Boundary behaviours of Leishmania mexicana: A hydrodynamic simulation study

Intraflagellar transport speed is sensitive to genetic and mechanical perturbations to flagellar beating

Two sets of motor proteins underpin motile cilia/flagella function. The axoneme-associated inner and outer dynein arms drive sliding of adjacent axoneme microtubule doublets to periodically bend the flagellum for beating, while intraflagellar transport (IFT) kinesins and dyneins carry IFT trains bidirectionally along the axoneme. Despite assembling motile cilia and flagella, IFT train speeds have only previously been quantified in immobilized flagella-mechanical immobilization or genetic paralysis. This has limited investigation of the interaction between IFT and flagellar beating. Here, in uniflagellate Leishmania parasites, we use high-frequency, dual-color fluorescence microscopy to visualize IFT train movement in beating flagella. We discovered that adhesion of flagella to a microscope slide is detrimental, reducing IFT train speed and increasing train stalling. In flagella free to move, IFT train speed is not strongly dependent on flagella beat type; however, permanent disruption of flagella beating by deletion of genes necessary for formation or regulation of beating showed an inverse correlation of beat frequency and IFT train speed.

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.

Performance of a Helical Microswimmer Traversing a Discrete Viscoelastic Network with Dynamic Remodeling

Microorganisms often navigate a complex environment composed of a viscous fluid with suspended microstructures such as elastic polymers and filamentous networks. These microstructures can have similar length scales to the microorganisms, leading to complex swimming dynamics. Some microorganisms secrete enzymes that dynamically change the elastic properties of the viscoelastic networks through which they move. In addition to biological organisms, microrobots have been engineered with the goals of mucin gel penetration or dissolving blood clots. In order to gain insight into the coupling between swimming performance and network remodeling, we used a regularized Stokeslet boundary element method to compute the motion of a microswimmer consisting of a rotating spherical body and counter-rotating helical flagellum. The viscoelastic network is represented by a network of points connected by virtual elastic linkages immersed in a viscous fluid. Here, we model the enzymatic dissolution of the network by bacteria or microrobots by dynamically breaking elastic linkages when the cell body of the swimmer falls within a given distance from the link. We investigate the swimming performance of the microbes as they penetrate and move through networks of different material properties, and also examine the effect of network remodeling.

Self-organized swimming with odd elasticity

We theoretically investigate self-oscillating waves of an active material, which were recently introduced as a nonsymmetric part of the elastic moduli, termed odd elasticity. Using Purcell's three-link swimmer model, we reveal that an odd-elastic filament at low Reynolds number can swim in a self-organized manner and that the time-periodic dynamics are characterized by a stable limit cycle generated by elastohydrodynamic interactions. Also, we consider a noisy shape gait and derive a swimming formula for a general elastic material in the Stokes regime with its elasticity modulus being represented by a nonsymmetric matrix, demonstrating that the odd elasticity produces biased net locomotion from random noise.

Modelling Motility: The Mathematics of Spermatozoa

In one of the first examples of how mechanics can inform axonemal mechanism, Machin's study in the 1950s highlighted that observations of sperm motility cannot be explained by molecular motors in the cell membrane, but would instead require motors distributed along the flagellum. Ever since, mechanics and hydrodynamics have been recognised as important in explaining the dynamics, regulation, and guidance of sperm. More recently, the digitisation of sperm videomicroscopy, coupled with numerous modelling and methodological advances, has been bringing forth a new era of scientific discovery in this field. In this review, we survey these advances before highlighting the opportunities that have been generated for both recent research and the development of further open questions, in terms of the detailed characterisation of the sperm flagellum beat and its mechanics, together with the associated impact on cell behaviour. In particular, diverse examples are explored within this theme, ranging from how collective behaviours emerge from individual cell responses, including how these responses are impacted by the local microenvironment, to the integration of separate advances in the fields of flagellar analysis and flagellar mechanics.

The single flagellum of Leishmania has a fixed polarisation of its asymmetric beat

Eukaryotic flagella undertake different beat types as necessary for different functions; for example, the Leishmania parasite flagellum undergoes a symmetric tip-to-base beat for forward swimming and an asymmetric base-to-tip beat to rotate the cell. In multi-ciliated tissues or organisms, the asymmetric beats are coordinated, leading to movement of the cell, organism or surrounding fluid. This coordination involves a polarisation of power stroke direction. Here, we asked whether the asymmetric beat of the single Leishmania flagellum also has a fixed polarisation. We developed high frame rate dual-colour fluorescence microscopy to visualise flagellar-associated structures in live swimming cells. This showed that the asymmetric Leishmania beat is polarised, with power strokes only occurring in one direction relative to the asymmetric flagellar machinery. Polarisation of bending was retained in deletion mutants whose flagella cannot beat but have a static bend. Furthermore, deletion mutants for proteins required for asymmetric extra-axonemal and rootlet-like flagellum-associated structures also retained normal polarisation. Leishmania beat polarisation therefore likely arises from either the nine-fold rotational symmetry of the axoneme structure or is due to differences between the outer doublet decorations.

Highlighted Article: By using high speed, high-resolution fluorescence microscopy of swimming Leishmania cells, we showed that the asymmetric flagellar beat always wafts in the same direction and investigate which structures are involved.

