Simple mechanosense and response of cilia motion reveal the intrinsic habits of ciliates

Thermodynamic Effects Are Essential for Surface Entrapment of Bacteria

The entrapment of bacteria near boundary surfaces is of biological and practical importance, yet the underlying physics is not well understood. We demonstrate that it is crucial to include a commonly neglected thermodynamic effect related to the spatial variation of hydrodynamic interactions, through a model that provides analytic explanation of bacterial entrapment in two dimensionless parameters: α_{1} the ratio of thermal energy to self-propulsion, and α_{2} an intrinsic shape factor. For α_{1} and α_{2} that match an Escherichia coli at room temperature, our model quantitatively reproduces existing experimental observations, including two key features that have not been previously resolved: The bacterial "nose-down" configuration, and the anticorrelation between the pitch angle and the wobbling angle. Furthermore, our model analytically predicts the existence of an entrapment zone in the parameter space defined by {α_{1},α_{2}}.

50-year history and perspective on biomechanics of swimming microorganisms: Part II. Collective behaviours

The paired review papers in Parts I and II describe the 50-year history of research on the biomechanics of swimming microorganisms and its prospects in the next 50 years. Parts I and II are divided not by the period covered, but by the content of the research: Part I explains the behaviours of individual microorganisms, and Part II explains collective behaviour. In the 1990s, the description of microbial suspensions as a continuum progressed, and macroscopic flow structures such as bioconvection were analysed. The continuum model was later extended to analyse various phenomena such as flow induced trapping of microorganisms and accumulation of cells at interfaces. In the 2000s, the collective behaviour of swimming microorganisms came into the limelight, and physicists as well as biomechanics researchers carried out many studies probing microorganism collectivity. In particular, research on the turbulence-like flow structure of dense bacterial suspensions has led to dramatic developments in the field of microbial biomechanics. Efforts to bridge the cellular scale to the macroscopic scale by extracting macroscopic physical quantities from the microstructure of cell suspensions are also underway. This Part II reviews these collective behaviours of swimming microorganisms and discusses future prospects of the field.

50-year History and perspective on biomechanics of swimming microorganisms: Part I. Individual behaviours

The paired review papers in Parts I and II describe the 50-year history of research on the biomechanics of swimming microorganisms and its prospects in the next 50 years: Part I explains the behaviour of individual microorganisms, and Part II explains collective behaviour. Since the discovery of microorganisms by van Leeuwenhoek in the 17th century, many natural scientists have been interested in their motility because it is directly associated with biological function. A research upsurge occurred in the 1970s, with the elucidation of swimming mechanisms among individual microorganisms and the theoretical derivation of swimming speeds. Various swimming strategies of three types of microorganisms, i.e. bacteria, ciliates and microalgae, are explained in this Part I. We show that some of the behaviours of microorganisms can be described by biomechanical equations and are to some extent predictable. Recent researches have revealed the behaviour of microorganisms in more complex environments and more realistic settings, which are also reviewed in the paper. Last, we provide future prospects for research on microbial behaviour.

Rheotaxis in Mycoplasma gliding

This review describes the upstream-directed movement in the small parasitic bacterium Mycoplasma. Many Mycoplasma species exhibit gliding motility, a form of biological motion over surfaces without the aid of general surface appendages such as flagella. The gliding motility is characterized by a constant unidirectional movement without changes in direction or backward motion. Unlike flagellated bacteria, Mycoplasma lacks the general chemotactic signaling system to control their moving direction. Therefore, the physiological role of directionless travel in Mycoplasma gliding remains unclear. Recently, high-precision measurements under an optical microscope have revealed that three species of Mycoplasma exhibited rheotaxis, that is, the direction of gliding motility is lead upstream by the water flow. This intriguing response appears to be optimized for the flow patterns encountered at host surfaces. This review provides a comprehensive overview of the morphology, behavior, and habitat of Mycoplasma gliding, and discusses the possibility that the rheotaxis is ubiquitous among them.

