2D is traceless). )( Dgg This term also includes both anisotropic and isotropic shifts
[2.25]
32
p p
Yesnowski et al JCP 89, 4600 (1988)
Bertini et al. “Solution NMR of Paramagnetic Molecules”
Calculation of Thermally Averaged Calculation of Thermally Averaged H fi ShiftH fi Shift d MASd MASHyperfine ShiftsHyperfine Shifts under MASunder MAS
Case 2: g-anitoropy NOT neglectedBy averaging the diagonal elements of the tensors ACg/T
and (C/geT)g·g·D, we obtain the isotropic shifts for t t d di l hift f llcontact and dipolar shifts as follows:
CAB<CON> 30 /}{ zzyyxxB
gggTCAB
cos 31 222 ggCdB
[2.26]
<PCS>cos){( 3
312
22
23
0
yyXX
zze
ggg
TRgCdB
34}cossin 2
62
22
yyXX gg [2.27]
Distance Information from Distance Information from I t i PC ShiftI t i PC ShiftIsotropic PC ShiftsIsotropic PC Shifts
cos 31 2222 yyXX ggCdB cos){(
331
222
23
0
yyXX
zze
gg
ggg
TRgCdB<PCS>=
}cossin 26
222
yyXX gg
[2.27]
where and are the polar and azimuthal angles of the dipolar vector with respect to the g-tensor frame (see Ref. below) The principal values gkk can be obtained from EPRbelow). The principal values gkk can be obtained from EPR.
R, , can be fitting parameters for structural studies!
35
Yesnowski et al JCP 89, 4600 (1988)
Use PCS in SSNMR of Paramagnetic Use PCS in SSNMR of Paramagnetic MetalloMetallo--proteinsproteinspp
Structural Information from Pseudo-contact ShiftsApplication to selectively 13CO-Leu, 15N-Phe, Gly labeled P450 BM-3 protein Application to uniformly
13C-labeled Co(II)-MMP
McDermott et al. JACS 127, 13816 (2005) Bertini et al .13816 (2005) Bertini et al .
JACS 129, 2219 (2007)
36
Relaxation PropertiesRelaxation Properties
The main source of the paramagneticThe main source of the paramagnetic relaxation in solids is thermally fluctuated fields due to hyperfine couplingsfields due to hyperfine couplings.
I S
37
CuCu2+2+ as a Structural Probe via Paramagnetic as a Structural Probe via Paramagnetic Relaxation Enhancement (PRE)Relaxation Enhancement (PRE)Relaxation Enhancement (PRE)Relaxation Enhancement (PRE)
Cu2+ binding to Influenza M2 protein Hong et al. JACS 134, 8693 (2012)
Cu2+ binding to β amyloid fibrilIshii et al. JACS 133, 3390 (2011)
Hi 13g ( )
His-13
F20H13
13C R for PRE @ 400 MHz38
13C R 1 for PRE @ 400 MHzR1 ~ 3.6 x 106/r6 Hz,where r is a 13C-Cu distance in Å.
Correlation timeCorrelation time
• We define the correlation time of theWe define the correlation time of the electron spin state S asC(t) = <S (t)S (0)> = <S (0)2>exp( |t|/ ) [2 28]C(t) = <Sz(t)Sz(0)> = <Sz(0)2>exp(-|t|/S) [2.28]
is in the range of 10-13 to 10-8 s ThisS is in the range of 10-13 to 10-8 s. This fluctuation can be introduced by electron spin relaxation, electron-electron spin couplingsrelaxation, electron electron spin couplings(dipolar & exchange couplings).
S can be significantly different between samples in solids and solution
39
S g y p(typically shorter in solids) because of intermolecular electron spin couplings.
Paramagnetic Relaxation in Solution• Two type of relaxation exists in solution: Curie relaxation & Solomon relaxation (seeCurie relaxation & Solomon relaxation (see
the reference below for R2).
