Publications by authors named "Raymond E Goldstein"

100 Publications

Morphoelasticity of large bending deformations of cell sheets during development.

Phys Rev E 2021 Feb;103(2-1):022411

Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.

Deformations of cell sheets during morphogenesis are driven by developmental processes such as cell division and cell shape changes. In morphoelastic shell theories of development, these processes appear as variations of the intrinsic geometry of a thin elastic shell. However, morphogenesis often involves large bending deformations that are outside the formal range of validity of these shell theories. Here, by asymptotic expansion of three-dimensional incompressible morphoelasticity in the limit of a thin shell, we derive a shell theory for large intrinsic bending deformations and emphasize the resulting geometric material anisotropy and the elastic role of cell constriction. Taking the invagination of the green alga Volvox as a model developmental event, we show how results for this theory differ from those for a classical shell theory that is not formally valid for these large bending deformations and reveal how these geometric effects stabilize invagination.
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http://dx.doi.org/10.1103/PhysRevE.103.022411DOI Listing
February 2021

Swirling Instability of the Microtubule Cytoskeleton.

Phys Rev Lett 2021 Jan;126(2):028103

Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WA, United Kingdom.

In the cellular phenomena of cytoplasmic streaming, molecular motors carrying cargo along a network of microtubules entrain the surrounding fluid. The piconewton forces produced by individual motors are sufficient to deform long microtubules, as are the collective fluid flows generated by many moving motors. Studies of streaming during oocyte development in the fruit fly Drosophila melanogaster have shown a transition from a spatially disordered cytoskeleton, supporting flows with only short-ranged correlations, to an ordered state with a cell-spanning vortical flow. To test the hypothesis that this transition is driven by fluid-structure interactions, we study a discrete-filament model and a coarse-grained continuum theory for motors moving on a deformable cytoskeleton, both of which are shown to exhibit a swirling instability to spontaneous large-scale rotational motion, as observed.
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http://dx.doi.org/10.1103/PhysRevLett.126.028103DOI Listing
January 2021

Nuclear crowding and nonlinear diffusion during interkinetic nuclear migration in the zebrafish retina.

Elife 2020 10 6;9. Epub 2020 Oct 6.

Department of Physiology, Development and Neuroscience, University of Cambridge, Cambridge, United Kingdom.

An important question in early neural development is the origin of stochastic nuclear movement between apical and basal surfaces of neuroepithelia during interkinetic nuclear migration. Tracking of nuclear subpopulations has shown evidence of diffusion - mean squared displacements growing linearly in time - and suggested crowding from cell division at the apical surface drives basalward motion. Yet, this hypothesis has not yet been tested, and the forces involved not quantified. We employ long-term, rapid light-sheet and two-photon imaging of early zebrafish retinogenesis to track entire populations of nuclei within the tissue. The time-varying concentration profiles show clear evidence of crowding as nuclei reach close-packing and are quantitatively described by a nonlinear diffusion model. Considerations of nuclear motion constrained inside the enveloping cell membrane show that concentration-dependent stochastic forces inside cells, compatible in magnitude to those found in cytoskeletal transport, can explain the observed magnitude of the diffusion constant.
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http://dx.doi.org/10.7554/eLife.58635DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7538155PMC
October 2020

Stress-Induced Dinoflagellate Bioluminescence at the Single Cell Level.

Phys Rev Lett 2020 Jul;125(2):028102

Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom.

One of the characteristic features of many marine dinoflagellates is their bioluminescence, which lights up nighttime breaking waves or seawater sliced by a ship's prow. While the internal biochemistry of light production by these microorganisms is well established, the manner by which fluid shear or mechanical forces trigger bioluminescence is still poorly understood. We report controlled measurements of the relation between mechanical stress and light production at the single cell level, using high-speed imaging of micropipette-held cells of the marine dinoflagellate Pyrocystis lunula subjected to localized fluid flows or direct indentation. We find a viscoelastic response in which light intensity depends on both the amplitude and rate of deformation, consistent with the action of stretch-activated ion channels. A phenomenological model captures the experimental observations.
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http://dx.doi.org/10.1103/PhysRevLett.125.028102DOI Listing
July 2020

CCDC61/VFL3 Is a Paralog of SAS6 and Promotes Ciliary Functions.

Structure 2020 06 5;28(6):674-689.e11. Epub 2020 May 5.