Interaction of the mechanosensitive microswimmer Paramecium with obstacles

In this work, we report investigations of the swimming behaviour of Paramecium tetraurelia, a unicellular microorganism, in micro-engineered pools that are decorated with thousands of cylindrical pillars. Two types of contact interactions are measured, either passive scattering of Paramecium along the obstacle or avoiding reactions (ARs), characterized by an initial backward swimming upon contact, followed by a reorientation before resuming forward motion. We find that ARs are only mechanically triggered approximately 10% of the time. In addition, we observe that only a third of all ARs triggered by contact are instantaneous while two-thirds are delayed by approximately 150 ms. These measurements are consistent with a simple electrophysiological model of mechanotransduction composed of a strong transient current followed by a persistent one upon prolonged contact. This is in apparent contrast with previous electrophysiological measurements where immobilized cells were stimulated with thin probes, which showed instantaneous behavioural responses and no persistent current. Our findings highlight the importance of ecologically relevant approaches to unravel the motility of mechanosensitive microorganisms in complex environments.

An electrophysiological and kinematic model of Paramecium, the "swimming neuron"

Paramecium is a large unicellular organism that swims in fresh water using cilia. When stimulated by various means (mechanically, chemically, optically, thermally), it often swims backward then turns and swims forward again in a new direction: this is called the avoiding reaction. This reaction is triggered by a calcium-based action potential. For this reason, several authors have called Paramecium the "swimming neuron". Here we present an empirically constrained model of its action potential based on electrophysiology experiments on live immobilized paramecia, together with simultaneous measurement of ciliary beating using particle image velocimetry. Using these measurements and additional behavioral measurements of free swimming, we extend the electrophysiological model by coupling calcium concentration to kinematic parameters, turning it into a swimming model. In this way, we obtain a model of autonomously behaving Paramecium. Finally, we demonstrate how the modeled organism interacts with an environment, can follow gradients and display collective behavior. This work provides a modeling basis for investigating the physiological basis of autonomous behavior of Paramecium in ecological environments.

Squirmer hydrodynamics near a periodic surface topography

The behaviour of microscopic swimmers has previously been explored near large-scale confining geometries and in the presence of very small-scale surface roughness. Here, we consider an intermediate case of how a simple microswimmer, the tangential spherical squirmer, behaves adjacent to singly and doubly periodic sinusoidal surface topographies that spatially oscillate with an amplitude that is an order of magnitude less than the swimmer size and wavelengths that are also within an order of magnitude of this scale. The nearest neighbour regularised Stokeslet method is used for numerical explorations after validating its accuracy for a spherical tangential squirmer that swims stably near a flat surface. The same squirmer is then introduced to different surface topographies. The key governing factor in the resulting swimming behaviour is the size of the squirmer relative to the surface topography wavelength. For instance, directional guidance is not observed when the squirmer is much larger, or much smaller, than the surface topography wavelength. In contrast, once the squirmer size is on the scale of the topography wavelength, limited guidance is possible, often with local capture in the topography troughs. However, complex dynamics can also emerge, especially when the initial configuration is not close to alignment along topography troughs or above topography crests. In contrast to sensitivity in alignment and topography wavelength, reductions in the amplitude of the surface topography or variations in the shape of the periodic surface topography do not have extensive impacts on the squirmer behaviour. Our findings more generally highlight that the numerical framework provides an essential basis to elucidate how swimmers may be guided by surface topography.

Most probable path of an active Brownian particle

In this study, we investigate the transition path of a free active Brownian particle (ABP) on a two-dimensional plane between two given states. The extremum conditions for the most probable path connecting the two states are derived using the Onsager-Machlup integral and its variational principle. We provide explicit solutions to these extremum conditions and demonstrate their nonuniqueness through an analogy with the pendulum equation indicating possible multiple paths. The pendulum analogy is also employed to characterize the shape of the globally most probable path obtained by explicitly calculating the path probability for multiple solutions. We comprehensively examine a translation process of an ABP to the front as a prototypical example. Interestingly, the numerical and theoretical analyses reveal that the shape of the most probable path changes from an I to a U shape and to the ℓ shape with an increase in the transition process time. The Langevin simulation also confirms this shape transition. We also discuss further method applications for evaluating a transition path in rare events in active matter.

