1. Dynamics / fluctuations in biological systems S. Longeville Laboratoire Léon Brillouin (CEA-CNRS) CEA Saclay

2. - Why studying dynamics in biological systems ? - Why neutrons for studying dynamics ? - The example of the dynamical transition - Principle of spin echo spectroscopy - Mechanisms of diffusion in crowded solutions

3. Dynamics in biological systems 1- Protein structure and stability ; folding / unfolding 2- Protein function 3- Protein diffusion and reaction kinetics

4. 1- folding / unfolding Quat. Rev. Biophys. 35 (2002) 111-167

5. 1- Protein structure and stability Thermal adaptation of constituents of thermophilic organisms - Increase the bond number/strengths more rigid to resist unfolding - Neutrons scattering experiments seems to indicate that thermophilic enzymes are less rigid (fluctuate more) than their mesophilic equivalent Fluctuations increase the structural disorder structure is stabilized by entropic terms G = U-TS

6. 2- Protein function Myoglobin : capture O 2 (CO) storage catalyse the reaction N0 -> NO 3 - Mb + O 2  MbO 2 From the structure : no path for O 2 to reach the heme Fluctuations : dynamical path H. Frauenfelder et al PNAS 100 (2003) 8615 Takeno et al J. Mol. Biol. 110 (1977) 569

7. 3- Protein diffusion and reaction kinetics Transition state theory (Kramers) AB Diffusion limited / assisted kinetics of reaction B B+C D C diffusion

8. R. Pynn Why neutrons for studying dynamics ?

9. Energy – wave vector plot Neutrons versus other techniques Local study by SANS and NSE http://www.ess-europe.de/en/data_images/N-complementarity.gif Study on inter- molecular lengths and the relevant time scales By neutron scattering Contrast variation methods (H/D, ZAC) High penetration, matching to study inside cells

10. Movements inside proteins Vibrations, harmonic motions 0.1-0.2Å E> 1 meV (t<0.6 ps) Internal motions /relaxations ~1 Å E~0.1-0.01 meV (t~1-100 ps) Global motions (diffusion) ~10 - 100 Å t ~ ns

11. Debye-Waller Lamb-Mossbauer (Back-scattering) Internal dynamics TOF Spin-echo Diffusion, Rotation Spin-echo

12. Protein function and the dynamical transition F. Parak et al, J. Mol. Biol. 161 (1982) 177-194 Mossbauer spectroscopy Fluctuations of the Fe of the heme in Myoglobin crystals

13. Protein function and the dynamical transition Relation to protein activity ? Lichtenegger et al. Biophys.J. 76 (1999) 414 Kleinert et al. Biochem. (1998) 37:717, Srajer et al. Biochem. (2001) Solvent viscosity controls dynamical transition and escape rate Biological activity correlated with dynamic transittion

14. Models : - two states model (transition from one to another at sufficient high energy) - mode coupling theory (Doster 1989) - Softening of the density of state (Parak 2003) Protein function and the dynamical transition W. Doster and Settles in Hydration processes in Biology (Nato science series ed: M.-C. Bellissent-Funel) H anharmonic motions are correlated to biological acticity conformational fluctuations Mb dynamical path for ligand binding

15. Principle of neutron spin-echo spectroscopy

16. Neutron spin, precession... S=1/2 B B o (G)  N ( msec -1 ) B0B0 10 100 1000 1 T 183 kHz 1,83 MHz 18,3 MHz 183 MHz 29 290 2900 29000

17. The measured quantity : the scattered beam polarisation... B 0 = 0  SiSi B0B0  SiSi z |-> |+> p |+> =cos 2 (  /2) p |-> =sin 2 (  /2) Analyser |+>, |-> |+>

18. Neutron spin echo : NSE, elastic scattering... B0B0 B1B1 x y F. Mezei Z. Physik, 255 (1972) 145 2 > 1 Whatever the neutron velocity, if the scattering process is elastic and the spectrometer perfect, the spin orientation after the second arm will be the same as before entering the first one at the echo point elasticQuasi-elastic

19. n Neutron spin echo : NSE,... 1 rst arm 0 = max. of the incident wavelength distribution

20. Elastic scattering II = I Neutron spin echo : NSE... Inelastic scattering II = I + 

21. Neutron spin echo : NSE, inelastic scattering... Quasielastic scattering :  hence

22. Neutron spin echo : NSE, inelastic scattering... Scattered beam Quasi-elastic

23. Diffusion mechanisms of protein in crowded solutions S. Longeville LLB (CEA-CNRS), W. Doster TU München

24. (A. P. Minton, J. Biol. Chem. 276 (2001) 10577) What is the crowding effect on biochemical reaction kinetics, transport mechanisms, protein folding...? In cells proteins are present in very crowded solutions  0.3

