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The Basics of Neutron Scattering Jill Trewhella, The University of Sydney EMBO Global Exchange Lecture Course April 28, 2011.

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Presentation on theme: "The Basics of Neutron Scattering Jill Trewhella, The University of Sydney EMBO Global Exchange Lecture Course April 28, 2011."— Presentation transcript:

1 The Basics of Neutron Scattering Jill Trewhella, The University of Sydney EMBO Global Exchange Lecture Course April 28, 2011

2 Conceptual diagram of the small-angle scattering experiment The conceptual experiment and theory is the same for X-rays and neutrons, the differences are the physics of the X-ray (electro-magnetic radiation) versus neutron (neutral particle) interactions with matter. Measurement is of the coherent (in phase) scattering from the sample. Incoherent scattering gives and constant background. [Note: q = 2  s]

3 Fundamentals   Neutrons have zero charge and negligible electric dipole and therefore interact with matter via nuclear forces   Nuclear forces are very short range (a few fermis, where 1 fermi = m) and the sizes of nuclei are typically 100,000 smaller than the distances between them.   Neutrons can therefore travel long distances in material without being scattered or absorbed, i.e. they are and highly penetrating (to depths of m).   Example: attenuation of low energy neutrons by Al is ~1%/mm compared to >99%/mm for x-rays

4 Neutrons are particles that have properties of plane waves They have amplitude and phase

5 They can be scattered elastically or inelastically Inelastic scattering changes both direction and magnitude of the neutron wave vector Elastic scattering changes direction but not the magnitude of the wave vector

6 It is the elastic, coherent scattering of neutrons that gives rise to small-angle scattering

7 Coherent scattering is “in phase” and thus can contribute to small-angle scattering. Incoherent scattering is isotropic and in a small-angle scattering experiment and thus contributes to the background signal and degrades signal to noise. Coherent scattering essentially describes the scattering of a single neutron from all the nuclei in a sample Incoherent scattering involves correlations between the position of an atom at time 0 and the same atom at time t

8 The neutron scattering power of an atom is given as b in units of length Circular wave scattered by nucleus at the origin is: (-b/r)e ikr b is the scattering length of the nucleus and measures the strength of the neutron-nucleus interaction. The scattering cross section  = 4πb 2..as if b were the radius of the nucleus as seen by the neutron.

9   For some nuclei, b depends upon the energy of the incident neutrons because compound nuclei with energies close to those of excited nuclear states are formed during the scattering process.   This resonance phenomenon gives rise to imaginary components of b. The real part of b gives rise to scattering, the imaginary part to absorption.   b has to be determined experimentally for each nucleus and cannot be calculated reliably from fundamental constants.

10 Neutron scattering lengths for isotopes of the same element can have very different neutron scattering properties

11 As nuclei are point scattering centers, neutron scattering lengths show no angular dependence

12 At very short wavelengths and low q, the X-ray coherent scattering cross-section of an atom with Z electrons is 4π(Zr 0 ) 2, where r 0 = e 2 /m e c 2 = 0.28 x cm. AtomNucleus ( cm) f x-ray for  = 0 in electrons (and in units of cm) a Hydrogen 1H1H (0.28) Deuterium 2H2H (0.28) Carbon 12 C (1.69) Nitrogen 14 N (1.97) Oxygen 16 O (2.25) Phosphorous 31 P (4.23) SulfurMostly 32 S (4.5) b values for nuclei typically found in bio-molecules

13 Scattering Length Density  The average scattering length density  for a particle is simply the sum of the scattering lengths (b)/unit volume

14 The basic scattering equation  For an ensemble of identical, randomly oriented particles, the intensity of coherently, elastically scattered radiation is dependant only upon the magnitude of q, and can be expressed as: N = molecules/unit volume V = molecular volume = contrast, the scattering density difference = contrast, the scattering density difference between the scattering particle and solvent between the scattering particle and solvent P(q) = form factor  particle shape S(q) = structure factor  inter-particle correlation distances

15 Inter-particle distance correlations between charged molecules D D D D D D - D - D ….. gives a non-unity S(q) term that is concentration dependent

16 I(q) =   |  e -i(qr) dr]| 2  where  =  particle -  solvent Average scattering length density  is simply the of the sum of the scattering lengths (b)/unit volume Because H ( 1 H) and D ( 2 H) have different signs, by manipulating the H/D ratio in a molecule and/or its solvent one can vary the contrast  Zero contrast = no small-angle scattering _ _ _ _ _ _ For a single particle in solution (i.e. S(q) = 1):

17  P(r) is calculated as the inverse Fourier transform of I(q) and yields the probable frequency of inter- atomic distances within the scattering particle. Svergun, D. I. & Koch, M. H. J. (2003). Small-angle scattering studies of biological macromolecules in solution. Rep. Prog. Phys. 66, P(r) provides a real space interpretation of I(q)

18 Contrast (or solvent) Matching  Solvent matching (i.e. matching the scattering density of a molecule with the solvent) facilitates study of on component by rendering another “invisible.”