Switching of behavioral modes and their modulation by a geometrical cue in the ciliate Stentor coeruleus

Protists ubiquitously live in nature and play key roles in the food web chain. Their habitats consist of various geometrical structures, such as porous media and rigid surfaces, affecting their motilities. A kind of protist, Stentor coeruleus, exhibits free swimming and adhering for feeding. Under environmental and culture conditions, these organisms are often found in sediments with complex geometries. The determination of anchoring location is essential for their lives. However, the factors that induce the behavioral transition from swimming to adhering are still unknown. In this study, we quantitatively characterized the behavioral transitions in S. coeruleus and observed the behavior in a chamber with dead ends made by a simple structure mimicking the environmental structures. As a result, the cell adheres and feeds in narrow spaces between the structure and the chamber wall. It may be reasonable for the organism to hide itself from predators and capture prey in these spaces. The behavioral strategy for the exploration and exploitation of spaces with a wide variety of geometries in their habitats is discussed.

The dynamic trophic architecture of open-ocean protist communities revealed through machine-guided metatranscriptomics

Mixotrophy is a ubiquitous nutritional strategy in marine ecosystems. Although our understanding of the distribution and abundance of mixotrophic plankton has improved significantly, the functional roles of mixotrophs are difficult to pinpoint, as mixotroph nutritional strategies are flexible and form a continuum between heterotrophy and phototrophy. We developed a machine learning–based method to assess the nutritional strategies of in situ planktonic populations based on metatranscriptomic profiles. We demonstrate that mixotrophic populations play varying functional roles along physicochemical gradients in the North Pacific Ocean, revealing a degree of physiological plasticity unique to aquatic mixotrophs. Our results highlight mechanisms that may dictate the flow of biogeochemical elements and ecology of the North Pacific Ocean, one of Earth's largest biogeographical provinces.

Intricate networks of single-celled eukaryotes (protists) dominate carbon flow in the ocean. Their growth, demise, and interactions with other microorganisms drive the fluxes of biogeochemical elements through marine ecosystems. Mixotrophic protists are capable of both photosynthesis and ingestion of prey and are dominant components of open-ocean planktonic communities. Yet the role of mixotrophs in elemental cycling is obscured by their capacity to act as primary producers or heterotrophic consumers depending on factors that remain largely uncharacterized. Here, we develop and apply a machine learning model that predicts the in situ trophic mode of aquatic protists based on their patterns of gene expression. This approach leverages a public collection of protist transcriptomes as a training set to identify a subset of gene families whose transcriptional profiles predict trophic mode. We applied our model to nearly 100 metatranscriptomes obtained during two oceanographic cruises in the North Pacific and found community-level and population-specific evidence that abundant open-ocean mixotrophic populations shift their predominant mode of nutrient and carbon acquisition in response to natural gradients in nutrient supply and sea surface temperature. Metatranscriptomic data from ship-board incubation experiments revealed that abundant mixotrophic prymnesiophytes from the oligotrophic North Pacific subtropical gyre rapidly remodeled their transcriptome to enhance photosynthesis when supplied with limiting nutrients. Coupling this approach with experiments designed to reveal the mechanisms driving mixotroph physiology provides an avenue toward understanding the ecology of mixotrophy in the natural environment.

Accumulation of Tetrahymena pyriformis on Interfaces

The behavior of ciliates has been studied for many years through environmental biology and the ethology of microorganisms, and recent hydrodynamic studies of microswimmers have greatly advanced our understanding of the behavioral dynamics at the single-cell level. However, the association between single-cell dynamics captured by microscopic observation and pattern dynamics obtained by macroscopic observation is not always obvious. Hence, to bridge the gap between the two, there is a need for experimental results on swarming dynamics at the mesoscopic scale. In this study, we investigated the spatial population dynamics of the ciliate, Tetrahymena pyriformis, based on quantitative data analysis. We combined the image processing of 3D micrographs and machine learning to obtain the positional data of individual cells of T. pyriformis and examined their statistical properties based on spatio-temporal data. According to the 3D spatial distribution of cells and their temporal evolution, cells accumulated both on the solid wall at the bottom surface and underneath the air–liquid interface at the top. Furthermore, we quantitatively clarified the difference in accumulation levels between the bulk and the interface by creating a simple behavioral model that incorporated quantitative accumulation coefficients in its solution. The accumulation coefficients can be compared under different conditions and between different species.

