Hemodynamic regulation allows stable growth of microvascular networks.

How do vessels find optimal radii? Capillaries are known to adapt their radii to maintain the shear stress of blood flow at the vessel wall at a set point, yet models of adaptation purely based on average shear stress have not been able to produce complex loopy networks that resemble real microvascular systems. For narrow vessels where red blood cells travel in a single file, the shear stress on vessel endothelium peaks sharply when a red blood cell passes through. We show that stable shear-stress-based adaptation is possible if vessel shear stress set points are cued to the stress peaks. Model networks that respond to peak stresses alone can quantitatively reproduce the observed zebrafish trunk microcirculation, including its adaptive trajectory when hematocrit changes or parts of the network are amputated. Our work reveals the potential for mechanotransduction alone to generate stable hydraulically tuned microvascular networks.

Mitigating transcription noise via protein sharing in syncytial cells.

Bursty transcription allows nuclei to concentrate the work of transcribing mRNA into short, intermittent intervals, potentially reducing transcriptional interference. However, bursts of mRNA production can increase noise in protein abundances. Here, we formulate models for gene expression in syncytia, or multinucleate cells, showing that protein abundance noise may be mitigated locally via spatial averaging of diffuse proteins. Our modeling shows a universal reduction in protein noise, which increases with the average number of nuclei per cell and persists even when the number of nuclei is itself a random variable. Experimental data comparing distributions of a cyclin mRNA that is conserved between brewer's yeast and a closely related filamentous fungus Ashbya gossypii confirm that syncytism is permissive of greater levels of transcriptional noise. Our findings suggest that division of transcriptional labor between nuclei allows syncytia to sidestep tradeoffs between efficiency and precision of gene expression.

Control of low flow regions in the cortical vasculature determines optimal arterio-venous ratios.

The energy demands of neurons are met by a constant supply of glucose and oxygen via the cerebral vasculature. The cerebral cortex is perfused by dense, parallel arterioles and venules, consistently in imbalanced ratios. Whether and how arteriole-venule arrangement and ratio affect the efficiency of energy delivery to the cortex has remained an unanswered question. Here, we show by mathematical modeling and analysis of the mapped mouse sensory cortex that the perfusive efficiency of the network is predicted to be limited by low-flow regions produced between pairs of arterioles or pairs of venules. Increasing either arteriole or venule density decreases the size of these low-flow regions, but increases their number, setting an optimal ratio between arterioles and venules that matches closely that observed across mammalian cortical vasculature. Low-flow regions are reshaped in complex ways by changes in vascular conductance, creating geometric challenges for matching cortical perfusion with neuronal activity.

Circadian rhythm shows potential for mRNA efficiency and self-organized division of labor in multinucleate cells.

Multinucleate cells occur in every biosphere and across the kingdoms of life, including in the human body as muscle cells and bone-forming cells. Data from filamentous fungi suggest that, even when bathed in a common cytoplasm, nuclei are capable of autonomous behaviors, including division. How does this potential for autonomy affect the organization of cellular processes between nuclei? Here we analyze a simplified model of circadian rhythm, a form of cellular oscillator, in a mathematical model of the filamentous fungus Neurospora crassa. Our results highlight a potential role played by mRNA-protein phase separation to keep mRNAs close to the nuclei from which they originate, while allowing proteins to diffuse freely between nuclei. Our modeling shows that syncytism allows for extreme mRNA efficiency-we demonstrate assembly of a robust oscillator with a transcription rate a thousand-fold less than in comparable uninucleate cells. We also show self-organized division of the labor of mRNA production, with one nucleus in a two-nucleus syncytium producing at least twice as many mRNAs as the other in 30% of cycles. This division can occur spontaneously, but division of labor can also be controlled by regulating the amount of cytoplasmic volume available to each nucleus. Taken together, our results show the intriguing richness and potential for emergent organization among nuclei in multinucleate cells. They also highlight the role of previously studied mechanisms of cellular organization, including nuclear space control and localization of mRNAs through RNA-protein phase separation, in regulating nuclear coordination.

Microvscular networks with uniform flow.

