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Intrinsic Mean Square Displacements in Proteins

Intrinsic Mean Square Displacements in Proteins. Henry R. Glyde Department of Physics and Astronomy University of Delaware, Newark, Delaware 19716. JINS-ORNL Oak Ridge, Tennessee 19 December 2013. Intrinsic Mean Square Displacements in Proteins. Collaborators:

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Intrinsic Mean Square Displacements in Proteins

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  1. Intrinsic Mean Square Displacements in Proteins Henry R. Glyde Department of Physics and Astronomy University of Delaware, Newark, Delaware 19716 JINS-ORNL Oak Ridge, Tennessee 19 December 2013

  2. Intrinsic Mean Square Displacements in Proteins Collaborators: Derya Vural University of Delaware Liang Hong UT/ORNL Centre for Molecular Biophysics Oak Ridge National Laboratory Oak Ridge, Tennessee Jeremy SmithUT/ORNL Centre for Molecular Biophysics Oak Ridge National Laboratory Oak Ridge, Tennessee

  3. Mean Square Displacements in Proteins: • MSDs widely measured with neutrons, quasi-elastic scattering • Observed MSD dominated by MSD of hydrogen. • MSD increases with increasing temperature. • MSD shows a “Dynamical Transition” (DT) to large • displacements at ~ 220 K in hydrated proteins. • 4. Large MSD is generally associated with protein function.

  4. Observed MSD in Lysozyme as a function of hydration h FWHM W= 1 μeV

  5. Goal 1 of Talk: • To obtain intrinsic, long time MSD <r2> from simulations, the same MSD as observed with neutrons. • Observed MSD is instrument resolution dependent. Observed MSD increases with increased resolution. • Simulated MSD, increases with increasing simulation time. • 3. Differing MSD observed on different instruments.

  6. Mean Square Displacements in Proteins

  7. Mean Square Displacement in Proteins

  8. Observed Mean Square Displacements in Proteins

  9. Define an Intrinsic MSD in Proteins

  10. Mean Square Displacements in Proteins Simulations of Lysozyme

  11. Intrinsic MSD in Proteins Simulations of Lysozyme (h = 0.4), 1000 ns. Δ(Q,t) out to 10 ns

  12. Why are we interested long-time Intrinsic MSDs? • To obtained well defined MSDs from experiment. • To obtain time converged values from simulations. • More profoundly and interestingly to obtain “equilibrium” values of the MSD, the MSD that reflect the properties of the protein and the potential landscapes that are confining the H • and setting the possible motions: ---- to obtain the MSD that would be predicted by statistical mechanics. • . Low T • . High T

  13. Long time Intrinsic MSD in Proteins

  14. Intrinsic MSD in Proteins Fits of I(Q,t) and S(Q,ω) to Observed S(Q,ω =0)

  15. Goal 2 of Talk: • To obtain intrinsic, wave vector, Q, independent MSD. • Observed MSD depends on Q value selected. • Observed MSD decreases with increasing Q. • 3. Does the Q dependence arise from? • Gaussian approximation (neglecting higher cumulants in the ISF) • Dynamical heterogeneity of H in the protein, • in the ISF • 3. Or is there an “intrinsic” Q dependence in the MSD? The MSD is length scale dependent.

  16. The Q dependence of the MSD

  17. The Q dependence of the MSD

  18. Outline of Talk: • 1. Simulations of Lysozyme, calculations of I(Q,t). • Fits of model I(Q,t) to obtain <r2> , • - also λ, β in stretched exponential. • Compare intrinsic MSD with resolution dependent MSD and with observed MSD. • Explore Dynamical Transition in the intrinsic MSD

  19. Simulations of Lysozyme • 1. Two proteins, arbitrary orientation, in water; h = 0.4. • Simulation 1: t = 100 ns, 19 temperatures • Calculate I(Q,t) out to 1 ns • Simulation 2: t = 1000 ns, 5 temperatures • Calculate I(Q,t) out to 10 ns. • Fit of model I(Q,t) to simulated I(Q,t) to obtain <r2>, • also (λ, β in stretched exponential).