MRC Laboratory of Molecular Biology, Cambridge Biomedical Campus, Francis Crick Avenue, Cambridge CB2 0QH, UK. Electronic address:

Centrioles are cylindrical assemblies whose peripheral microtubule array displays a 9-fold rotational symmetry that is established by the scaffolding protein SAS6. Centriole symmetry can be broken by centriole-associated structures, such as the striated fibers in Chlamydomonas that are important for ciliary function. The conserved protein CCDC61/VFL3 is involved in this process, but its exact role is unclear. Here, we show that CCDC61 is a paralog of SAS6. Crystal structures of CCDC61 demonstrate that it contains two homodimerization interfaces that are similar to those found in SAS6, but result in the formation of linear filaments rather than rings. Furthermore, we show that CCDC61 binds microtubules and that residues involved in CCDC61 microtubule binding are important for ciliary function in Chlamydomonas. Together, our findings suggest that CCDC61 and SAS6 functionally diverged from a common ancestor while retaining the ability to scaffold the assembly of basal body-associated structures or centrioles, respectively.
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http://dx.doi.org/10.1016/j.str.2020.04.010DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7267773PMC
June 2020

Motility and phototaxis of Gonium, the simplest differentiated colonial alga.

Phys Rev E 2020 Feb;101(2-1):022416

Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.

Green algae of the Volvocine lineage, spanning from unicellular Chlamydomonas to vastly larger Volvox, are models for the study of the evolution of multicellularity, flagellar dynamics, and developmental processes. Phototactic steering in these organisms occurs without a central nervous system, driven solely by the response of individual cells. All such algae spin about a body-fixed axis as they swim; directional photosensors on each cell thus receive periodic signals when that axis is not aligned with the light. The flagella of Chlamydomonas and Volvox both exhibit an adaptive response to such signals in a manner that allows for accurate phototaxis, but in the former the two flagella have distinct responses, while the thousands of flagella on the surface of spherical Volvox colonies have essentially identical behavior. The planar 16-cell species Gonium pectorale thus presents a conundrum, for its central 4 cells have a Chlamydomonas-like beat that provide propulsion normal to the plane, while its 12 peripheral cells generate rotation around the normal through a Volvox-like beat. Here we combine experiment, theory, and computations to reveal how Gonium, perhaps the simplest differentiated colonial organism, achieves phototaxis. High-resolution cell tracking, particle image velocimetry of flagellar driven flows, and high-speed imaging of flagella on micropipette-held colonies show how, in the context of a recently introduced model for Chlamydomonas phototaxis, an adaptive response of the peripheral cells alone leads to photoreorientation of the entire colony. The analysis also highlights the importance of local variations in flagellar beat dynamics within a given colony, which can lead to enhanced reorientation dynamics.
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http://dx.doi.org/10.1103/PhysRevE.101.022416DOI Listing
February 2020

Optimal Design of Multilayer Fog Collectors.

ACS Appl Mater Interfaces 2020 Feb 30;12(6):7736-7743. Epub 2020 Jan 30.

Faculty of Engineering and Sciences , Universidad Adolfo Ibáñez , Av. Padre Hurtado 750 , Viña del Mar 2562340 , Chile.

The growing concerns over desertification have spurred research into technologies aimed at acquiring water from nontraditional sources such as dew, fog, and water vapor. Some of the most promising developments have focused on improving designs to collect water from fog. However, the absence of a shared framework to predict, measure, and compare the water collection efficiencies of new prototypes is becoming a major obstacle to progress in the field. We address this problem by providing a general theory to design efficient fog collectors as well as a concrete experimental protocol to furnish our theory with all the necessary parameters to quantify the effective water collection efficiency. We show in particular that multilayer collectors are required for high fog collection efficiency and that all efficient designs are found within a narrow range of mesh porosity. We support our conclusions with measurements on simple multilayer harp collectors.
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http://dx.doi.org/10.1021/acsami.9b19727DOI Listing
February 2020

A theory for the slip and drag of superhydrophobic surfaces with surfactant.

J Fluid Mech 2020 Jan 25;883. Epub 2019 Nov 25.

Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106, USA.