Within animals, oxygen exchange occurs within vascular transport networks containing potentially billions of microvessels that are distributed throughout the body. By comparison, large blood vessels are theorized to minimize transport costs, leading to tree-like networks that satisfy Murray's law. We know very little about the principles underlying the organization of healthy micro-vascular networks. Indeed capillary networks must also perfuse tissues with oxygen, and efficient perfusion may be incompatible with minimization of transport costs. While networks that minimize transport costs have been well-studied, other optimization principles have received much less scrutiny. In this work we derive the morphology of networks that uniformize blood flow distribution, inspired by the zebrafish trunk micro-vascular network. To find uniform flow networks, we devise a gradient descent algorithm able to optimize arbitrary differentiable objective functions on transport networks, while exactly respecting arbitrary differentiable constraint functions. We prove that in a class of networks that we call stackable, which includes a model capillary bed, the uniform flow network will have the same flow as a uniform conductance network, i.e., in which all edges have the same conductance. This result agrees with uniform flow capillary bed network found by the algorithm. We also show that the uniform flow completely explains the observed radii within the zebrafish trunk vasculature. In addition to deriving new results on optimization of uniform flow in micro-vascular networks, our algorithm provides a general method for testing hypotheses about possible optimization principles underlying real microvascular networks, including exposing tradeoffs between flow uniformity and transport cost.

Mushrooms use convectively created airflows to disperse their spores.

Thousands of basidiomycete fungal species rely on mushroom spores to spread across landscapes. It has long been thought that spores depend on favorable winds for dispersal--that active control of spore dispersal by the parent fungus is limited to an impulse delivered to the spores to carry them clear of the gill surface. Here we show that evaporative cooling of the air surrounding the pileus creates convective airflows capable of carrying spores at speeds of centimeters per second. Convective cells can transport spores from gaps that may be only 1 cm high and lift spores 10 cm or more into the air. This work reveals how mushrooms tolerate and even benefit from crowding and explains their high water needs.

Optimal occlusion uniformly partitions red blood cells fluxes within a microvascular network.

In animals, gas exchange between blood and tissues occurs in narrow vessels, whose diameter is comparable to that of a red blood cell. Red blood cells must deform to squeeze through these narrow vessels, transiently blocking or occluding the vessels they pass through. Although the dynamics of vessel occlusion have been studied extensively, it remains an open question why microvessels need to be so narrow. We study occlusive dynamics within a model microvascular network: the embryonic zebrafish trunk. We show that pressure feedbacks created when red blood cells enter the finest vessels of the trunk act together to uniformly partition red blood cells through the microvasculature. Using mathematical models as well as direct observation, we show that these occlusive feedbacks are tuned throughout the trunk network to prevent the vessels closest to the heart from short-circuiting the network. Thus occlusion is linked with another open question of microvascular function: how are red blood cells delivered at the same rate to each micro-vessel? Our analysis shows that tuning of occlusive feedbacks increase the total dissipation within the network by a factor of 11, showing that uniformity of flows rather than minimization of transport costs may be prioritized by the microvascular network.

Defining individual size in the model filamentous fungus Neurospora crassa.

It is challenging to apply the tenets of individuality to filamentous fungi: a fungal mycelium can contain millions of genetically diverse but totipotent nuclei, each capable of founding new mycelia. Moreover, a single mycelium can potentially stretch over kilometres, and it is unlikely that its distant parts share resources or have the same fitness. Here, we directly measure how a single mycelium of the model ascomycete Neurospora crassa is patterned into reproductive units (RUs), meaning subpopulations of nuclei that propagate together as spores, and function as reproductive individuals. The density of RUs is sensitive to the geometry of growth; we detected 50-fold smaller RUs when mycelia had expanding frontiers than when they were constrained to grow in one direction only. RUs fragmented further when the mycelial network was perturbed. In mycelia with expanding frontiers, RU composition was strongly influenced by the distribution of genotypes early in development. Our results provide a concept of fungal individuality that is directly connected to reproductive potential, and therefore to theories of how fungal individuals adapt and evolve over time. Our data show that the size of reproductive individuals is a dynamic and environment-dependent property, even within apparently totally connected fungal mycelia.

Nuclear dynamics in a fungal chimera.

A fungal colony is a syncytium composed of a branched and interconnected network of cells. Chimerism endows colonies with increased virulence and ability to exploit nutritionally complex substrates. Moreover, chimera formation may be a driver for diversification at the species level by allowing lateral gene transfer between strains that are too distantly related to hybridize sexually. However, the processes by which genomic diversity develops and is maintained within a single colony are little understood. In particular, both theory and experiments show that genetically diverse colonies may be unstable and spontaneously segregate into genetically homogenous sectors. By directly measuring patterns of nuclear movement in the model ascomycete fungus Neurospora crassa, we show that genetic diversity is maintained by complex mixing flows of nuclei at all length scales within the hyphal network. Mathematical modeling and experiments in a morphological mutant reveal some of the exquisite hydraulic engineering necessary to create the mixing flows. In addition to illuminating multinucleate and multigenomic lifestyles, the adaptation of a hyphal network for mixing nuclear material provides a previously unexamined organizing principle for understanding morphological diversity in the more-than-a-million species of filamentous fungi.

