Self-organized mechano-chemical dynamics in amoeboid locomotion of Physarum fragments

Abstract

The aim of this work is to quantify the spatio-temporal dynamics of flow-driven amoeboid locomotion in small (~100 µm) fragments of the true slime mold Physarum polycephalum. In this model organism, cellular contraction drives intracellular flows, and these flows transport the chemical signals that regulate contraction in the first place. As a consequence of these non-linear interactions, a diversity of migratory behaviors can be observed in migrating Physarum fragments. To study these dynamics, we measure the spatio-temporal distributions of the velocities of the endoplasm and ectoplasm of each migrating fragment, the traction stresses it generates on the substratum, and the concentration of free intracellular calcium. Using these unprecedented experimental data, we classify migrating Physarum fragments according to their dynamics, finding that they often exhibit spontaneously coordinated waves of flow, contractility and chemical signaling. We show that Physarum fragments exhibiting symmetric spatio-temporal patterns of endoplasmic flow migrate significantly slower than fragments with asymmetric patterns. In addition, our joint measurements of ectoplasm velocity and traction stress at the substratum suggest that forward motion of the ectoplasm is enabled by a succession of stick-slip transitions, which we conjecture are also organized in the form of waves. Combining our experiments with a simplified convection-diffusion model, we show that the convective transport of calcium ions may be key for establishing and maintaining the spatiotemporal patterns of calcium concentration that regulate the generation of contractile forces.

Keywords: amoeboid motility; cell migration; mechano-chemical interactions; particle image velocimetry; physarum; traction force microscopy.

Figure 1

(a) Instantaneous endoplasmic flow speed and traction stresses exerted on the substrate by a migrating Physarum fragment. Arrows exhibit the flow speed and colormap shows the magnitude of traction stresses. (b, c) Instantaneous traction stresses exerted by two Physarum fragments with different dynamical behaviors, with the stress vectors along the cell boundary removed. Black circles indicate the location of contraction centers.

Figure 2

Kymographs of longitudinal endoplasm flow velocity (a, d), peripheral traction stress (b, e), and longitudinal traction stress (c, f) for a peristaltic (a–c) and an amphistaltic (d–f) Physarum fragment.

Figure 3

Kymographs of flow and traction stress of two Physarum that exhibited uncommon spatio-temporal dynamics. (a, b, c) Kymographs for a fragment exhibiting organized dynamics with two consecutive backward flow waves for each forward flow wave (reminiscent of a period doubling state). (d, e, f) Kymographs for a fragment exhibiting disorganized dynamics.

Figure 4

(a)–(e) Box plots of motility parameters corresponding to peristaltic (N = 20) and amphistaltic (N = 8) Physarum fragments. (a) Average oscillation period. (b) Average magnitude of the traction stresses. (c) Average endoplasmic flow speed. (d) Average fragment length. (e) Shape factor. (f) Average shape of peristaltic (red line) and amphistaltic (blue line) types. Shaded regions contain 90% of the statistical distribution of shapes for each fragment type.

Figure 5

(a) Box plot of average migration speeds in peristaltic (N = 20) and amphistaltic (N = 8) Physarum fragments. Two asterisks denote statistically significant differences between medians (p < 0.01). (b) Simplified model schematic for the distance traveled by endoplasmic fluid particles per oscillation cycle. Top panel, peristaltic fragments; bottom panel, amphistaltic fragments. (c) Scatter plot of the distance Δx_cent traveled by the centroid of the Physarum fragment per oscillation cycle vs. the net distance Δx_flow traveled by an endoplasmic fluid particle. , peristaltic fragments; , amphistaltic fragments. The dashed line is Δx_cent = Δx_flow.

Figure 6

Instantaneous snapshots showing velocity vectors for endoplasm (blue) and ectoplasm (green) flows in a migrating Physarum, superimposed on the bright field image of the fragment. The pseudo-color map indicates the magnitude of velocity according to the colorbar in the right hand side of the panel. (a) Frontal part of the fragment. (b) Rear part of the fragment.

Figure 7

Kymographs of longitudinal ectoplasm flow velocity (a, d), longitudinal traction stress (b, e), and longitudinal endoplasm flow velocity (c, f) for a peristaltic (a–c) and an amphistaltic (d–f) Physarum fragment. In panels (a, d), we have added bright green and purple at the floor and ceiling of the colormaps to emphasize asymmetries in the velocity data.

Figure 8

Time histories of longitudinal ectoplasm velocity ( ) and longitudinal traction stresses ( ) at two specific locations in the front (panel a) and the back (panel b) of the peristaltic Physarum fragment shown in Figure 7. The tiled bars at the top of the plots represent the time-dependent phase differences (in radians) between the ectoplasm velocity and the traction stresses. Blue and orange tiles represent phase differences near −π/2 (cell and substrate stick) and zero (cell and substrate slip) respectively, as indicated by the color scale at the top of the figure.

Figure 9

Time sequence of ratiometric measurememt of [Ca²⁺]i during the locomotion of a typical peristaltic cell showing a Ca²⁺ wave propagating forward.

Figure 10

(a) Kymograph of ratiometric measurement of [Ca²⁺]i in a typical peristaltic fragment. (b) Kymograph of instantaneous longitudinal velocities of endoplasmic flow of the same peristaltic fragment in Figure 10(a). (c) Kymograph of ratiometric measurement of [Ca²⁺]i in a typical amphistaltic fragment. (d) Kymograph of instantaneous longitudinal velocities of endoplasmic flow of the same amphistaltic fragment in Figure 10(]c).

Figure 11

(a) Kymograph of concentration of passive scalar in a mimic peristaltic fragment. (b) Kymograph of longitudinal velocities of endoplasmic flow representative of a peristaltic fragment. (c) Kymograph of concentration of passive scalar in a mimic amphistaltic fragment. (d) Kymograph of longitudinal velocities of endoplasmic flow of endoplasmic flow representative of an amphistaltic fragment.

Figure 12

Top row (a, c, e, g): Time histories of endoplasmic flow velocity ( ) and ratiometric measurement of [Ca²⁺]i ( ), averaged along the width of a peristaltic fragment (panels a and c) and an amphistaltic fragment (panels e and g). Bottom row (b, d, f, h): Time histories of endoplasmic flow velocity ( ) and peripheral traction stress ( ), averaged along the width of a peristaltic fragment (panels b and d) and an amphistaltic fragment (panels f and h). Panels (a, b, e, f): Fragment front. Panels (c, d, g, h): Fragment rear.