Superhydrophobic surfaces (SHSs) have the potential to reduce drag at solid boundaries. However, multiple independent studies have recently shown that small amounts of surfactant, naturally present in the environment, can induce Marangoni forces that increase drag, at least in the laminar regime. To obtain accurate drag predictions, one must solve the mass, momentum, bulk surfactant and interfacial surfactant conservation equations. This requires expensive simulations, thus preventing surfactant from being widely considered in SHS studies. To address this issue, we propose a theory for steady, pressure-driven, laminar, two-dimensional flow in a periodic SHS channel with soluble surfactant. We linearise the coupling between flow and surfactant, under the assumption of small concentration, finding a scaling prediction for the local slip length. To obtain the drag reduction and interfacial shear, we find a series solution for the velocity field by assuming Stokes flow in the bulk and uniform interfacial shear. We find how the slip and drag depend on the nine dimensionless groups that together characterize the surfactant transport near SHSs, the gas fraction and the normalized interface length. Our model agrees with numerical simulations spanning orders of magnitude in each dimensionless group. The simulations also provide the constants in the scaling theory. Our model significantly improves predictions relative to a surfactant-free one, which can otherwise overestimate slip and underestimate drag by several orders of magnitude. Our slip length model can provide the boundary condition in other simulations, thereby accounting for surfactant effects without having to solve the full problem.
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http://dx.doi.org/10.1017/jfm.2019.857DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6894944PMC
January 2020

Swimming eukaryotic microorganisms exhibit a universal speed distribution.

Elife 2019 07 16;8. Epub 2019 Jul 16.

Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, United Kingdom.

One approach to quantifying biological diversity consists of characterizing the statistical distribution of specific properties of a taxonomic group or habitat. Microorganisms living in fluid environments, and for whom motility is key, exploit propulsion resulting from a rich variety of shapes, forms, and swimming strategies. Here, we explore the variability of swimming speed for unicellular eukaryotes based on published data. The data naturally partitions into that from flagellates (with a small number of flagella) and from ciliates (with tens or more). Despite the morphological and size differences between these groups, each of the two probability distributions of swimming speed are accurately represented by log-normal distributions, with good agreement holding even to fourth moments. Scaling of the distributions by a characteristic speed for each data set leads to a collapse onto an apparently universal distribution. These results suggest a universal way for ecological niches to be populated by abundant microorganisms.
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http://dx.doi.org/10.7554/eLife.44907DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6634970PMC
July 2019

Nonlinear and nonlocal elasticity in coarse-grained differential-tension models of epithelia.

Phys Rev E 2019 Feb;99(2-1):022411

Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.

The shapes of epithelial tissues result from a complex interplay of contractile forces in the cytoskeleta of the cells in the tissue and adhesion forces between them. A host of discrete, cell-based models describe these forces by assigning different surface tensions to the apical, basal, and lateral sides of the cells. These differential-tension models have been used to describe the deformations of epithelia in different living systems, but the underlying continuum mechanics at the scale of the epithelium are still unclear. Here, we derive a continuum theory for a simple differential-tension model of a two-dimensional epithelial monolayer and study the buckling of this epithelium under imposed compression. The analysis reveals how the cell-level properties encoded in the differential-tension model lead to linear and nonlinear elastic as well as nonlocal, nonelastic behavior at the continuum level.
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http://dx.doi.org/10.1103/PhysRevE.99.022411DOI Listing
February 2019

Embryonic Inversion in : The Flipping and Peeling of Elastic Lips.

Phys Rev E 2018 Nov;98(5)

Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.

The embryos of the green alga are spherical sheets of cells that turn themselves inside out at the close of their development through a programme of cell shape changes. This process of inversion is a model for morphogenetic cell sheet deformations; it starts with four lips opening up at the anterior pole of the cell sheet, flipping over and peeling back to invert the embryo. Experimental studies have revealed that inversion is arrested if some of these cell shape changes are inhibited, but the mechanical basis for these observations has remained unclear. Here, we analyse the mechanics of this inversion by deriving an averaged elastic theory for these lips and we interpret the experimental observations in terms of the mechanics and evolution of inversion.
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http://dx.doi.org/10.1103/PhysRevE.98.052415DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6276994PMC
November 2018

Time Irreversibility and Criticality in the Motility of a Flagellate Microorganism.

Phys Rev Lett 2018 Aug;121(5):058103

Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WA, United Kingdom.

