The Basics of Neutron Scattering Jill Trewhella The
The Basics of Neutron Scattering Jill Trewhella, The University of Sydney EMBO Global Exchange Lecture Course April 28, 2011
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]
Fundamentals Neutrons have zero charge and negligible electric dipole and therefore interact with matter via nuclear forces Ø Nuclear forces are very short range (a few fermis, where 1 fermi = 10 -15 m) and the sizes of nuclei are typically 100, 000 smaller than the distances between them. Ø Neutrons can therefore travel long distances in material without being scattered or absorbed, i. e. they are and highly penetrating (to depths of 0. 1 -0. 01 m). Ø Example: attenuation of low energy neutrons by Al is ~1%/mm compared to >99%/mm for x-rays Ø
Neutrons are particles that have properties of plane waves They have amplitude and phase
They can be scattered elastically or inelastically Elastic scattering changes direction but not the magnitude of the wave vector Inelastic scattering changes both direction and magnitude of the neutron wave vector
It is the elastic, coherent scattering of neutrons that gives rise to small-angle scattering
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
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)eikr 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.
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. Ø This resonance phenomenon gives rise to imaginary components of b. The real part of b gives rise to scattering, the imaginary part to absorption. Ø b has to be determined experimentally for each nucleus and cannot be calculated reliably from fundamental constants. Ø
Neutron scattering lengths for isotopes of the same element can have very different neutron scattering properties
As nuclei are point scattering centers, neutron scattering lengths show no angular dependence
b values for nuclei typically found in bio-molecules (10 -12 cm) fx-ray for = 0 in electrons (and in units of 10 -12 cm)a 1. 000 (0. 28) Atom Nucleus Hydrogen 1 H -0. 3742 Deuterium 2 H 0. 6671 1. 000 Carbon 12 C 0. 6651 6. 000 (1. 69) Nitrogen Oxygen 14 N 16 O 0. 940 0. 5804 7. 000 (1. 97) 8. 000 (2. 25) Phosphorous 31 P 0. 517 15. 000 (4. 23) Sulfur Mostly 32 S 0. 2847 16. 000 (4. 5) (0. 28) 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/mec 2 = 0. 28 x 10 -12 cm.
Scattering Length Density Ø The average scattering length density for a particle is simply the sum of the scattering lengths (b)/unit volume
The basic scattering equation ØFor 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 between the scattering particle and solvent P(q) = form factor particle shape S(q) = structure factor inter particle correlation distances
Inter-particle distance correlations between charged molecules D D D - D D …. . gives a non-unity S(q) term that is concentration dependent
For a single particle in solution (i. e. S(q) = 1): _ I(q) = | e-i(q • r) 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
P(r) provides a real space interpretation of I(q) Ø P(r) is calculated as the inverse Fourier transform of I(q) and yields the probable frequency of interatomic 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, 1735 -1782
Contrast (or solvent) Matching Ø Solvent matching (i. e. matching the scattering density of a molecule with the solvent) facilitates study of on component by rendering another “invisible. ”
Optical Contrast Matching Example
Using small-angle X-ray scattering we showed that the N-terminal domains of cardiac myosin binding protein C (C 0 C 2) form an extended modular structure with a defined disposition of the modules Jeffries, Whitten et al. (2008)J. Mol. Biol. 377, 1186 -1199
Mixing monodisperse solutions of C 0 C 2 with G actin results in a dramatic increase in scattering signal due to the formation of a large, rod-shaped assembly
Neutron contrast variation on actin thinfilaments with deuterated the C 002 stabilizes F-actin filaments
Solvent matching for the C 0 C 2 -actin assembly Whitten, Jeffries, Harris, Trewhella (2008) Proc Natl Acad Sci USA 105, 18360 -18365
Contrast Variation Ø To determine the shapes and dispositions of labeled and unlabelled components in a complex
I 1 I 12 I 2 For a complex of H- and D-proteins: _ _ H(D) (= H(D)protein - solvent ) is the mean contrast of the H and D components, IDP, IHP their scattering profiles, and Icrs 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 ID, IH, and IHD.
