moniulotteinen moniydin nmr-spektroskopia proteiinien rakennetutkimusmenetelmä
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Moniulotteinen moniydin NMR-spektroskopiaMoniulotteinen moniydin NMR-spektroskopiaProteiinien rakennetutkimusmenetelmä Proteiinien rakennetutkimusmenetelmä
)(,)(
tHidt
td
S
I
t1
t2
NMR-spektroskopian perusteetNMR-spektroskopian perusteet
M(t)
B(t)
M+(t)
t)()()(
ttdt
tdBM
M
NMR-spektroskopian teoriaa NMR-spektroskopian teoriaa
(t)
H(t)
)(,)(
tHidt
td
M+(t) Tr{ (t)F+}M+(t) Tr{ (t)F+}
M(t)
B(t)
M+(t)
)()()(
ttdt
tdBM
M t
OdotusarvoOdotusarvo
(t)
c3(t)
c1(t)c2(t)
||AA
nm
mn nmtctcA ||)()( * A
nm
mn nmtctcA ||)()( * A
nmmn mnmntctc ||||)()( * P
TiheysmatriisiTiheysmatriisi
AAA Tr |||||| nmnm
nnnmmnA
OdotusarvoOdotusarvo
Poikittainen magnetisaatioPoikittainen magnetisaatio
FM )(Tr)( tNt
K
kkyxk
K
kk iIII
11
FA M(t)
B(t)
M+(t)t
...
...
...
...
...
...
...
...
.....
.....
.....
.
.
.
AAA Tr |||||| nmnm
nnnmmnA
OdotusarvoOdotusarvo
Poikittainen magnetisaatioPoikittainen magnetisaatio
FM )(Tr)( tNt
M(t)
B(t)
M+(t)t
?)(t
Tiheysoperaattorin liikeTiheysoperaattorin liike
***||)(
mkm
kmk c
dt
dc
dt
dcc
dt
ccd
dt
mkd
dt
td
(t)
c3(t)
c1(t)c2(t)
)()(
tHdt
tdi
Schrödingerin yhtälöSchrödingerin yhtälö
nHtcndt
tdci
nn
n |)(|)(
nHktcnkdt
tdci
nn
n ||)(|)(
nHktcdt
tdci
nn
k ||)()(
knnk ,0|
Tiheysoperaattorin liikeyhtälöTiheysoperaattorin liikeyhtälö
***||)(
mkm
kmk c
dt
dc
dt
dcc
dt
ccd
dt
mkd
dt
td
nHkccimHnccin
mnn
nk |||| **
mnnHkimHnnkinn
||||||||
mHkmHki ||||
)(,,)()(
tHiHtidt
td
Liouville-von Neumann yhtälöLiouville-von Neumann yhtälö
iHtiHt eet )0()(
RatkaisuRatkaisu
HHitHidt
td )(,
)(
Liouville − von Neumann yhtälöLiouville − von Neumann yhtälö
iHtiHt ee 01
21 Ht
NK
kkk Ktbt 4,)()(
1
B
Tiheysoperaattori kantaoperaattoreinaTiheysoperaattori kantaoperaattoreina
Tiheysoperaattorin liikeTiheysoperaattorin liike
21 Ht
(t)b3(t)
b1(t)b2(t) B2
B3
B1zyx IIIE
KantaoperaattoritKantaoperaattorit
zyx SSS
zzyzxz
zyyyxy
zxyxxx
SISISI
SISISI
SISISI
222
222
222
VuorovaikutuksetVuorovaikutukset
SDISI 2ISzSzI JSIH
zzISzSzI SIJSIH 2
LiikeLiike
zzISzSzI SIJSIH 2
xzrfIe IIH 1)( tIIH rfxzI cos1 xe IH 1
)(,)(
tHidt
td re
r
tiHtiHr ee eet 0)(
VuorovaikutuksetVuorovaikutukset
SDISI 2ISzSzI JSIH
zzISzSzI SIJSIH 2
LiikeLiike
zzISzSzI SIJSIH 2
xe IH 1
)(,)(
tHidt
td re
r
tiHtiHr ee eet 0)(
tHit e sin,cos 00 iCBA ,
0
eH
0,eHi
t
rfrf-pulssi-pulssi
xe IH 1
yzx iIII ,
xI
zI
yI
t1
zI0
tItI
tIIitII
yz
zxzI
zx
11
11
sincos
sin,cos1
I
0 1
Prekessio BPrekessio B00-kentässä-kentässä
zIe IH
xyz iIII ,xI
zI
yI
1tI
yI1
11
11
sincos
sin,cos
tItI
tIIitII
IxIy
IyzIyI
yzI
I
0 1 2
t1
KytkentäKytkentä
zzIS SIJH 2
zyxzz SIiISI 2,2 xI
zzSI2
yI
J
xI2
JSIJI
JISIiJII
zyx
xzzxSIJ
xzz
sin2cos
