Summary

1. Rigler, R., U. Mets, J. Widengren and P. Kask (1993). European Biophysics Journal22(3): 169-175. Fluorescence correlation spectroscopy with high count rate and low background: Analysis of translational diffusion.

2. How to increase signal to noise ratio? Small measurement volume (sample size) Overfill back-aperture Small pinhole Is the double Gauss approximation valid? Yes, for small enough pinhole size and correct laser focusing Summary

3. 2. Theoretical background Aragon, S. R. and R. Pecora (1976). "Fluorescence correlation spectroscopy as a probe of molecular dynamics." Journal of Chemical Physics64(4): 1791-1803. (1) (2)

4. Double Gauss not exact, because: Focused laser beam Detection along z not exactly Gaussian Double Gauss is used, because: Analytical solution available When is double Gauss adequate? Intensity profile in z not critical 2. Theoretical background

5. 2. Theoretical background Fig. 1

6. CEF (collection efficiency function) describes the effect of the pinhole on the emitted fluorescence light 2. Theoretical background (5) (4) Koppel, D. E., D. Axelrod, et al. (1976). "Dynamics of fluorescence marker concentration as a probe of mobility." Biophys J16: 1315-29.

7. Excitation intensity profile is Gauss-Lorentzian 2. Theoretical background (7) (6)

8. 3. Molecular detection efficiency calculations Fig. 2

9. MDE determines effective sample volume Independent parameters: Numerical aperture of objective including refractive index Pinhole radius projected to sample space Focusing angle of laser beam δ≤α/2 Radius of sample volume defined by laser beam within projected pinhole 3. Molecular detection efficiency calculations

10. Maximum increment of 10% for beam radius: 3. Molecular detection efficiency calculations (4) (6) (9)

11. Estimate of half-length of sample in z-direction 1/e2 points of CEF(0,z) Area PSF = e2 times pinhole area 3. Molecular detection efficiency calculations (10) (11) with • Far from resolution limit of objective • No spherical aberration • Practical limit z0 not smaller than 1μm

12. 4. Experimental • 40x 0.9 • Laser focusing angle: 0.33 rad • Max. pinhole: 20μm • Min. pinhole: 15 μm • 63x 1.2 • Laser focusing angle: 0.45 rad • Max. pinhole: 35μm • Min. pinhole: 15 μm

13. Strong focused laser results in small sample volume Increased fluctuation amplitude High signal to noise Shorter translational correlation times Slower molecules can be measured Large molecules High viscosity S/N increases with square root of total counting time over correlation time High count rate regime 5. Results and discussion Koppel, D. E. (1974). "Statistical accuracy in fluorescence correlation spectroscopy." Physical Review Letters10: 1938-1945.

14. Compare measured and calculated volumes W0 within 10% for pinhole 25μm and 15μm Z0 not accurate because of spherical aberrations 5. Results and discussion

15. 2D vs. 3D model Error when using 2D model not large for correlation time 2D will miss additional processes 5. Results and discussion Fig. 3

16. 200 seconds vs. 200 milliseconds 5. Results and discussion Fig. 4 Fig. 5

17. Apparent number of molecules: 5. Results and discussion Koppel, D. E. (1974). "Statistical accuracy in fluorescence correlation spectroscopy." Physical Review Letters10: 1938-1945.

18. For fast measurements use z0 and w0 from more accurate measurments In contrast to findings by Qian and Elson 3D Gauss can be used. Exposure dose and thus bleaching independent of beam radius Light intensity and thus saturation is proportional to w0-2 5. Results and discussion Qian, H. and E. L. Elson (1991). "Analysis of confocal laser-microscopy optics for 3-D fluorescence correlation spectroscopy." Applied Optics30(10): 1185-1195.