A general allometric and life-history model for cellular differentiation in the transition to multicellularity.

The transition from unicellular, to colonial, to larger multicellular organisms has benefits, costs, and requirements. Here we present a model inspired by the volvocine green algae that explains the dynamics involved in the unicellular-multicellular transition using life-history theory and allometry. We model the two fitness components (fecundity and viability) and compare the fitness of hypothetical colonies of different sizes with varying degrees of cellular differentiation to understand the general principles that underlie the evolution of multicellularity. We argue that germ-soma separation may have evolved to counteract the increasing costs and requirements of larger multicellular colonies. The model shows that the cost of investing in soma decreases with size. For lineages such as the Volvocales, as reproduction costs increase with size for undifferentiated colonies, soma specialization benefits the colony indirectly by decreasing such costs and directly by helping reproductive cells acquire resources for their metabolic needs. Germ specialization is favored once soma evolves and takes care of vegetative functions. To illustrate the model, we use some allometric relationships measured in Volvocales. Our analysis shows that the cost of reproducing an increasingly larger group has likely played an important role in the transition to multicellularity and cellular differentiation.

Confinement stabilizes a bacterial suspension into a spiral vortex.

Confining surfaces play crucial roles in dynamics, transport, and order in many physical systems, but their effects on active matter, a broad class of dynamically self-organizing systems, are poorly understood. We investigate here the influence of global confinement and surface curvature on collective motion by studying the flow and orientational order within small droplets of a dense bacterial suspension. The competition between radial confinement, self-propulsion, steric interactions, and hydrodynamics robustly induces an intriguing steady single-vortex state, in which cells align in inward spiraling patterns accompanied by a thin counterrotating boundary layer. A minimal continuum model is shown to be in good agreement with these observations.

Intraspecies variation in cotton border cell production: rhizosphere microbiome implications.

PREMISE OF THE STUDY: Border cells, which separate from the root cap, can comprise >90% of carbon-based exudates released into the rhizosphere, but may not provide a general source of nutrients for soil microorganisms. Instead, this population of specialized cells appears to function in defense of the root tip by an extracellular trapping process similar to that of mammalian white blood cells. Border cell production is tightly regulated, and direct tests of their impact on crop production have been hindered by lack of intraspecies variation. • METHODS: Border cell number, viability, and clumping were compared among 22 cotton cultivars. Slime layer "extracellular trap" production by border cells in response to copper chloride, an elicitor of plant defenses, was compared in two cultivars with divergent border cell production. Trapping of bacteria by border cells in these lines also was measured. • KEY RESULTS: Emerging roots of some cultivars produced more than 20000 border cells per root, a 100% increase over previously reported values for this species. No differences in border cell morphology, viability, or clumping were found. Copper chloride-induced extracellular trap formation by border cells from a cultivar that produced 27921 ± 2111 cells per root was similar to that of cells from a cultivar with 10002 ± 614 cells, but bacterial trapping was reduced. • CONCLUSIONS: Intraspecific variation in border cell production provides a tool to measure their impact on plant development in the laboratory, greenhouse, and field. Further research is needed to determine the basis for this variation, and its impact on rhizosphere community structure.

Model for dynamical coherence in thin films of self-propelled microorganisms.

Concentrated bacterial suspensions spontaneously develop transient spatiotemporal patterns of coherent locomotion whose correlation lengths greatly exceed the size of individual organisms. Continuum models have indicated that a state of uniform swimming order is linearly unstable at finite wavelengths, but have not addressed the nonlinear dynamics of the coherent state, with its biological implications for mixing, transport, and intercellular communication. We investigate a specific model incorporating hydrodynamic interactions in thin-film geometries and show by numerical studies that it displays large scale persistently recurring vortices, as actually observed.

A hydrodynamics approach to the evolution of multicellularity: flagellar motility and germ-soma differentiation in volvocalean green algae.

During the unicellular-multicellular transition, there are opportunities and costs associated with larger size. We argue that germ-soma separation evolved to counteract the increasing costs and requirements of larger multicellular colonies. Volvocalean green algae are uniquely suited for studying this transition because they range from unicells to multicellular individuals with germ-soma separation. Because Volvocales need flagellar beating for movement and to avoid sinking, their motility is modeled and analyzed experimentally using standard hydrodynamics. We provide comparative hydrodynamic data of an algal lineage composed of organisms of different sizes and degrees of complexity. In agreement with and extending the insights of Koufopanou, we show that the increase in cell specialization as colony size increases can be explained in terms of increased motility requirements. First, as colony size increases, soma must evolve, the somatic-to-reproductive cell ratio increasing to keep colonies buoyant and motile. Second, increased germ-soma specialization in larger colonies increases motility capabilities because internalization of nonflagellated germ cells decreases colony drag. Third, our analysis yields a limiting maximum size of the volvocalean spheroid that agrees with the sizes of the largest species known. Finally, the different colony designs in Volvocales reflect the trade-offs between reproduction, colony size, and motility.

Reversal of bacterial locomotion at an obstacle.

