arXiv subjects

Raymond E. Goldstein

Publications and source records attributed to Raymond E. Goldstein.

At least 73 records · Page 4Linked to original sources

arXiv2016

Directed collective motion of bacteria under channel confinement

Dense suspensions of swimming bacteria are known to exhibit collective behaviour arising from the interplay of steric and hydrodynamic interactions. Unconfined suspensions exhibit transient, recurring vortices and jets, whereas those confinedin circular domains may exhibit order in the form of a spiral vortex. Here we show that confinement into a long and narrow macroscopic `racetrack' geometry stabilises bacterial motion to form a steady unidirectional circulation. This motion is reproduced in simulations of discrete swimmers that reveal the crucial role that bacteria-driven fluid flows play in the dynamics. In particular, cells close to the channel wall produce strong flows which advect cells in the bulk against their swimming direction. We examine in detail the transition from a disordered state to persistent directed motion as a function of the channel width,and show that the width at the crossover point is comparable to the typical correlation length of swirls seen in the unbounded system. Our results shed light on the mechanisms driving the collective behaviour of bacteria and other active matter systems, and stress the importance of the ubiquitous boundaries found in natural habitats.

physics.bio-ph↗

arXiv2016

Instabilities and Solitons in Minimal Strips

We show that highly twisted minimal strips can undergo a non-singular transition, unlike the singular transitions seen in the Möbius strip and the catenoid. If the strip is non-orientable this transition is topologically frustrated, and the resulting surface contains a helical defect. Through a controlled analytic approximation the system can be mapped onto a scalar $ϕ^4$ theory on a non-orientable line bundle over the circle, where the defect becomes a topologically protected kink soliton or domain wall, thus establishing their existence in minimal surfaces. Experimental studies of soap films confirm these results and demonstrate how the position of the defect can be controlled through boundary deformation.

cond-mat.soft↗

arXiv2015

Motility of Colonial Choanoflagellates and the Statistics of Aggregate Random Walkers

We illuminate the nature of the three-dimensional random walks of microorganisms composed of individual organisms adhered together. Such $aggregate~random~walkers$ are typified by choanoflagellates, eukaryotes that are the closest living relatives of animals. In the colony-forming species $Salpingoeca~rosetta$ we show that the beating of each flagellum is stochastic and uncorrelated with others, and the vectorial sum of the flagellar propulsion manifests as stochastic helical swimming. A quantitative theory for these results is presented and species variability discussed.

cond-mat.soft↗

arXiv2015

Ferromagnetic and antiferromagnetic order in bacterial vortex lattices

Despite their inherent non-equilibrium nature, living systems can self-organize in highly ordered collective states that share striking similarities with the thermodynamic equilibrium phases of conventional condensed matter and fluid systems. Examples range from the liquid-crystal-like arrangements of bacterial colonies, microbial suspensions and tissues to the coherent macro-scale dynamics in schools of fish and flocks of birds. Yet, the generic mathematical principles that govern the emergence of structure in such artificial and biological systems are elusive. It is not clear when, or even whether, well-established theoretical concepts describing universal thermostatistics of equilibrium systems can capture and classify ordered states of living matter. Here, we connect these two previously disparate regimes: Through microfluidic experiments and mathematical modelling, we demonstrate that lattices of hydrodynamically coupled bacterial vortices can spontaneously organize into distinct phases of ferro- and antiferromagnetic order. The preferred phase can be controlled by tuning the vortex coupling through changes of the inter-cavity gap widths. The emergence of opposing order regimes is tightly linked to the existence of geometry-induced edge currents, reminiscent of those in quantum systems. Our experimental observations can be rationalized in terms of a generic lattice field theory, suggesting that bacterial spin networks belong to the same universality class as a wide range of equilibrium systems.

cond-mat.soft↗

arXiv2015

Cortical microtubule nucleation can organise the cytoskeleton of $Drosophila$ oocytes to define the anteroposterior axis

Many cells contain non-centrosomal arrays of microtubules (MT), but the assembly, organisation and function of these arrays are poorly understood. We present the first theoretical model for the non-centrosomal MT cytoskeleton in $Drosophila$ oocytes, in which $bicoid$ and $oskar$ mRNAs become localised to establish the anterior-posterior body axis. Constrained by experimental measurements, the model shows that a simple gradient of cortical MT nucleation is sufficient to reproduce the observed MT distribution, cytoplasmic flow patterns and localisation of $oskar$ and naive $bicoid$ mRNAs. Our simulations exclude a major role for cytoplasmic flows in localisation and reveal an organisation of the MT cytoskeleton that is more ordered than previously thought. Furthermore, modulating cortical MT nucleation induces a bifurcation in cytoskeletal organisation that accounts for the phenotypes of polarity mutants. Thus, our three-dimensional model explains many features of the MT network and highlights the importance of differential cortical MT nucleation for axis formation.

