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Brock University Neutrons for Biology – 1 / 74

Neutron scattering for biologyApplications in membrane biophysics

Thad HarrounCanadian Neutron Beam Centre

28 September, 2005

Outline


■ Some important properties of neutrons.■ How do neutrons interact with matter?■ How are neutrons “made”?■ Survey of neutron scattering experiments in membrane biophysics.

Properties of neutrons

Properties ofneutrons


■ Mechanical

◆ Mass◆ Angular momentum◆ . . .

■ Electrical

◆ Charge◆ Magnetic dipole moment◆ Electric dipole moment◆ . . .

■ Nuclear

◆ Free lifetime◆ Decay modes◆ Intrinsic Parity, P◆ Isospin, I◆ Baryon number, B◆ Strangeness, S◆ . . .

Mass



The mass of the neutron is Mn = 1.008 664 915 60(55) atomicmass units.

Note that Mn > Mp + Me, which makes beta decay possible.[Mn 939.565 MeV - Mp 938.272 MeV - Me 0.510 MeV = 0.782 MeV]

The reaction n → p + e + νe is the prototype for essentially allnaturally occurring radioactivity.

The lifetime of free neutron is about 15 minutes.

Electric and magnetic moments



Since the neutron has internal charge and distribution due to thequarks, in principle it can have various electric/magneticmoments, but:

■ The total charge is zero.■ Magnetic dipole moment = -0.966 x 10−26 J T−1

■ Spin = 12

Energy and wavelength



A neutron traveling at velocity v has a wavelength ofλ = h/(mv), where h is Planck’s constant, m is the neutronmass, and has a kinetic energy E = 1

2mv2.

The neutron’s momentum is given by ~p = m~v = h̄~k, and|~k| = 2πλ

Elastic scattering

Interactions ofneutrons


Neutrons that scatter undergo a change in momemtum,~q = ~k0 − ~k1.

k0 k1

d

θθ

Bragg scattering



If |~q| = 2πd =4π sin θ

λ , we get constructive interference in thedirection θ.

k0 k1

d

θθ

q

k0

k1 2πd

θ

θ

X-ray interactions with matter



X-rays scatter from the electrons in the electron cloud. Since thecloud fills most of the atom volume, the source of the scatteredwaves are “fuzzy”.

Neutron interaction with matter - 1



Nuclear dimensions ∼ 10−15m, a pin-point compared to thetypical neutron wavelength, ∼ 10−10m. For neutrons, materialsare mostly empty space.

Neutron interaction with matter - 2



There is also the interaction between unpaired electron spins inmagnetic materials and the neutron magnetic moment. Notmuch use in biology!

Scattering length



Neutron-atom interactions are due to the short range nuclearstrong force. The neutron interacts only within an effectiveimpact radius b ∼ Rn + RA.

A

n

“cross section”Effective

b has the units of length and ∼ 10−12cm.

Scattering cross section



We measure the differential cross section, defined as

dσ

dΩ=

neutrons s−1 scattered into dΩ

flux dΩ= |b2|

Neutrons

Sample

Detector

dΩ

The total cross section is then σ =∫

(dσdΩ)dΩ = 4πb2.

(1 barn = 10−24 cm2)

Scattering length



So, what is this value b? It is a measure of the ability of an atomto scatter neutrons.

It is a characteristic of every isotope of every element, that mustbe determined empirically.