Contrast Variation Experiment Ø 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: Mod. ULes for the Analysis of Small angle Neutron Contrast Variation Data from Biomolecular Complexes, ” J. Appl. Cryst. 41, 222 226, 2008. 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, pp 307 23, 2009. Email: jill. trewhella@sydney. edu. au for reprint requests.
Use Rg values for Sturhman analysis RH = 25. 40 Å RD = 25. 3 Å D = 27. 0 Å
Stuhrmann showed that the observed Rg for a scattering object with internal density fluctuations _ can be expressed as a quadratice function of the contrast : where Rm is the Rg 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
implies a homogeneous scattering particle Ø positive implies the higher scattering density is on average more toward the outside of the particle Ø negative places the higher scattering density is on average more toward the inside of the particle Ø zero
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 Rg values for the individual components and their separation using the following relationships:
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, IDP, IHP their scattering profiles, and Icrs 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 ID, IH, and IHD.
Solve the resulting simultaneous equations for I(q)H, I(q)D, I(q)HD I 12 I 2
Use ab initio shape determination or rigid body refinement of the components against the scattering data if you have coordinates
The sensor histidine kinase Kin. A - response regulator spo 0 A in Bacillus subtilis Failure to initiate DNA replication DNA damage Sda Change in N 2 source Kip. A Kip. I Kin. A Spo 0 F Spo 0 B Spo 0 A Sporulation Environmental signal
Our molecular actors Kin. A Sda Based on H 853 Thermotoga maritima to sensor domains Kip. I Pyrococcus horikoshi CA Pro 410 His 405 DHp Trp
HK 853 based Kin. A model predicts the Kin. A 2 contracts upon binding 2 Sda molecules X-ray scattering data Sda 2 Rg = 15. 4 Å, dmax = 55 Å Kin. A 2 Rg = 29. 6 Å, dmax = 95 Å Kin. A 2 -Sda 2 Rg = 29. 1 Å, dmax = 80 Å
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 D 65, 574 -581, 2009.
Kip. I dimerizes via its N-terminal domains and 2 Kip. I molecules bind Kin. A 2 Kip. I 2 Rg = 31. 3 Å, dmax = 100 Å Kin. A 2 Rg = 29. 6 Å, dmax = 80 Å Kin. A 2 -2 Kip. I Rg = 33. 4 Å, dmax = 100 Å
Neutron contrast variation: Kin. A 2: 2 DSda Rg Kin. A 2 Rg 2 Sda I(Q) A 1 in complex 25. 40 Å 25. 3 Å uncomplexed 29. 6 Å 15. 4 Å Separation of centres of mass = 27. 0 Å
MONSA: 3 D shape restoration for Kin. A 2: 2 DSda
Component analysis
Rigid-body refinement Kin. A 2 -2 Sda components 90 Whitten, Jacques, Langely et al. , J. Mol. Biol. 368, 407, 2007 I(Q) A 1
Kin. A 2 -2 Kip. I 90 Jacques, Langely, Jeffries et al (2008) J. Mol. Biol. 384, 422 -435 I(Q) A 1
The Kin. A helix containing Pro 410 sits in the Kip. IC domain hydrophobic groove
A possible role for cis-trans isomerization of Pro 410 in tightening the helical bundle to transmit the Kip. I signal to the catalytic domains? Or is the Kip. I cyclophilin-like domain simply a proline binder?
Sda Kip. I Sda and binding interacts Kip. Idoes induce bind withnot at the appear theregion same basetocontraction of ofprovide the Kin. A DHp forof domain Kin. A dimerization steric upon mechanism thatbinding includes phosphotransfer of(4 inhibition the Å in conserved Rg, (DHp) 15 Å in Pro domain D 410 max) DHp helical bundle is a critical conduit for signaling
Mean scattering length density (1010 cm 2) 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
DNA and protein have inherent differences in scattering density that can be used in neutron contrast variation experiments
Under some circumstances, SAXS data can yield reliable polynucleotide protein structure interpretation 3 Cpro. RNA complex; Claridge et al. (2009) J. Struct. Biol. 166, 251 -262
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