Encoding memory in tube diameter hierarchy of living flow network

Abstract

The concept of memory is traditionally associated with organisms possessing a nervous system. However, even very simple organisms store information about past experiences to thrive in a complex environment-successfully exploiting nutrient sources, avoiding danger, and warding off predators. How can simple organisms encode information about their environment? We here follow how the giant unicellular slime mold Physarum polycephalum responds to a nutrient source. We find that the network-like body plan of the organism itself serves to encode the location of a nutrient source. The organism entirely consists of interlaced tubes of varying diameters. Now, we observe that these tubes grow and shrink in diameter in response to a nutrient source, thereby imprinting the nutrient's location in the tube diameter hierarchy. Combining theoretical model and experimental data, we reveal how memory is encoded: a nutrient source locally releases a softening agent that gets transported by the cytoplasmic flows within the tubular network. Tubes receiving a lot of softening agent grow in diameter at the expense of other tubes shrinking. Thereby, the tubes' capacities for flow-based transport get permanently upgraded toward the nutrient location, redirecting future decisions and migration. This demonstrates that nutrient location is stored in and retrieved from the networks' tube diameter hierarchy. Our findings explain how network-forming organisms like slime molds and fungi thrive in complex environments. We here identify a flow networks' version of associative memory-very likely of relevance for the plethora of living flow networks as well as for bioinspired design.

Keywords: adaptive networks; behavior; decision making; flow networks.

Fig. 1.

Memory of a nutrient stimulus’ position is encoded in network hierarchy. Bright-field images of a foraging P. polycephalum network subject to a localized nutrient stimulus (red arrow) applied at 0 min. The network previously migrating to the right reorganizes migration direction facing the nutrient within 45 min. Subsequently, nutrient is exhausted (90 min) until foraging is resumed (310 min). Nutrient location is imprinted in the network hierarchy by thick tubes formed around the nutrient source—persisting long after the nutrient is consumed.

Fig. 2.

Rapidly after nutrient stimulus application, hierarchy of tube diameters changes, establishing a new migration direction. (A) Bright-field images of a network before and after the application of a nutrient stimulus (red arrow). A new migration direction is being created at the top of the network. (B) Relative tube growth over the 45 min after stimulus (red dot) application. While overall mass is redistributed from the bottom to the top of the network, close to the stimulus site, initially larger tubes lose less mass, thus increasing network hierarchy. N(tubes) = 2,165.

Fig. 3.

Tube dilation propagates by flow transport velocity from stimulus site. Here depicted is the evolution of relative tube diameters in the entire network. Individual tubes are sorted by their Euclidean distance to the stimulus site. Stimulus time is denoted by the white vertical line. The speed of the dilation front triggered by stimulus matches flow advection velocity of P. polycephalum networks. N(tubes) = 2,165.

Fig. 4.

Theoretical model of elastic tube dilation triggered by flow-transported softening agent captures characteristic tube dynamics observed in the experiment. (A) Predictions of a theoretical model of a closed peristaltic tube (sketch) on the tube diameter dynamics at the marked segments. Releasing a soluble wall-softening agent (red symbol/vertical line) within the elastic tube predicts characteristic tube dilation and relaxation. Tube dilation response time (dotted line) is shifted in time due to the agent being transported by peristaltic flow. (B) A decrease in contraction frequency slowing down flows directly increases the tube segment’s response time until dilation. (C) Experimental tube diameter dynamics are fully classified into the two characteristic dynamics predicted by the model (sketch). The dynamics of the mean tube diameter averaged over each ensemble of tubes follow theoretically predicted tube dynamics. N(tubes) = 2,165. (D) Quantification of the response time until dilation in experimental datasets shows increase of response time with decreasing contraction frequency, in line with theory. Error bars show the full range of tube response times in every dataset. N(tubes) = 2,165, 486, 438, and 45 for 10, 8, 6, and 4 mHz, respectively.

Fig. 5.

Network reads out memory encoded in network hierarchy by previous stimuli. (A) Bright-field image of the plasmodial network right after stimulus application as in Fig. 2. (B) Within the part of the network overall undergoing shrinkage (Fig. 4C), thick transport tubes positioned close (red) and far (orange) with respect to stimulus differ in dynamics. The average tube diameters of the tubes closer by flow-based travel time to stimulus undergo negligible shrinkage and recover their prestimulus diameter, whereas the tubes farther away shrink overall permanently.