This document summarizes techniques for single particle and single molecule tracking using fluorescence microscopy. It discusses how relative measurements can be used to track labeled objects in living cells in real time without requiring absolute measurements. It also describes methods for labeling particles or molecules, considerations for sample preparation and imaging, techniques for identifying particle locations, and calculations for determining tracking precision based on measurements of photon counts and point spread functions.

1. Single Particle and Single Molecule Tracking Multiple Measurements Provide Increased Tracking Accuracy Michael Chelen October 14th 2003 Biological Imaging and Fluorescence Microscopy

2. What is Particle Tracking Relative measurements Absolute measurements not required Brownian motion vs. restricted movement Labeled objects Real time observation of living cells Data oriented labeling

3. Labeling Single Particle Tracking Inorganic beads Smallest beads 40um Crosslinked to target Single Molecule Tracking Single fluorophore molecule

4. Sample Micrograph First frame of 400ms recording 0.23um green fluorescent microspheres 40X 1.3NA oil-immersion objective. Additional 2.5X magnifier was used Total magnification of 100X. Images courtesty Lanni F.

5. Sample Micrograph Apparently Low Noise Histogram-adjusted Contrast

6. Abbe Model and Resolution p min = λ 0 (2 n sin Ө max ) n is refractive index Λ is wavelength Ө max is the maximum angle due to aperture p is the period of resolved slits p min =2NA

7. Identification of Particle Location Particles are too small to resolve Assuming ideal conditions, best resolution is of Airy pattern Dimensions of pattern set by wave length, focal length, and aperture.

8. 0.23um green fluorescent microsphere 400ms Elapsed Time

9. Identification of Particle Location Measurement at points surrounding particle center Calculate position of center based on weighted values Accuracy dependent on signal to noise ratio at each measurement point

10. 400ms / 10 Frames X Y

11. 100ms / 10 Frames X Y

12. Dealing with Airy Pattern 2D Point Spread Function Airy pattern is the ideal in-focus 2D PSF Brightness and sharpness affected by axial focus Identification of particle position can be calculated in different ways

13. Precision Suppose that the point-spread function of a microscope is given by psf(n), where n is measurement of pixels along an axis. For any point, psf(n) is the fraction of total photons detected at that point. M(n) is expected photon count Detection of photons has inherent variability Poisson Root-mean-square variation of M is SQRT(M) Also depends on background photon count, M 0 RMS noise is SQRT[M(n)] = SQRT[psf(n) M 0 ] M = Expected Photon Count M 0 = is total photon count above background For Pixel “n” expected photon count M(n) = psf(n) x M 0 Precision = RMS(ΔX) =

14. Sample Precision Calculation Suppose the PSF is peaked in the middle, normalized, only five pixels wide, and has the form: { 0, ......, 0, 0.1, 0.2, 0.4, 0.2, 0.1, 0, ........, 0 } RMSΔX = = If the particle image contains 10,000 counts (M0 = 10,000), RMSΔX = 1.0954 / 100 = 0.011 pixels Precision will be approximately 1/90 of a pixel.

15. References Kues T, Peters R, Kubitscheck U, Visualization and Tracking of Single Protein Molecules in the Cell Nucleus Lanni F. and Keller E., Imaging Neurons Japan Association of Remote Sensing http:// www.profc.udec.cl/~gabriel/tutoriales/rsnote/contents.htm Inoué, S., Imaging Superresolution, and Precision Measurement Lanni F., Email and Conversation