Flow-induced size-dependent distribution of probes. (a) The expected distribution of a large probe diffusing with D = 1 μm² s^–1 as a function of distance from the leading edge for different flow rates along the anterior–posterior axis. (b) The expected distribution of a probe as a function of distance from the leading edge at a constant flow rate of V_f = 0.1 μm s^–1 towards the leading edge for different values of the probe's diffusion coefficient. (c, d) Confocal images of probe distribution in live keratocytes. The distribution of small probe (AlexaFluor488 in c, Texas red conjugated 3 kD dextran in d; upper images), large probe (QD655 in c, Fluorescein-conjugated 500K dextran in d; centre images) and the ratio between large probe to small probe (lower images) are shown. Plots of the probe density along cross-sections in the central lamellipodium show enhancement of large probe near the leading edge (lower panel). The density was measured along the lines shown in the ratio images, and averaged over a width of 2 μm (small probe, green line; large probe, red line; ratio, black line). Control experiments measuring the ratio of two small probes (AF488 and AF594) showed a flat profile (Supplementary Information, Fig. S2). Note that the QDs are excluded from the region very close (<1 μm) to the leading edge, probably because of size exclusion by the dense brush-like actin network present there11.

Effects of blebbistatin on fluid flow. (a) Confocal ratio imaging of a cell treated with blebbistatin. The distribution of small probe (upper image), large probe (centre image) and the ratio between large probe to small probe (lower image) are shown. Plots of the probe density along a cross-section in the central lamellipodium show depletion of large probe near the leading edge (lower panel). The density was measured along the line shown in the ratio image, and averaged over a width of 2 μm (small probe, green line; large probe, red line; ratio, black line). (b) The normalized ratio density profiles as a function of distance from the leading edge along a cross-section in the central lamellipodium for different cells were averaged. The bold lines and shaded regions represent the mean and standard deviation (respectively) of the profiles of all cells for untreated (red) and blebbistatin-treated (blue) cells. (c) A simulation of the steady-state distribution of 30,000 particles diffusing with D = 1 μm² s^–1 within a fluid flowing with the velocity distribution showed in d. Fluid-flow-induced depletion of QDs near the leading edge is visible both in the experimental (a) and simulated (c) distributions. The comparison between experimental results and model should be limited to the lamellipodium, as the model does not address pressure, fluid flow and probe distribution in the cell body at the rear. (d) The Darcy flow equations described in the text were solved numerically in 2D for a blebbistatin-treated cell (with boundary condition that P_r = P_out; see Supplementary Information for details) and the fluid flow velocity distribution is shown. (e) Phase-contrast and fluorescence images of an untreated and a blebbistatin-treated cell fixed and stained with phalloidin to visualize actin filaments. The ordered actin meshwork in the lamellipodium is apparent in both the untreated and treated cell.

Single-particle tracking of QDs in the lamellipodia of live keratocytes. (a) Phase-contrast (top) and fluorescence (middle; white line: cell outline) images of a keratocyte with 655QDs. The QD trajectories during 100 frames (dt = 0.15 s) are shown in the cell frame of reference (bottom; dots indicates t = 0). Gaps in the tracks caused by QD blinking are depicted as dashed lines. (b) MSD(t) = 〈δr(t)²〉 (mean ± s.e.m.) of 655QDs as a function of time lag calculated on non-overlapping time intervals for data pooled from 12 cells, acquired with an exposure of 0.008 s and frame interval of 0.038 s. The MSD was slightly subdiffusive on all the timescales observed (0.038s < t < 10s; Supplementary Information, Supplementary Text B1), with MSD(t) ~t^y and γ = 0.89 ± 0.01. (c) Analysis of the distribution of apparent diffusion coefficient, D = MSD(t)/4t; t = 0.038 s, for the data shown in b; n = 611 tracks, truncated to 20 time-points, were included in the analysis (individual QD tracks may be split into several tracks because of long blinking events). The line represents the error distribution16, assuming a homogenous underlying diffusion coefficient equal to the mean of the distribution, D = 1.07 μm² s^–1. The experimental distribution is substantially broader than the error distribution, reflecting heterogeneity in the surroundings, probably because of variation in the density and organization of the actin cytoskeleton in different regions within the lamellipodium, and more substantially between different cells. (d) Examples of the distribution of apparent diffusion coefficient as in c for tracks from two different cells; n = 57 (cell A) and n = 105 (cell B) tracks, truncated to 15 time-points, were included in the analysis. The QDs in the two cells show markedly different diffusion rates. (e) MSD of 655QDs as a function of time lag for individual untreated cells (left) and for blebbistatin-treated cells (right). Each line represents average values for a single cell calculated on non-overlapping time intervals. The apparent diffusion varied considerably among individual cells between about 0.4–2.5 μm² s^–1 with an average of D = 1.15 ± 0.5 μm² s^–1 (mean ± s.d., D = MSD(t)/4t; t = 0.3 s; n = 37 cells) for untreated cells and D = 0.9 ± 0.3 μm² s^–1 (n = 16 cells) for blebbistatin-treated cells. The apparent diffusion coefficient in cells was approximately an order of magnitude lower than in water (D = 14 ± 0.5 μm² s^–1, from dynamic light scattering measurements) because of the crowded intracellular environment19.

Measurements of fluid flow based on the distribution of 655QDs. (a) An illustration of a keratocyte in the cell frame of reference depicting the model parameters and variables. Side (left) and top (right) views are shown. (b, c) The density distribution (left panels) and cross-sections along the black anterior–posterior (centre panels) and grey side–side (right panels) lines (averaged over a width of 2 μm) are shown. The experimental results (b) are compared with the results of a simulation (c) of the steady-state distribution of 30,000 particles (~ the number of 655QDs in b) diffusing with D = 1 μm² s^–1 within a fluid flowing with the velocity distribution shown in e. Note the fluid-flow induced enhancement of QDs near the leading edge and towards the sides in both the experimental (b) and simulated (c) distributions. (d, e) The Darcy flow equations described in the text were solved numerically in 2D (see Supplementary Information for details). The resulting pressure distribution (d) and fluid flow velocity distribution (e) are shown. The hydrostatic pressure drops from rear to front and sides and drives a fountain-like flow against the drag of the actin cytoskeleton. The fluid encounters more resistance flowing forwards against the retrograde actin meshwork flow, than flowing towards the sides, hence some of the fluid escapes to the lamellipodial sides. As the fluid is incompressible, this leads to a decrease in the flow rate towards the leading edge.