2
D i i lid
222222
2
30
16
13
141512
CSI
C
CI
C
CSI
CSI
RSS
)()()( R1
SL =
21 CASS )(
20
20
222 31 rSIS BSS )(
Dominant term in solidswhen C>> 1/S ~10-12
R1Curie =
22131
CS
C
hASS
)(
2232 1435 rIRkT
“S f ”
where r is the rotation correlation time of the molecule,1/C = 1/S + 1/r.
~ 0 in solids (r )R1
(tr for protein ~ns)
40
Bertini “Solution NMR of paramagnetic Molecules”In solids, r ~ . R1Curie ~0
& C ~ S. About the absence of Curie relaxationEmsley JACS 129 14118 (2007)
Structural Info from Paramagnetic R1Structural Info from Paramagnetic R1
• R1SL 1/R6 Distance informationR1 1/R Distance information
Cu(II)-13C distance determinationusing 13C R1 measurements
for unlabeled Cu(Ala-Thr)
Seven 13C-Cu distances were determined without requirements of 13C-labeled qsamples
41
R2 Paramagnetic Relaxation
2 6631SS )(
Solomon relaxationR2
SL =
2222222230
16
16
13
14
4151
CSI
C
CS
C
CI
C
CSI
Cc
SI
RSS
)()()(
Dominant dipolar terms in solids
21 C
CASS )(
20
20
222 341 rSIS BSS )(
Dominant dipolar terms in solids(First term dominant when C < 10-9.)
~ 0 in solidsR2Curie =
2213 CSCh
2232 1
4435 rI
rRkT
0 in solidsR2
Ratio (R1/R2)
0.80.91.0
R2SL I
2
0.30.40.50.60.7
R1/
R2
R2 I
Even if 1H Signals are very broad, 13C, 15N signals may be observable.
420.00.10.2
-12 -10 -8 -6 -4Log(tau)
Spin Labeling RR11/R/R22 for Different for Different Correlation TimeCorrelation Time
0 80.91.0
0 50.60.70.8
R2
8
0 20.30.40.5
R1/ Tau >10-8s
Very broad
0.00.10.2
-12 -10 -8 -6 -4-12 -10 -8 -6 -4Log() NO Spin Labeling Gd2+Tau <10-11s
Limited ~10-11 -10-9 s
43Cu2+relaxation R2 ~ R1
Moderate broadening
2 6312 SS )(
Comparison of the 3 terms
222222
2
30
1 16
13
141512
CSI
C
CI
C
CSI
CSISL
RSSR
)()()(
6.0E-10
7.0E-10
J(wI-JS) C = 1/2I
3 0E-10
4.0E-10
5.0E-103J(wI)
6J(wI+wS)
J Log(
J)
J C = 1/2I
1.0E-10
2.0E-10
3.0E 10 L
C = 1/2S
0.0E+00-16 -14 -12 -10 -8 -6 -4
Log(C) Log(C)
45
g( C)
2 663)1(2 SS
Comparison of the 5 terms
22222222
2
30
2 )(16
16
13
)(14
415)1(2
CSI
C
CS
C
CI
C
CSI
CC
SISL
RSSR
1E-09
log(4tau)log(J(wI-wS)log(3J(wI))log(6J(ws))log(6J(wI+wS)
6E-10
8E-10
4tauJ(wI-JS)3J(wI)6J(wI+wS)
0.0
5.0
16 14 12 10 8 6 4J)
log(6J(wI+wS)
C = 1/2I J )J
2E-10
4E-10
6J(wI wS)6J(ws)
-10.0
-5.0-16 -14 -12 -10 -8 -6 -4
Log(
J
Log(
J)
0
-16 -14 -12 -10 -8 -6 -4-20.0
-15.0
( )Log(C)
Log( )Log(tau)
46
g( C)Log(C)
Sec. 3 Examples & ApplicationsSec. 3 Examples & Appl cat ons3.1 Sensitivity & Resolution Enhancement
3.1.2 Very-Fast MASy3.1.2 Polarization transfer3.1.3 Protein example
3.2 Structural Information3.2.1 Small molecules 3.2.2 Metallo-proteins3 2 3 Metal bound proteins3.2.3. Metal-bound proteins
3.3 Use of Paramagnetic Interactions on Non-Paramagnetic Proteins a a ag et c ote s3.3.1 Sensitivity Enhancement3.3.2 Structural Information
47
1H & 13C High Resolution Paramagnetic SSNMRP bl P ti Shift A L (1H & 13C)
Fundamental RF methods fail (1H-1H or 1H decoupling, CP) 2D labeling (D b t l 1990 Oldfi ld t l )
Problems Paramagnetic Shifts Are Large (1H & 13C)
2D labeling (Dobson et al. 1990; Oldfield et al.) Resolution under MAS at ~10 kHz in a few cases (1H Yesinowski et al. 1988;
