An active poroelastic model for mechanochemical patterns in protoplasmic droplets of Physarum polycephalum

Influence of physical interactions on spatiotemporal patterns

Spatiotemporal patterns are often modeled using reaction-diffusion equations, which combine complex reactions between constituents with ideal diffusive motion. Such descriptions neglect physical interactions between constituents, which might affect resulting patterns. To overcome this, we study how physical interactions affect cyclic dominant reactions, like the seminal rock-paper-scissors game, which exhibits spiral waves for ideal diffusion. Generalizing diffusion to incorporate physical interactions, we find that weak interactions change the length- and time scales of spiral waves, consistent with a mapping to the complex Ginzburg-Landau equation. In contrast, strong repulsive interactions typically generate oscillating lattices, and strong attraction leads to an interplay of phase separation and chemical oscillations, like droplets co-locating with cores of spiral waves. Our work suggests that physical interactions are relevant for forming spatiotemporal patterns in nature, and it might shed light on how biodiversity is maintained in ecological settings.

Emergence of behaviour in a self-organized living matter network

What is the origin of behaviour? Although typically associated with a nervous system, simple organisms also show complex behaviours. Among them, the slime mold Physarum polycephalum, a giant single cell, is ideally suited to study emergence of behaviour. Here, we show how locomotion and morphological adaptation behaviour emerge from self-organized patterns of rhythmic contractions of the actomyosin lining of the tubes making up the network-shaped organism. We quantify the spatio-temporal contraction dynamics by decomposing experimentally recorded contraction patterns into spatial contraction modes. Notably, we find a continuous spectrum of modes, as opposed to a few dominant modes. Our data suggests that the continuous spectrum of modes allows for dynamic transitions between a plethora of specific behaviours with transitions marked by highly irregular contraction states. By mapping specific behaviours to states of active contractions, we provide the basis to understand behaviour’s complexity as a function of biomechanical dynamics.

Living systems are smarter bots: Slime mold semiosis versus AI symbol manipulation

Although machines may be good at mimicking, they are not currently able, as organisms are, to act creatively. We offer an understanding of the emergent qualities of biological sign processing in terms of generalization, association, and encryption. We use slime mold as a model of minimal cognition and compare it to deep-learning video game bots, which some claim have evolved beyond their merely quantitative algorithms. We find that these discrete Turing machine bots are not able to make productive, yet unanticipated, "errors"-necessary for biological learning-which, based on the physicality of signs, their relatively similar shapes, and relative physical positions spatially and temporally, lead to emergent effects and make learning and evolution possible. In organisms, stochastic resonance at the local level can be leveraged for self-organization at the global level. We contrast all this to the symbolic processing of today's machine learning, whereby each logic node and memory state is discrete. Computer codes are produced by external operators, whereas biological symbols are evolved through an internal encryption process.

Adaptive behaviour and learning in slime moulds: the role of oscillations

The slime mould Physarum polycephalum, an aneural organism, uses information from previous experiences to adjust its behaviour, but the mechanisms by which this is accomplished remain unknown. This article examines the possible role of oscillations in learning and memory in slime moulds. Slime moulds share surprising similarities with the network of synaptic connections in animal brains. First, their topology derives from a network of interconnected, vein-like tubes in which signalling molecules are transported. Second, network motility, which generates slime mould behaviour, is driven by distinct oscillations that organize into spatio-temporal wave patterns. Likewise, neural activity in the brain is organized in a variety of oscillations characterized by different frequencies. Interestingly, the oscillating networks of slime moulds are not precursors of nervous systems but, rather, an alternative architecture. Here, we argue that comparable information-processing operations can be realized on different architectures sharing similar oscillatory properties. After describing learning abilities and oscillatory activities of P. polycephalum, we explore the relation between network oscillations and learning, and evaluate the organism's global architecture with respect to information-processing potential. We hypothesize that, as in the brain, modulation of spontaneous oscillations may sustain learning in slime mould. This article is part of the theme issue 'Basal cognition: conceptual tools and the view from the single cell'.

