Microbeads are Tracked and Mean-Squared Displacement

Video is tracked with Video Spot Tracker (http://cismm.cs.unc.edu/downloads/) and edited in MATLAB. A script called evt_GUI allows the data to be analyzed and plots of the tracks to be produced. Among other analysis tools the program allows us to produce plots of mean-squared displacement (MSD). Mean-squared displacement is a measure of the spatial extent of random motion. It is a measure of the displacement squared versus the change in time ( = t). The MSD is determined mathematically by Equation 6.3.

(6.3) where x is the position of the bead and t is time. The plot of MSD can be used to characterize the type of observed movement in the experiment (Kulic, Brown et al. 2008). The slope of an MSD curve reveals information about the displacement of the bead. The slope in log-log space of an MSD plot is indicative of purely diffusive motions. A slope between 0 and 1 is indicative of sub-diffusive behavior whereas a slope between 1 and 2 is indicative of driven, sub-ballistic behavior. A slope very close to 2 would be considered ballistic motion. Applying this analysis to the tracks we can judge the type of motions that are observed in the internalized 1m beads. An example a radial displacement of a transported bead is shown in the left column of Figure 6.4. On the right column is the track of a bead in the same field of view that is stuck to the glass. Below each is the respective plot of mean squared displacement.

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Figure 6.4 Left column shows the radial displacement plot of an internalized 1m bead along with plot of MSD. The right column shows the same type of data for a 1m bead that is stuck to the glass. Data are shown in blue. In both MSD plots, a line of slope = 1 is shown in black. The internalized bead has a slope greater than one (m = 1.63), confirming the active transport. The bead stuck to the glass substrate shows a slope less than 1 (m = 0.6), showing that it is not diffusing or transporting in any way.

The transported bead shows a clear distinction from the stuck bead. The bi-directional transport can be seen in the radial displacement plot. The slope of the MSD plot is shown to be 1.63, in the sub-ballistic, driven transport regime. The stuck bead shows no long- scale displacement which is also shown in its MSD plot, where the slope of the curve is 0.6, well within the sub-diffusive range. It is clearly possible then to distinguish which beads are undergoing active transport from ones that are not using this methodology.

6.4.3 3-D Isosurfaces Can Show the Position of the Microbead and Verify Internalization

To visualize the internalization of the beads be the cells, HeLa wild types cells were transfected with Fluorescent Protein Cellular Labels: Cellular Lights™ Reagents. These reagents use baculoviruses to introduce DNA into the host cell that codes for the cytoskeletal monomer subunits with an attached fluorescent protein. Cells were transfected with a GFP-Actin actin according to the manufacturer’s guidelines, and results were verified with fluorescence microscopy. Stacks were taken on the Nikon epifluorescence microscope described previously. The images in the stacks were taken in green and red and red channels consecutively at each z-height. The stacks were then modeled into a 3D isosurface using Image Surfer software from CISMM (http://cismm.cs.unc.edu/downloads/). The models depict the positioning of the beads relative to the membrane of the cell. We are able to identify beads that are being transported by the cell and the 3D models can confirm that the beads are inside of the cell.

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Figure 6.5 (a) Slice from a red-green stack of Hela GFP-Actin cell and Alexa Fluor Hydrazide 568 beads. (b) Isosurface of combined red-green stack from ImageSurfer. (c) Same isosurface as b. with the opacity of the green channel reduced. Red 1m beads can be seen inside of the isosurface. (d) Slice taken from another stack of a different cell. (e) Isosurface of d. (f) View of isosurface from underneath the cell. The 1m bead can be seen beneath the outer membrane in proximity to the nucleus.

The isosurfaces depicted in Figure 6.5 show two examples of a bead internalized in a cell. The images in the left column are slices from the respective z-stacks. The middle column of the figure shows the two stacks merged and rendered into an isosurface. The top right image (c.) shows the isosurface of the top cell with the opacity of the green channel reduced so that the area beneath the membrane is visible. The nucleus is visible and the red fluorescent 1 micron bead is visible at the lower right. The bottom right image (e.) shows the isosurface rotated and so that the region underneath the membrane is visible. The 1 micron bead can be clearly seen in proximity to the nucleus. Images like this confirm that the beads we identify as undergoing active transport are indeed internalized within the cell, and are suitable candidates for probing the intracellular environment.