Active living organisms exhibit behavioral variability, partitioning between fast and slow dynamics. Such variability may be key to generating rapid responses in a heterogeneous, unpredictable environment wherein cellular activity effects continual exchanges of energy fluxes. We demonstrate a novel, noninvasive strategy for revealing nonequilibrium control of swimming-specifically, in an octoflagellate microalga. These organisms exhibit surprising features of flagellar excitability and mechanosensitivity, which characterize a novel, time-irreversible "run-stop-shock" motility comprising forward runs, knee-jerk shocks with dramatic beat reversal, and long stops during which cells are quiescent yet continue to exhibit submicron flagellar vibrations. Entropy production, associated with flux cycles arising in a reaction graph representation of the gait-switching dynamics, provides a direct measure of detailed balance violation in this primitive alga.
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http://dx.doi.org/10.1103/PhysRevLett.121.058103DOI Listing
August 2018

Are theoretical results 'Results'?

Elife 2018 07 23;7. Epub 2018 Jul 23.

Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Cambridge, United Kingdom.

Yes.
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http://dx.doi.org/10.7554/eLife.40018DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6056240PMC
July 2018

The noisy basis of morphogenesis: Mechanisms and mechanics of cell sheet folding inferred from developmental variability.

PLoS Biol 2018 07 12;16(7):e2005536. Epub 2018 Jul 12.

Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Cambridge, United Kingdom.

Variability is emerging as an integral part of development. It is therefore imperative to ask how to access the information contained in this variability. Yet most studies of development average their observations and, discarding the variability, seek to derive models, biological or physical, that explain these average observations. Here, we analyse this variability in a study of cell sheet folding in the green alga Volvox, whose spherical embryos turn themselves inside out in a process sharing invagination, expansion, involution, and peeling of a cell sheet with animal models of morphogenesis. We generalise our earlier, qualitative model of the initial stages of inversion by combining ideas from morphoelasticity and shell theory. Together with three-dimensional visualisations of inversion using light sheet microscopy, this yields a detailed, quantitative model of the entire inversion process. With this model, we show how the variability of inversion reveals that two separate, temporally uncoupled processes drive the initial invagination and subsequent expansion of the cell sheet. This implies a prototypical transition towards higher developmental complexity in the volvocine algae and provides proof of principle of analysing morphogenesis based on its variability.
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http://dx.doi.org/10.1371/journal.pbio.2005536DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6063725PMC
July 2018

Why Clothes Don't Fall Apart: Tension Transmission in Staple Yarns.

Phys Rev Lett 2018 Apr;120(15):158001

Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.

The problem of how staple yarns transmit tension is addressed within abstract models in which the Amontons-Coulomb friction laws yield a linear programing (LP) problem for the tensions in the fiber elements. We find there is a percolation transition such that above the percolation threshold the transmitted tension is in principle unbounded. We determine that the mean slack in the LP constraints is a suitable order parameter to characterize this supercritical state. We argue the mechanism is generic, and in practical terms, it corresponds to a switch from a ductile to a brittle failure mode accompanied by a significant increase in mechanical strength.
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http://dx.doi.org/10.1103/PhysRevLett.120.158001DOI Listing
April 2018

Microbial mutualism at a distance: The role of geometry in diffusive exchanges.

Phys Rev E 2018 Feb;97(2-1):022411

Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom.

The exchange of diffusive metabolites is known to control the spatial patterns formed by microbial populations, as revealed by recent studies in the laboratory. However, the matrices used, such as agarose pads, lack the structured geometry of many natural microbial habitats, including in the soil or on the surfaces of plants or animals. Here we address the important question of how such geometry may control diffusive exchanges and microbial interaction. We model mathematically mutualistic interactions within a minimal unit of structure: two growing reservoirs linked by a diffusive channel through which metabolites are exchanged. The model is applied to study a synthetic mutualism, experimentally parametrized on a model algal-bacterial co-culture. Analytical and numerical solutions of the model predict conditions for the successful establishment of remote mutualisms, and how this depends, often counterintuitively, on diffusion geometry. We connect our findings to understanding complex behavior in synthetic and naturally occurring microbial communities.
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http://dx.doi.org/10.1103/PhysRevE.97.022411DOI Listing
February 2018

Spontaneous oscillations of elastic filaments induced by molecular motors.

