1. Proteins are dynamic systems Concerted motions of the p53 binding domain of MDM2

2. protein dynamics: –Timescale: from s to fs. –Inhomogeneity within same structure. –Conformational substates – Temperature dependence. Motions of tyrosine kinase

3. Observation of protein dynamics –Mössbauer spectroscopy: based on the interaction between x-ray (e. g. synchrotron radiation) and atomic nucleus in solids or some liquids (nuclear resonance scattering). Lamb-Mössbauer factor f:

4. –Incoherent neutron scattering:

5. Experimental observation Linear up to about T c =180K. T>T c : a dramatic increase of the slope  new modes of motion contribute to MSD, even in dry Mb. This phenomenon has been found in a large number of proteins. Data from incoherent neutron scattering (open symbols), and Mössbauer absorption (full symbols) with different Mb-crystals.

6. Experimental observation How fast are these new modes of motion? –Consider the relation of energy and time resolution: The new protein specific motions (T>T c ) occur on a timesacle < 4ps! Symbols: data from several Mössbauer experiments "—": calculated data from phonon density.

7. Example: photosystem II of spinach Average mean square displacements of iron in photosystem II of spinach () and efficiency of the electron transfer from quinone A to quinone B as a function of temperature.

8. Proteins and glasses Glasses are better studied and much simpler than proteins, so they can serve as guides to formulate concepts and theories for proteins. AttributesGlassProtein Structurally disordered  Many mimina in the energy landscape   -,  -relaxation 

9. Glass transition Unlike crystalline solids, glasses do not have a certain melting temperature. The viscosity changes gradually with increasing temperature. Glass transition temperature T g : At which the viscosity of a material reaches 10^13p = poise (=0.1kg/ms). SiO 2 crystal SiO 2 glass

10. Glass transition T<T g : „Frozen“ in one of many local minima, very little mobility. T>T g : The energy barriers can be overcome and other local minima explored. Energy landscape

11. Glass-like transition in proteins Proteins also possess a glass transition temperature T g : –Near T g : Dynamical transition to a glass-like solid, –T<T g : Quenched anharmonic motions and long-range correlated motion. (functionally relevant motions) From computer simulations: Glassy behaviour of solvent drives the transition of protein.

12. Atomic-Detail Computer Simulation Model System Molecular Mechanics Potential Energy Surface  Exploration by Simulation..

13. Mountain Landscape Energy Landscapes

14. More realistic pictures of energy landscapes

15. Dynamical Transition Mean-Square Displacement Nonlinear in T

16. The Protein Glass Transition d d n n Onset of Protein Function Harmonic Liquid Glass

17. Dynamics & Activity of Glutamate Dehydrogenase in a Cryosolvent [70% MeOD; 30%; D 2 O] VALERIE REAT RACHEL DUNN ROY DANIEL JOHN FINNEY.

18. Principal Component Analysis of the Myoglobin Glass Transition ALEX TOURNIER 7500

19. ALEX TOURNIER Anharmonicity Factor =  N/  P Normal Mode Frequency,  N Principal Mode Frequency,  P NN PP

20. Good Fit Bad Fit Error in Gaussian Fit P(r)

21. Free Energy Profiles of Dominant Principal Components

22. Mode Incipient at Myoglobin Glass Transition

23. Low temperature onset of anharmonic dynamics Simulation details : Hydrated Myoglobin crystal Hydrated Myoglobin crystal 10 ns MD trajectory (NPT) 10 ns MD trajectory (NPT) Methyl dynamics at 150 K Methyl dynamics at 150 K Mean Square Displacement Protein dynamical transition~220K Protein dynamical transition~220K Onset of anharmonic dynamics~150K Onset of anharmonic dynamics~150K Methyl dynamic heterogeneity Site-specific spectral analysis Low frequency methyl dynamics is sensitive to local packing Low frequency methyl dynamics is sensitive to local packing Role of Xenon cavities Mobile CH3 groups are populated near xenon cavities Mobile CH3 groups are populated near xenon cavities

24. Isolated Protein Dynamical Transition in an Isolated Protein: MD Simulation of Myoglobin. KRZYSZTOF KUCZERA MARTIN KARPLUS

25. 5 4321 Radial Dependence of Dynamical Transition JIANCONG XU ALEX TOURNIER Hydrated Myoglobin 5 4 3 2 1

26. System Heatbaths ProtSolv. Nose-Hoover-Chain Multiple Heatbath Simulation Algorithm System 1 st Heatbath 2 nd Heatbath ProtSolv. Canonical Distribution of Temperatures

27. KEEP COLD VARY T T1T1 T2T2 DUAL HEAT-BATH SIMULATIONS e.g. ALEX TOURNIER

28. Translation Rotation Water Diffusion on a Protein Surface Translation ALEX TOURNIER

29. Water Diffusion and the Glass Transition ALEX TOURNIER Protein Water Translational Diffusion Protein Fluctuations Rotation

30. Effect of Approximations in Experimental Neutron Scattering Data Analysis  u 2  1 ns Low-q, 20  eV resolution ‘High’-q, (0  q 2  23Å -2 ),20  eV resolution ‘Low’-q (0  q 2  1.44Å -2 ) perfect resolution Harmonic JENNIFER HAYWARD