X-ray scattering length


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

1

H0.282

2

He0.564

3

Li0.846

4

Be1.128

5

B1.41

6

C1.692

7

N1.974

8

O2.256

9

F2.538

10

Ne2.82

11

Na3.102

12

Mg3.384

13

Al3.666

14

Si3.948

15

P4.23

16

S4.512

17

Cl4.794

18

Ar5.076

19

K5.358

20

Ca5.64

21

Sc5.922

22

Ti6.204

23

V6.486

24

Cr6.768

25

Mn7.05

26

Fe7.332

27

Co7.614

28

Ni7.896

29

Cu8.178

30

Zn8.46

31

Ga8.742

32

Ge9.024

33

As9.306

34

Se9.588

35

Br9.87

36

Kr10.152

37

Rb10.434

38

Sr10.716

39

Y10.998

40

Zr11.28

41

Nb11.562

42

Mo11.844

43

Tc12.126

44

Ru12.408

45

Rh12.69

46

Pd12.972

47

Ag13.254

48

Cd13.536

49

In13.818

50

Sn14.1

51

Sb14.382

52

Te14.664

53

I14.946

54

Xe15.228

55

Cs15.51

56

Ba15.792

57

La16.074

72

Hf20.304

73

Ta20.586

74

W20.868

75

Re21.15

76

Os21.432

77

Ir21.714

78

Pt21.996

79

Au22.278

80

Hg22.56

81

Tl22.842

82

Pb23.124

83

Bi23.406

84

Po23.688

85

At23.97

86

Rn24.252

87

Fr24.534

88

Ra24.816

89

Ac25.098

58

Ce16.356

59

Pr16.638

60

Nd16.92

61

Pm17.202

62

Sm17.484

63

Eu17.766

64

Gd18.048

65

Tb18.33

66

Dy18.612

67

Ho18.894

68

Er19.176

69

Tm19.458

70

Yb19.74

71

Lu20.022

90

Th25.38

91

Pa25.662

92

U25.944

93

Np26.226

94

Pu26.508

95

Am26.79

96

Cm27.072

bX−ray = Z × re = Z × 0.2382 × 10−12 cm

Neutron scattering length


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

1

H−3.739

2

He3.26

3

Li−1.9

4

Be7.79

5

B5.3

6

C6.646

7

N9.36

8

O5.803

9

F5.654

10

Ne4.566

11

Na3.63

12

Mg5.375

13

Al3.449

14

Si4.1491

15

P5.13

16

S2.847

17

Cl9.577

18

Ar1.909

19

K3.67

20

Ca4.7

21

Sc12.29

22

Ti−3.438

23

V−0.3824

24

Cr3.635

25

Mn−3.73

26

Fe9.45

27

Co2.49

28

Ni10.3

29

Cu7.718

30

Zn5.68

31

Ga7.288

32

Ge8.185

33

As6.58

34

Se7.97

35

Br6.795

36

Kr7.81

37

Rb7.09

38

Sr7.02

39

Y7.75

40

Zr7.16

41

Nb7.054

42

Mo6.715

43

Tc6.8

44

Ru7.03

45

Rh5.88

46

Pd5.91

47

Ag5.922

48

Cd4.87

49

In4.065

50

Sn6.225

51

Sb5.57

52

Te5.8

53

I5.28

54

Xe4.92

55

Cs5.42

56

Ba5.07

57

La8.24

72

Hf7.7

73

Ta6.91

74

W4.86

75

Re9.2

76

Os10.7

77

Ir10.6

78

Pt9.6

79

Au7.63

80

Hg12.692

81

Tl8.776

82

Pb9.405

83

Bi8.532

84

Po0

85

At0

86

Rn0

87

Fr0

88

Ra10

89

Ac0

58

Ce4.84

59

Pr4.58

60

Nd7.69

61

Pm12.6

62

Sm0.8

63

Eu7.22

64

Gd6.5

65

Tb7.38

66

Dy16.9

67

Ho8.01

68

Er7.79

69

Tm7.07

70

Yb12.43

71

Lu7.21

90

Th10.31

91

Pa9.1

92

U8.417

93

Np10.55

94

Pu0

95

Am8.3

96

Cm0

Incoherent scattering and absorption



1. Neutron-nucleus system has two spin states: I ± 12, with two

scattering lengths: b+, b−.Thermally averaged scattering length

〈b〉 =1

2I + 1

[

(I + 1) b+ + Ib−]

〈

b2〉

=1

2I + 1

[

(I + 1) (b+)2 + I(b−)2]

,

σcoherent = 4π 〈b〉2. σtotal = 4π

〈

b2〉

.σtotal − σcoherent = σincoherent.

