Simulating the complex cell design of Trypanosoma brucei and its motility

Trajectory-driven computational analysis for element characterization in Trypanosoma cruzi video microscopy

Optical microscopy videos enable experts to analyze the motion of several biological elements. Particularly in blood samples infected with Trypanosoma cruzi (T. cruzi), microscopy videos reveal a dynamic scenario where the parasites' motions are conspicuous. While parasites have self-motion, cells are inert and may assume some displacement under dynamic events, such as fluids and microscope focus adjustments. This paper analyzes the trajectory of T. cruzi and blood cells to discriminate between these elements by identifying the following motion patterns: collateral, fluctuating, and pan-tilt-zoom (PTZ). We consider two approaches: i) classification experiments for discrimination between parasites and cells; and ii) clustering experiments to identify the cell motion. We propose the trajectory step dispersion (TSD) descriptor based on standard deviation to characterize these elements, outperforming state-of-the-art descriptors. Our results confirm motion is valuable in discriminating T. cruzi of the cells. Since the parasites perform the collateral motion, their trajectory steps tend to randomness. The cells may assume fluctuating motion following a homogeneous and directional path or PTZ motion with trajectory steps in a restricted area. Thus, our findings may contribute to developing new computational tools focused on trajectory analysis, which can advance the study and medical diagnosis of Chagas disease.

Multi-particle collision dynamics with a non-ideal equation of state. II. Collective dynamics of elongated squirmer rods

Simulations of flow fields around microscopic objects typically require methods that both solve the Navier-Stokes equations and also include thermal fluctuations. One such method popular in the field of soft-matter physics is the particle-based simulation method of multi-particle collision dynamics (MPCD). However, in contrast to the typically incompressible real fluid, the fluid of the traditional MPCD methods obeys the ideal-gas equation of state. This can be problematic because most fluid properties strongly depend on the fluid density. In a recent article, we proposed an extended MPCD algorithm and derived its non-ideal equation of state and an expression for the viscosity. In the present work, we demonstrate its accuracy and efficiency for the simulations of the flow fields of single squirmers and of the collective dynamics of squirmer rods. We use two exemplary squirmer-rod systems for which we compare the outcome of the extended MPCD method to the well-established MPCD version with an Andersen thermostat. First, we explicitly demonstrate the reduced compressibility of the MPCD fluid in a cluster of squirmer rods. Second, for shorter rods, we show the interesting result that in simulations with the extended MPCD method, dynamic swarms are more pronounced and have a higher polar order. Finally, we present a thorough study of the state diagram of squirmer rods moving in the center plane of a Hele-Shaw geometry. From a small to large aspect ratio and density, we observe a disordered state, dynamic swarms, a single swarm, and a jammed cluster, which we characterize accordingly.

Expansion microscopy facilitates quantitative super-resolution studies of cytoskeletal structures in kinetoplastid parasites

Expansion microscopy (ExM) has become a powerful super-resolution method in cell biology. It is a simple, yet robust approach, which does not require any instrumentation or reagents beyond those present in a standard microscopy facility. In this study, we used kinetoplastid parasites Trypanosoma brucei and Leishmania major, which possess a complex, yet well-defined microtubule-based cytoskeleton, to demonstrate that this method recapitulates faithfully morphology of structures as previously revealed by a combination of sophisticated electron microscopy (EM) approaches. Importantly, we also show that due to the rapidness of image acquisition and three-dimensional reconstruction of cellular volumes ExM is capable of complementing EM approaches by providing more quantitative data. This is demonstrated on examples of less well-appreciated microtubule structures, such as the neck microtubule of T. brucei or the pocket, cytosolic and multivesicular tubule-associated microtubules of L. major. We further demonstrate that ExM enables identifying cell types rare in a population, such as cells in mitosis and cytokinesis. Three-dimensional reconstruction of an entire volume of these cells provided details on the morphology of the mitotic spindle and the cleavage furrow. Finally, we show that established antibody markers of major cytoskeletal structures function well in ExM, which together with the ability to visualize proteins tagged with small epitope tags will facilitate studies of the kinetoplastid cytoskeleton.