Active poroelastic two-phase model for the motion of physarum microplasmodia

The onset of self-organized motion is studied in a poroelastic two-phase model with free boundaries for Physarum microplasmodia (MP). In the model, an active gel phase is assumed to be interpenetrated by a passive fluid phase on small length scales. A feedback loop between calcium kinetics, mechanical deformations, and induced fluid flow gives rise to pattern formation and the establishment of an axis of polarity. Altogether, we find that the calcium kinetics that breaks the conservation of the total calcium concentration in the model and a nonlinear friction between MP and substrate are both necessary ingredients to obtain an oscillatory movement with net motion of the MP. By numerical simulations in one spatial dimension, we find two different types of oscillations with net motion as well as modes with time-periodic or irregular switching of the axis of polarity. The more frequent type of net motion is characterized by mechano-chemical waves traveling from the front towards the rear. The second type is characterized by mechano-chemical waves that appear alternating from the front and the back. While both types exhibit oscillatory forward and backward movement with net motion in each cycle, the trajectory and gel flow pattern of the second type are also similar to recent experimental measurements of peristaltic MP motion. We found moving MPs in extended regions of experimentally accessible parameters, such as length, period and substrate friction strength. Simulations of the model show that the net speed increases with the length, provided that MPs are longer than a critical length of ≈ 120 μm. Both predictions are in line with recent experimental observations.

A lumped parameter model of endoplasm flow in Physarum polycephalum explains migration and polarization-induced asymmetry during the onset of locomotion

The plasmodial slime mold Physarum polycephalum exhibits strong, periodic flow of cytoplasm through the veins of its network. In the special case of mesoplasmodia, a newly described starvation-induced, shape-constant morphotype, this periodic endoplasm streaming is the basis of locomotion. Furthermore, we presume that cytoplasm flow is also involved in signal transmission and signal processing. Mesoplasmodia motility resembles amoeboid locomotion. In contrast to other amoebae, however, mesoplasmodia move without extending pseudopods and retain a coherent, fan-shaped morphology throughout their steady locomotion. Attaining sizes of up to 2 mm², mesoplasmodia are also much bigger than other amoebae. We characterize this particular type of locomotion and identify patterns of movement. By using the analogy between pulsatile fluid flow through a network of elastic tubes and electrical circuits, we build a lumped model that explains observed fluid flow patterns. Essentially, the mesoplasmodium acts as a low-pass filter, permitting only low-frequency oscillations to propagate from back to front. This frequency selection serves to optimize flow and reduces power dissipation. Furthermore, we introduce a distributed element into the lumped model to explain cell polarization during the onset of chemotaxis: Biochemical cues (internal or external) lead to a local softening of the actin cortex, which in turn causes an increased flow of cytoplasm into that area and, thus, a net forward movement. We conclude that the internal actin-enclosed vein network gives the slime mold a high measure of control over fluid transport, especially by softening or hardening, which in turn leads to polarization and net movement.

Oscillatory fluid flow drives scaling of contraction wave with system size

Flows over remarkably long distances are crucial to the functioning of many organisms, across all kingdoms of life. Coordinated flows are fundamental to power deformations, required for migration or development, or to spread resources and signals. A ubiquitous mechanism to generate flows, particularly prominent in animals and amoebas, is actomyosin cortex-driven mechanical deformations that pump the fluid enclosed by the cortex. However, it is unclear how cortex dynamics can self-organize to give rise to coordinated flows across the largely varying scales of biological systems. Here, we develop a mechanochemical model of actomyosin cortex mechanics coupled to a contraction-triggering, soluble chemical. The chemical itself is advected with the flows generated by the cortex-driven deformations of the tubular-shaped cell. The theoretical model predicts a dynamic instability giving rise to stable patterns of cortex contraction waves and oscillatory flows. Surprisingly, simulated patterns extend beyond the intrinsic length scale of the dynamic instability-scaling with system size instead. Patterns appear randomly but can be robustly generated in a growing system or by flow-generating boundary conditions. We identify oscillatory flows as the key for the scaling of contraction waves with system size. Our work shows the importance of active flows in biophysical models of patterning, not only as a regulating input or an emergent output, but also as a full part of a self-organized machinery. Contractions and fluid flows are observed in all kinds of organisms, so this concept is likely to be relevant for a broad class of systems.

