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

Abstract

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.

Emergence of behaviour in a self-organized living matter network

“…The most powerful aspect of P. polycephalum as a model organism of behaviour lies in the direct link between actomyosin contractions, resulting in cytoplasmic flows and emerging behaviours. The broad understanding of the theory of active contractions ( Bois et al, 2011 ; Radszuweit et al, 2013 ; Radszuweit et al, 2014 ; Julien and Alim, 2018 ; Kulawiak et al, 2019 ) might therefore well be the foundation to formulate the physics of behaviour not only in P. polycephalum but also in other simple organisms. This would not only open up an new perspective on life but also guide the design of bio-inspired soft robots with a behavioural repertoire comparable to higher organisms.…”

“…So far, only one type of network-spanning peristaltic contraction pattern has been described experimentally ( Alim et al, 2013 ; Oettmeier et al, 2017 ). However, for small P. polycephalum plasmodial fragments various other short-range contraction patterns have been observed ( Lewis et al, 2015 ; Zhang et al, 2017 ) and predicted by theory of active contractions ( Bois et al, 2011 ; Radszuweit et al, 2013 ; Radszuweit et al, 2014 ; Julien and Alim, 2018 ; Kulawiak et al, 2019 ). Similarly, up to now unknown complex, large-scale contraction patterns might play a role in generating the behaviour of large P. polycephalum networks.…”

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

“…Yochelis et al [ 151 ] showed that the minimal IAW model in one space dimension, in the setting of Equations (5), may indeed support rich and robust spatiotemporal dynamics following pulse collisions, in contrast to IAW models which do not contain explicit mass conservation [ 28 , 55 , 81 , 163 , 164 ]: Annihilation, reflection, and “birth” of new pulses after reflection, as shown in Figure 3 . In a broader RD context, where similar aspects have been also observed, these dynamics do not require special properties, such as non-locality [ 165 , 166 , 167 , 168 ], cross-diffusion [ 169 ], and heterogeneity [ 170 , 171 , 172 ].…”

“…More specifically, we are interested in IAW that are affected by a large-scale mode—a situation that arises due to the conservation of actin monomers (over the time-scale of the IAW phenomenon). We note that phenomena such as waves are, in general, beyond the scope of this perspective as they involve the transport of ions between the cell interior and the extracellular space (which acts as an infinite reservoir) [ 26 , 27 , 28 ], unless conservation can be accounted for [ 29 ]. Moreover, we emphasize that we aim to provide a perspective and not a comprehensive review, as such reviews are already available, see, e.g., in [ 30 , 31 , 32 , 33 , 34 , 35 , 36 ].…”

Emergence of behavior in a self-organized living matter network

“…So far only one type of network-spanning peristaltic contraction pattern has been described experimentally (22,29). However, for small P. polycephalum plasmodial fragments various other short-range contraction patterns have been observed (25,26) and predicted by theory of active contractions (30)(31)(32)(33)(34). Similarly, up to now unknown complex, largescale contraction patterns might play a role in generating the behavior of large P. polycephalum networks.…”