A new angle on microscopic suspension feeders near boundaries.

Microscopic sessile suspension feeders are a critical component in aquatic ecosystems, acting as an intermediate trophic stage between bacteria and higher eukaryotic taxa. Because they live attached to boundaries, it has long been thought that recirculation of the feeding currents produced by sessile suspension feeders inhibits their ability to access fresh fluid. However, previous models for the feeding flows of these organisms assume that they feed by pushing fluid perpendicular to surfaces they live upon, whereas we observe that sessile suspension feeders often feed at an angle to these boundaries. Using experiments and calculations, we show that living suspension feeders (Vorticella) likely actively regulate the angle that they feed relative to a substratum. We then use theory and simulations to show that angled feeding increases nutrient and particle uptake by reducing the reprocessing of depleted water. This work resolves an open question of how a key class of suspension-feeding organisms escapes physical limitations associated with their sessile lifestyle.

Cooperatively generated stresslet flows supply fresh fluid to multicellular choanoflagellate colonies.

The flagellated protozoan Salpingoeca rosetta is one of the closest relatives of multicellular animals. Unicellular S. rosetta can be induced to form multicellular colonies, but colonies swim more slowly than individual cells so the advantages conferred by colony formation are uncertain. Here we use theoretical models to show that hydrodynamic cooperation between cells can increase the fluid supply to the colony, an important predictor of feeding rate. Our results suggest that hydrodynamic benefits may have been an important selective factor in the evolution of early multicellular animals.

Dispersal of fungal spores on a cooperatively generated wind.

Because of their microscopic size, the forcibly ejected spores of ascomycete fungi are quickly brought to rest by drag. Nonetheless some apothecial species, including the pathogen Sclerotinia sclerotiorum, disperse with astonishing rapidity between ephemeral habitats. Here we show that by synchronizing the ejection of thousands of spores, these fungi create a flow of air that carries spores through the nearly still air surrounding the apothecium, around intervening obstacles, and to atmospheric currents and new infection sites. High-speed imaging shows that synchronization is self-organized and likely triggered by mechanical stresses. Although many spores are sacrificed to produce the favorable airflow, creating the potential for conflict among spores, the geometry of the spore jet physically targets benefits of the airflow to spores that cooperate maximally in its production. The ability to manipulate a local fluid environment to enhance spore dispersal is a previously overlooked feature of the biology of fungal pathogens, and almost certainly shapes the virulence of species including S. sclerotiorum. Synchronous spore ejection may also provide a model for the evolution of stable, self-organized behaviors.

A nonperturbative approximation for the moderate Reynolds number Navier-Stokes equations.

The nonlinearity of the Navier-Stokes equations makes predicting the flow of fluid around rapidly moving small bodies highly resistant to all approaches save careful experiments or brute force computation. Here, we show how a linearization of the Navier-Stokes equations captures the drag-determining features of the flow and allows simplified or analytical computation of the drag on bodies up to Reynolds number of order 100. We illustrate the utility of this linearization in 2 practical problems that normally can only be tackled with sophisticated numerical methods: understanding flow separation in the flow around a bluff body and finding drag-minimizing shapes.

Bacillus subtilis spreads by surfing on waves of surfactant.

The bacterium Bacillus subtilis produces the molecule surfactin, which is known to enhance the spreading of multicellular colonies on nutrient substrates by lowering the surface tension of the surrounding fluid, and to aid in the formation of aerial structures. Here we present experiments and a mathematical model that demonstrate how the differential accumulation rates induced by the geometry of the bacterial film give rise to surfactant waves. The spreading flux increases with increasing biofilm viscosity. Community associations are known to protect bacterial populations from environmental challenges such as predation, heat, or chemical stresses, and enable digestion of a broader range of nutritive sources. This study provides evidence of enhanced dispersal through cooperative motility, and points to nonintuitive methods for controlling the spread of biofilms.

Vascular Injury in the Zebrafish Tail Modulates Blood Flow and Peak Wall Shear Stress to Restore Embryonic Circular Network.

