Dispersion-Relation Fluorescence Spectroscopy

Because of its ability to study specifically labeled structures, fluorescence microscopy is the most widely used technique for investigating live cell dynamics and function. Fluorescence correlation spectroscopy is an established method for studying molecular transport and diffusion coefficients at a fixed spatial scale. We propose a new approach, dispersion-relation fluorescence spectroscopy (DFS), to study the transport dynamics over a broad range of spatial and temporal scales. The molecules of interest are labeled with a fluorophore whose motion gives rise to spontaneous fluorescence intensity fluctuations that are analyzed to quantify the governing mass transport dynamics. These data are characterized by the effective dispersion relation. We report on experiments demonstrating that DFS can distinguish diffusive from advection motion in a model system, where we obtain quantitatively accurate values of both diffusivities and advection velocities. Because of its spatially resolved information, DFS can distinguish between directed and diffusive transport in living cells. Our data indicate that the fluorescently labeled actin cytoskeleton exhibits active transport motion along a direction parallel to the fibers and diffusive in the perpendicular direction.

Figure 1

(a) Fluorescence images of $1.2\mu \mathrm{m}$ polystyrene fluorescence beads in water under Brownian motion. (b) Trajectories of individual beads in (a). (c) Fluorescence images of $1.2\mu \mathrm{m}$ polystyrene fluorescence beads drifting from left to the right. (d) Trajectories of individual beads in (c).

Figure 2

Mean-squared displacement (MSD) obtained by tracking individual beads in Fig. 1a. (b) Decay rate versus spatial mode, $\Gamma ({\mathbf{q}}_{\mathbf{x}},{\mathbf{q}}_{\mathbf{y}})$, associated with the beads in (a). The dashed ring indicates the maximum $q$ values allowed by the resolution limit of the microscope. (c) Azimuthal average of data in (b) to yield $\Gamma (q)$. The fits with the quadratic function yield the value of the diffusion coefficient as indicated. (d) Mean-squared displacement along the $x$ direction and the $y$ direction of beads in Fig. 1c. (e) Temporal frequency versus spatial frequency. The slope yields the drifting velocity along the $x$ direction. (f) Temporal frequency versus spatial frequency. The slope yields the drifting velocity along the $y$ direction.

Figure 3

Fluorescence images of culture of S2 drosophila cells whose peroxisomes were labeled with GFP. (b) Dispersion curve measured for the cell in (a). The quadratic curve fitting indicates dominant diffusion motion and the fitting coefficients yields the diffusion coefficient. Inset shows the $\Gamma (q_x,q_y)$ map. (c) Trajectories of peroxisomes in (a). (d) MSD obtained tracking the trajectories of peroxisomes. The linear relationship indicates diffusive motion, and the fitting coefficient gives rise to the corresponding diffusion coefficient.

Figure 4

(a) Fluorescence images of culture of mouse embryonic fibroblast whose actin was labeled with GFP. (b) Dispersion curve measured for the cell in (a). The black square and red circle curves indicate directed motion and diffusion along ${\theta }_1$ and ${\theta }_2$ direction, respectively. The blue lines on top of black and red curves denote their $q^1$ and $q^2$ dependence. Inset shows the $\Gamma (q_x,q_y)$ map associated with (a).