Oscillatory motion of a droplet in an active poroelastic two-phase model

Kulawiak, Dirk Alexander; Löber, Jakob; Bär, Markus; Engel, Harald

doi:10.1088/1361-6463/aae41d

Cited by 9 publications

(36 citation statements)

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“…flows give rise to pattern formation in a resting droplet [37]. In [38], we have studied 49 this model with free boundary conditions and linear friction between droplet and 50 substrate. While we were able to observe back and forth motion of the boundaries, the 51 center of mass (COM) position remained fixed.…”

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“…52 Moreover, we derived an argument that COM motion is impossible with a spatially 53 homogeneous substrate friction. Furthermore, numerical simulations have shown that 54 an additional mechanism establishing an axis of polarity that is stable on long 55 timescales is necessary for net motion [38]. 56 In this work, we proceed in two steps.…”

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“…56 In this work, we proceed in two steps. First we extend the model described in [38] 57 with a nonlinear slip-stick friction between droplet and substrate to create a spatially 58 heterogeneous substrate friction. Second, we consider a specific model derived for 59 Physarum MP that contains a reaction kinetics.…”

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“…To 109 May 6, 2019 3/20 circumvent this problem, we formulate the model in a co-moving body reference frame. 110 The details of the transformation from the laboratory to the body reference frame can 111 be found in [37][38][39]. S1 Fig displays a visual comparison of a quantity plotted in the 112 body reference and the laboratory frame.…”

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confidence: 99%

“…In [38], we identified a heterogeneous substrate friction as a requisite for motion of 123 the MP's center of mass (COM). While the exact nature of the Physarum friction 124 dynamics is not known, recent experiments indicate that MP exhibit nonlinear slip-stick 125 friction with an underlying substrate resulting in a heterogeneous friction [13].…”

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Active Poroelastic Two-Phase Model for the Motion of Physarum Microplasmodia

Kulawiak

LoÌˆber

BaÌˆr

et al. 2019

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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. 1 Introduction 1 Dynamic processes in biological systems such as cells are examples of when 2 spatio-temporal patterns develop far from thermodynamic equilibrium [1, 2]. One 3 fascinating instance of such active matter are intracellular molecular motors that 4 consume ATP [3] and can drive mechano-chemical contraction-expansion patterns [4] 5 and, ultimately, cell locomotion. Further biological examples of such phenomena are 6 discussed in [5-7]. 7 The true slime mold Physarum polycephalum is a well known model organism [8] 8 that exhibits mechano-chemical spatio-temporal patterns. Previous research in 9 Physarum has addressed many different topics in biophysics, such as genetic activity [9], 10 habituation [10], decision making [11] and cell locomotion [12, 13]. Physarum is an 11 May 6, 2019 1/20 unicellular organism, which builds large networks that exhibit self-organized 12 synchronized contraction patterns [8, 14, 15]. These contractions enable shuttle 13 streaming in the tubular veins of the network and allow for efficient nutrient transport 14 throughout the organism [16]. Many groups have investigated the network's 15 dynamics [17-19], however size and complex topology of these networks make analyzing 16 and modeling them challenging. 17 Physarum microplasmodia (MP) allow one to study Physarum's internal dynamics 18 in a simpler setup. These MPs ca...

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