Mechanism of signal propagation in Physarum polycephalum

Abstract

Complex behaviors are typically associated with animals, but the capacity to integrate information and function as a coordinated individual is also a ubiquitous but poorly understood feature of organisms such as slime molds and fungi. Plasmodial slime molds grow as networks and use flexible, undifferentiated body plans to forage for food. How an individual communicates across its network remains a puzzle, but Physarum polycephalum has emerged as a novel model used to explore emergent dynamics. Within P. polycephalum, cytoplasm is shuttled in a peristaltic wave driven by cross-sectional contractions of tubes. We first track P. polycephalum's response to a localized nutrient stimulus and observe a front of increased contraction. The front propagates with a velocity comparable to the flow-driven dispersion of particles. We build a mathematical model based on these data and in the aggregate experiments and model identify the mechanism of signal propagation across a body: The nutrient stimulus triggers the release of a signaling molecule. The molecule is advected by fluid flows but simultaneously hijacks flow generation by causing local increases in contraction amplitude as it travels. The molecule is initiating a feedback loop to enable its own movement. This mechanism explains previously puzzling phenomena, including the adaptation of the peristaltic wave to organism size and P. polycephalum's ability to find the shortest route between food sources. A simple feedback seems to give rise to P. polycephalum's complex behaviors, and the same mechanism is likely to function in the thousands of additional species with similar behaviors.

Keywords: Taylor dispersion; acellular slime mold; behavior; transport network.

Fig. 1.

Propagating amplitude front. (A) Bright-field images of a P. polycephalum network before ($-$3 s, including approaching pipette) and after stimulation with a droplet of nutrient media. Droplet added at 0 s. Tubes swell where they make contact with the droplet (green arrow). (Scale bar, 2 mm.) (B) The same time points as in A showing contraction amplitude relative to the average over the last 10 periods before stimulation. Stimulation site marked by black arrow. The front (hot colors) spreads preferentially through tubes of larger radii. (C) Amplitude front and particle speeds extracted from bright-field dataset. (i) Locations of particle speed (blue) and front speed (magenta) measures. (ii) Contraction patterns at three different points further and further away from stimulation site. Dotted vertical lines mark sudden changes in contraction amplitude. (iii) Kymograph along trace in i showing change in contraction amplitude, observed as increased contrast during a contraction cycle. Front of increased amplitude propagates over time (red dashed line). (iv) Inset of iii: Particles advected along the tube appear as dark spotted trajectories. (v) Representative maximal speeds of particles (blue), located as pictured in i. Average front propagation speed (red) along trajectory in i as shown in iii.

Fig. S1.

Amplitude front propagation in two additional data sets. For both sets (A and B) i shows network morphology and stimulus site (green arrow). ii shows contraction patterns at three different points further and further away from stimulation site. Dotted vertical lines indicate a sudden change in contraction amplitude. iii shows a kymograph along the trace shown in i.

Fig. S2.

Maximal particle speed compared with net particle propagation speed. Shuttle flow of material can be seen in kymographs as sinusoidal patterns. Maximal particle speed (faster, yellow dashed line) corresponds to the steepest part of this sinusoid, whereas net propagation speed (slower, red dashed line) corresponds to incremental movements of the tips of the sinusoids along the tube.

Fig. 2.

Front speed identifies mechanism. (A) Propagation speeds for elastic waves (red), action potentials (blue), (19, 20), and P. polycephalum (green). Wave velocity in a fluid filled elastic tube varies between wave speed in the elastic wall (lower bound) and the fluid only (upper bound) (21). (B) Front speed increases with tube radius as predicted by the model. Amplitude fronts along tubes of a network centrally stimulated by nutrient droplet. Data show average speed and tube diameter with one SD error measured at five locations along the corresponding route (Inset). (Scale bar, 5 mm.)

Fig. 3.

Signal propagation in a theoretical model. (A) Sketch of a tube and the concentration of a signaling molecule within the tube over time (color gradient, see legend of C). The signal increases the amplitude of radial contractions (smaller radius at high concentration) and so establishes a self-propagating front of increased signal concentration and contraction amplitude. When a region of large contraction amplitude contracts (between two white lines marking amplitude front location) surroundings expand, or vice versa. (B) Kymograph of tube radius along the tube over time. Amplitude front is marked by phase jump between stimulated region and surroundings (white line). (C) Map of the time-averaged signal concentration; spread is caused by flow. The location of the front as measured by the position of the phase jump coincides with the mean averaged concentration across the tube at every time point (white line).

Fig. S3.

Quantification of front propagation in model. (A) Comparison of maximal flow velocity and front velocity over the course of the initial 15 periods after a concentration stimulus in the center for a tube. (B) Comparison of observed front diffusivity calculated from the variance of the time-averaged concentration over time, $\mathrm{var}(⟨c⟩)/2t$, the absolute value of the effective Taylor diffusivity according to Eq. 7 averaged over the area within the two fronts spreading right and left of stimulation site, and the molecular diffusivity.

Fig. S4.

Balance of tension and elastic forces approximates observed contraction and flow dynamics. Comparison of simulated (A) and calculated tube radius (B) according to Eq. 9 and the respective flow velocities (C and D). The calculated flow velocity follows from solving Eq. 5 given the approximated contractions. Note a fivefold decrease in scale for the flow velocities.

Fig. 4.

Decay into a stationary state of a single wavelength matching organism size. The initial condition is set as three undulations in radius along a tube (A) and a slightly randomized but otherwise constant concentration of the signaling molecule concentration (B). The feedback between concentration and contraction amplitude drives the system to a single undulation in radius and concentration; the wavelength matches the tube length. Note that high and low concentrations and radii at early time points are not representing their true value to accommodate the range generated at final time points.