Recent experiments have shown large-scale dynamic coherence in suspensions of the bacterium B. subtilis, characterized by quorum polarity, collective parallel swimming of cells. To probe mechanisms leading to this, we study the response of individual cells to steric stress, and find that they can reverse swimming direction at spatial constrictions without turning the cell body. The consequences of this propensity to flip the flagella are quantified by measurements of the inward and outward swimming velocities, whose asymptotic values far from the constriction show near perfect symmetry, implying that "forwards" and "backwards" are dynamically indistinguishable, as with E. coli.

Dynamics of swimming bacteria: transition to directional order at high concentration.

At high cell concentrations, bacterial suspensions are known to develop a state of collective swimming (the "zooming bionematic phase," or ZBN) characterized by transient, recurring regions of coordinated motion greatly exceeding the size of individual cells. Recent theoretical studies of semidilute suspensions have suggested that long-range hydrodynamic interactions between swimming cells are responsible for long-wavelength instabilities that lead to these patterns, while models appropriate for higher concentrations have suggested that steric interactions between elongated cells play an important role in the self-organization. Using particle imaging velocimetry in well-defined microgeometries, we examine the statistical properties of the transition to the ZBN in suspensions of Bacillus subtilis, with particular emphasis on the distribution of cell swimming speeds and its correlation with orientational order. This analysis reveals a nonmonotonic relationship between mean cell swimming speed and cell concentration, with a minimum occurring near the transition to the ZBN. Regions of high orientational order in the ZBN phase have locally high swimming speeds, while orientationally disordered regions have lower speeds. A model for steric interactions in concentrated suspensions and previous observations on the kinetics of flagellar rebundling associated with changes in swimming direction are used to explain this observation. The necessity of incorporating steric effects on cell swimming in theoretical models is emphasized.

Flagellar phenotypic plasticity in volvocalean algae correlates with Péclet number.

Flagella-generated fluid stirring has been suggested to enhance nutrient uptake for sufficiently large micro-organisms, and to have played a role in evolutionary transitions to multicellularity. A corollary to this predicted size-dependent benefit is a propensity for phenotypic plasticity in the flow-generating mechanism to appear in large species under nutrient deprivation. We examined four species of volvocalean algae whose radii and flow speeds differ greatly, with Péclet numbers (Pe) separated by several orders of magnitude. Populations of unicellular Chlamydomonas reinhardtii and one- to eight-celled Gonium pectorale (Pe ∼ 0.1-1) and multicellular Volvox carteri and Volvox barberi (Pe ∼ 100) were grown in diluted and undiluted media. For C. reinhardtii and G. pectorale, decreasing the nutrient concentration resulted in smaller cells, but had no effect on flagellar length and propulsion force. In contrast, these conditions induced Volvox colonies to grow larger and increase their flagellar length, separating the somatic cells further. Detailed studies on V. carteri found that the opposing effects of increasing beating force and flagellar spacing balance, so the fluid speed across the colony surface remains unchanged between nutrient conditions. These results lend further support to the hypothesized link between the Péclet number, nutrient uptake and the evolution of biological complexity in the Volvocales.

Disruption of vertical motility by shear triggers formation of thin phytoplankton layers.

Thin layers of phytoplankton are important hotspots of ecological activity that are found in the coastal ocean, meters beneath the surface, and contain cell concentrations up to two orders of magnitude above ambient concentrations. Current interpretations of their formation favor abiotic processes, yet many phytoplankton species found in these layers are motile. We demonstrated that layers formed when the vertical migration of phytoplankton was disrupted by hydrodynamic shear. This mechanism, which we call gyrotactic trapping, can be responsible for the thin layers of phytoplankton commonly observed in the ocean. These results reveal that the coupling between active microorganism motility and ambient fluid motion can shape the macroscopic features of the marine ecological landscape.

Unexpected bipolar flagellar arrangements and long-range flows driven by bacteria near solid boundaries.

Experiments and mathematical modeling show that complex flows driven by unexpected flagellar arrangements are induced when peritrichously flagellated bacteria are confined in a thin layer of fluid, between asymmetric boundaries. The flagella apparently form a dynamic bipolar assembly rather than the single bundle characteristic of free swimming bacteria, and the resulting flow is observed to circulate around the cell body. It ranges over several cell diameters, in contrast to the small extent of the flows surrounding free swimmers. Results also suggest that flagellar bundles on bacteria that lie flat on a solid substrate have an effective rotation rate slower than "free" flagella. This discovery extends our knowledge of the dynamic geometry of bacteria and their flagella, and reveals new mechanisms for motility-associated molecular transport and intercellular communication.

Concentration dependence of the collective dynamics of swimming bacteria.

At concentrations near the maximum allowed by steric repulsion, swimming bacteria form a dynamical state exhibiting extended spatiotemporal coherence. The viscous fluid into which locomotive energy of individual microorganisms is transferred also carries interactions that drive the coherence. The concentration dependence of correlations in the collective state is probed here with a novel technique that herds bacteria into condensed populations of adjustable concentration. For the particular thin-film geometry employed, the correlation lengths vary smoothly and monotonically through the transition from individual to collective behavior.