Near-wall rheotaxis of the ciliate Tetrahymena induced by the kinesthetic sensing of cilia

To survive in harsh environments, single-celled microorganisms autonomously respond to external stimuli, such as light, heat, and flow. Here, we elucidate the flow response of Tetrahymena, a well-known single-celled freshwater microorganism. Tetrahymena moves upstream against an external flow via a behavior called rheotaxis. While micrometer-sized particles are swept away downstream in a viscous flow, what dynamics underlie the rheotaxis of the ciliate? Our experiments reveal that Tetrahymena slides along walls during upstream movement, which indicates that the cells receive rotational torque from shear flow to control cell orientation. To evaluate the effects of the shear torque and propelling speed, we perform a numerical simulation with a hydrodynamic model swimmer adopting cilia dynamics in a shear flow. The swimmer orientations converge to an upstream alignment, and the swimmer slides upstream along a boundary wall. The results suggest that Tetrahymena automatically responds to shear flow by performing rheotaxis using cilia-stalling mechanics.

Three-dimensional tracking of the ciliate Tetrahymena reveals the mechanism of ciliary stroke-driven helical swimming

Helical swimming in free-space is a common behavior among microorganisms, such as ciliates that are covered with thousands hair-like motile cilia, and is thought to be essential for cells to orient directly to an external stimulus. However, a direct quantification of their three-dimensional (3D) helical trajectories has not been reported, in part due to difficulty in tracking 3D swimming behavior of ciliates, especially Tetrahymena with a small, transparent cell body. Here, we conducted 3D tracking of fluorescent microbeads within a cell to directly visualize the helical swimming exhibited by Tetrahymena. Our technique showed that Tetrahymena swims along a right-handed helical path with right-handed rolling of its cell body. Using the Tetrahymena cell permeabilized with detergent treatment, we also observed that influx of Ca²⁺ into cilia changed the 3D-trajectory patterns of Tetrahymena swimming, indicating that the beating pattern of cilia is the determining factor in its swimming behavior.

Straight-to-Curvilinear Motion Transition of a Swimming Droplet Caused by the Susceptibility to Fluctuations

In this Letter, a water-in-oil swimming droplet's transition from straight to curvilinear motion is investigated experimentally and theoretically. An analysis of the experimental results and the model reveal that the motion transition depends on the susceptibility of the droplet's direction of movement to external stimuli as a function of environmental parameters such as droplet size. The simplicity of the present experimental system and the model suggests implications for a general class of transitions in self-propelled swimmers.

An effective and efficient model of the near-field hydrodynamic interactions for active suspensions of bacteria

Active suspensions of microswimmers demonstrate novel emergent behaviors (self-organizations, active turbulence, etc.) on macroscopic length scales. For such systems with, minimally, thousands of microswimmers, direct numerical simulations of the hydrodynamic interactions are computationally infeasible, and reduced models are needed. We demonstrated that existing models are not satisfactory in describing the hydrodynamic interactions for microswimmers in close proximity with even qualitatively erroneous predictions, indicating a pressing need for an adequate model. We propose a model that is both physically effective and computationally efficient in describing such hydrodynamics. The main novelty of our model is the description of hydrodynamic interactions through a resistance tensor, as opposed to an effective steric interaction in existing models.

