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SCATTERING OF NEUTRONS AND X-RAYS

SCATTERING OF NEUTRONS AND X-RAYS. hω ENERGY TRANSFER h q MOMENTUM TRANSFER. k i - k f = q. k f. k i. COHERENT INCOHERENT SCATTERING SCATTERING g ( r ,t) g s ( r ,t). .

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SCATTERING OF NEUTRONS AND X-RAYS

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  1. SCATTERING OF NEUTRONS AND X-RAYS hω ENERGY TRANSFER hqMOMENTUM TRANSFER ki - kf = q kf ki COHERENT INCOHERENT SCATTERING SCATTERING g (r,t) gs(r,t)  ei(ωt-q·r) g(r,t) dr dt S (q,ω) = Dynamic structure factor r,t O QUASIELASTIC DIFFUSIVE MOTIONS INELASTIC VIBRATIONAL COHERENT INCOHERENT STRUCTURAL FT [gs (r, )] Elastic ELASTIC Δωe Quasielastic Inelastic Δωqe Energy transfer, ω NUCLEAR PROB. DISTRIBUTION

  2. Neutron Diffraction 1) Scattering from nuclei - combined x-n analysis of small molecules. 2) Scattering power does not depend on atomic number. - hydrogens scatter strongly - deuterium and hydrogen opposite signs. 3) Small-angle scattering - contrast matching. 4) Solution scattering with isotope substitution - partial structure factors. 4) Enzyme structures - proton positions - water structure - no solution to phase problem - large crystals required - need nuclear reactor or spallation source.

  3. FRANCI MERZEL Protein Hydration. Svergun et al: First 3Å hydration layer ~10% denser than bulk water

  4. RADII OF GYRATION Geometric Rg from MD simulation = 14.10.1Å SMALL-ANGLE SCATTERING

  5. Statistical Models of a Strongly Unfolded Protein

  6. Small Angle Neutron Scattering P(q) q(Å-1) Include Higher q : Chain Configurational Statistics Low q : Size Radius of Gyration (Rg)

  7. ANDREI PETRESCU PATRICK CALMETTES DOMINIQUE DURAND Phosphoglycerate Kinase in 4M GdnDCl Freely Jointed Chains Excluded Volume Chains RgNat~ 23Å RgDen~ 90Å P(q) FJChains q(Å-1)

  8. Low Resolution MC Simulation Scattering Profile of the Models Atomic Level Modeling 180 Y 0 EVN (Exluded Volume Native) -180 0 -180 180  180 Y 0 EVB (Exluded Volume Beta) -180 -180 0 180  180 LE (Locally Extended) Y 0 -180 -180 0 180 

  9. Snapshots of Atomic-Detail Models of Strongly-Unfolded PGK EVN EVB EVN LE EVB LE

  10. Lattice Vibrations - PERIODIC in TIME and SPACE. - DISPERSION RELATIONSHIP between FREQUENCY and WAVEVECTOR l OPTICAL   ACOUSTICAL =180o= =2l q=/l 0 1 COHERENT INELASTIC NEUTRON SCATTERING

  11. CRYSTALLINE L-ALANINE : LATTICE DYNAMICS EXPERIMENT - Triple-Axis Coherent Inelastic Neutron Scattering THEORY - (i) Ab Initio Quantum Chemistry  H-Bond and Rotational Potentials (ii) Energy Minimization + Harmonic Analysis. PHONON DISPERSION CURVES THz CM-1 Experimental Calculated

  12. COHERENT INELASTIC NEUTRON SCATTERING INTENSITIES INTENSITY SCATTERING VECTOR MODE POLARIZATION VECTOR CALCULATED b*direction EXPERIMENTAL

  13. UREA-ALKANE INCLUSION COMPOUND DIFFUSIVE ALKANE DYNAMICS AT 180K Three Simulation Models Urea ‘HOST’ C19H40 ‘GUEST’

  14. QUASIELASTIC INCOHERENT NEUTRON SCATTERING Experiment compared with Simulation 10 chains DIRECTION PARALLEL TO CHAIN AXIS 5 chains 3 chains = experiment 1 chain DIRECTION PERPENDICULAR TO CHAIN AXIS

  15. ROTATIONAL PROBABILITY DISTRIBUTIONS OF ALKANE CHAINS Average Over Chains Potential of Mean Force=-kTlogP() ROTATIONAL ANGLE,  V()= Rotational Potential TWO SINGLE CHAINS Elastic Incoherent Structure Factor Experiment & Simulation Probability Distributions, P() Converged (t)

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