J R Soc Interface 2017 11;14(136)

Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK

It is known from the wave-like motion of microtubules in motility assays that the piconewton forces that motors produce can be sufficient to bend the filaments. In cellular phenomena such as cytosplasmic streaming, molecular motors translocate along cytoskeletal filaments, carrying cargo which entrains fluid. When large numbers of such forced filaments interact through the surrounding fluid, as in particular stages of oocyte development in , complex dynamics are observed, but the detailed mechanics underlying them has remained unclear. Motivated by these observations, we study here perhaps the simplest model for these phenomena: an elastic filament, pinned at one end, acted on by a molecular motor treated as a point force. Because the force acts tangential to the filament, no matter what its shape, this 'follower-force' problem is intrinsically non-variational, and thereby differs fundamentally from Euler buckling, where the force has a fixed direction, and which, in the low-Reynolds-number regime, ultimately leads to a stationary, energy-minimizing shape. Through a combination of linear stability theory, analytical study of a solvable simplified 'two-link' model and numerical studies of the full elastohydrodynamic equations of motion, we elucidate the Hopf bifurcation that occurs with increasing forcing of a filament, leading to flapping motion analogous to the high-Reynolds-number oscillations of a garden hose with a free end.
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http://dx.doi.org/10.1098/rsif.2017.0491DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5721157PMC
November 2017

Localised dynactin protects growing microtubules to deliver mRNA to the posterior cortex of the oocyte.

Elife 2017 10 16;6. Epub 2017 Oct 16.

The Gurdon Institute and the Department of Genetics, University of Cambridge, Cambridge, United Kingdom.

The localisation of mRNA to the posterior of the oocyte defines where the abdomen and germ cells form in the embryo. Kinesin 1 transports mRNA to the oocyte posterior along a polarised microtubule cytoskeleton that grows from non-centrosomal microtubule organising centres (ncMTOCs) along the anterior/lateral cortex. Here, we show that the formation of this polarised microtubule network also requires the posterior regulation of microtubule growth. A missense mutation in the dynactin Arp1 subunit causes most mRNA to localise in the posterior cytoplasm rather than cortically. mRNA transport and anchoring are normal in this mutant, but the microtubules fail to reach the posterior pole. Thus, dynactin acts as an anti-catastrophe factor that extends microtubule growth posteriorly. Kinesin 1 transports dynactin to the oocyte posterior, creating a positive feedback loop that increases the length and persistence of the posterior microtubules that deliver mRNA to the cortex.
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http://dx.doi.org/10.7554/eLife.27237DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5643094PMC
October 2017

Scattering of biflagellate microswimmers from surfaces.

Phys Rev E 2017 Aug 10;96(2-1):023102. Epub 2017 Aug 10.

Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom.

We use a three-bead-spring model to investigate the dynamics of biflagellate microswimmers near a surface. While the primary dynamics and scattering are governed by geometric-dependent direct contact, the fluid flows generated by the swimmer locomotion are important in orienting it toward or away from the surface. Flagellar noise and in particular cell spinning about the main axis help a surface-trapped swimmer escape, whereas the time a swimmer spends at the surface depends on the incident angle. The dynamics results from a nuanced interplay of direct collisions, hydrodynamics, noise, and the swimmer geometry. We show that to correctly capture the dynamics of a biflagellate swimmer, minimal models need to resolve the shape asymmetry.
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http://dx.doi.org/10.1103/PhysRevE.96.023102DOI Listing
August 2017

Traces of surfactants can severely limit the drag reduction of superhydrophobic surfaces.

Proc Natl Acad Sci U S A 2017 07 27;114(28):7254-7259. Epub 2017 Jun 27.

Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106

Superhydrophobic surfaces (SHSs) have the potential to achieve large drag reduction for internal and external flow applications. However, experiments have shown inconsistent results, with many studies reporting significantly reduced performance. Recently, it has been proposed that surfactants, ubiquitous in flow applications, could be responsible by creating adverse Marangoni stresses. However, testing this hypothesis is challenging. Careful experiments with purified water already show large interfacial stresses and, paradoxically, adding surfactants yields barely measurable drag increases. To test the surfactant hypothesis while controlling surfactant concentrations with precision higher than can be achieved experimentally, we perform simulations inclusive of surfactant kinetics. These reveal that surfactant-induced stresses are significant at extremely low concentrations, potentially yielding a no-slip boundary condition on the air-water interface (the "plastron") for surfactant concentrations below typical environmental values. These stresses decrease as the stream-wise distance between plastron stagnation points increases. We perform microchannel experiments with SHSs consisting of stream-wise parallel gratings, which confirm this numerical prediction, while showing near-plastron velocities significantly slower than standard surfactant-free predictions. In addition, we introduce an unsteady test of surfactant effects. When we rapidly remove the driving pressure following a loading phase, a backflow develops at the plastron, which can only be explained by surfactant gradients formed in the loading phase. This demonstrates the significance of surfactants in deteriorating drag reduction and thus the importance of including surfactant stresses in SHS models. Our time-dependent protocol can assess the impact of surfactants in SHS testing and guide future mitigating designs.
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http://dx.doi.org/10.1073/pnas.1702469114DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5514732PMC
July 2017

Theory of Shape-Shifting Droplets.