Biofilms at interfaces: microbial distribution in floating films

Cellular motility is a key function guiding microbial adhesion to interfaces, which is the first step in the formation of biofilms. The close association of biofilms and bioremediation has prompted extensive research aimed at comprehending the physics of microbial locomotion near interfaces. We study the dynamics and statistics of microorganisms in a 'floating biofilm', i.e., a confinement with an air-liquid interface on one side and a liquid-liquid interface on the other. We use a very general mathematical model, based on a multipole representation and probabilistic simulations, to ascertain the spatial distribution of microorganisms in films of different viscosities. Our results reveal that microorganisms can be distributed symmetrically or asymmetrically across the height of the film, depending on their morphology and the ratio of the film's viscosity to that of the fluid substrate. Long-flagellated, elongated bacteria exhibit stable swimming parallel to the liquid-liquid interface when the bacterial film is less viscous than the underlying fluid. Bacteria with shorter flagella on the other hand, swim away from the liquid-liquid interface and accumulate at the free surface. We also analyze microorganism dynamics in a flowing film and show how a microorganism's ability to resist 'flow-induced-erosion' from interfaces is affected by its elongation and mode of propulsion. Our study generalizes past efforts on understanding microorganism dynamics under confinement by interfaces and provides key insights on biofilm initiation at liquid-liquid interfaces.

Glycan–glycan interactions determine Leishmania attachment to the midgut of permissive sand fly vectors

Force spectroscopy was used to measure the adhesion of Leishmania to synthetic mimics of galectins on the sand fly midgut.

High-speed multifocal plane fluorescence microscopy for three-dimensional visualisation of beating flagella

Analysis of flagellum and cilium beating in three dimensions (3D) is important for understanding cell motility, and using fluorescence microscopy to do so would be extremely powerful. Here, high-speed multifocal plane fluorescence microscopy, where the light path is split to visualise multiple focal planes simultaneously, was used to reconstruct Trypanosoma brucei and Leishmania mexicana movement in 3D. These species are uniflagellate unicellular parasites for which motility is vital. It was possible to use either a fluorescent stain or a genetically-encoded fluorescent protein to visualise flagellum and cell movement at 200 Hz frame rates. This addressed two open questions regarding Trypanosoma and Leishmania flagellum beating, which contributes to their swimming behaviours: 1) how planar is the L. mexicana flagellum beat, and 2) what is the nature of flagellum beating during T. brucei 'tumbling'? We showed that L. mexicana has notable deviations from a planar flagellum beat, and that during tumbling the T. brucei flagellum bends the cell and beats only in the distal portion to achieve cell reorientation. This demonstrates high-speed multifocal plane fluorescence microscopy as a powerful tool for the analysis of beating flagella.

Automated identification of flagella from videomicroscopy via the medial axis transform

Ubiquitous in eukaryotic organisms, the flagellum is a well-studied organelle that is well-known to be responsible for motility in a variety of organisms. Commonly necessitated in their study is the capability to image and subsequently track the movement of one or more flagella using videomicroscopy, requiring digital isolation and location of the flagellum within a sequence of frames. Such a process in general currently requires some researcher input, providing some manual estimate or reliance on an experiment-specific heuristic to correctly identify and track the motion of a flagellum. Here we present a fully-automated method of flagellum identification from videomicroscopy based on the fact that the flagella are of approximately constant width when viewed by microscopy. We demonstrate the effectiveness of the algorithm by application to captured videomicroscopy of Leishmania mexicana, a parasitic monoflagellate of the family Trypanosomatidae. ImageJ Macros for flagellar identification are provided, and high accuracy and remarkable throughput are achieved via this unsupervised method, obtaining results comparable in quality to previous studies of closely-related species but achieved without the need for precursory measurements or the development of a specialised heuristic, enabling in general the automated generation of digitised kinematic descriptions of flagellar beating from videomicroscopy.

Response of monoflagellate pullers to a shearing flow: A simulation study of microswimmer guidance

Microscale swimming may be intuited to be dominated by background flows, sweeping away any untethered bodies with the prevalent flow direction. However, it has been observed that many microswimmers utilize ambient flows as guidance cues, in some cases resulting in net motion upstream, contrary to the dominant background fluid direction and our accompanying intuition. Thus the hydrodynamic response of small-scale motile organisms requires careful analysis of the complex interaction between swimmer and environment. Here we investigate the effects of a Newtonian shear flow on monoflagellated swimmers with specified body symmetry, representing, for instance, the Leishmania mexicana promastigote, a parasitic hydrodynamic puller that inhabits the microenvironment of a sandfly vector midgut and is the cause of a major and neglected human tropical disease. We observe that a lack of symmetry-breaking cellular geometry results in the periodic tumbling of swimmers in the bulk, with the rotations exhibiting a linear response to changes in shearing rate enabling analytic approximation. In order to draw comparisons with the better-studied pushers, we additionally consider virtual Leishmania promastigotes in a confined but typical geometry, that of a no-slip planar solid boundary, and note that in general stable guided taxis is not exhibited amongst the range of observed behaviors. However, a repulsive boundary gives rise to significant continued taxis in the presence of shearing flow, a phenomenon that may be of particular pertinence to the infective lifecycle stage of such swimmers subject to the assumption of a Newtonian medium. We finally propose a viable and general in vitro method of controlling microswimmer boundary accumulation using temporally evolving background shear flows, based on the analysis of phase-averaged dynamics and verified in silico.