13C McDermott et al. 1995, 13C Kohler et al. 2001) Labeling required & Limited sensitivity/resolution Labeling required & Limited sensitivity/resolution
Numerous sidebands due to large anisotropic shifts Assignments are difficult
Selective 2D or 13C-labeling required Sophisticated experiments rarely attempted (2D, Distance)
2D 13C/13C correlation (Terao et al. 1999; Emsley et al. 2000)
Low Resolution/Sensitivity Assignment Difficult
( ; y ) 13C labeled samples even for small molecules
Very Fast Magic Angle (VFMAS) Changes48
Low Resolution/Sensitivity, Assignment Difficult Only handful studies over 30 years before 2000
Very Fast Magic Angle (VFMAS) Changes the Situations !
13C High Resolution Paramagnetic SSNMRProblems Paramagnetic Shifts Are Large (1H & 13C)
1H (1H-1H) RF decoupling ineffectiveProblems Paramagnetic Shifts Are Large (1H & 13C)
Decoupling by Very Fast MAS Numerous sidebands Decoupling by Very Fast MAS
Removal by Very Fast MAS CP ineffective
N OH2O
Cu(DL-Ala)2 1 min (600 scans)13C MAS at 5 kHz
Cu
NH2 O
N O
MAS 24 kHz + No Decoupling1 min (600 scans)
CH3CH
CO2-
NH2
CH CO
CH49400 0 -400(ppm) 400 0 -400(ppm)
CH3
13C High Resolution Paramagnetic SSNMRProblems Paramagnetic Shifts Are Large (1H & 13C)
1H (1H-1H) RF decoupling ineffectiveProblems Paramagnetic Shifts Are Large (1H & 13C)
Decoupling by Very Fast MAS MAS 24 kH Di l INEPT Numerous sidebands Decoupling by Very Fast MAS
Removal by Very Fast MAS
MAS 24 kHz + Dipolar INEPT1min (13k scans)
CH3CH
Recoupling-based transferusing strong RF fields
CP ineffective
Cu(DL-Ala)2 1 min (600 scans)13C MAS at 5 kHz
CO2-
using strong RF fields
CH3CH
CO2-
*
50400 0 -400(ppm) 400 0 -400(ppm) Ishii et al. JACS 125, 3438-3439 (2003)
13C VFMAS Spectrum with Dipolar INEPTwith Dipolar INEPTfor Mn(III)(acac)3
MAS: 26.3 kHzMAS: 26.3 kHz
51Wickramasinghe & Ishii J. Magn. Reson. (2006)
More PCS are visible for More PCS are visible for 11H & H & 1313C closer to C closer to CoCo2+2+--MMP 12 under fast MAS at 60 kHz MMP 12 under fast MAS at 60 kHz CoCo MMP 12 under fast MAS at 60 kHz MMP 12 under fast MAS at 60 kHz Under MAS at 20 kHz, 13C signal is visible only outside 10 Å radius from Co2+
52At 60 kHz MAS, signals at ~5.5 Å from Co2+ are visible
Bertini, Emsley, Luchinat et al JACS 132 5558 (2010)
Dipolar INEPT Pulse SequenceDipolar INEPT Pulse SequenceDipolar INEPT Pulse SequenceDipolar INEPT Pulse Sequence
x
Frydman et al JMR (2001)Ishii et al. JMR (2006)
53
Assignment using Dipolar INEPTAssignment using Dipolar INEPTEffective transfer-time () dependence of signal intensities
54
2D 13C/1H Correlation of Cu(Ala-Thr)Sec 3.2 Structural Measurements:Sec 3.2 Structural Measurements:Distance Measurements for Cu(AlaDistance Measurements for Cu(Ala--ThrThr))
With CP (ct = 0.5 ms)(( ))
(c) Pseudo-Contact Shift
0
(c)OH
CβH
CO2
CαH COCγH3 2.62 Å
(2.78)
Pseudo Contact Shift
fts(p
pm) 25
Ala
CβH
C H
1 H s
hif
5075
Ala
Thr
CβH3
**
*
**
*
SSNMR
200 100 0 -300 -400
100
7 Thr
CαH
SSNMR(X-ray)
Agree Well !55Exp Time ~ 30 hours
13C shifts(ppm)
[Ishii et al. JACS 2003, JMR 2006 Wickramasinghe et al JPC B 2007]
Agree Well !
