Dynamics / fluctuations in biological systems

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 O2 (CO) storage catalyse the reaction N0 -> NO3- Mb + O2 MbO2 From the structure : no path for O2 to reach the heme Takeno et al J. Mol. Biol. 110 (1977) 569 Fluctuations : dynamical path H. Frauenfelder et al PNAS 100 (2003) 8615

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

8. Why neutrons for studying dynamics ? R. Pynn

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

10. Movements inside proteins

11. Debye-Waller Lamb-Mossbauer (Back-scattering) Diffusion, Rotation Spin-echo Internal dynamics TOF 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. Protein function and the dynamical transition W. Doster andSettles 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 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)

15. Principle of neutron spin-echo spectroscopy

16. Neutron spin , precession ... S=1/2 B B0 Bo (G) w N (msec-1) 10 183 kHz 29 100 1,83 MHz 290 1000 18,3 MHz 2900 1 T 183 MHz 29000

17. The measured quantity : the scattered beam polarisation ... |+>, |-> |+> B0= 0 B0 Analyser z p|+>=cos2(a/2) Si |+> a Si a p|->=sin2(a/2) |->

18. Neutron spin echo : NSE, elastic scattering ... F. Mezei Z. Physik, 255 (1972) 145 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 x B0 y elastic Quasi-elastic B1 l2>l1

19. n Neutron spin echo : NSE,... l0 = max. of the incident wavelength distribution 1rst arm

20. Neutron spin echo : NSE ... Elastic scattering lII=lI Inelastic scattering lII=lI+dl

21. Neutron spin echo : NSE, inelastic scattering ... Quasielastic scattering : dl<<l 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. In cells proteins are present in very crowded solutions F0.3 (A. P . Minton, J. Biol. Chem. 276 (2001) 10577) What is the crowding effect on biochemical reaction kinetics, transport mechanisms, protein folding ...?

25. Oxygen transport proteins myoglobin and hemoglobin Hemoglobin is the main component of red blood cells, it stores oxygen in lungs and release it in muscles (R~26Å) 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)

26. Small Angle Neutron Scattering : the contrast H-protein D2O

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

28. Coherent scattering lengths (fm) D C N O H -3.74 6.67 6.65 9.36 5.81 P S 5.13 2.85

29. Coherent scattering lengths (fm) D C N O H -3.74 6.67 6.65 9.36 5.81 P S 5.13 2.85 H20/D20 contrast

30. Coherent scattering lengths (fm) D C N O H -3.74 6.67 6.65 9.36 5.81 P S 5.13 2.85 H20/D20 contrast H-Prot. in D20

31. Coherent scattering lengths (fm) D C N O H -3.74 6.67 6.65 9.36 5.81 P S 5.13 2.85 H20/D20 contrast H-Prot. in D20 H-Prot. in H20

32. Coherent scattering lengths (fm) D C N O H -3.74 6.67 6.65 9.36 5.81 P S 5.13 2.85 H20/D20 contrast H-Prot. in 40%D20-60%H20 H-Prot. in D20 H-Prot. in H20

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

34. In the high Q limit (QR>1) : self-diffusion coefficient QR>>1 a small Dr induces a strong phase term Q(ri-rj)

35. P(v) for an HSS in which no energy change is associated with volume redistribution V* critical volume Vf free volume D(v)is very slowly dependent of v a adjustable parameter 1 Rah & Eu, J. Chem. Phys.115 (2001) 2634 Myoglobine T=37°C D/Do 0.1 Free Volume HS cavity a =3.1 0.1 F Volume fraction The Free volume theories Cohen & Turnbull, J. Chem. Phys.31 (1959) 1164

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

37. |Zp|  20.4 e Dp  323 Å

38. hydrodynamic effect F=0.2 F=0.4

39. - Protein : charge Zp, density np(r,t) - Anions : charge Za, density na(r,t) - Cations : charge Zc, density nc(r,t) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - P Zp P Zp P Zp - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + Solvent e,h The “plasmon mode” approach :

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

41. Zp1.5 e Ds 0.041 10-5 cm2s-1

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

43. H-Prot. in D20 Matching the RBC membrane? SANS

44. H-Prot. in D20 Matching the RBC membrane? SANS H-Prot. in H20

45. H-Prot. in D20 Matching the RBC membrane? SANS H-Prot. in H20 Match Prot.

46. H-Prot. in D20 Matching the RBC membrane? SANS H-Prot. in H20 Match Prot. Match Memb.

47. ~ 10 mm ~ 1 mm - self-diffusion NSE Ds0.021 10-5 cm2s-1 r t NO2 Ds 10 mm ~ 0.8 sec - Collective behavior, what is the driving force ? 0.5 mm ~ 0.001 sec Electrostatic Mechanical motions F What can we learn from such study with respect to oxygen transport ? Hemoglobin has to catch O2 at the membrane surface ! In lungs t ~ 0.1 sec

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) - self and collective diffusion - direct interactions (electrostatic +HSS) - indirect interactions (hydrodynamic) Simple systems (spherical like shape molecules) In cells ? More complex systems (H probe protein in D-cells, D-cells with H20)