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