Phys Rev Lett 2017 Feb 21;118(8):088001. Epub 2017 Feb 21.

Department of Chemical and Pharmaceutical Engineering, Faculty of Chemistry and Pharmacy, University of Sofia, 1164 Sofia, Bulgaria.

Recent studies of cooled oil emulsion droplets uncovered transformations into a host of flattened shapes with straight edges and sharp corners, driven by a partial phase transition of the bulk liquid phase. Here, we explore theoretically the simplest geometric competition between this phase transition and surface tension in planar polygons and recover the observed sequence of shapes and their statistics in qualitative agreement with experiments. Extending the model to capture some of the three-dimensional structure of the droplets, we analyze the evolution of protrusions sprouting from the vertices of the platelets and the topological transition of a puncturing planar polygon.
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http://dx.doi.org/10.1103/PhysRevLett.118.088001DOI Listing
February 2017

Filter-feeding, near-field flows, and the morphologies of colonial choanoflagellates.

Phys Rev E 2016 Nov 1;94(5-1):052401. Epub 2016 Nov 1.

Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.

Efficient uptake of prey and nutrients from the environment is an important component in the fitness of all microorganisms, and its dependence on size may reveal clues to the origins of evolutionary transitions to multicellularity. Because potential benefits in uptake rates must be viewed in the context of other costs and benefits of size, such as varying predation rates and the increased metabolic costs associated with larger and more complex body plans, the uptake rate itself is not necessarily that which is optimized by evolution. Uptake rates can be strongly dependent on local organism geometry and its swimming speed, providing selective pressure for particular arrangements. Here we examine these issues for choanoflagellates, filter-feeding microorganisms that are the closest relatives of the animals. We explore the different morphological variations of the choanoflagellate Salpingoeca rosetta, which can exist as a swimming cell, as a sessile thecate cell, and as colonies of cells in various shapes. In the absence of other requirements and in a homogeneously nutritious environment, we find that the optimal strategy to maximize filter-feeding by the collar of microvilli is to swim fast, which favors swimming unicells. In large external flows, the sessile thecate cell becomes advantageous. Effects of prey diffusion are discussed and also found to be to the advantage of the swimming unicell.
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http://dx.doi.org/10.1103/PhysRevE.94.052401DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6054299PMC
November 2016

Long-range interactions, wobbles, and phase defects in chains of model cilia.

Phys Rev Fluids 2016 Dec;1:081201

Physics Department, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, United Kingdom.

Eukaryotic cilia and flagella are chemo-mechanical oscillators capable of generating long-range coordinated motions known as metachronal waves. Pair synchronization is a fundamental requirement for these collective dynamics, but it is generally not sufficient for collective phase-locking, chiefly due to the effect of long-range interactions. Here we explore experimentally and numerically a minimal model for a ciliated surface: hydrodynamically coupled oscillators rotating above a no-slip plane. Increasing their distance from the wall profoundly affects the global dynamics, due to variations in hydrodynamic interaction range. The array undergoes a transition from a traveling wave to either a steady chevron pattern or one punctuated by periodic phase defects. Within the transition between these regimes the system displays behavior reminiscent of chimera states.
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http://dx.doi.org/10.1103/PhysRevFluids.1.081201DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6097603PMC
December 2016

Aerotaxis in the closest relatives of animals.

Elife 2016 11 24;5. Epub 2016 Nov 24.

Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Cambridge, United Kingdom.

As the closest unicellular relatives of animals, choanoflagellates serve as useful model organisms for understanding the evolution of animal multicellularity. An important factor in animal evolution was the increasing ocean oxygen levels in the Precambrian, which are thought to have influenced the emergence of complex multicellular life. As a first step in addressing these conditions, we study here the response of the colony-forming choanoflagellate to oxygen gradients. Using a microfluidic device that allows spatio-temporal variations in oxygen concentrations, we report the discovery that displays positive aerotaxis. Analysis of the spatial population distributions provides evidence for logarithmic sensing of oxygen, which enhances sensing in low oxygen neighborhoods. Analysis of search strategy models on the experimental colony trajectories finds that choanoflagellate aerotaxis is consistent with stochastic navigation, the statistics of which are captured using an effective continuous version based on classical run-and-tumble chemotaxis.
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http://dx.doi.org/10.7554/eLife.18109DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5122458PMC
November 2016

Elastohydrodynamic Synchronization of Adjacent Beating Flagella.

