Tracking of single fluorescent particles in three dimensions: use of cylindrical optics to encode particle position

Abstract

We present a novel optical technique for three-dimensional tracking of single fluorescent particles using a modified epifluorescence microscope containing a weak cylindrical lens in the detection optics and a microstepper-controlled fine focus. Images of small, fluorescent particles were circular in focus but ellipsoidal above and below focus; the major axis of the ellipsoid shifted by 90 degrees in going through focus. Particle z position was determined from the image shape and orientation by applying a peak detection algorithm to image projections along the x and y axes; x, y position was determined from the centroid of the particle image. Typical spatial resolution was 12 nm along the optical axis and 5 nm in the image plane with a maximum sampling rate of 3-4 Hz. The method was applied to track fluorescent particles in artificial solutions and living cells. In a solution of viscosity 30 cP, the mean squared distance (MSD) traveled by a 264 nm diameter rhodamine-labeled bead was linear with time to 20 s. The measured diffusion coefficient, 0.0558 +/- 0.001 micron2/s (SE, n = 4), agreed with the theoretical value of 0.0556 micron2/s. Statistical variability of MSD curves for a freely diffusing bead was in quantitative agreement with Monte Carlo simulations of three-dimensional random walks. In a porous glass matrix, the MSD data was curvilinear and showed reduced bead diffusion. In cytoplasm of Swiss 3T3 fibroblasts, bead diffusion was restricted. The water permeability in individual Chinese Hamster Ovary cells was measured from the z movement of a fluorescent bead fixed at the cell surface in response osmotic gradients; water permeability was increased by > threefold in cells expressing CHIP28 water channels. The simplicity and precision of this tracking method may be useful to quantify the complex trajectories of fluorescent particles in living cells.

Particle imaging techniques for volumetric three-component (3D3C) velocity measurements in microfluidics

“…Kao and Verkman (1994) applied this technique to the measurement of the position of fluorescent particles in living cells. They used a 609 oil immersion lens to image 93 nm fluorescent latex beads over a depth range of 4 lm.…”

Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function

“…In the third (z) dimension, diffraction also limits resolution to Ϸ2n /NA 2 with n the index of refraction, corresponding to a depth of field of Ϸ500 nm in the visible wavelength region with modern microscopes. Improvements in 3D localization beyond this limit are also possible by using astigmatism (10,11), defocusing (12), or simultaneous multiplane viewing (13).…”

3D Particle Tracking on a Two-Photon Microscope

“…The first method is a 3D volumetric scanning that localizes the particle by scanning several images at different depths into the sample. The second technique is similar to Kao and Verkman's approach in that it utilizes aberrations in the PSF to determine the axial position of the particle [14].…”

“…Spedel developed a method using off-focus imaging to track particles at 10 Hz rate but it is limited to a few micrometers in axial extent [13]. Kao and Verkman developed 3D SPT system by employing cylindrical optics that broke the axial symmetry of the optical system [14]. In a well-corrected optical system, the image of a point source should look identical at equivalent distances above or below the focus of the objective.…”