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

Calcium regulates cortex contraction inPhysarum polycephalum

The tubular network-forming slime moldPhysarum polycephalumis able to maintain long-scale contraction patterns driven by an actomyosin cortex. The resulting shuttle streaming in the network is crucial for the organism to respond to external stimuli and reorganize its body mass giving rise to complex behaviors. However, the chemical basis of the self-organized flow pattern is not fully understood. Here, we present ratiometric measurements of free intracellular calcium in simple morphologies ofPhysarumnetworks. The spatiotemporal patterns of the free calcium concentration reveal a nearly anti-correlated relation to the tube radius, suggesting that calcium is indeed a key regulator of the actomyosin activity. We compare the experimentally observed phase relation between the radius and the calcium concentration to the predictions of a theoretical model including calcium as an inhibitor. Numerical simulations of the model suggest that calcium indeed inhibits the contractions inPhysarum, although a quantitative difference to the experimentally measured phase relation remains. Unraveling the mechanism underlying the contraction patterns is a key step in gaining further insight into the principles ofPhysarum's complex behavior.

From actin waves to mechanism and back: How theory aids biological understanding

Actin dynamics in cell motility, division, and phagocytosis is regulated by complex factors with multiple feedback loops, often leading to emergent dynamic patterns in the form of propagating waves of actin polymerization activity that are poorly understood. Many in the actin wave community have attempted to discern the underlying mechanisms using experiments and/or mathematical models and theory. Here, we survey methods and hypotheses for actin waves based on signaling networks, mechano-chemical effects, and transport characteristics, with examples drawn from Dictyostelium discoideum, human neutrophils, Caenorhabditis elegans, and Xenopus laevis oocytes. While experimentalists focus on the details of molecular components, theorists pose a central question of universality: Are there generic, model-independent, underlying principles, or just boundless cell-specific details? We argue that mathematical methods are equally important for understanding the emergence, evolution, and persistence of actin waves and conclude with a few challenges for future studies.

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.

Why a Large-Scale Mode Can Be Essential for Understanding Intracellular Actin Waves

During the last decade, intracellular actin waves have attracted much attention due to their essential role in various cellular functions, ranging from motility to cytokinesis. Experimental methods have advanced significantly and can capture the dynamics of actin waves over a large range of spatio-temporal scales. However, the corresponding coarse-grained theory mostly avoids the full complexity of this multi-scale phenomenon. In this perspective, we focus on a minimal continuum model of activator-inhibitor type and highlight the qualitative role of mass conservation, which is typically overlooked. Specifically, our interest is to connect between the mathematical mechanisms of pattern formation in the presence of a large-scale mode, due to mass conservation, and distinct behaviors of actin waves.