Near-field hydrodynamic interactions in active fluids are essential to determine many important emergent behaviors observed, but have not been successfully modeled so far. In this work, we propose an effective model capturing the essence of the near-field hydrodynamic interactions through a tensorial coefficient of resistance, validated numerically by a pedagogic model system consisting of an Escherichia coli bacterium and a passive sphere. In a critical test case that studies the scattering angle of the bacterium–sphere pair dynamics, we prove that the near-field hydrodynamics can make a qualitative difference even for this simple two-body system: Calculations based on the proposed model reveal a region in parameter space where the bacterium is trapped by the passive sphere, a phenomenon that is regularly observed in experiments but cannot be explained by any existing model. In the end, we demonstrate that our model also leads to efficient simulation of active fluids with tens of thousands of bacteria, sufficiently large for investigations of many emergent behaviors.

Integrative Neuroscience of Paramecium, a "Swimming Neuron"

Paramecium is a unicellular organism that swims in fresh water by beating thousands of cilia. When it is stimulated (mechanically, chemically, optically, thermally…), it often swims backward then turns and swims forward again. This "avoiding reaction" is triggered by a calcium-based action potential. For this reason, some authors have called Paramecium a "swimming neuron." This review summarizes current knowledge about the physiological basis of behavior of Paramecium.

Circular swimming motility and disordered hyperuniform state in an algae system

Active matter comprises individually driven units that convert locally stored energy into mechanical motion. Interactions between driven units lead to a variety of nonequilibrium collective phenomena in active matter. One of such phenomena is anomalously large density fluctuations, which have been observed in both experiments and theories. Here we show that, on the contrary, density fluctuations in active matter can also be greatly suppressed. Our experiments are carried out with marine algae ([Formula: see text]), which swim in circles at the air-liquid interfaces with two different eukaryotic flagella. Cell swimming generates fluid flow that leads to effective repulsions between cells in the far field. The long-range nature of such repulsive interactions suppresses density fluctuations and generates disordered hyperuniform states under a wide range of density conditions. Emergence of hyperuniformity and associated scaling exponent are quantitatively reproduced in a numerical model whose main ingredients are effective hydrodynamic interactions and uncorrelated random cell motion. Our results demonstrate the existence of disordered hyperuniform states in active matter and suggest the possibility of using hydrodynamic flow for self-assembly in active matter.

Uni-cellular integration of complex spatial information in slime moulds and ciliates

Single-celled organisms show a fascinating faculty for integrating spatial information and adapting their behaviour accordingly. As such they are of potential interest for elucidating fundamental mechanisms of developmental biology. In this mini-review we highlight current research on two organisms, the true slime mould Physarum polycephalum and the ciliates Paramecium and Tetrahymena. For each of these, we present a case study how applying physical principles to explain behaviour can lead to the understanding of general principles possibly relevant to developmental biology.

Nutrient Transport Driven by Microbial Active Carpets

We demonstrate that active carpets of bacteria or self-propelled colloids generate coherent flows towards the substrate, and propose that these currents provide efficient pathways to replenish nutrients that feed back into activity. A full theory is developed in terms of gradients in the active matter density and velocity, and applied to bacterial turbulence, topological defects and clustering. Currents with complex spatiotemporal patterns are obtained, which are tunable through confinement. Our findings show that diversity in carpet architecture is essential to maintain biofunctionality.

Influence of cellular shape on sliding behavior of ciliates

Some types of ciliates accumulate on solid/fluid interfaces. This behavior is advantageous to survival in nature due to the presence of sufficient nutrition and stable environments. Recently, the accumulating mechanisms of Tetrahymena pyriformis at the interface were investigated. The synergy of the ellipsoidal shape of the cell body and the mechanosensing feature of the cilia allow for cells to slide on interfaces, and the sliding behavior leads to cell accumulation on the interfaces. Here, to examine the generality of the sliding behavior of ciliates, we characterized the behavior of Paramecium caudatum, which is a commonly studied ciliate. Our experimental and numerical results confirmed that P. caudatum also slid on the solid/fluid interface by using the same mechanism as T. pyriformis. In addition, we evaluated the effects of cellular ellipticity on their behaviors near the wall with a phase diagram produced via numerical simulation.