q-bio.SC↗

arXiv2015

Feeding ducks, bacterial chemotaxis, and the Gini index

Classic experiments on the distribution of ducks around separated food sources found consistency with the `ideal free' distribution in which the local population is proportional to the local supply rate. Motivated by this experiment and others, we examine the analogous problem in the microbial world: the distribution of chemotactic bacteria around multiple nearby food sources. In contrast to the optimization of uptake rate that may hold at the level of a single cell in a spatially varying nutrient field, nutrient consumption by a population of chemotactic cells will modify the nutrient field, and the uptake rate will generally vary throughout the population. Through a simple model we study the distribution of resource uptake in the presence of chemotaxis, consumption, and diffusion of both bacteria and nutrients. Borrowing from the field of theoretical economics, we explore how the Gini index can be used as a means to quantify the inequalities of uptake. The redistributive effect of chemotaxis can lead to a phenomenon we term `chemotactic levelling', and the influence of these results on population fitness are briefly considered.

physics.bio-ph↗

arXiv2015

Elasticity and Glocality: Initiation of Embryonic Inversion in ${\it Volvox}$

Elastic objects across a wide range of scales deform under local changes of their intrinsic properties, yet the shapes are ${\it glocal}$, set by a complicated balance between local properties and global geometric constraints. Here, we explore this interplay during the inversion process of the green alga ${\it Volvox}$, whose embryos must turn themselves inside out to complete their development. This process has recently been shown [S. Höhn ${\it et~al}.$, ${\it Phys. Rev. Lett.}$ $\textbf{114}$, 178101 (2015)] to be well described by the deformations of an elastic shell under local variations of its intrinsic curvatures and stretches, although the detailed mechanics of the process have remained unclear. Through a combination of asymptotic analysis and numerical studies of the bifurcation behavior, we illustrate how appropriate local deformations can overcome global constraints to initiate inversion.

cond-mat.soft↗

arXiv2015

A physical perspective on cytoplasmic streaming (invited)

Organisms show a remarkable range of sizes, yet the dimensions of a single cell rarely exceed $100$ $μ$m. While the physical and biological origins of this constraint remain poorly understood, exceptions to this rule give valuable insights. A well-known counterexample is the aquatic plant $Chara$, whose cells can exceed $10$ cm in length and $1$ mm in diameter. Two spiraling bands of molecular motors at the cell periphery drive the cellular fluid up and down at speeds up to $100$ $μ$m/s, motion that has been hypothesized to mitigate the slowness of metabolite transport on these scales and to aid in homeostasis. This is the most organized instance of a broad class of continuous motions known as "cytoplasmic streaming", found in a wide range of eukaryotic organisms - algae, plants, amoebae, nematodes, and flies - often in unusually large cells. In this overview of the physics of this phenomenon, we examine the interplay between streaming, transport and cell size, and discuss the possible role of self-organization phenomena in establishing the observed patterns of streaming.

physics.bio-ph↗

arXiv2015

Metachronal waves in the flagellar beating of $Volvox$ and their hydrodynamic origin

Groups of eukaryotic cilia and flagella are capable of coordinating their beating over large scales, routinely exhibiting collective dynamics in the form of metachronal waves. The origin of this behaviour -- possibly influenced by both mechanical interactions and direct biological regulation -- is poorly understood, in large part due to lack of quantitative experimental studies. Here we characterise in detail flagellar coordination on the surface of the multicellular alga $Volvox~carteri$, an emerging model organism for flagellar dynamics. Our studies reveal for the first time that the average metachronal coordination observed is punctuated by periodic phase defects during which synchrony is partial and limited to specific groups of cells. A minimal model of hydrodynamically coupled oscillators can reproduce semi-quantitatively the characteristics of the average metachronal dynamics, and the emergence of defects. We systematically study the model's behaviour by assessing the effect of changing intrinsic rotor characteristics, including oscillator stiffness and the nature of their internal driving force, as well as their geometric properties and spatial arrangement. Our results suggest that metachronal coordination follows from deformations in the oscillators' limit cycles induced by hydrodynamic stresses, and that defects result from sufficiently steep local biases in the oscillators' intrinsic frequencies. Additionally, we find that random variations in the intrinsic rotor frequencies increase the robustness of the average properties of the emergent metachronal waves.