Phys Rev Fluids 2016 Nov;1

Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.

It is now well established that nearby beating pairs of eukaryotic flagella or cilia typically synchronize in phase. A substantial body of evidence supports the hypothesis that hydrodynamic coupling between the active filaments, combined with waveform compliance, provides a robust mechanism for synchrony. This elastohydrodynamic mechanism has been incorporated into 'bead-spring' models in which the beating flagella are represented by microspheres tethered by radial springs as they are driven about orbits by internal forces. While these low-dimensional models reproduce the phenomenon of synchrony, their parameters are not readily relatable to those of the filaments they represent. More realistic models which reflect the underlying elasticity of the axonemes and the active force generation, take the form of fourth-order nonlinear PDEs. While computational studies have shown the occurrence of synchrony, the effects of hydrodynamic coupling between nearby filaments governed by such continuum models have been theoretically examined only in the regime of interflagellar distances large compared to flagellar length . Yet, in many biological situations ≪ 1. Here, we first present an asymptotic analysis of the hydrodynamic coupling between two extended filaments in the regime ≪ 1, and find that the form of the coupling is independent of the microscopic details of the internal forces that govern the motion of the individual filaments. The analysis is analogous to that yielding the localized induction approximation for vortex filament motion, extended to the case of mutual induction. In order to understand how the elastohydrodynamic coupling mechanism leads to synchrony of extended objects, we introduce a heuristic model of flagellar beating. The model takes the form of a single fourth-order nonlinear PDE whose form is derived from symmetry considerations, the physics of elasticity, and the overdamped nature of the dynamics. Analytical and numerical studies of this model illustrate how synchrony between a pair of filaments is achieved through the asymptotic coupling.
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http://dx.doi.org/10.1103/PhysRevFluids.1.073201DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5939993PMC
November 2016

The Evolution of Silicon Transport in Eukaryotes.

Mol Biol Evol 2016 12 11;33(12):3226-3248. Epub 2016 Oct 11.

Howard Hughes Medical Institute and Department of Molecular and Cell Biology, University of California, Berkeley, CA.

Biosilicification (the formation of biological structures from silica) occurs in diverse eukaryotic lineages, plays a major role in global biogeochemical cycles, and has significant biotechnological applications. Silicon (Si) uptake is crucial for biosilicification, yet the evolutionary history of the transporters involved remains poorly known. Recent evidence suggests that the SIT family of Si transporters, initially identified in diatoms, may be widely distributed, with an extended family of related transporters (SIT-Ls) present in some nonsilicified organisms. Here, we identify SITs and SIT-Ls in a range of eukaryotes, including major silicified lineages (radiolarians and chrysophytes) and also bacterial SIT-Ls. Our evidence suggests that the symmetrical 10-transmembrane-domain SIT structure has independently evolved multiple times via duplication and fusion of 5-transmembrane-domain SIT-Ls. We also identify a second gene family, similar to the active Si transporter Lsi2, that is broadly distributed amongst siliceous and nonsiliceous eukaryotes. Our analyses resolve a distinct group of Lsi2-like genes, including plant and diatom Si-responsive genes, and sequences unique to siliceous sponges and choanoflagellates. The SIT/SIT-L and Lsi2 transporter families likely contribute to biosilicification in diverse lineages, indicating an ancient role for Si transport in eukaryotes. We propose that these Si transporters may have arisen initially to prevent Si toxicity in the high Si Precambrian oceans, with subsequent biologically induced reductions in Si concentrations of Phanerozoic seas leading to widespread losses of SIT, SIT-L, and Lsi2-like genes in diverse lineages. Thus, the origin and diversification of two independent Si transporter families both drove and were driven by ancient ocean Si levels.
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http://dx.doi.org/10.1093/molbev/msw209DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5100055PMC
December 2016

A model for the effects of germanium on silica biomineralization in choanoflagellates.

J R Soc Interface 2016 Sep;13(122)

Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK.

