Pruning to Increase Taylor Dispersion inPhysarum polycephalumNetworks

Abstract

How do the topology and geometry of a tubular network affect the spread of particles within fluid flows? We investigate patterns of effective dispersion in the hierarchical, biological transport network formed by Physarum polycephalum. We demonstrate that a change in topology -pruning in the foraging state -causes a large increase in effective dispersion throughout the network. By comparison, changes in the hierarchy of tube radii result in smaller and more localized differences. Pruned networks capitalize on Taylor dispersion to increase the dispersion capability.PACS numbers: 87.18. Vf, 87.16.Wd Transport due to fluid flowing through tubular networks is of great interest, because it has technological applications to biomimetic microfluidic devices [1][2][3], foams [4], fuel cells [5], and other filtration systems [6] and lies at the heart of extended organisms that rely on transport networks to function: animal vasculature [7,8], fungal mycelia [9], and plant tubes [10][11][12]. A big challenge regarding transport networks is to understand how network architecture changes the efficiency of particle spread throughout a network. While it is experimentally tedious to map particle transport in a network, predicting the spread of particles is also a theoretical challenge [13][14][15][16][17][18][19][20]. Attempts to understand how the network topology and geometry affect the transport of particles are scarce [17]. Alternatively, we can study the dynamic changes of tubular network architecture in living beings. Organisms spontaneously reorganize their transport networks, including tube pruning [21][22][23][24]. Examples are vessel development in zebra fish brain development [21], or growth of a large foraging fungal body [22]. Here, we study the slime mold Physarum polycephalum which emerged as an inspiring and yet puzzling model for 'intelligent' living transport networks.P. polycephalum like foraging fungi, actively adapts its network to environmental cues [25][26][27][28][29]. Networks connecting multiple food sources are a good compromise between efficiency, reliability, and cost, comparable to human transport networks [29]. Fluid cytoplasm enclosed in the tubular network exhibits nonstationary shuttle flows [30][31][32] driven by a peristaltic wave of contractions spanning the entire organism [33]. Investigations of transport in these networks are so far limited to estimates based on the minimal distance between tubes [29,34,35]. We tracked a well-reticulated individual trimmed from a larger network (Fig. 1). After several hours, the thin central tubes were abandoned in favor of a few large central tubes and globular structures at the periphery. How does this radical change of topology affect the transport capabilities of the individual? What role do hierarchical tube radii play? We present a method to efficiently map the effective dispersion of particles from any initiation site throughout any network with nonstationary but periodic fluid flows. We use this method to study the change in dispersion patterns ...

Mechanism of signal propagation in Physarum polycephalum

“…Signals may propagate via elastic waves (14) or an advected molecular stimulus (15,16) or electrical impulses (17). Our very recent work tentatively suggests the second hypothesis; flows generated from the coordinated contractions of tube walls are used to increase the effective dispersion of molecules substantially beyond their pure molecular diffusivity, a phenomenon known as Taylor dispersion (18). However, these different possibilities can be definitively distinguished by their velocities for signal propagation, which differ dramatically, and recognition of this fact opens up the possibility of understanding communication, the key to understanding behaviors.…”

“…Building on our previous observations (12,18), we now report and characterize the mechanism of communication in P. polycephalum and demonstrate that a simple feedback between a signaling molecule and a propagating contraction front is sufficient to explain P. polycephalum's sophisticated behaviors. The key experiment demonstrates that a localized nutrient stimulus…”

Mode Selection in Compressible Active Flow Networks

“…(2). This also promises that Bayesian methods like vbFRET will function as reliable inference tools for experimental data from reallife active flow networks [3,10].…”

“…Identifying generic self-organization principles [6,7] that control the dynamics of these biological or artificial far-fromequilibrium systems remains one of the foremost challenges of modern statistical physics. Despite promising experimental [3,[8][9][10] and theoretical [1,4,[11][12][13] advances over the past decade, it is not well understood how the interactions between local energy input, dissipation, and network topology determine the coordinated global behaviors of cells [8], plasmodia [3], or tissues [14]. Further progress requires analytically tractable models that help clarify the underlying nonequilibrium mode-selection principles [15].…”

“…Identifying generic self-organization principles [6,7] that control the dynamics of these biological or artificial far-fromequilibrium systems remains one of the foremost challenges of modern statistical physics. Despite promising experimental [3,[8][9][10] and theoretical [1,4,[11][12][13] advances over the past decade, it is not well understood how the interactions between local energy input, dissipation, and network topology determine the coordinated global behaviors of cells [8] [19], the theory accounts for network activity through a nonlinear friction [19][20][21]. We work in a fully compressible framework allowing accumulated matter at vertices to affect flow through network pressure gradients, generalizing previous work on incompressible pseudoequilibrium active flow networks [22,23], as suited to the many biological systems exhibiting flexible network geometry [3] or variations in the density of active components [7].…”