2. Neutron capture by the nucleus σabsorption.

X-ray scattering cross section


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

1

H0.655

2

He1.94

3

Li5.76

4

Be16.6

5

B41.5

6

C89.9

7

N173

8

O304

9

F498

10

Ne768

11

Na1140

12

Mg1610

13

Al2220

14

Si2970

15

P3880

16

S4970

17

Cl6240

18

Ar7720

19

K9400

20

Ca11300

21

Sc13500

22

Ti15900

23

V18500

24

Cr21300

25

Mn24600

26

Fe28000

27

Co31400

28

Ni4760

29

Cu5470

30

Zn6290

31

Ga7190

32

Ge8190

33

As9290

34

Se10500

35

Br11800

36

Kr13200

37

Rb14800

38

Sr16500

39

Y18300

40

Zr20300

41

Nb22300

42

Mo24600

43

Tc27000

44

Ru29500

45

Rh32300

46

Pd35200

47

Ag38200

48

Cd41500

49

In45000

50

Sn48600

51

Sb52500

52

Te56500

53

I60700

54

Xe65200

55

Cs70000

56

Ba75000

57

La80300

72

Hf46000

73

Ta48500

74

W51300

75

Re57200

76

Os58000

77

Ir62400

78

Pt63400

79

Au66900

80

Hg66800

81

Tl111000

82

Pb117000

83

Bi123000

84

Po129000

85

At126000

86

Rn143000

87

Fr149000

88

Ra149000

89

Ac174000

58

Ce85700

59

Pr91200

60

Nd96800

61

Pm102000

62

Sm108000

63

Eu110000

64

Gd105000

65

Tb84700

66

Dy97700

67

Ho34700

68

Er36700

69

Tm39300

70

Yb41000

71

Lu45000

90

Th172000

91

Pa153000

92

U161000

93

Np169000

94

Pu165000

95

Am181000

96

Cm179000

Neutron total cross section


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

1

H82.3526

2

He1.34747

3

Li71.87

4

Be7.6376

5

B772.24

6

C5.5545

7

N13.41

8

O4.23219

9

F4.0276

10

Ne2.667

11

Na3.81

12

Mg3.773

13

Al1.734

14

Si2.338

15

P3.484

16

S1.556

17

Cl50.3

18

Ar1.358

19

K4.06

20

Ca3.26

21

Sc51

22

Ti10.44

23

V10.18

24

Cr6.54

25

Mn15.45

26

Fe14.18

27

Co42.78

28

Ni22.99

29

Cu11.81

30

Zn5.241

31

Ga9.58

32

Ge10.8

33

As10

34

Se20

35

Br12.8

36

Kr7.68

37

Rb7.18

38

Sr7.53

39

Y8.98

40

Zr6.645

41

Nb7.405

42

Mo8.19

43

Tc26.3

44

Ru9.16

45

Rh149.4

46

Pd11.38

47

Ag68.29

48

Cd2526.5

49

In196.42

50

Sn5.518

51

Sb8.81

52

Te9.02

53

I9.96

54

Xe23.9

55

Cs32.9

56

Ba4.48

57

La18.63

72

Hf114.3

73

Ta26.61

74

W22.9

75

Re101.2

76

Os30.7

77

Ir439

78

Pt22.01

79

Au106.4

80

Hg399.1

81

Tl13.32

82

Pb11.289

83

Bi9.1898

84

Po0

85

At0

86

Rn12.6

87

Fr0

88

Ra25.8

89

Ac0

58

Ce3.57

59

Pr14.16

60

Nd67.1

61

Pm189.7

62

Sm5961

63

Eu4539.2

64

Gd49880

65

Tb30.24

66

Dy1084.3

67

Ho73.12

68

Er167.7

69

Tm106.38

70

Yb58.2

71

Lu81.2

90

Th20.73

91

Pa211.1

92

U16.478

93

Np190.4

94

Pu0

95

Am84.3

96

Cm0

The penetrating power of neutrons



Neutron sources

Neutron sources


Where can you get neutrons?