sin,2cos2
I
0 1 2
t1
zySI2
3
S
1515N-N-11H korrelaatiokoeH korrelaatiokoe
11 sin2cos222 tSItSISISII SxzSyzyzzxz
11 sin2cos tSItI SxySx
21 coscos ttI ISx
1515N-N-11H korrelaatiospektriH korrelaatiospektri
H
N
C
CO
Gz
1515N-N-1313CC--11H korrelaatiospektriH korrelaatiospektri
Kolmiulotteinen korrelaatiospektriKolmiulotteinen korrelaatiospektri
Informaatiota kolmiulotteisesta rakenteestaInformaatiota kolmiulotteisesta rakenteestaLyhyet protoni-protoni etäisyydetLyhyet protoni-protoni etäisyydet
Informaatiota kolmiulotteisesta rakenteestaInformaatiota kolmiulotteisesta rakenteestaDiedrikulmatDiedrikulmat
Informaatiota kolmiulotteisesta rakenteestaInformaatiota kolmiulotteisesta rakenteestaSidossuunnatSidossuunnat
1H
1 5N),( ABDJ
Dd
Sidossuunntien mSidossuunntien määrittäminenäärittäminenjäännösdipolikytkennöistäjäännösdipolikytkennöistä
JJCACOCACO
JJHACAHACA
JJHACOHACO
JJHACBHACB
JJCACBCACB
JJHANHAN
JJHANHAN
Esim.Esim.
JHACO-kytkennän mittaus
C’
C
H
Gz
N
t1
t22C
zC’z
Cx
2CyC’z
JCC’
2CzC’z
Cx
2CyC’z
JCC’
t3
JCACO ja JHACO-kytkentöjen mittaus
JHACO
JCACO
H
CO
Kolmiulotteisen rakenteen määrittäminenKolmiulotteisen rakenteen määrittäminen
SASA
Rakenteettomien proteiinien rakenteistaRakenteettomien proteiinien rakenteista
““PrP Gedanken experiment”PrP Gedanken experiment”
Burns CS, et al. Biochemistry. 2002 41, 3991-4001. , Biochemistry. 2002 42, 6794-6803.
-8.0
-6.0
-4.0
-2.0
0.0
2.0
4.0
6.0
8.0
20 70 120 170 220
COCA
CACB
COHA
-50
-40
-30
-20
-10
0
10
20
30
40
50
20 40 60 80 100 120 140 160 180 200 220
HN
HACA
Simuloidut Simuloidut jjäännösdipolikytkennätäännösdipolikytkennät
How to use Residual Dipolar Couplings to How to use Residual Dipolar Couplings to study Flexible Protein Segments − A Practical study Flexible Protein Segments − A Practical
GuideGuide
0.0
5.0
10.0
15.0
20.0
0 5 10 15 20 25 30 35 40 45 50
Residue
HA
CA
xXxX
-4.0
-3.0
-2.0
-1.0
0.0
1.0
2.0
0 5 10 15 20 25 30 35 40 45 50
Residue
CA
CO
xXxX
-3.0
-2.0
-1.0
0.0
1.0
2.0
3.0
0 5 10 15 20 25 30 35 40 45 50
Residue
HA
CO
xXxX
How to use Residual Dipolar Couplings to How to use Residual Dipolar Couplings to study Flexible Protein Segments − A Practical study Flexible Protein Segments − A Practical
GuideGuide
0.0
2.04.0
6.0
8.0
10.012.0
14.0
16.0
0 5 10 15 20 25 30 35 40 45 50
Residue
HA
CA
xXxX
-4.0
-3.0
-2.0
-1.0
0.0
1.0
2.0
0 5 10 15 20 25 30 35 40 45 50
Residue
CA
CO
xXxX
-3.0
-2.0
-1.0
0.0
1.0
2.0
3.0
0 5 10 15 20 25 30 35 40 45 50
Residue
HA
CO
xXxX
Moniulotteinen moniydin NMR-spektroskopiaMoniulotteinen moniydin NMR-spektroskopiaProteiinien rakennetutkimusmenetelmä Proteiinien rakennetutkimusmenetelmä
)(,)(
tHidt
td
S
I
t1
t2
OdotusarvoOdotusarvo
M(t)
B(t)
M+(t)
t
t
Beff(t)