19 Optical Contrast Matching Example

20 Using small-angle X-ray scattering we showed that the N-terminal domains of cardiac myosin binding protein C (C0C2) form an extended modular structure with a defined disposition of the modules Jeffries, Whitten et al. (2008)J. Mol. Biol. 377,

21 Mixing mono- disperse solutions of C0C2 with G actin results in a dramatic increase in scattering signal due to the formation of a large, rod-shaped assembly

22 Neutron contrast variation on actin thin- filaments with deuterated the C002 stabilizes F-actin filaments

23 Solvent matching for the C0C2-actin assembly Whitten, Jeffries, Harris, Trewhella (2008) Proc Natl Acad Sci USA 105,

24 Contrast Variation   To determine the shapes and dispositions of labeled and unlabelled components in a complex

25 For a complex of H- and D-proteins:  H(D) (=  H(D)protein -  solvent ) is the mean contrast of the H and D components, I DP, I HP their scattering profiles, and I crs is the cross term that contains information about their relative positions. The contrast terms can be calculated from the chemical composition, so one can solve for I D, I H, and I HD. __ I1I1I1I1 I 12 I2I2I2I2

26 Contrast Variation Experiment   Measure I(q) for a complex of labelled and unlabelled proteins in different concentrations of D 2 O References: Whitten, A. E., Cai, S., and Trewhella, J. “MULCh: ­ModULes for the Analysis of Small-angle Neutron Contrast Variation Data from Biomolecular Complexes,” J. Appl. Cryst. 41, , Whitten, A. E. and Trewhella, J. “Small-Angle Scattering and Neutron Contrast Variation for Studying Bio-molecular Complexes,” Microfluids, Nanotechnologies, and Physical Chemistry (Science) in Separation, Detection, and Analysis of Biomolecules, Methods in Molecular Biology Series, James W. Lee Ed., Human Press, USA, Volume 544, pp307-23, for reprint

27 Use Rg values for Sturhman analysis R H = Å R D = 25.3 Å D = 27.0 Å

28 Stuhrmann showed that the observed R g for a scattering object with internal density fluctuations can be expressed as a quadratice function of the contrast  : where R m is the R g at infinite contrast,  the second moment of the internal density fluctuations within the scattering object, and  is a measure of the displacement of the scattering length distribution with contrast _

29   zero  implies a homogeneous scattering particle   positive  implies the higher scattering density is on average more toward the outside of the particle   negative  places the higher scattering density is on average more toward the inside of the particle

30 For a two component system in which the difference in scattering density between the two components is large enough, the Stuhhmann relationship can provide information on the R g values for the individual components and their separation using the following relationships:

31 Each experimental scattering profile of a contrast series can be approximated by:  H(D) (=  H(D)protein -  solvent ) is the mean contrast of the H and D components, I DP, I HP their scattering profiles, and I crs is the cross term that contains information about their relative positions. The contrast terms can be calculated from the chemical composition, so one can solve for I D, I H, and I HD. __

32 Solve the resulting simultaneous equations for I(q) H, I(q) D, I(q) HD I1I1I1I1 I 12 I2I2I2I2

33 Use ab initio shape determination or rigid body refinement of the components against the scattering data if you have coordinates

34 The sensor histidine kinase KinA - response regulator spo0A in Bacillus subtilis Sda KinA Spo0A KipA KipI Failure to initiate DNA replication DNA damage Change in N 2 source Sporulation Spo0F Spo0B Environmental signal

35 Our molecular actors KipI Pyrococcus horikoshi Sda KinA Based on H853 Thermotoga maritima Pro 410 His 405 Trp CA DHp to sensor domains

36 Sda 2 R g = 15.4 Å, d max = 55 Å KinA 2 R g = 29.6 Å, d max = 95 Å KinA 2 -Sda 2 R g = 29.1 Å, d max = 80 Å HK853 based KinA model predicts the KinA X-ray scattering data KinA 2 contracts upon binding 2 Sda molecules

37 Sda is a trimer in solution! Jacques, et al “Crystal Structure of the Sporulation Histidine Kinase Inhibitor Sda from Bacillus subtilis – Implications for the Solution State of Sda,” Acta D65, , 2009.

38 KipI dimerizes via its N-terminal domains and 2 KipI molecules bind KinA 2 KipI 2 R g = 31.3 Å, d max = 100 Å KinA 2 R g = 29.6 Å, d max = 80 Å KinA 2 -2KipI R g = 33.4 Å, d max = 100 Å

39 Neutron contrast variation: KinA 2 :2 D Sda in complexuncomplexed R g KinA Å29.6 Å R g 2Sda 25.3 Å15.4 Å Separation of centres of mass = 27.0 Å I(Q) A -1

40 MONSA: 3D shape restoration for KinA 2 :2 D Sda

41 Component analysis

42 Rigid-body refinement KinA 2 -2Sda components Whitten, Jacques, Langely et al., J. Mol.Biol. 368, 407,  I(Q) A -1

43 KinA 2 -2KipI Jacques, Langely, Jeffries et al (2008) J. Mol.Biol. 384, 

44 The KinA helix containing Pro 410 sits in the KipI- C domain hydrophobic groove

45 A possible role for cis-trans isomerization of Pro 410 in tightening the helical bundle to transmit the KipI signal to the catalytic domains? Or is the KipI cyclophilin-like domain simply a proline binder?

46 Sda and KipI bind at the base of the KinA dimerization phosphotransfer (DHp) domain Sda binding does not appear to provide for steric mechanism of inhibition KipI interacts with that region of the DHp domain that includes the conserved Pro 410 Sda and KipI induce the same contraction of KinA upon binding (4 Å in R g, 15 Å in D max ) DHp helical bundle is a critical conduit for signaling

47 Contrast variation in biomolecules can take advantage of the fortuitous fact that the major bio-molecular constituents of have mean scattering length densities that are distinct and lie between the values for pure D 2 O and pure H 2 O Mean scattering length density (10 10 cm 2 )

48 DNA and protein have inherent differences in scattering density that can be used in neutron contrast variation experiments

49 Under some circumstances, SAXS data can yield reliable polynucleotide-protein structure interpretation 3C pro RNA complex; Claridge et al. (2009) J. Struct. Biol. 166, C pro RNA 3C pro


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