Recall that free neutrons have a half-life of about 15 mins.

There are lots of “stored” neutrons in the very heavy elements.

Reactor sources

Neutron sources


CNBC, Chalk River, Ontario

Neutron sources


Fission production

Neutron sources


235U(92p + 143n) + n → X + Y + 2.5n + Q

■ X,Y are nuclei with atomic mass ∼ 95 - 140 u■ ∼ 2.5n per fission■ Q ∼ 210 MeV per fission released

Reactor sources

Neutron sources


CORE

WARM WATER

TO HEAT

EXCHANGERS

COOL WATER

FROM PUMPS

BEAM

TUBES

STEEL

SHIELDING

CONCRETE

SHIELDING

DECK PLATE

MAIN

FLOOR

10 m

9 m

NEUTRONS

n(v) = 4√π

(

m2kBT

)3/2v2 exp

(

− mv2

2kBT

)

Neutron energies

Neutron sources


0

10

20

30

40

50

100 1000

Neutron velocity (m/s)

5 K50 K

300 K

0.0001 0.001 0.01 0.1

Neutron energy (eV)

1 10

Neutron wavelength (Å)

NRU spectrometers

Neutron sources


NIST, Gaithersberg, Maryland

Neutron sources


Spallation sources

Neutron sources


ISIS, Oxford, U.K.

Neutron sources


SNS, Oak Ridge, Tennesse

Neutron sources


Neutron flux

Neutron sources


X-ray synchrotron flux ∼ 1013 − 1015 photons/mm2-sec-1% spectrum

Neutrons and biology

Neutrons andbiology


Bound Atom Scattering Lengths and Cross Sections for Typical Elements in

Biomaterials

Atom Nucleus bc σc σi σabs* f

(10−12 cm) (10−24 cm2) (10−24 cm2) (10−24 cm2) (

Hydrogen 1H -0.374 1.76 79.7 0.33 0.28Deuterium 2H 0.667 5.59 2.01 0 0.28Carbon 12C 0.665 5.56 0 0 1.69Nitrogen 14N 0.930 11.1 0 1.88 1.97Oxygen 16O 0.580 4.23 0 0 2.25Fluorine 19F 0.556 4.03 0 0 2.53

Phosphorous P† 0.513 3.31 0 0.17 4.22

Chlorine Cl† 0.958 11.53 5.9 33.6 4.74

The structure of membrane lipids

Neutrons andbiology


Hydrogen/Deuterium contrast

Neutrons andbiology


0

0.02

0.04

0.06

0 20 40 60 80 100

ρ (1

0−12

cm

Å−

3 )

% D2O

Water

RNA

Protein

Lipid head group

CH2

The structure of membrane lipids

Neutrons andmembranebiophysics


The cell membrane



Composition of cell membranes.



Membrane Protein (%) Lipid (%) Carbohydrate (%)Myelin 18 79 3Human erythrocyte plasma membrane 49 43 8Amoeba plasma membrane 54 42 4Mycoplasma cell membrane 58 37 1.5Halobacterium purple membrane 75 25 0

Lipid bilayers



Sample preparation - 1



Incident Diffracted

d

2q

q

Si Substrate

Sample preparation - 2



Experimental data



hq = hd =2h sin θ

λ

I ∝ |F (q)|2 = |∑

bi exp(−iqzi)|2

100

1000

0 2 4 6 8 10 12 14 16 18

Neu

tron

cou

nts

2θ (°)

Data analysis



ρ(z) = ρ0 +hmax∑

h=1

Fh cos(2πhz/d)

−0.01

−0.005

0

0.005

0.01

0.015

0.02

−30 −20 −10 0 10 20 30

Sca

tterin

g Le

ngth

Den

sity

(ar

b. u

nits

)

z (Å)