Moniulotteinen moniydin NMR-spektroskopiaMoniulotteinen moniydin NMR-spektroskopiaProteiinien rakennetutkimusmenetelmä Proteiinien rakennetutkimusmenetelmä
Moniulotteinen moniydin NMR-spektroskopiaMoniulotteinen moniydin NMR-spektroskopiaProteiinien rakennetutkimusmenetelmä Proteiinien rakennetutkimusmenetelmä
Shortle D. and Ackerman M.S.Persistence of native-like topology in a denatured protein in 8 M urea.
Science. 2001 293, 487-9.
RDCs = 0
RDCs 0
RDCs 0
0
5
10
1 11 21 31 41 51 61 71
Residue
D (H
z)
Sign Size Form Variation
Origin of RDCs from a flexible segmentOrigin of RDCs from a flexible segment
The elongated conformation will fit closer to the wall.The elongated conformation will fit closer to the wall.
RDCs are biased RDCs are biased towards elongated conformations!towards elongated conformations!
There is more volume for the elongated conformation.There is more volume for the elongated conformation.
Concentration of the elongated conformation is higher!Concentration of the elongated conformation is higher!
Random-flight chainRandom-flight chainA model of a denatured proteinA model of a denatured protein
z
dYWDD iii )()( 20
max
dYDD ii )(20
max
l
n
N-n
0.0
2.0
4.0
6.0
8.0
S l,zz
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
-12 -8 -4 0 4 8 12Segment
S l,zz*10-3
Glu
Pro
Gly
Calculated alignments for chainsCalculated alignments for chains
y
z
PolyGlu Terminus PolyGlu Center
Random Flight
Size Form VariationSignSign
On obstruction induced conformational changesOn obstruction induced conformational changes
Does the medium perturb the ensemble?Does the medium perturb the ensemble?
Calculation of segmental alignments Calculation of segmental alignments with and without conformational changeswith and without conformational changes
z
n
z
Without With
Expected results on the basis of calculationsExpected results on the basis of calculationsNo evidence of conformational changesNo evidence of conformational changes
0
50
100
150
200
250
300
0 10 200
50
100
150
200
250
300
0 10 20
Without
0
5
10
1 11 21 31 41 51 61 71
Residue
D (H
z)Sign Size Form Variation
0
5
10
1 11 21 31 41 51 61 71
Residue
D (H
z)Sign Size Form Variation
21-merpolyglutamate
JJCACOCACO
JJHACAHACA
JJHACOHACO
JJHACBHACBJJCACBCACB
JJHANHAN
JJHANHAN
0
5
10
1 11 21 31 41 51 61 71
Residue
D (H
z)Sign Size Form Variation
What is the source of variation in RDCs?What is the source of variation in RDCs?
-8 .0
-6 .0
-4 .0
-2 .0
0 .0
2.0
4.0
6.0
8.0
4 8 12 16 20
R es id u e
D[Hz]
HACA
COCA -8 .0
-6 .0
-4 .0
-2 .0
0 .0
2.0
4.0
6.0
8.0
4 8 12 16 20
R es id u e
D[Hz]
NH
NCO
Glu/Pro/Gly
0
5
10
1 11 21 31 41 51 61 71
Residue
D (H
z)
Sign Size Form Variation
Variation in flexibility?Variation in flexibility?