  20. Mean Square Displacements in Proteins Simulations of Proteins (Lysozyme)

  21. Mean Square Displacements in Proteins

  22. Application of Model I(Q,t) • 1. Experiment, measure: • Use model I(Q,t) to calculate S(Q,0) and fit to experiment. • 2. Simulation, calculate: • Fit model I(Q,t) to the simulated Iinc(Q,t) • Obtain <r2>, (also λ, β in stretched exponential) from fit.

  23. Mean Square Displacement in Proteins Simulations of Lysozyme, 100 ns I(Q,t) calculated out to 1 ns

  24. Intrinsic MSD in Proteins Simulations of Lysozyme, 100 ns. I(Q,t) out to 1 ns

  25. Intrinsic MSD in Proteins Simulations of Lysozyme, 100 ns. I(Q,t) out to 1 ns

  26. Intrinsic MSD in Proteins Simulations of Lysozyme, 100 ns. I(Q,t) out to 1 ns

  27. Intrinsic MSD in Proteins Simulations of Lysozyme, 100 ns. I(Q,t) out to 1 ns

  28. Mean Square Displacement in Proteins Simulations of Lysozyme, 1000 ns I(Q,t) calculated out to 10 ns

  29. Intrinsic MSD in Proteins Simulations of Lysozyme, 1000 ns. I(Q,t) out to 10 ns

  30. Intrinsic MSD in Proteins Simulations of Lysozyme, 1000 ns. I(Q,t) out to 10 ns

  31. Intrinsic MSD in Proteins Simulations of Lysozyme (h = 0.4), 1000 ns. Δ(Q,t) out to 10 ns

  32. Compare long-time, Intrinsic MSD with: • Resolution broadened MSD • Other simulated MSD for Lysozyme. • Observed MSD in Lysozyme. • Intrinsic MSD shows a “Dynamical Transition” (DT). • Thus DT an intrinsic property, not a “time window” effect. • “time window” effect modifies the DT (increases TD)

  33. Observed Mean Square Displacements in Proteins

  34. Intrinsic MSD and Resolution Broadened MSD Compared: identical I(Q,t) for Lysozyme

  35. Intrinsic and Resolution Broadened MSD Compared Simulations of Lysozyme, Roh et al. for h = 0.43

  36. Present Intrinsic MSD (Lysozyme (h = 0.4) Compared with Experiment (Lysozyme, variable h, W = 1 microeV)

  37. Observed MSD in Lysozyme, h = 0.4 g water/g protein FWHM W= 3.5 μeV

  38. Intrinsic MSD shows a Dynamical Transition Resolution Broadening moves TD to higher T

  39. Intrinsic MSD shows a Dynamical Transition Resolution Broadening moves TD to higher T

  40. Summary • Observed MSD depends on instrument resolution FWHM. • Simulated MSD increase with increasing simulation time. • 3. Can extract the long time, intrinsic MSD • 3. Concept is to fit a model which contains long time, intrinsic as a parameter to data or finite time I(Q,t). • Obtain <r2> , also (λ, β in stretched exponential) as fitting parameters.

  41. Conclusions: • An intrinsic <r2> can be defined and determined from simulations. The <r2> always greater than <r2>R. • In lysozyme <r2>R ~ 2 <r2>R for W = 1 μeV. • The intrinsic MSD <r2> relative to <r2> R depends on the decay times in the protein relative to the cut off time τ ~ ħ/W set by the instrument resolution. Rapid decay times means <r2>close to <r2> R . • Intrinsic MSD also depends on the function used to represent C(t). A stretched exponential rather than simple exponential, means a larger intrinsic <r2> . • The intrinsic MSD, <r2>, shows a Dynamical Transition. • A finite resolution displaces TD to a higher temperature.

  42. Goal 2 of Talk: • Obtain a wave vector, Q, independent MSD. • Exploring beyond the Gaussian Approximation • (higher cumulants) • Does the Q dependence arise from limits of the analysis? • Gaussian approximation • Dynamical diversity of H in the protein • An intrinsic Q dependence?

  43. The Q dependence of the MSD

  44. The Full Ii(Q,t) and the Gaussian approximation IiG(Q,t)

  45. Mean Square Displacements in Proteins

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