25. myoglobin is located in muscles, it stores oxygen and is suspected to support oxygen diffusion from the cell surface to the mitochondries (R~18 Å) Hemoglobin is the main component of red blood cells, it stores oxygen in lungs and release it in muscles (R~26Å) Oxygen transport proteins myoglobin and hemoglobin

26. Small Angle Neutron Scattering : the contrast H-protein D2OD2O

27. Measures the scattering length density fluctuations Scattering by a solution of spherical shape molecules

28. Coherent scattering lengths (fm) H DCNO PS -3.746.676.659.365.81 5.132.85

29. H 2 0/D 2 0 contrast Coherent scattering lengths (fm) H DCNO PS -3.746.676.659.365.81 5.132.85

30. H-Prot. in D 2 0 H 2 0/D 2 0 contrast Coherent scattering lengths (fm) H DCNO PS -3.746.676.659.365.81 5.132.85

31. H-Prot. in H 2 0H-Prot. in D 2 0 H 2 0/D 2 0 contrast Coherent scattering lengths (fm) H DCNO PS -3.746.676.659.365.81 5.132.85

32. H-Prot. in 40%D 2 0-60%H 2 0 H-Prot. in D 2 0 H 2 0/D 2 0 contrast Coherent scattering lengths (fm) H DCNO PS -3.746.676.659.365.81 5.132.85 H-Prot. in H 2 0

33. Myoglobine in-vitro Dynamics : Neutron spin echo spectroscopy Diffusion by coherent scattering ? NRSE - LLB

34. In the high Q limit (QR>1) : self-diffusion coefficient QR>>1 a small  r induces a strong phase term Q(r i -r j )

35. The Free volume theories Cohen & Turnbull, J. Chem. Phys. 31 (1959) 1164 V* critical volume V f free volume  adjustable parameter Rah & Eu, J. Chem. Phys. 115 (2001) 2634 P(v) for an HSS in which no energy change is associated with volume redistribution D(v) is very slowly dependent of v

36. The interactions : What is S(Q) ? MSA HS+Yukawa potential Ornstein-Zernike Mean spherical approximation (hayter penfold, belloni) V ij (r) S(Q)

37. |Zp|  2  0.4 e Dp  32  3 Å

38. hydrodynamic effect  =0.2  =0.4

39. The “plasmon mode” approach : - Protein : charge Z p, density n p (r,t) - Cations : charge Z c, density n c (r,t) - Anions : charge Z a, density n a (r,t) - - - - - - - - - - - - - -- - PZpPZp -- - - - - - - - - - - - - - - -- - PZpPZp - - - - - - - - - - - - - -- - PZpPZp - - - - - - - - - + + + + + + + + + + + + + + + + + + Solvent 

40. The “plasmon mode” approach : Continuity equation Poisson equation

41. Z p  1.5 e Ds  0.041 10 -5 cm 2 s -1

42. Hemoglobin in red blood cells ( in-vivo ) IN15 - ILL

43. Matching the RBC membrane? SANS H-Prot. in D 2 0

44. Matching the RBC membrane? SANS H-Prot. in D 2 0 H-Prot. in H 2 0

45. Matching the RBC membrane? SANS H-Prot. in D 2 0 H-Prot. in H 2 0Match Prot.

46. Matching the RBC membrane? SANS H-Prot. in D 2 0 H-Prot. in H 2 0Match Prot.Match Memb.

47. What can we learn from such study with respect to oxygen transport ? ~ 10  m ~ 1  m rt 10  m 0.5  m ~ 0.8 sec ~ 0.001 sec In lungs t ~ 0.1 sec Hemoglobin has to catch O 2 at the membrane surface ! Ds N O2  - Collective behavior, what is the driving force ? Electrostatic Mechanical motions NSE D s  0.021 10 -5 cm 2 s -1 - self-diffusion

48. Conclusion : Local study of the protein-protein interaction effects on the diffusion mechanisms by SANS and NSE (in crowded Solutions and in blood cells) - direct interactions (electrostatic +HSS) - indirect interactions (hydrodynamic) - self and collective diffusion Simple systems (spherical like shape molecules) In cells ? More complex systems (H probe protein in D-cells, D-cells with H 2 0)