Silica biomineralization is a widespread phenomenon of major biotechnological interest. Modifying biosilica with substances like germanium (Ge) can confer useful new properties, although exposure to high levels of Ge disrupts normal biosilicification. No clear mechanism explains why this disruption occurs. Here, we study the effect of Ge on loricate choanoflagellates, a group of protists that construct a species-specific extracellular lorica from multiple siliceous costal strips. High Ge exposures were toxic, whereas lower Ge exposures produced cells with incomplete or absent loricae. These effects can be ameliorated by restoring the germanium : silicon ratio, as observed in other biosilicifying organisms. We developed simulations of how Ge interacts with polymerizing silica. In our models, Ge is readily incorporated at the ends of silica forming from silicic acid condensation, but this prevents further silica polymerization. Our 'Ge-capping' model is supported by observations from loricate choanoflagellates. Ge exposure terminates costal strip synthesis and lorica formation, resulting in disruption to cytokinesis and fatal build-up of silicic acid. Applying the Ge-capping model to other siliceous organisms explains the general toxicity of Ge and identifies potential protective responses in metalloid uptake and sensing. This can improve the design of new silica biomaterials, and further our understanding of silicon metabolism.
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http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5046948PMC
http://dx.doi.org/10.1098/rsif.2016.0485DOI Listing
September 2016

Instabilities and Solitons in Minimal Strips.

Phys Rev Lett 2016 Jul 1;117(1):017801. Epub 2016 Jul 1.

Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.

We show that highly twisted minimal strips can undergo a nonsingular transition, unlike the singular transitions seen in the Möbius strip and the catenoid. If the strip is nonorientable, this transition is topologically frustrated, and the resulting surface contains a helicoidal defect. Through a controlled analytic approximation, the system can be mapped onto a scalar ϕ^{4} theory on a nonorientable line bundle over the circle, where the defect becomes a topologically protected kink soliton or domain wall, thus establishing their existence in minimal surfaces. Demonstrations with soap films confirm these results and show how the position of the defect can be controlled through boundary deformation.
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http://dx.doi.org/10.1103/PhysRevLett.117.017801DOI Listing
July 2016

Ferromagnetic and antiferromagnetic order in bacterial vortex lattices.

Nat Phys 2016 Apr 4;12:341-345. Epub 2016 Jan 4.

Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, U.K.

Despite their inherent non-equilibrium nature1, living systems can self-organize in highly ordered collective states2,3 that share striking similarities with the thermodynamic equilibrium phases4,5 of conventional condensed matter and fluid systems. Examples range from the liquid-crystal-like arrangements of bacterial colonies6,7, microbial suspensions8,9 and tissues10 to the coherent macro-scale dynamics in schools of fish11 and flocks of birds12. Yet, the generic mathematical principles that govern the emergence of structure in such artificial13 and biological6-9,14 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 currents15,16, reminiscent of those in quantum systems17-19. 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.
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http://dx.doi.org/10.1038/nphys3607DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4869837PMC
April 2016

Coordinated beating of algal flagella is mediated by basal coupling.

Proc Natl Acad Sci U S A 2016 May 2;113(20):E2784-93. Epub 2016 May 2.

Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom

Cilia and flagella often exhibit synchronized behavior; this includes phase locking, as seen in Chlamydomonas, and metachronal wave formation in the respiratory cilia of higher organisms. Since the observations by Gray and Rothschild of phase synchrony of nearby swimming spermatozoa, it has been a working hypothesis that synchrony arises from hydrodynamic interactions between beating filaments. Recent work on the dynamics of physically separated pairs of flagella isolated from the multicellular alga Volvox has shown that hydrodynamic coupling alone is sufficient to produce synchrony. However, the situation is more complex in unicellular organisms bearing few flagella. We show that flagella of Chlamydomonas mutants deficient in filamentary connections between basal bodies display markedly different synchronization from the wild type. We perform micromanipulation on configurations of flagella and conclude that a mechanism, internal to the cell, must provide an additional flagellar coupling. In naturally occurring species with 4, 8, or even 16 flagella, we find diverse symmetries of basal body positioning and of the flagellar apparatus that are coincident with specific gaits of flagellar actuation, suggesting that it is a competition between intracellular coupling and hydrodynamic interactions that ultimately determines the precise form of flagellar coordination in unicellular algae.
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http://dx.doi.org/10.1073/pnas.1518527113DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4878519PMC
May 2016