cond-mat.soft↗

arXiv2014

Rhythmicity, Recurrence, and Recovery of Flagellar Beating

The eukaryotic flagellum beats with apparently unfailing periodicity, yet responds rapidly to stimuli. Like the human heartbeat, flagellar oscillations are now known to be noisy. Using the alga \textit{C. reinhardtii}, we explore three aspects of nonuniform flagellar beating. We report the existence of rhythmicity, waveform noise peaking at transitions between power and recovery strokes, and fluctuations of interbeat intervals that are correlated and even recurrent, with memory extending to hundreds of beats. These features are altered qualitatively by physiological perturbations. Further, we quantify the recovery of periodic breastroke beating from transient hydrodynamic forcing. These results will help constrain microscopic theories on the origins and regulation of flagellar beating.

cond-mat.soft↗

arXiv2014

Green Algae as Model Organisms for Biological Fluid Dynamics

In the past decade the volvocine green algae, spanning from the unicellular $Chlamydomonas$ to multicellular $Volvox$, have emerged as model organisms for a number of problems in biological fluid dynamics. These include flagellar propulsion, nutrient uptake by swimming organisms, hydrodynamic interactions mediated by walls, collective dynamics and transport within suspensions of microswimmers, the mechanism of phototaxis, and the stochastic dynamics of flagellar synchronization. Green algae are well suited to the study of such problems because of their range of sizes (from 10 $μ$m to several millimetres), their geometric regularity, the ease with which they can be cultured and the availability of many mutants that allow for connections between molecular details and organism-level behavior. This review summarizes these recent developments and highlights promising future directions in the study of biological fluid dynamics, especially in the context of evolutionary biology, that can take advantage of these remarkable organisms.

cond-mat.soft↗

arXiv2014

Dynamics of a $Volvox$ Embryo Turning Itself Inside Out

Spherical embryos of the algal genus $Volvox$ must turn themselves inside out to complete their embryogenesis. This `inversion', which shares important features with morphological events such as gastrulation in animals, is perhaps the simplest example of a topological transition in developmental biology. Waves of cell shape changes are believed to play a major role in the process, but quantification of the dynamics and formulation of a mathematical description of the process have been lacking. Here, we use selective plane illumination microscopy on $V. globator$ to obtain the first quantitative three-dimensional visualizations of inversion $in~vivo$. A theory is formulated for inversion based on local variations of intrinsic curvature and stretching of an elastic shell, and for the mechanics of an elastic snap-through resisted by the surrounding fluid.

cond-mat.soft↗

arXiv2014

Boundary Singularities Produced by the Motion of Soap Films

Recent work has shown that a Möbius strip soap film rendered unstable by deforming its frame changes topology to that of a disk through a 'neck-pinching' boundary singularity. This behavior is unlike that of the catenoid, which transitions to two disks through a bulk singularity. It is not yet understood whether the type of singularity is generally a consequence of the surface topology, nor how this dependence could arise from an equation of motion for the surface. To address these questions we investigate experimentally, computationally, and theoretically the route to singularities of soap films with different topologies, including a family of punctured Klein bottles. We show that the location of singularities (bulk or boundary) may depend on the path of the boundary deformation. In the unstable regime the driving force for soap-film motion is the mean curvature. Thus, the narrowest part of the neck, associated with the shortest nontrivial closed geodesic of the surface, has the highest curvature and is the fastest-moving. Just before onset of the instability there exists on the stable surface a shortest closed geodesic, which is the initial condition for evolution of the neck's geodesics, all of which have the same topological relationship to the frame. We make the plausible conjectures that if the initial geodesic is linked to the boundary then the singularity will occur at the boundary, whereas if the two are unlinked initially then the singularity will occur in the bulk. Numerical study of mean curvature flows and experiments support these conjectures.

cond-mat.soft↗

arXiv2014

Rheotaxis facilitates upstream navigation of mammalian sperm cells

A major puzzle in biology is how mammalian sperm determine and maintain the correct swimming direction during the various phases of the sexual reproduction process. Whilst chemotaxis is assumed to dominate in the immediate vicinity of the ovum, it is unclear which biochemical or physical cues guide spermatozoa on their long journey towards the egg cell. Currently debated mechanisms range from peristaltic pumping to temperature sensing (thermotaxis) and direct response to fluid flow variations (rheotaxis), but little is known quantitatively about their relative importance. Here, we report the first quantitative experimental study of mammalian sperm rheotaxis. Using microfluidic devices, we investigate systematically the swimming behavior of human and bull sperm over the whole range of physiologically relevant shear rates and viscosities. Our measurements show that the interplay of fluid shear, steric surface-interactions and chirality of the flagellar beat leads to a stable upstream spiraling motion of sperm cells, thus providing a generic and robust rectification mechanism to support mammalian fertilisation. To rationalise these findings, we identify a minimal mathematical model that is capable of describing quantitatively the experimental observations. The combined experimental and theoretical evidence supports the hypothesis that the shape and beat patterns of mammalian sperm cells have evolved to optimally exploit rheotaxis for long-distance navigation.