DMPC−d3DMPC

−0.005

0

0.005

0.01

0.015

0.02

0.025

−30 −20 −10 0 10 20 30

Sca

tterin

g Le

ngth

Den

sity

(ar

b. u

nits

)

DMPC−d3 Label

Area 0.077Width 4.2 Center 0.0

Label distributionFit

Deuterium labelling



ρ(z) = ρ0 +hmax∑

h=1

(

FDh − FHh

)

cos(2πhz/d)

−0.01

−0.005

0

0.005

0.01

0.015

0.02

−30 −20 −10 0 10 20 30

Sca

tterin

g Le

ngth

Den

sity

(ar

b. u

nits

)

z (Å)

DMPC−d3DMPC

−0.005

0

0.005

0.01

0.015

0.02

0.025

−30 −20 −10 0 10 20 30

Sca

tterin

g Le

ngth

Den

sity

(ar

b. u

nits

)

DMPC−d3 Label

Area 0.077Width 4.2 Center 0.0

Label distributionFit

cholesterol in polyunsaturated lipids



0

0.02

0.04

0.06

0.08

−30 −20 −10 0 10 20 30

Distance from bilayer center (Å)

20:4−20:4 PC

0

0.02

0.04

0.06

Net

uron

sca

tteri

ng le

ngth

den

sity

(x1

0−7

Å−2

)

18:0−20:4 PC

0

0.02

0.04

0.06 18:1−18:1 PC

0

0.02

0.04

0.0616:0−18:1 PC

Center of bilayer

Headgroup

Water

Acyl chain

A B C

Labelling membrane bound proteins



Finding amino acids in the bilayer



−0.02

0.02

0.06

0.1

0.14

0 5 10 15 20 25

Labe

l Pro

file

Phe4DifferenceGauss fit

0 5 10 15 20 25

z (°)

Phe8

0 5 10 15 20 25

Phe12

We see the time-averaged fluctuation amplitude for each residuethat was deuterium labeled.

Protein structure modeling



X

Y

Z

Combined with a model of protein structure, determining theorientation is a simple problem of geometry.

Protein structure modeling



Insights into the protein’s behavior while part of the membranecan be gained through modeling the data.



The mesh represents the interface between the membrane and the

water.

Slightly different structures have very different orientations,which are clues to the protein’s function.

Small angle scattering



Recall Bragg’s law: q = 4πλ sin θ =2πd

The angles at which neutrons are diffracted scales inversely withthe size of the scattering object:2θ ∼ λd

To probe the shape and size of objects on the length scales of60∼1000 Å, then 2θ = 0.3◦ ∼ 5◦ (λ =10 Å).

We are no longer on the atomic scale. Consider the sample as a

continuum of scattering density.

Instead of bi for each atom i, consider b(~r).

Small angle scattering



The neutron scattering from variations in b(~r) depends on twoterms:

■ F (q) depends on the shape of the scattering objects■ S(q) depends on the distribution of the objects

Solvent

Object

b(r)

Membrane pore formation



Antimicrobial proteins work by forming pores in the membrane,which causes cell death.How big are these pores? What is their lateral density?

In-plane diffraction



The theory is drawn from liquid scattering, only this liquid is 2D.It accounts for pore size and correlations intra- and inter-bilayer.

q = qr r̂ + qz ẑ

I(qz,qr) = N | F (qz,qr) |2 S(qz,qr)

S(qz,qr) = S00(qr) + 2 cos(qzD)S01(qr) + ...

S0m(qr) = δ0m +

∫

(n0m(r) − n̄)J0(qr)2πrdr




Mellitin pores detected by off-plane diffraction.




Melittin pores can semi-crystallize into a 3D lattice.

AFMnet: potential drug delivery



Bicellar mixtures



It is currently thought that mixtures of long and short chain lipidsform a liquid crystalline phase of bicelles - bilayered micelles.