Multicellularity and the functional interdependence of motility and molecular transport.

Benefits, costs, and requirements accompany the transition from motile totipotent unicellular organisms to multicellular organisms having cells specialized into reproductive (germ) and vegetative (sterile soma) functions such as motility. In flagellated colonial organisms such as the volvocalean green algae, organized beating by the somatic cells' flagella yields propulsion important in phototaxis and chemotaxis. It has not been generally appreciated that for the larger colonies flagellar stirring of boundary layers and remote transport are fundamental for maintaining a sufficient rate of metabolite turnover, one not attainable by diffusive transport alone. Here, we describe experiments that quantify the role of advective dynamics in enhancing productivity in germ soma-differentiated colonies. First, experiments with suspended deflagellated colonies of Volvox carteri show that forced advection improves productivity. Second, particle imaging velocimetry of fluid motion around colonies immobilized by micropipette aspiration reveals flow fields with very large characteristic velocities U extending to length scales exceeding the colony radius R. For a typical metabolite diffusion constant D, the associated Peclet number Pe = 2UR/D >> 1, indicative of the dominance of advection over diffusion, with striking augmentation at the cell division stage. Near the colony surface, flows generated by flagella can be chaotic, exhibiting mixing due to stretching and folding. These results imply that hydrodynamic transport external to colonies provides a crucial boundary condition, a source for supplying internal diffusional dynamics.

Flows driven by flagella of multicellular organisms enhance long-range molecular transport.

Evolution from unicellular organisms to larger multicellular ones requires matching their needs to the rate of exchange of molecular nutrients with the environment. This logistic problem poses a severe constraint on development. For organisms whose body plan is a spherical shell, such as the volvocine green algae, the current (molecules per second) of needed nutrients grows quadratically with radius, whereas the rate at which diffusion alone exchanges molecules grows linearly, leading to a bottleneck radius beyond which the diffusive current cannot meet metabolic demands. By using Volvox carteri, we examine the role that advection of fluid by the coordinated beating of surface-mounted flagella plays in enhancing nutrient uptake and show that it generates a boundary layer of concentration of the diffusing solute. That concentration gradient produces an exchange rate that is quadratic in the radius, as required, thus circumventing the bottleneck and facilitating evolutionary transitions to multicellularity and germ-soma differentiation in the volvocalean green algae.

Bacterial swimming and oxygen transport near contact lines.

Aerobic bacteria often live in thin fluid layers near solid-air-water contact lines, in which the biology of chemotaxis, metabolism, and cell-cell signaling is intimately connected to the physics of buoyancy, diffusion, and mixing. Using the geometry of a sessile drop, we demonstrate in suspensions of Bacillus subtilis the self-organized generation of a persistent hydrodynamic vortex that traps cells near the contact line. Arising from upward oxygentaxis and downward gravitational forcing, these dynamics are related to the Boycott effect in sedimentation and are explained quantitatively by a mathematical model consisting of oxygen diffusion and consumption, chemotaxis, and viscous fluid dynamics. The vortex is shown to advectively enhance uptake of oxygen into the suspension, and the wedge geometry leads to a singularity in the chemotactic dynamics near the contact line.

Coiling, entrainment, and hydrodynamic coupling of decelerated fluid jets.

From algal suspensions to magma upwellings, one finds jets which exhibit complex symmetry-breaking instabilities as they are decelerated by their surroundings. We consider here a model system--a saline jet descending through a salinity gradient--which produces dynamics unlike those of standard momentum jets or plumes. The jet coils like a corkscrew within a conduit of viscously entrained fluid, whose upward recirculation braids the jet, and nearly confines transverse mixing to the narrow conduit. We show that the underlying jet structure and certain scaling relations follow from similarity solutions to the fluid equations and the physics of Kelvin-Helmholtz instabilities.

Self-concentration and large-scale coherence in bacterial dynamics.

Suspensions of aerobic bacteria often develop flows from the interplay of chemotaxis and buoyancy. We find in sessile drops that flows related to those in the Boycott effect of sedimentation carry bioconvective plumes down the slanted meniscus and concentrate cells at the drop edge, while in pendant drops such self-concentration occurs at the bottom. On scales much larger than a cell, concentrated regions in both geometries exhibit transient, reconstituting, high-speed jets straddled by vortex streets. A mechanism for large-scale coherence is proposed based on hydrodynamic interactions between swimming cells.

Periodic chirality transformations propagating on bacterial flagella.

When a helical bacterial flagellum, clamped at one end, is placed in an external flow, it has been observed that regions of the flagellum transform to the opposite chirality, and travel as pulses down the length of the filament, the process repeating periodically [H. Hotani, J. Mol. Biol. 156, 791 (1982)]]. We propose a theory for this phenomenon based on a treatment of the flagellum as an elastic object with multiple stable configurations. The simplest possible implementation of the model accurately reproduces key features seen in experiment.