Structural Information ?♦ Pseudo-Contact (Anisotropic) Shift
|11 – i | = cS(S+1)/R3 |11 iso| cS(S+1)/R♦ Paramagnetic Relaxation Time: T1
1/T1 = k S(S+1)S / {(1+I2S
2)R6}1/T1 k S(S 1)S / {(1 I S )R }
R: Metal-13C DistanceS: Electron Spin NumberS: Electron Spin NumberS: Electron Spin Correlation TimeI : 13C NMR Frequencyc, k: Known Constant
13Cm
13CR
{(T1m)/(T1
n)}1/6 = (Rm/Rn)
13CnRm
RnCu
56No Labeling Necessary !
Cu
2D 13C/1H Correlation of Cu(Ala-Thr)Distance Measurements for Cu(Ala-Thr)With CP (ct = 0.5 ms)
(c) Pseudo-Contact Shift13C T
0
(c)OH
CβH
CO2
CαH COCγH3
4.15 Å2.62 Å
2 97 Å
3.83 Å(4.19) (2.78)(3.94)
Pseudo Contact Shift
13C T1
fts(p
pm) 25
Ala
CβH
C H
3.21 Å2.97 Å
4.30 Å
Å
(2.88)(2.86)
(3.94)
1 H s
hif
5075
Ala
Thr
CβH3
**
*
**
*2.49 Å(2.76)
SSNMR
200 100 0 -300 -400
100
7 Thr
CαH
SSNMR(X-ray)
All Agree Well !57Exp Time ~ 30 hours
13C shifts(ppm)
[Wickramasinghe et al JPC B 2007 ]
All Agree Well !
13C VFMAS Characterization of Solid-State Reaction for Cu(II)(8-quinolinol)State Reaction for Cu(II)(8-quinolinol)2
Anti-cancer drugs for leukemia
α-Cu(II)Q2 β-Cu(II)Q2
210ºC/2 hours
** ********
58750 500 250 0 -250 -500
(ppm)750 500 250 0 -250 -500
(ppm)
What is the origin of the difference?What is the origin of the difference?
(a) α-form (b) β-formC
(a) α o (b) β oC
CH C
CH
CH
CCH
CH
CH
CCH
CH CH
CC
CHCH
∗ ∗ ∗∗∗
∗∗ ∗ ∗ ∗∗ ∗∗∗∗ ∗∗∗∗ Monomer
↑
59M. Shaibat, Y. Ishii et al JACS (2007)Collaboration with Dr. A. de Dios & L Casabianca at Georgetown
↑ Dimer
CuCu2+2+ as a Structural Probe via Paramagnetic as a Structural Probe via Paramagnetic Relaxation Enhancement (PRE) IRelaxation Enhancement (PRE) IRelaxation Enhancement (PRE) IRelaxation Enhancement (PRE) I
Cu2+ binding to β amyloid fibril Ishii et al. JACS 133, 3390 (2011)
Hi 13His-13Phe-20His-13
Extent of signal quenching by Cu2+ binding
61
Green: 15%Orange 15-25%Red: >25%
CuCu2+2+ as a Structural Probe via Paramagnetic as a Structural Probe via Paramagnetic Relaxation Enhancement (PRE) IIRelaxation Enhancement (PRE) IIRelaxation Enhancement (PRE) IIRelaxation Enhancement (PRE) II
Cu2+ binding to Influenza M2 protein Hong et al. JACS 134, 8693 (2012)
13C R 1 for PRE @ 400 MHzR1 ~ 3.6 x 106/(RC Cu)6 Hz, (T1e ~2.5 ns)
62
R1 3.6 x 10 /(RC-Cu) Hz, (T1e 2.5 ns)where RC-Cu is a 13C-Cu distance in Å.
