1. Fluorescence Correlation Spectroscopy technique and its applications to DNA dynamics Oleg Krichevsky Ben-Gurion University in the Negev

2. Outline Tutorial on FCS 1)The basic idea of the technique 2)Instrumentation 3)Standard applications: - measurements of concentrations - diffusion kinetics - binding assay DNA dynamics

3. 1)DNA hairpin opening-closing kinetics  o (k - )  c (k + ) 2) DNA “breathing” 3) Polymer conformational dynamics - flexible polymers (ssDNA) - semi-flexible polymers (dsDNA) - semi-rigid polymers (F-actin)

4. Tools: specific fluorescence labeling: attaching fluorophores at precise positions Fluorescence Correlation Spectroscopy (FCS)

5. Magde, Elson & Webb (1972); Rigler et al (1993) t (ms)

6. General Properties of FCS Correlation Function

7. t (ms) Rh6G Correlation function for simple diffusion:

8. Principles of confocal setup Sampling volume 0.5 fl (Ø 0.45 x 2  m) Incident light power 10 - 50  W 0.1-300 molecules per sampling volume on average

13. Enhancements and variations of the standard setup: 1)Two-color FCS (Schwille et al) 2)Two-photon FCS (Berland et al) 3)Scanning FCS (Petersen et al) References and technical details in G. Bonnet and O.K., Reports on Progress in Physics, 65(2002), 251-297

14. Standard applications: 1)Amplitude of G(t) → concentration of moving molecules 2)Decay → diffusion kinetics (in vitro and in vivo ) 3)Binding assay

15. FCS as a Binding Assay Few nm Protein DNA Few  m + Fast Diffusion Slow Diffusion

16. Methyltransferase + Lambda-DNA ( methyltransferase – courtesy of Albert Jeltsch and Vikas Handa ) In general, for two-component diffusion:

17. 1)DNA hairpin opening-closing kinetics  o (k - )  c (k + ) with Grégore Altan-Bonnet Noel Goddard Albert Libchaber Rockefeller University

18. DNA hairpin fluctuations: Molecular beacon design Tyagi&Kramer (1996) 5’ - Rh6G – CCCAA – (Xn) – TTGGG – [DABCYL] – 3’ (n=12-30)Signal/background: I o / I c ~ 50-100  o (k - )  c (k + ) I (kHz) T ( o C)

19. FCS on Molecular beacons: two processes – two characteristic time scales

20. G t (ms) Correlation function of a molecular beacon: HOPE!!! structural fluctuations diffusion

21. Control:  o (k - )  c (k + )  o (k - )  c (k + ) Beacon:

22. Correlation functions of beacon & control t (ms) Ratio of the correlation functions: pure conformational kinetics

23. t (ms) G conf Conformational kinetics at different temperatures:

24. 1) Melting curves: I(T) 2) FCS on beacons: 3) FCS on controls: The experimental procedure: I T

25. Characteristic time scales of opening and closing of T 21 loop hairpin:

26. Different lengths of T-loops:

27. The loops of equal length but different sequence: T 21 vs. A 21

28. Stacking interaction between bases

29. Opening and closing times of different poly-A loops Closing enthalpy (kcal/mol) vs. loop length (poly-A) 0.55 kcal/mol/stacked base

30. Placing a defect in a poly-A loop no defect PNAS 95, 8602-8606 (1998) Phys. Rev. Letters 85, 2400-2403 (2000)

31. In some simple situations we have some understanding of the sequence-dependence of hairpin closing kinetics In a number of other situations we have no undersanding - poly-C loops - short poly-T loops (below 7 bases(

32. The experimental construct: 2) DNA “breathing”

36. Phys. Rev. Letters 90, 138101 (2003)

37. Conformational dynamics of polymers in good solvents: on the model of dsDNA and ssDNA molecules

38. lag (ms) G(t) lag (ms) Diffusion of dsDNA 6700bp

41. Polymer Statistics Freely Jointed Chain model: Random Walks in Space R ee b

42. Polymer conformational dynamics: center of mass polymer end The kinetics of monomer random motion: double-stranded DNA (dsDNA) single-stranded DNA (ssDNA) Rouse (1953) Zimm (1956)

43. t Theory: b2b2

44. Rouse theory of Polymer Dynamics: Basic length scale: b Basic timescale:Polymer size: N b 

45. Rouse modes: n 0 N Mean-square displacement of an end-monomer: Center-of-massinternal

46. Rouse model: connectivity + friction of polymer segments Exact: r

47. Rouse model is nice but wrong: 1) Experimental measurements of polymer coil diffusion (dynamic light scattering) 2) Hydrodynamic interactions between polymer segments cannot be neglected

48. Diverge with N => cannot be neglected even for distant monomers Zimm model: Rouse model + hydrodynamic interactions

50. Hydrodynamic shell: r Exact

51. Zimm model is right Rouse model is wrong From polymer coil diffusion measurements: What about monomer motion? Zimm Rouse

52. Real polymers: limited flexibility b - Kuhn length: defines polymer flexibility b ~ several monomers: flexible polymer b >> monomer size: semi-flexible or stiff polymer Polymer can be considered as flexible at the length scale > b dsDNA: semi-flexible,b=100nm~340bp, dsDNA width d=2nm ssDNA: flexible,b~1-5nm~2-10bases

54. Results: 2400 bp fragment t (ms) r2(m2)r2(m2) R 2 ee b2b2 b - Kuhn length (b=2l p ~100nm~340bp) R ee – end-to-end distance: Why no Zimm behavior? 2400bp = 7b small polymer

55. still small ? 9400bp = 30 b still small r2r2 9400bp = 30 b 6700bp = 20 b 23000bp = 70 b hmm... 48000bp = 140 b

56. Interpretation of  the friction of cylinder with length b=100nm and diameter d=2nm:

57. Why not Zimm-model behavior? dsDNA is semi-flexible, the hydrodynamic interactions are weak Korteweg-Helmholtz theorem: when inertia can be neglected, the flow is organized to have minimal viscous losses Rouse model: Zimm model: Rouse regime below:

58. For dsDNA b=100nm, d=2nm: Rouse regime from b 2 (0.01  m 2 ) to 18b 2 (0.2  m 2 ) or R 2 ee

59. Above r 2 c : Zimm behavior 23000bp Best power fit gives power 0.64 Zimm regime: No free parameters, No polymer parameters

60. For flexible polymer: No Rouse regime, Zimm regime only

61. Single-stranded DNA:

62. Theory for semi-flexible polymers: parameters b,d. Harnau, Winkler, Reineker (1996)

63. Conclusions: Phys. Rev. Lett. 92, 048303 (2004) 1) First measurements of individual monomer dynamics within large polymer coil 2) There is a large range of dsDNA dynamics unaffected by hydrodynamic interactions (Rouse model) 3) The dynamics of ssDNA is dominated by hydrodynamic interactions (Zimm theory)

64. Thanks to my group: Roman Shusterman Sergey Alon Tatiana Gavrinyov Carmit Gabay And to friends and collaborators Grégoire Altan-Bonnet Noel Goddard Albert Libchaber Didier Chatenay Rony Granek David Mukamel Albert Jeltsch Vikas Handa Dina Raveh Anna Bakhrat