three R2 values for the fits to the equations for random, directed, and caged movement was below 0.015, movement was also considered as ‘‘random’’. This approach was necessary to ensure that trajectories with a nearly linear MSD were not assigned to either directed or caged movements, because these equations have more parameters than the equation for random movement. More 2 parameters generally result in a lower value for R . Two - dimensional tracking analysis Essentially, the same approach was used to analyze 2D trajectories obtained from TIRF microscopy measurements. For tracking vesicles in 2D, we used MatLab algorithms adapted by Daniel Blair and Eric Dufresne (http://physics.georgetown.edu/ matlab/) from particle tracking procedures originally written for IDL by David Grier, John Crocker, and Eric Weeks. In this case, however, random diffusion with a diffusion coefficient D is described by the equation MSDðDtÞ~4DDtzk directed diffusion at velocity v with a diffusion coefficient D is described by the equation MSDðDtÞ~4DDtzv2ðDtÞ2zk and restricted diffusion within a cage of radius R and a diffusion coefficient of D0 is described by equation [62] MSDðDtÞ~R2=3 1 exp 12D0Dt= R2 zk In all equations, k is the constant offset of the MSD at all time steps [61]. More than 95% of the LG recorded in the NKL-GFP- FasL fixed by 4% freshly-prepared paraformaldehyde for 15–30 minutes at room temperature, were found to have a maximum 2 MSD value of 0.2 mm . Hence, all tracked LG, which never exceed this MSD value within the total observation time of 50s, were defined as ‘‘immobile’’. Track properties To further quantify the movement of LG, the length, straightness, and displacement were calculated for each track. For a multi-step trajectory its length is defined as the sum of all step-displacements, its total displacement is the displacement between the start and end of the track and its straightness is defined as the ratio between its total displacement and length. Lower straightness values correspond to constrained trajectories. Key parameters from the automated tracking analysis (i.e. length, displacement, straightness, and velocity) are presented as both histograms and cumulative probability distributions. The cumulative probability distribution and histograms plot the same information for a given data set; however, the histogram plots the frequency distribution (y-axis) as a function of the binned data set (x-axis). The cumulative probability distribution displays the distribution of the data set from the smallest (from the left on the x-axis) to the greatest value (at the right of the x-axis) and provides the probability (y-axis) of whether a particular value will occur at or less than a specified point on the x-axis. Moreover, the cumulative probability distributions are less sensitive to noise and they are continuous, i.e. bin-sizes do not affect their appearance as they do in histogram plots. Since most readers are familiar with standard histogram plots, we present histogram plots (an overview of the distribution) and cumulative probability distributions (rapid 4 ð Þ 5 ð Þ 6 ð Þ Granules Movement in NK Cells identification of the median value of the data set by interpolation at 50% on the y-axis). Statistical analysis For normally distributed data, averages were given as mean 6 SEM (standard error of the mean) and statistical significance was tested using the Student’s t-test. For exponential distribution data, averages were given as median 6 SEM and statistical significance was tested using the Kolmogorov-Smirnov test. Supporting Information Figure S1 Disruption of the cytoskeleton decreased the mobility of LG at the PM. 2D track length, displacement, and straightness in NKL cells either untreated (Control) or treated with 10 mM Nocod (A), 10 mM LatB (B), or both (C). Found at: doi:10.1371/journal.pone.0012870.s001 (0.71 MB TIF) Figure S2 Disruption of the cytoskeleton decreased the fraction of LG with directed movement and increased the fraction of immobile LG. The relative occurrence of each type of movement for each indicated condition is summarized. The numbers of tracking events (n) are listed on the right. Found at: doi:10.1371/journal.pone.0012870.s002 (0.25 MB TIF) Figure S3 Long-range directed movement of single LG depended on microtubule, but not F-actin and Rab27a. Representative single LG tracked among different conditions, as indicated. An accumulated view of trajectories recorded during ,50 seconds is shown. All trajectories are centered with their initial time point in the middle of each figure. Note the extension of the cloud of tracks obtained from measurements of fixed granules provides a conservative estimate for the spatial resolution achieved by the tracking method in all three dimensions. Found at: doi:10.1371/journal.pone.0012870.s003 (0.96 MB TIF) Figure S4 Stabilization of F-actin and disruption of microtu- bules impaired cytosolic LG movement. Straightness of trajectories is shown as histograms and cumulative probability plots, as observed after treatment with 10 mM LatB (A), 1.0 mM Jasp (B), and 10 mM Nocod (C). Images were acquired by 3-D spinning disc confocal microscopy. Found at: doi:10.1371/journal.pone.0012870.s004 (0.76 MB TIF) Figure S5 High concentration of LatB slightly increased the 3D tracks length of LG in the cytosol. 3D length of tracking is shown as histograms (A) and cumulative probability plots (B), as observed after treatment with DMSO vehicle control (black line), 1.0 mM LatB (blue line), and 10 mM LatB (red line). Images were acquired by 3-D spinning disc confocal microscopy. Found at: doi:10.1371/journal.pone.0012870.s005 (0.29 MB TIF) Figure S6 Disruption of microtubules decreased the mobility of cytosolic LG. The length of trajectories of vesicles observed in NKL cells pretreated with 10 mM Nocod are shown as histograms (A) and cumulative probability plots (B). For the same trajectories, displacement (C and D) and velocity (E and F) are shown as histograms and cumulative probability plots, respectively. Found at: doi:10.1371/journal.pone.0012870.s006 (0.66 MB TIF) Figure S7 Data from additional two independent Rab27a knockdown NKL clones are comparable. The tracks length of single vesicle trajectories observed in Rab27a knockdown (Rab27a-KD-A1) NKL cells (red), NKL cells expressing control shRNA (control, black), as well as fixed cells (gray) are shown as histograms (A) and cumulative probability plots (B). The straightness of single trajectories during 10 seconds in NK cells PLoS ONE | www.plosone.org 10 September 2010 | Volume 5 | Issue 9 | e12870