31. GERALD KNELLER FIT RIGID REFERENCE STRUCTURES TO EACH FRAME OF FULLY-FLEXIBLE TRAJECTORY TRAJECTORY OF RIGID BODIES

32. 6543621 Atomic Dynamics as a function of Distance from Protein Centre Concentric Shells SERGE DELLERUE, ANDREI PETRESCU, MARIE-CLAIRE BELLISSENT-FUNEL

33. 10 -1 10 0 10 1 10 2 10 3 t (ps) 0.0 0.2 0.4 0.6 0.8 1.0 A I(q,t) B 0.0 0.2 0.4 0.6 0.8 1.0 I(q,t) 10 -1 10 0 10 1 10 2 10 3 t (ps) Derivation of Simplified Dynamical Description from Molecular Dynamics Simulation Data: Fit of a Stretched Exponential Model to the Intermediate Scattering Function.

34. Radially-Softening Dynamical Model R av = radius of sphere in which atom diffuses.  = dynamical correlation time  = stretch factor (range of timescales spanned) Atom in Sphere

35. Some “Predictions” for the Spallation Neutron Source….

36. Pressure Transition in Protein Dynamics LARS MEINHOLD WATER THE FREQUENCIES AFFECTED PROTEIN Crystalline Staphylococcal Nuclease

37. solvent Pressure-induced transition in protein dynamics Meinhold, Smith. PRE 72:061908 (2005) DoS: mode 1 mode 5 mode 30 mode 100 PMF: protein MSD: t r()r() r(+t)r(+t)

38. Protein:Protein Interactions. Vibrations at 150K VANDANA KURKAL-SIEBERT

39. GERALD KNELLER FIT RIGID REFERENCE STRUCTURES TO EACH FRAME OF FULLY-FLEXIBLE TRAJECTORY TRAJECTORY OF RIGID BODIES

40. Scattering of X-Rays by Protein Crystals Real Crystal = Ideal Crystal + Perturbations STÉPHANIE HÉRY DANIEL GENEST SVEN LAMMERS

41. PROTEIN FUNCTION Collective Motions Dynamics Structure NMR (13%) X-ray (87%)X-ray beam detector Bragg  el (r) phase problem disorder static - dynamic DIFFUSE Scattering Diff. Scatt. (B factors) CORRELATION

42. Rigid-Body Decomposition Rigid-Body Fit (R-factor re: Full Trajectory = 5.3%) Molecular Dynamics of Lysozyme Unit Cell Experimental Full Trajectory STÉPHANIE HÉRY DANIEL GENEST

43. X-Ray Diffuse Scattering LARS MEINHOLD Staphylococcal Nuclease

44. Staph nuclease S Gruner et al still exposurediffuse scattering after removal of Bragg peaks

45. Staph nuclease S Gruner et al h l k

46. Interpreting the experimental data … data reduction 3D – 2D – 1D MD simulations unit cell: 15993 atoms 4 proteins 2115 TIP3P + 48 Cl - C HARMM (param:22) PME Nose-Hoover (300K,1bar) 4 X 10ns,  t =1fs

47. Unit cell of Staphylococcal nuclease Space group P 41 (4 proteins) Water box with unit cell dimensions (1972 molecules) 36 chloride ions Total number of atoms 15540 S.LAMMERS

48. Intensity in hk0 plane Experimental intensity distribution Theoretical intensity distribution

49. Scattering vector in hk0 plane

50. Intensity in hk0 plane 25 frames 250 frames 2500 frames 12000 frames

51. R-factor for hk0 plane

52. LARS MEINHOLD X-Ray Diffuse Scattering

53. 1D decomposition unit cell scattering protein scattering Meinhold, Smith. PRL 95:218103 (2005)

54. 2D variance-covariance matrix Which parts of the protein and which types of motion cause the intense scattering features? pairs (k,k’)PCA decomposition

55. Protein Scattering Solvent Scattering LARS MEINHOLD Solvent Ring ?

56. decomposition Protein Scattering? Solvent Scattering? LARS MEINHOLD PROTEIN SOLVENT Helix Repeat Interstrand Distance Water O…O

57. 2D Meinhold, Smith. PRL 95:218103 (2005)

58. Specific Motions in Diffuse Scattering Pattern Feature F2 LARS MEINHOLD

59. N. Calimet, CMB Characterisation of PCA modes:

60. 3D without hydrogens including Agreement factor: EXP - MD MD scattering not converged Meinhold, Smith. BiophysJ 88:2554 (2005)

61. Convergence properties of collective variables protein topology Meinhold, Smith. BiophysJ 88:2554 (2005) an-isotropicisotropic linear correlation

62. PROTEIN FUNCTION Collective Motions ?? temperature pressure Tournier, Smith. PRL 91:208106 (2003) MD Simulation s a m p l i n g p r o b l e m brute force replica exchange conformational flooding (T2,p2)(T2,p2)(T1,p1)(T1,p1)

63. Bragg & Diffuse X-ray Scattering r e f i n e m e n t PROTEIN FUNCTION DynamicsStructure Computer Simulation Neutron Scattering 4 th generation X-ray sources Collective Motions - new concepts - Systems Biology - networks - ab-initio Folding