Differential Activity-Driven Instabilities in Biphasic Active Matter

Active stresses can cause instabilities in contractile gels and living tissues. Here we provide a generic hydrodynamic theory that treats these systems as a mixture of two phases of varying activity and different mechanical properties. We find that differential activity between the phases causes a uniform mixture to undergo a demixing instability. We follow the nonlinear evolution of the instability and characterize a phase diagram of the resulting patterns. Our study complements other instability mechanisms in mixtures driven by differential adhesion, differential diffusion, differential growth, and differential motion.

Current reinforcement model reproduces center-in-center vein trajectory of Physarum polycephalum

Vein networks span the whole body of the amoeboid organism in the plasmodial slime mould Physarum polycephalum, and the network topology is rearranged within an hour in response to spatio-temporal variations of the environment. It has been reported that this tube morphogenesis is capable of solving mazes, and a mathematical model, named the 'current reinforcement rule', was proposed based on the adaptability of the veins. Although it is known that this model works well for reproducing some key characters of the organism's maze-solving behaviour, one important issue is still open: In the real organism, the thick veins tend to trace the shortest possible route by cutting the corners at the turn of corridors, following a center-in-center trajectory, but it has not yet been examined whether this feature also appears in the mathematical model, using corridors of finite width. In this report, we confirm that the mathematical model reproduces the center-in-center trajectory of veins around corners observed in the maze-solving experiment.

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

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.

Coordination of contractility, adhesion and flow in migrating Physarum amoebae

This work examines the relationship between spatio-temporal coordination of intracellular flow and traction stress and the speed of amoeboid locomotion of microplasmodia of Physarum polycephalum. We simultaneously perform particle image velocimetry and traction stress microscopy to measure the velocity of cytoplasmic flow and the stresses applied to the substrate by migrating Physarum microamoebae. In parallel, we develop a mathematical model of a motile cell which includes forces from the viscous cytosol, a poro-elastic, contractile cytoskeleton and adhesive interactions with the substrate. Our experiments show that flow and traction stress exhibit back-to-front-directed waves with a distinct phase difference. The model demonstrates that the direction and speed of locomotion are determined by this coordination between contraction, flow and adhesion. Using the model, we identify forms of coordination that generate model predictions consistent with experiments. We demonstrate that this coordination produces near optimal migration speed and is insensitive to heterogeneity in substrate adhesiveness. While it is generally thought that amoeboid motility is robust to changes in extracellular geometry and the nature of extracellular adhesion, our results demonstrate that coordination of adhesive forces is essential to producing robust migration.

Patterns of cell thickness oscillations during directional migration of Physarum polycephalum

The functional relationship between the velocity of cell locomotion and intracellular spatial patterns of thickness oscillations in the acellular slime mould Physarum polycephalum was studied. The freely migrating plasmodial cells of 300-800 µm length were tadpole-shaped and displayed thickness oscillations along their longitudinal (body) axis. Two distinct patterns of intracellular thickness oscillations were observed in dependence on the locomotive velocity. The first mode consisted of a single travelling wave that propagated from the rear to the front of the cell. This pattern occurred when the plasmodium migrated slowly. The second mode was a multinodal standing wave that was found during events of fast propagation. Transitions between these two types of cell thickness oscillation patterns took place in narrow propagation velocity intervals. We discuss the possible mechanism leading to these patterns, which are conjectured to modulate both the intracellular pressure and the velocity of free locomotion of the cell.