-25.0
-20.0
-15.0
-10.0
-5.0
0.0
5.0
10.0
15.0
20.0
25.0
1 6 11 16 21
Residue #
D (
HZ
)
-6.0
-4.0
-2.0
0.0
2.0
4.0
6.0
D (
Hz)
Glu Glu
Asp
SerCys
Glu Asp
Glu
Cys
Ser
What is the source of variation in RDCs?What is the source of variation in RDCs?
Variation in amino acid orientations?Variation in amino acid orientations?
-10.0
-5.0
0.0
5.0
10.0
15.0
1 6 11 16 21
Residue #
D (
HZ
)
-2.0
-1.0
0.0
1.0
2.0
3.0
D (
Hz)
-12.5
-7.5
-2.5
2.5
7.5
12.5
1 6 11 16 21
Residue #
D (
Hz)
-3.0
-2.0
-1.0
0.0
1.0
2.0
3.0
D (
Hz)
Glu Glu
Asp
SerCys
Glu Asp
Glu
Cys
Ser
0
5
10
1 11 21 31 41 51 61 71
Residue
D (H
z)
Sign Size Form Variation
What is the source of variation in RDCs?What is the source of variation in RDCs?
Variation in amino acid orientations?
2x
-25.0
-20.0
-15.0
-10.0
-5.0
0.0
5.0
10.0
15.0
20.0
25.0
1 6 11 16 21
Residue #
D (
HZ
)
-6.0
-4.0
-2.0
0.0
2.0
4.0
6.0
D (
Hz)
Glu Asp
Glu
Cys
Ser
Glu
Glu
Asp
SerCys
What is the source of variation in RDCs?What is the source of variation in RDCs?
Variation due to local structures?Variation due to local structures?
0
5
10
1 11 21 31 41 51 61 71
Residue
D (H
z)
Sign Size Form Variation
low pH
0
5
10
1 11 21 31 41 51 61 71
Residue
D (H
z)
Sign Size Form Variation
Glu
Glu
Asp
Ser
Cys
What is the source of variation in RDCs?What is the source of variation in RDCs?
Variation due to motifs?Variation due to motifs?
-25.0
-20.0
-15.0
-10.0
-5.0
0.0
5.0
10.0
15.0
20.0
25.0
1 6 11 16 21
Residue #
D (
Hz)
-6.0
-4.0
-2.0
0.0
2.0
4.0
6.0
D (
Hz)
Glu
Asp
Glu
Cys
Ser
-12.5
-7.5
-2.5
2.5
7.5
12.5
1 6 11 16 21
Residue #
D (
Hz)
-3.0
-2.0
-1.0
0.0
1.0
2.0
3.0
D (
Hz)
0
5
10
1 11 21 31 41 51 61 71
Residue
D (H
z)
Sign Size Form Variation
0 5 10 15 20
What about electrostatics?What about electrostatics?
Repulsion
What about electrostatics?What about electrostatics?
Attraction
Repulsion
0 5 10 15 20
What about electrostatics?What about electrostatics?
Attraction
0 5 10 15 20
Uniform RDCs are Uniform RDCs are characteristics of a random coil.characteristics of a random coil.
SummarySummary
Good part of variation in RDCsGood part of variation in RDCs stems stems from the variation in amino acid sequence.from the variation in amino acid sequence.
Large variation in RDCsLarge variation in RDCs and increase increase in local alignment indicate local structure.in local alignment indicate local structure.
Long tail may compromise refinement of a core.Long tail may compromise refinement of a core.
ColleaguesColleagues
The study has been supported byThe study has been supported by
the Academy Finland and Technology Agency of Finland the Academy Finland and Technology Agency of Finland (TEKES)(TEKES)
Kai FredrikssonKai Fredriksson
Martti LouhivuoriMartti Louhivuori
Kimmo PKimmo Pääääkkkköönennen
Perttu PermiPerttu Permi
Peter WPeter Wüürtzrtz
PALES by Markus Zweckstetter, PALES by Markus Zweckstetter, Gerd Hummer, Ad BaxGerd Hummer, Ad Bax
CYANA by Peter GüntertCYANA by Peter Güntert
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