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Biomedical subjects

Raymond E Goldstein

Publications and source records attributed to Raymond E Goldstein.

15 recordsLinked to original sources

Dynamic buckling of morphoelastic filaments.

The equilibrium shapes of biological structures as diverse as plant tendrils and bacterial filaments can be altered by externally imposed stresses of sufficient duration. We study the simplest model for this morphoelasticity--a filament whose intrinsic curvatures relax to the local curvatures--and illustrate its properties in the context of dynamic Euler buckling and writhing. When a thrust or twist is ramped in time the effective elastic properties of the filament depend on the load rate. Slow ramps interrupted by removal of the external forces can leave in equilibrium any of a whole continuum of buckled shapes. Morphoelastic relaxation can also allow a filament to bypass a bifurcation.

Animals↗

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.

Animals↗

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.

Bacillus subtilis↗

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.

Algal Proteins↗

The flagellar cytoskeleton of the spirochetes.

The recent discoveries of prokaryotic homologs of all three major eukaryotic cytoskeletal proteins (actin, tubulin, intermediate filaments) have spurred a resurgence of activity in the field of bacterial morphology. In spirochetes, however, it has long been known that the flagellar filaments act as a cytoskeletal protein structure, contributing to their shape and conferring motility on this unique phylum of bacteria. Therefore, revisiting the spirochete cytoskeleton may lead to new paradigms for exploring general features of prokaryotic morphology. This review discusses the role that the periplasmic flagella in spirochetes play in maintaining shape and producing motility. We focus on four species of spirochetes: Borrelia burgdorferi, Treponema denticola, Treponema phagedenis and Leptonema (formerly Leptospira) illini. In spirochetes, the flagella reside in the periplasmic space. Rotation of the flagella in the above species by a flagellar motor induces changes in the cell morphology that drives motility. Mutants that do not produce flagella have a markedly different shape than wild-type cells.

Borrelia burgdorferi↗

Precipitative growth templated by a fluid jet.

Tubular growth by chemical precipitation at the interface between two fluids, a jet and its surroundings, underlies the development of such important structures as chimneys at hydrothermal vents. This growth is associated with strong thermal and/or solute gradients localized at those interfaces, and these gradients, in turn, often produce radial compositional stratification of the resulting tube wall. A fundamental question underlying these processes is how the interplay between diffusion, advection, and precipitation determines the elongation rate of the tubes. Here we report experimental and theoretical results that reveal a regime in which there exists a new scaling law for tube growth. The model system studied consists of a jet of aqueous ammonia injected into a ferrous sulfate solution, precipitating iron hydroxides with varying oxidation states at the jet boundary. Despite the complex chemistry and dynamics underlying the precipitation, the tube growth exhibits a strikingly simple scaling form, with characteristic lengths and times increasing linearly with the mean velocity of the jet. These observations follow from a kinetic model of advection-dominated flows.

Letter↗

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.

Journal Article↗

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.

Bacillus subtilis↗

Stalactite growth as a free-boundary problem: a geometric law and its platonic ideal.

The chemical mechanisms underlying the growth of cave formations such as stalactites are well known, yet no theory has yet been proposed which successfully accounts for the dynamic evolution of their shapes. Here we consider the interplay of thin-film fluid dynamics, calcium carbonate chemistry, and CO2 transport in the cave to show that stalactites evolve according to a novel local geometric growth law which exhibits extreme amplification at the tip as a consequence of the locally-varying fluid layer thickness. Studies of this model show that a broad class of initial conditions is attracted to an ideal shape which is strikingly close to a statistical average of natural stalactites.

Journal Article↗

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.

Bacillus subtilis↗

Tubular precipitation and redox gradients on a bubbling template.

Tubular structures created by precipitation abound in nature, from chimneys at hydrothermal vents to soda straws in caves. Their formation is controlled by chemical gradients within which precipitation occurs, defining a surface that templates the growing structure. We report a self-organized periodic templating mechanism producing tubular structures electrochemically in iron-ammonium-sulfate solutions; iron oxides precipitate on the surface of bubbles that linger at the tube rim and then detach, leaving behind a ring of material. The acid-base and redox gradients spontaneously generated by diffusion of ammonia from the bubble into solution organize radial compositional layering within the tube wall, a mechanism studied on a larger scale by complex Liesegang patterns of iron oxides formed as ammonia diffuses through a gel containing FeSO(4). When magnetite forms within the wall, a tube may grow curved in an external magnetic field. Connections with free-boundary problems in speleothem formation are emphasized.

Journal Article↗

Quantum necking in stressed metallic nanowires.

When a macroscopic metallic wire is subject to tensile stress, it necks down smoothly as it elongates. We show that nanowires with radii comparable to the Fermi wavelength display remarkably different behavior. Using concepts from fluid dynamics, a partial differential equation for nanowire shape evolution is derived from a semiclassical energy functional that includes electron-shell effects. A rich dynamics involving movement and interaction of kinks connecting locally stable radii is found, and a new class of universal equilibrium shapes is predicted.

Journal Article↗

Inertially driven buckling and overturning of jets in a Hele-Shaw cell.

We study a fluid jet descending through stratified surroundings at low Reynolds number in Hele-Shaw flow. The jet buckles and overturns inside a conduit of entrained fluid which supports smooth or unstable traveling waves. A model of the recirculating flow within the conduit shows that buckling and waves arise from Kelvin-Helmholtz instabilities and quantitatively accounts for the main experimental observations. Beyond the onset of the instability, a damped, forced Burgers' equation obtained from corrections to Darcy's law for small Reynolds number governs the interface dynamics and supports singularities corresponding to the observed jet overturning and unstable waves.

Journal Article↗

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.

Bacterial Physiological Phenomena↗

Fluid-membrane tethers: minimal surfaces and elastic boundary layers.

Thin cylindrical tethers are common lipid bilayer membrane structures, arising in situations ranging from micromanipulation experiments on artificial vesicles to the dynamic structure of the Golgi apparatus. We study the shape and formation of a tether in terms of the classical soap-film problem, which is applied to the case of a membrane disk under tension subject to a point force. A tether forms from the elastic boundary layer near the point of application of the force, for sufficiently large displacement. Analytic results for various aspects of the membrane shape are given.

Cytoplasmic Vesicles↗