Random network peristalsis in Physarum polycephalum organizes fluid flows across an individual

Abstract

Individuals can function as integrated organisms only when information and resources are shared across a body. Signals and substrates are commonly moved using fluids, often channeled through a network of tubes. Peristalsis is one mechanism for fluid transport and is caused by a wave of cross-sectional contractions along a tube. We extend the concept of peristalsis from the canonical case of one tube to a random network. Transport is maximized within the network when the wavelength of the peristaltic wave is of the order of the size of the network. The slime mold Physarum polycephalum grows as a random network of tubes, and our experiments confirm peristalsis is used by the slime mold to drive internal cytoplasmic flows. Comparisons of theoretically generated contraction patterns with the patterns exhibited by individuals of P. polycephalum demonstrate that individuals maximize internal flows by adapting patterns of contraction to size, thus optimizing transport throughout an organism. This control of fluid flow may be the key to coordinating growth and behavior, including the dynamic changes in network architecture seen over time in an individual.

Keywords: acellular; fungi; myxomycete.

Fig. 1.

(A) Bright-field image of P. polycephalum, a true slime mold (myxomycete) that grows as a network of tubes. (B) Transmitted light intensity at two sample tubes as a function of time. Vertical lines indicate maxima of oscillations. The oscillating cross-sectional contractions of a tube directly modulate the intensity of transmitted light (Fig. S1), enabling the contraction state and the phase of contractions over time to be identified and tracked. Phase as a function of time is shown at the top of each graph, using a periodic color code that cycles from black at zero to blue, green, and red and then back to black at 2π.

Fig. 2.

Testing for a causal relationship between cross-sectional tube contractions and cytoplasmic flows. (A) Overlay of bright-field (gray) and fluorescent (red and green) images, to simultaneously measure tube radius along a tube over time and track fluorescent beads advected by the flow. Moving beads, indicated by arrows, are red in an initial time frame and green in the time frame taken 1 s later. (B) Illustration of how cross-sectional contractions (black arrows) of a tube of radius a drive fluid flow (blue streamlines) along a 3D tube extending in radial r and longitudinal z dimensions. (C) Flows predicted by the contracting tube model based on experimentally obtained tube radii. Flow to the right, away from the tube end (0 mm), is shown in red and that toward the tube end is in blue, highlighting flow arrests (marked by asterisks) and reversals in white. Overlaid experimental time points of real flow reversals (dashed lines) show very good agreement with the model. Moreover, time points where the model predicts that the flow arrests without reversing its direction (asterisks) correspond to what is observed experimentally (Movie S1).

Fig. 3.

(A–C) Typical phase patterns of P. polycephalum networks ranging from approximately (A) 17 mm to (C) 3 mm. Independently of size, an almost linear phase gradient establishes across the network. The gradient encompasses a single cycle of zero to 2π extending along the longest axis of an individual. Colors mark the phases of contractions calculated as the fraction of the contraction cycle elapsed relative to the last maximum (Fig. 1B). (A and B, Top) Black rectangles mark the approximate regions cut at the end of each experiment to obtain the medium network (B) from the large network (A) and the small network (C) from the medium network (B), respectively. For tube architecture see bright-field data in Fig. S6.

Fig. 4.

Networks optimized for minimal local phase difference maximize particle transport. Numerically calculated mean displacement of tracer particles within the large real P. polycephalum network architecture of Fig. 3A is shown here for theoretically optimized (Inset A, solid line) and random (Inset B, dashed line) phase patterns. The mean displacement is normalized by the largest distance L in the network. Arrows mark the site of tracer initiation.

Fig. 5.

(A and B) Qualitative agreement between measured (A) and theoretically derived (B) phase correlations for individuals shown in Fig. 3. All phase correlations display a single minimum, as predicted for a single wavelength along a tube shown in B. At large distances correlations are averaged out because much of the network extends perpendicular to the direction of the gradient. Experimental data are mean values averaged from a 276-s time frame; theoretical data are the mean of 100 independent runs, and so the statistical error is less than line thickness.