Isotropic bicelles


10-1

100

101

102

103

104

I (a

rbitr

ary

unit)

5 60.01

2 3 4 5 60.1

2 3

q (Å-1

)

35 oC

10 oC

55 oC

45 oC

q-1

Chiral nematic ribbons


10-1

100

101

102

103

104

I (a

rbitr

ary

unit)

5 60.01

2 3 4 5 60.1

2 3

q (Å-1

)

35 oC

10 oC

55 oC

45 oC

q-1

Chiral nematic ribbons



Multilamellar vesicles


10-1

100

101

102

103

104

I (a

rbitr

ary

unit)

5 60.01

2 3 4 5 60.1

2 3

q (Å-1

)

35 oC

10 oC

55 oC

45 oC

q-1

Multilamellar vesicles



Smectic lamellae


10-1

100

101

102

103

104

I (a

rbitr

ary

unit)

5 60.01

2 3 4 5 60.1

2 3

q (Å-1

)

35 oC

10 oC

55 oC

45 oC

q-1

Smectic lamellae



Liposomes


10-2

10-1

100

101

102

103

104

I (ar

bitr

ary

unit)

4 6 80.01

2 4 6 80.1

2

q (Å-1

)

0.1 wt%10

oC

45 oC

10 oC

Acknowledgments



■ NPMR NRC Chalk River, Canada■ AFMnet, University of Gueplh

◆ John Katsaras◆ Mu-Ping Nieh◆ Jeremy Pencer◆ Staecie Institute of Molecular Sciences

■ University of Edinburgh, Scotland, U.K.

◆ Jeremy Bradshaw◆ Richard Ashley◆ Malcolm Darkes◆ Sarah Davies◆ Biotechnology and Biological Sciences Research Council◆ Welcome Trust

■ Rice University, Houston, Texas

◆ Huey W. Huang◆ William Heller◆ Lin Yang◆ NIH - Houston Molecular Biophysics Program

OutlineProperties of neutronsProperties of neutronsMassElectric and magnetic momentsEnergy and wavelength

Interactions of neutronsElastic scatteringBragg scatteringX-ray interactions with matterNeutron interaction with matter - 1Neutron interaction with matter - 2Scattering lengthScattering cross sectionScattering lengthX-ray scattering lengthNeutron scattering lengthIncoherent scattering and absorptionX-ray scattering cross sectionNeutron total cross sectionThe penetrating power of neutronsThe penetrating power of neutrons

Neutron sourcesNeutron sourcesReactor sourcesCNBC, Chalk River, OntarioFission productionReactor sourcesNeutron energiesNRU spectrometersNRU spectrometersNRU spectrometersNRU spectrometersNIST, Gaithersberg, MarylandNIST, Gaithersberg, MarylandSpallation sourcesISIS, Oxford, U.K.ISIS, Oxford, U.K.SNS, Oak Ridge, TennesseNeutron flux

Neutrons and biologyNeutrons and biologyThe structure of membrane lipidsHydrogen/Deuterium contrast

Neutrons and membrane biophysicsThe structure of membrane lipidsThe cell membraneComposition of cell membranes.Lipid bilayersSample preparation - 1Sample preparation - 2Experimental dataData analysisDeuterium labellingcholesterol in polyunsaturated lipidsLabelling membrane bound proteinsFinding amino acids in the bilayerProtein structure modelingProtein structure modelingSmall angle scatteringSmall angle scatteringMembrane pore formationIn-plane diffractionIn-plane diffractionIn-plane diffractionIn-plane diffractionAFMnet: potential drug deliveryBicellar mixturesIsotropic bicellesChiral nematic ribbonsChiral nematic ribbonsMultilamellar vesiclesMultilamellar vesiclesSmectic lamellaeSmectic lamellaeLiposomesAcknowledgments

neutron scattering for biology applications in membrane ...tharroun/docs/talk.pdf · kr 7.81 37 rb...

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