Use of PCS for Paramagnetic Use of PCS for Paramagnetic MetalloMetallo--proteinsproteinsSt t l I f ti f P d t t ShiftppStructural Information from Pseudo-contact Shifts
Application to selectively 13CO-Leu, 15N-Phe, Gly labeled P450 BM-3 protein Application to uniformly
13C-labeled Co(II)-MMP
McDermott et al. JACS 127, 13816 (2005) Bertini et al .13816 (2005) Bertini et al .
JACS 129, 2219 (2007)
63
Sec 3.3 Applications to NonSec 3.3 Applications to Non--paramagnetic paramagnetic SystemsSystemsSystemsSystems
A V Simpl 30A V Simpl 30 Y Q ti n Y Q ti n A Very Simple 30A Very Simple 30--Year Question Year Question on Solidon Solid--State NMR State NMR
Most SSNMR Experiments (including 2D, 3D, 4D for Proteins)( g , , ) Time-Consuming!
Q. How are we using TIME?
11H MAS spectra of Cu(DLH MAS spectra of Cu(DL--Ala)Ala)22(a) 24 kHz
CH3 Sample: 13 mg (~50 mol), Exp time: 20 ms (4 scans)
S/N x14 Compared
CH
S/N x14, Compared with 10 kHz
S/N 800 for CH3
* * * *
S/N 800 for CH3
(c) 5 kHz
(b) 10 kHz* * * * * * Numerous Sidebands !
65100 0 -100 (ppm) Ishii et al. JACS 2005
HighHigh--Sensitivity Sensitivity 11H SSNMR for H SSNMR for Paramagnetic Systems ?Paramagnetic Systems ?
a) Cu(L-Ala) 2 Sample: 13 mg (~50 mol), Exp time: 20 ms (4 scans)CH3CH3
Sample: ~ 5 g (20 nmol) Difference Spectra
T t l E Ti 4 i
Sensitivity Compared CH
CH
Total Exp Time 4 mins
*y p
with Diamagnetic Systems x10-12 CH3
b) Cu(DL-Ala)2
CH
3
Recycle Delays Only 3 msSensitivity (T2/T1)1/2
c) DL-Ala
Solid-State NMR Analysis Possible in a Nano-Mol Scale NH3
+ Bkg +CH3
661H shift (ppm)
100 0 -100[Ishii et al. JACS 2005]
Our “GoldOur “Gold--Standard” Experiments (CP/CPMAS)Standard” Experiments (CP/CPMAS)Pines, Gibby, Waugh (1972); Schaefer et al. (1977)
CP Dec1H
CP
CP Acq13C
I 13C SSNMR f t i 95 99 % f th hi ti i~2 s ~20 ms
● In 13C SSNMR of proteins, 95-99 % of the machine time istypically consumed for recycle delays.
