SCATTERING OF NEUTRONS AND X-RAYS kiki k i - k f = q hω ENERGY TRANSFER hq MOMENTUM TRANSFER kfkf Dynamic structure factor O r,t COHERENT INCOHERENT SCATTERING.

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Presentation transcript:

SCATTERING OF NEUTRONS AND X-RAYS kiki k i - k f = q hω ENERGY TRANSFER hq MOMENTUM TRANSFER kfkf Dynamic structure factor O r,t COHERENT INCOHERENT SCATTERING g (r,t) g s (r,t) QUASIELASTIC DIFFUSIVE MOTIONS INELASTIC VIBRATIONAL COHERENT INCOHERENT STRUCTURAL FT [ g s (r,  )] NUCLEAR PROB. DISTRIBUTION ELASTIC Elastic Quasielastic Inelastic Energy transfer, ω Δω e Δω q e  S (q,ω) = e i(ωt-q·r) g(r,t) dr dt

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.

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

Geometric R g from MD simulation = 14.1  0.1Å SMALL-ANGLE SCATTERING RADII OF GYRATION

Statistical Models of a Strongly Unfolded Protein

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

P(q) q(Å -1 ) Freely Jointed ChainsExcluded Volume Chains Phosphoglycerate Kinase in 4M GdnDCl R g Nat ~ 23Å R g Den ~ 90Å FJChains ANDREI PETRESCU PATRICK CALMETTES DOMINIQUE DURAND

          EVB (Exluded Volume Beta) EVN (Exluded Volume Native) Low Resolution MC Simulation    Scattering Profile of the Models Atomic Level Modeling LE (Locally Extended)    

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

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

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 CM -1 THz Calculated Experimental

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

UREA-ALKANE INCLUSION COMPOUND DIFFUSIVE ALKANE DYNAMICS AT 180K Three Simulation Models Urea ‘HOST’ C 19 H 40 ‘GUEST’

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

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