physics.bio-ph↗

arXiv2014

Flagellar Synchronization Through Direct Hydrodynamic Interactions

Microscale fluid flows generated by ensembles of beating eukaryotic flagella are crucial to fundamental processes such as development, motility and sensing. Despite significant experimental and theoretical progress, the underlying physical mechanisms behind this striking coordination remain unclear. Here, we present a novel series of experiments in which the flagellar dynamics of two micropipette-held somatic cells of Volvox carteri, with measurably different intrinsic beating frequencies, are studied by high-speed imaging as a function of their mutual separation and orientation. From analysis of beating time series we find that the interflagellar coupling, which is constrained by the lack of chemical and mechanical connections between the cells to be purely hydrodynamical, exhibits a spatial dependence that is consistent with theoretical predictions. At close spacings it produces robust synchrony which can prevail for thousands of flagellar beats, while at increasing separations this synchrony is systematically degraded by stochastic processes. Manipulation of the relative flagellar orientation reveals the existence of both in-phase and antiphase synchronized states, which is consistent with dynamical theories. Through dynamic flagellar tracking with exquisite spatio-temporal precision, we quantify changes in beating waveforms that result from altered coupling configuration and distance of separation. The experimental results of this study prove unequivocally that flagella coupled solely through a fluid medium can achieve robust synchrony despite significant differences in their intrinsic properties.

cond-mat.soft↗

arXiv2013

Lag, lock, sync, slip: the many "phases" of coupled flagella

In a multitude of life's processes, cilia and flagella are found indispensable. Recently, the biflagellated chlorophyte alga Chlamydomonas has become a model organism for the study of ciliary coordination and synchronization. Here, we use high-speed imaging of single pipette-held cells to quantify the rich dynamics exhibited by their flagella. Underlying this variability in behaviour, are biological dissimilarities between the two flagella - termed cis and trans, with respect to a unique eyespot. With emphasis on the wildtype, we use digital tracking with sub-beat-cycle resolution to obtain limit cycles and phases for self-sustained flagellar oscillations. Characterizing the phase-synchrony of a coupled pair, we find that during the canonical swimming breaststroke the cis flagellum is consistently phase-lagged relative to, whilst remaining robustly phase-locked with, the trans flagellum. Transient loss of synchrony, or phase-slippage, may be triggered stochastically, in which the trans flagellum transitions to a second mode of beating with attenuated beat-envelope and increased frequency. Further, exploiting this alga's ability for flagellar regeneration, we mechanically induced removal of one or the other flagellum of the same cell to reveal a striking disparity between the beating of the cis vs trans flagellum, in isolation. This raises further questions regarding the synchronization mechanism of Chlamydomonas.

physics.bio-ph↗

arXiv2013

Auto-chemotactic micro-swimmer suspensions: modeling, analysis and simulations

Microorganisms can preferentially orient and move along gradients of a chemo-attractant (i.e., chemotax) while colonies of many microorganisms can collectively undergo complex dynamics in response to chemo-attractants that they themselves produce. For colonies or groups of micro-swimmers we investigate how an "auto-chemotactic" response that should lead to swimmer aggregation is affected by the non-trivial fluid flows that are generated by collective swimming. For this, we consider chemotaxis models based upon a hydrodynamic theory of motile suspensions that are fully coupled to chemo-attractant production, transport, and diffusion. Linear analysis of isotropically ordered suspensions reveals both an aggregative instability due to chemotaxis that occurs independently of swimmer type, and a hydrodynamic instability when the swimmers are "pushers". Nonlinear simulations show nonetheless that hydrodynamic interactions can significantly modify the chemotactically-driven aggregation dynamics in suspensions of "pushers" or "pullers". Different states of the dynamics resulting from these coupled interactions in the colony are discussed.

physics.bio-ph↗

arXiv2013

Spontaneous ordering of a bacterial drop into a spiral vortex

In this fluid dynamics video we explore the nature and causes of the spontaneous ordering that emerges in a dense bacterial suspension under confinement. Recent experiments with B. Subtilis confined within small flattened drops show that the bacteria form a steady single-vortex state with a counterrotating cell boundary layer. Using simulations that capture oriented cell-cell and cell-fluid interactions, we show that hydrodynamics is crucial in reproducing and explaining the phenomenon. We give new insights into the microscopic arrangement of the bacteria, which are confirmed by new experiments.

cond-mat.soft↗