Q. How are we using TIME?
1313C SSNMR CPMAS Spectra of Protein C SSNMR CPMAS Spectra of Protein Microcrystals at 40 kHz MASMicrocrystals at 40 kHz MASMicrocrystals at 40 kHz MASMicrocrystals at 40 kHz MAS
Lysozyme Speed up! UbiquitinSpeed up!x 8.3 x 13.8
Ubiquitin
(d l 0 18 )(delay 0.18 s) (delay 0.18 s)
2 ho r e p 4 ho r e p
(delay 1.5 s) (delay 2.5 s)
pulse decoupling at every rotor period (rf duty ~ 10 %)
2 hour exp 4 hour expWickramasinghe et al. JMR (2007)
SolidSolid--state NMR state NMR for Ubiquitin using PACCfor Ubiquitin using PACC13C- &15N-labeled Microcrystal Sample: ~1.8 mg (210 nmol)
5.4 h Ishii et al. Nat. Methods (2009)
1 4 h1.4 h 13C-13C J decoupled in t1
New 750 MHz SSNMR@ U of I Chicago
1.3 mm SSNMR probe
New 750 MHz SSNMR DataNew 750 MHz SSNMR DataNew 750 MHz SSNMR Data New 750 MHz SSNMR Data Control (400 MHz)750 MHz Data
Distance Measurements using PRE for Distance Measurements using PRE for NonNon--paramagneticparamagnetic ProteinsProteinsp gp g
Long-range Distance Measurements for SSNMR of Proteins using
15N T1 Relaxation Data
of Proteins using Paramagnetic-tag Jaroniec et al. JACS 129 7502
(2007)Cu2+-EDTA@8
Zn-EDTA@8
(2007) Nat. Chem 4 410 (2012)
T51
RSL k/ 6
T5351
RSL1 = k/r6
T53
75
1313C PRE from CuC PRE from Cu2+2+--EDTA in EDTA in l i Al i Aββ fib ilfib ilsolution to Asolution to Aββ fibrilfibril
76
4.4. Experimental AspectsExperimental Aspects.. E p m pE p m p
• Temperature Dependence of ShiftsTemperature Dependence of Shifts Line broadening due to temperature distributiondistribution
Choose optimum spinning (T R2)
Enough VT Air & Optimize Line Shape for Standards (Cu(DL-Ala)2 & Lead Nitrate) ( ( )2 )
77
Practical Protocols to Examine Practical Protocols to Examine P ti S tP ti S tParamagnetic SystemsParamagnetic Systems
(1) 1H VFMAS(1) H VFMAS Check Line shape & 1H T1
(2) 13C Dipolar INEPT (with two values) Line shape & 13C Assignments Line shape & 13C Assignments
(3) 13C 1 pulse & Inversion recovery(3) 13C 1 pulse & Inversion recovery 13C T1 (Distances)
78(4) 2D 13C/1H correlation 1H Assignments
Selected ReferencesSelected ReferencesSelected ReferencesSelected ReferencesParamagnetic Solution NMR• I. Bertini, C. Luchinat, and G. Parigi, “Solution NMR of paramagnetic molecules”
P ti SSNMRParamagnetic SSNMR• A. Nayeem and J.P. Yesinowski, J. Chem. Phys., 1988. 89(8): p. 4600-4608. • K. Liu, D. Ryan, K. Nakanishi, and A. McDermott, J. Am. Chem. Soc., 1995. 117(26):
p. 6897-6906.• N P Wickramasinghe M Shaibat L B Casabianca A C de Dios J S Harwood and• N.P. Wickramasinghe, M. Shaibat, L.B. Casabianca, A.C. de Dios, J.S. Harwood, and
Y. Ishii, J. Chem. Phys. 2008, 128:p52210•
RelaxationRelaxation • A. Abragam, Principles of nuclear magnetism. International series of monographs.
1961, New York: Oxford University Press.• Emsley et al. J. Am. Chem. Soc. 2007. 129 14118-14119.
Biomolecular Application Solid State Nucl. Magn. Reson. 2012, 43-44:p1-
Magnetism
79
• C. Kittel “Introduction to Solid-state Physics” • C.P. Slichter, “Principles of Magnetic Resonance”
ConclusionConclusionConclusionConclusion
• Paramagnetic interactions are useful forParamagnetic interactions are useful for obtaining structural information for biomolecules!biomolecules!
• Long-range distance constraint can be obtainedobtained
• Structural analysis is possible for- Small unlabeled paramagnetic compounds - Labeled paramagnetic proteins.
80
81