Fluid flows shaping organism morphology

A dynamic self-organized morphology is the hallmark of network-shaped organisms like slime moulds and fungi. Organisms continuously re-organize their flexible, undifferentiated body plans to forage for food. Among these organisms the slime mould Physarum polycephalum has emerged as a model to investigate how organism can self-organize their extensive networks and act as a coordinated whole. Cytoplasmic fluid flows flowing through the tubular networks have been identified as key driver of morphological dynamics. Inquiring how fluid flows can shape living matter from small to large scales opens up many new avenues for research.Comment: 5 pages, 2 figures, perspectiv

Flow rate of transport network controls uniform metabolite supply to tissue

Life and functioning of higher organisms depends on the continuous supply of metabolites to tissues and organs. What are the requirements on the transport network pervading a tissue to provide a uniform supply of nutrients, minerals, or hormones? To theoretically answer this question, we present an analytical scaling argument and numerical simulations on how flow dynamics and network architecture control active spread and uniform supply of metabolites by studying the example of xylem vessels in plants. We identify the fluid inflow rate as the key factor for uniform supply. While at low inflow rates metabolites are already exhausted close to flow inlets, too high inflow flushes metabolites through the network and deprives tissue close to inlets of supply. In between these two regimes, there exists an optimal inflow rate that yields a uniform supply of metabolites. We determine this optimal inflow analytically in quantitative agreement with numerical results. Optimizing network architecture by reducing the supply variance over all network tubes, we identify patterns of tube dilation or contraction that compensate sub-optimal supply for the case of too low or too high inflow rate.Comment: 11 pages, 4 figures, 8 pages supplemen

Shapes of Semiflexible Polymer Rings

The shape of semiflexible polymer rings is studied over their whole range of flexibility. Investigating the joint distribution of asphericity and nature of asphericity as well as their respective averages we find two distinct shape regimes depending on the flexibility of the polymer. For small perimeter to persistence length the fluctuating rings exhibit only planar, elliptical configurations. At higher flexibilities three dimensional, crumpled structures arise. Analytic calculations for tight polymer rings confirm an elliptical shape in the stiff regime.Comment: 4 pages, 3 figures, Version as published in Phys. Rev. Let

Spatial mapping reveals multi-step pattern of wound healing in Physarum polycephalum

Wounding is a severe impairment of function, especially for an exposed organism like the network-forming true slime mould Physarum polycephalum. The tubular network making up the organism's body plan is entirely interconnected and shares a common cytoplasm. Oscillatory contractions of the enclosing tube walls drive the shuttle streaming of the cytoplasm. Cytoplasmic flows underlie the reorganization of the network for example by movement toward attractive stimuli or away from repellants. Here, we follow the reorganization of Physarum polycephalum networks after severe wounding. Spatial mapping of the contraction changes in response to wounding reveal a multi-step pattern. Phases of increased activity alternate with cessation of contractions and stalling of flows, giving rise to coordinated transport and growth at the severing site. Overall, severing surprisingly acts like an attractive stimulus enabling healing of severed tubes. The reproducible cessation of contractions arising during this wound-healing response may open up new venues to investigate the biochemical wiring underlying Physarum polycephalum's complex behaviours.Comment: Felix B\"auerle and Mirna Kramar contributed equally to this wor

Buckling of stiff polymer rings in weak spherical confinement

Confinement is a versatile and well-established tool to study the properties of polymers either to understand biological processes or to develop new nanobiomaterials. We investigate the conformations of a semiflexible polymer ring in weak spherical confinement imposed by an impenetrable shell. We develop an analytic argument for the dominating polymer trajectory depending on polymer flexibility considering elastic and entropic contributions. Monte Carlo simulations are performed to assess polymer ring conformations in probability densities and by the shape measures asphericity and nature of asphericity. Comparison of the analytic argument with the mean asphericity and the mean nature of asphericity confirm our reasoning to explain polymer ring conformations in the stiff regime, where elastic response prevails

Local pore size correlations determine flow distributions in porous media

The relationship between the microstructure of a porous medium and the observed flow distribution is still a puzzle. We resolve it with an analytical model, where the local correlations between adjacent pores, which determine the distribution of flows propagated from one pore downstream, predict the flow distribution. Numerical simulations of a two-dimensional porous medium verify the model and clearly show the transition of flow distributions from $\delta$-function-like via Gaussians to exponential with increasing disorder. Comparison to experimental data further verifies our numerical approach.Comment: 5 pages, 3 figures, supplemental materia

Controlling effective dispersion within a channel with flow and active walls

Channels are fundamental building blocks from biophysics to soft robotics, often used to transport or separate solutes. As solute particles inevitably transverse between streamlines along the channel by molecular diffusion, the effective diffusion of the solute along the channel is enhanced - an effect known as Taylor dispersion. Here, we investigate how the Taylor dispersion effect can be suppressed or enhanced in different settings. Specifically, we study the impact of flow profile and active or pulsating channel walls on Taylor dispersion. We derive closed analytic expressions for the effective dispersion equation in all considered scenarios providing hands-on effective dispersion parameters for a multitude of applications. In particular, we find that active channel walls may lead to three regimes of dispersion: either dispersion decrease by entropic slow down at small Peclet number, or dispersion increase at large Peclet number dominated either by shuttle dispersion or by Taylor dispersion. This improves our understanding of solute transport e.g. in biological active systems such as blood flow and opens a number of possibilities to control solute transport in artificial systems such as soft robotics

Pruning to Increase Taylor Dispersion in Physarum polycephalum Networks

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.Comment: 5 pages, 4 figures, 11 pages supplemental materia

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 amoeba, is acto-myosin cortex driven mechanical deformations that pump the fluid enclosed by the cortex. Yet, 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 acto-myosin 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 rather 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.Comment: 7 pages, 5 figure

Regulatory Role of Cell Division Rules on Tissue Growth Heterogeneity

The coordination of cell division and cell expansion are critical to normal development of tissues. In plants, cell wall mechanics and the there from arising cell shapes and mechanical stresses can regulate cell division and cell expansion and thereby tissue growth and morphology. Limited by experimental accessibility it remains unknown how cell division and expansion cooperatively affect tissue growth dynamics. Employing a cell-based two dimensional tissue simulation we investigate the regulatory role of a range of cell division rules on tissue growth dynamics and in particular on the spatial heterogeneity of growth. We find that random cell divisions only add noise to the growth and therefore increase growth heterogeneity, while cell divisions following the shortest new wall or along the direction of maximal mechanical stress reduce growth heterogeneity by actively enhancing the regulation of growth by mechanical stresses. Thus, we find that, beyond tissue geometry and topology, cell divisions affect the dynamics of growth, and that their signature is embedded in the statistics of tissue growth.Engineering and Applied Science