3-D Particle Tracking in a Two-Photon Microscope: Application to the Study of Molecular Dynamics in Cells  Valeria Levi, QiaoQiao Ruan, Enrico Gratton  Biophysical Journal  Volume 88, Issue 4, Pages 2919-2928 (April 2005) DOI: 10.1529/biophysj.104.044230 Copyright © 2005 The Biophysical Society Terms and Conditions

Figure 1 Schematic diagram of the two-photon fluorescence microscope setup. Biophysical Journal 2005 88, 2919-2928DOI: (10.1529/biophysj.104.044230) Copyright © 2005 The Biophysical Society Terms and Conditions

Figure 2 Intensity profile simulated during a cycle of the tracking routine. (A) The coordinates x (solid), y (dashed), and z (dotted) of the scanner during one cycle of tracking are represented as a function of time. (B) The fluorescence intensity signal as a function of time was calculated according to Eqs. 1 and 2 considering the following positions for the particle (in nm): (0,0,0), (100,0,0); (0,0,100); (100,0,1000). For the simulation, we considered the following parameter values: wo=500nm, B=0, Fo=106, rx,y=500nm, rz=1500nm, f=250Hz, λ=780nm. Biophysical Journal 2005 88, 2919-2928DOI: (10.1529/biophysj.104.044230) Copyright © 2005 The Biophysical Society Terms and Conditions

Figure 3 Tracking accuracy. 500-nm fluorescent beads dried onto a coverslip were moved in a sine wave of amplitudes in the range 0.1–10μm and frequency of 0.02Hz (A) or in 20 steps of 20–100nm separated in time by 3s (B). The tracking routine was run as described in Materials and Methods with fdata=16kHz, forbit=250Hz, n=8, rx,y=0.7μm, and rz=2.5μm. Trajectories recovered for beads moving 1μm in a sine wave (A) or in 60nm steps (B). The insets to the figures show the amplitude recovered by fitting the bead trajectories to sine waves plotted as a function of the input amplitude (A) and the average step size recovered plotted as a function of the input step size (B). Dependence of the tracking accuracy on the signal/noise ratio (C). The position of fixed beads with diameters (nm): 552 (□), 100 (○), 24 (■), and 14 (●) were determined at different laser powers in the range 0.1–15 mW, using the following parameters for the tracking routine: fdata=32kHz, forbit=250Hz, n=16, rx,y=0.7μm, and rz=2.5μm. The accuracy of the tracking was calculated as described in the text. The continuous line represents the fitting of the following function: accuracy=α(S/N)β with α=49±5nm, β=0.54±0.08. The dashed line represents the theoretical accuracy. Biophysical Journal 2005 88, 2919-2928DOI: (10.1529/biophysj.104.044230) Copyright © 2005 The Biophysical Society Terms and Conditions

Figure 4 Tracking fluorescent beads in glycerol solutions. Suspensions of 500nm fluorospheres in solutions of glycerol (0%–80%) were placed between a slide and a coverslip previously treated with octadecyltrichlorosilane. (A) Trajectories obtained for six different beads in 80% glycerol. The initial point for the trajectories was arbitrarily set in (0,0,0). (B) Histogram of diffusion coefficients obtained by fitting Eq. 5 to the MSD versus τ plot for trajectories of beads in 80% glycerol. The continuous line represents the Gaussian distribution function fitted to the experimental data. The tracking routine was run as described in Materials and Methods with fdata=16kHz, forbit=250Hz, n=4, rx,y=0.7μm, and rz=2.5μm. The temperature was 23.0°C. Biophysical Journal 2005 88, 2919-2928DOI: (10.1529/biophysj.104.044230) Copyright © 2005 The Biophysical Society Terms and Conditions

Figure 5 Diffusion of fluorescent beads in glycerol solutions. The experimental diffusion coefficients obtained as described in the legend to Fig. 4 are represented as a function of the inverse of the viscosity (circles). The continuous line represents the values of D obtained from the Stokes-Einstein relation (Eq. 7). Biophysical Journal 2005 88, 2919-2928DOI: (10.1529/biophysj.104.044230) Copyright © 2005 The Biophysical Society Terms and Conditions

Figure 6 Phagocytosis of BSA-coated beads. Trajectories of a bead loosely attached to a cell (A) and of another bead moving through a linear path toward the perinuclear region (B). The bright spot corresponds to the position of the laser at the beginning of the tracking. The yellow lines correspond to the 2-D projections of the trajectories. The tracking routine was run as described in Materials and Methods with fdata=16kHz, forbit=250Hz, n=8, rx,y=0.7μm, and rz=2.5μm and lasted 11min (A) and 16min (B). Bars=5μm. Biophysical Journal 2005 88, 2919-2928DOI: (10.1529/biophysj.104.044230) Copyright © 2005 The Biophysical Society Terms and Conditions

Figure 7 Phagocytosis of collagen-coated beads. 3-D trajectories of a collagen-coated bead loosely attached to a cell (A) and following a linear path (C). (B) and (D) MSD versus τ plots for these trajectories. The dashed lines correspond to the fitting of anomalous motion (Eq. 5) and diffusion+transport (Eq. 6) models, respectively. The best fitting parameters for these trajectories were D=2.75×10−3±2×10−5μm2/s and α=0.759±0.002 (B) and D=4.4×10−4±1.6×10−7μm2/s and v=1.6×10−2±9×10−6μm/s (D). The trajectories lasted for 5 and 8.7min, respectively. The tracking routine was run as described in Materials and Methods with fdata=16kHz, forbit=250Hz, n=4, rx,y=0.7μm, and rz=2.5μm. Biophysical Journal 2005 88, 2919-2928DOI: (10.1529/biophysj.104.044230) Copyright © 2005 The Biophysical Society Terms and Conditions

Figure 8 Tracking two particles. 3-D trajectories obtained simultaneously for two beads coated with collagen interacting with a cell. The tracking routine was run as described in Materials and Methods with fdata=16kHz, forbit=250Hz, n=4, rx,y=0.7μm, and rz=2.5μm. The tracking lasted 4min. Biophysical Journal 2005 88, 2919-2928DOI: (10.1529/biophysj.104.044230) Copyright © 2005 The Biophysical Society Terms and Conditions