Mechano-responsive signaling pathways enable blood vessels within a connected network to structurally adapt to partition of blood flow between organ systems. Wall shear stress (WSS) modulates endothelial cell proliferation and arteriovenous specification. Here, we study vascular regeneration in a zebrafish model by using tail amputation to disrupt the embryonic circulatory loop (ECL) at 3 days post fertilization (dpf). We observed a local increase in blood flow and peak WSS in the Segmental Artery (SeA) immediately adjacent to the amputation site. By manipulating blood flow and WSS via changes in blood viscosity and myocardial contractility, we show that the angiogenic Notch-ephrinb2 cascade is hemodynamically activated in the SeA to guide arteriogenesis and network reconnection. Taken together, ECL amputation induces changes in microvascular topology to partition blood flow and increase WSS-mediated Notch-ephrinb2 pathway, promoting new vascular arterial loop formation and restoring microcirculation.

Microscopic artificial swimmers.

Microorganisms such as bacteria and many eukaryotic cells propel themselves with hair-like structures known as flagella, which can exhibit a variety of structures and movement patterns. For example, bacterial flagella are helically shaped and driven at their bases by a reversible rotary engine, which rotates the attached flagellum to give a motion similar to that of a corkscrew. In contrast, eukaryotic cells use flagella that resemble elastic rods and exhibit a beating motion: internally generated stresses give rise to a series of bends that propagate towards the tip. In contrast to this variety of swimming strategies encountered in nature, a controlled swimming motion of artificial micrometre-sized structures has not yet been realized. Here we show that a linear chain of colloidal magnetic particles linked by DNA and attached to a red blood cell can act as a flexible artificial flagellum. The filament aligns with an external uniform magnetic field and is readily actuated by oscillating a transverse field. We find that the actuation induces a beating pattern that propels the structure, and that the external fields can be adjusted to control the velocity and the direction of motion.

Explosively launched spores of ascomycete fungi have drag-minimizing shapes.

The forcibly launched spores of ascomycete fungi must eject through several millimeters of nearly still air surrounding fruiting bodies to reach dispersive air flows. Because of their microscopic size, spores experience great fluid drag, and although this drag can aid transport by slowing sedimentation out of dispersive air flows, it also causes spores to decelerate rapidly after launch. We hypothesize that spores are shaped to maximize their range in the nearly still air surrounding fruiting bodies. To test this hypothesis we numerically calculate optimal spore shapes-shapes of minimum drag for prescribed volumes-and compare these shapes with real spore shapes taken from a phylogeny of >100 species. Our analysis shows that spores are constrained to remain within 1% of the minimum possible drag for their size. From the spore shapes we predict the speed of spore launch, and confirm this prediction through high-speed imaging of ejection in Neurospora tetrasperma. By reconstructing the evolutionary history of spore shapes within a single ascomycete family we measure the relative contributions of drag minimization and other shape determinants to spore shape evolution. Our study uses biomechanical optimization as an organizing principle for explaining shape in a mega-diverse group of species and provides a framework for future measurements of the forces of selection toward physical optima.

Fungal Biology: Bidirectional Communication across Fungal Networks.

Protoplasmic flow carries signals through fungal networks, alerting distant regions to predators or new food sources. A new study now shows that, by regularly alternating its direction, this flow links up all parts of the network, revealing new degrees of control over flow within fungal networks.

Correction: A Biologically-Inspired Symmetric Bidirectional Switch.

[This corrects the article DOI: 10.1371/journal.pone.0169856.].

A Biologically-Inspired Symmetric Bidirectional Switch.

Stimuli-sensitive hydrogels have been intensively studied because of their potential applications in drug delivery, cell culture, and actuator design. Although hydrogels with directed unidirectional response, i.e. capable of bending actuated by different chemical components reaction in response to several stimuli including water and electric fields, these hydrogels are capable of being actuated in one direction only by the stimulus. By contrast the challenge of building a device that is capable of responding to the same cue (in this case a temperature gradient) to bend in either direction remains unmet. Here, inspired by the structure of pine cone scales, we design a temperature-sensitive hydrogel with bending directed an imposed fishing line. The layers with same PNIPAAm always shrinks in response to the heat. Even the layers made with different chemical property, bends away from a warm surface, whether the warm surface is applied at its upper or lower boundary. To design the bending hydrogel we exploited the coupled responses of the hydrogel; a fishing line intercalating structure and change its construction. In addition to revealing a new capability of stimulus sensitive hydrogels, our study gives insight into the structural features of pine cone bending.