Structure of the trypanosome paraflagellar rod and insights into non-planar motility of eukaryotic cells

Eukaryotic flagella (synonymous with cilia) rely on a microtubule-based axoneme, together with accessory filaments to carryout motility and signaling functions. While axoneme structures are well characterized, 3D ultrastructure of accessory filaments and their axoneme interface are mostly unknown, presenting a critical gap in understanding structural foundations of eukaryotic flagella. In the flagellum of the protozoan parasite Trypanosoma brucei (T. brucei), the axoneme is accompanied by a paraflagellar rod (PFR) that supports non-planar motility and signaling necessary for disease transmission and pathogenesis. Here, we employed cryogenic electron tomography (cryoET) with sub-tomographic averaging, to obtain structures of the PFR, PFR-axoneme connectors (PACs), and the axonemal central pair complex (CPC). The structures resolve how the 8 nm repeat of the axonemal tubulin dimer interfaces with the 54 nm repeat of the PFR, which consist of proximal, intermediate, and distal zones. In the distal zone, stacked "density scissors" connect with one another to form a "scissors stack network (SSN)" plane oriented 45° to the axoneme axis; and ~370 parallel SSN planes are connected by helix-rich wires into a paracrystalline array with ~90% empty space. Connections from these wires to the intermediate zone, then to overlapping layers of the proximal zone and to the PACs, and ultimately to the CPC, point to a contiguous pathway for signal transmission. Together, our findings provide insights into flagellum-driven, non-planar helical motility of T. brucei and have broad implications ranging from cell motility and tensegrity in biology, to engineering principles in bionics.

Microgel that swims to the beat of light

Complementary to the quickly advancing understanding of the swimming of microorganisms, we demonstrate rather simple design principles for systems that can mimic swimming by body shape deformation. For this purpose, we developed a microswimmer that could be actuated and controlled by fast temperature changes through pulsed infrared light irradiation. The construction of the microswimmer has the following features: (i) it is a bilayer ribbon with a length of 80 or 120 [Formula: see text]m, consisting of a thermo-responsive hydrogel of poly-N-isopropylamide coated with a 2-nm layer of gold and equipped with homogeneously dispersed gold nanorods; (ii) the width of the ribbon is linearly tapered with a wider end of 5 [Formula: see text]m and a tip of 0.5 [Formula: see text]m; (iii) a thickness of only 1 and 2 [Formula: see text]m that ensures a maximum variation of the cross section of the ribbon along its length from square to rectangular. These wedge-shaped ribbons form conical helices when the hydrogel is swollen in cold water and extend to a filament-like object when the temperature is raised above the volume phase transition of the hydrogel at [Formula: see text]. The two ends of these ribbons undergo different but coupled modes of motion upon fast temperature cycling through plasmonic heating of the gel-objects from inside. Proper choice of the IR-light pulse sequence caused the ribbons to move at a rate of 6 body length/s (500 [Formula: see text]m/s) with the wider end ahead. Within the confinement of rectangular container of 30 [Formula: see text]m height and 300 [Formula: see text]m width, the different modes can be actuated in a way that the movement is directed by the energy input between spinning on the spot and fast forward locomotion.

The biomechanical role of extra-axonemal structures in shaping the flagellar beat of Euglena gracilis

We propose and discuss a model for flagellar mechanics in Euglena gracilis. We show that the peculiar non-planar shapes of its beating flagellum, dubbed 'spinning lasso', arise from the mechanical interactions between two of its inner components, namely, the axoneme and the paraflagellar rod. The spontaneous shape of the axoneme and the resting shape of the paraflagellar rod are incompatible. Thus, the complex non-planar configurations of the coupled system emerge as the energetically optimal compromise between the two antagonistic components. The model is able to reproduce the experimentally observed flagellar beats and the characteristic geometric signature of spinning lasso, namely, traveling waves of torsion with alternating sign along the length of the flagellum.

Single-cell motile behaviour of [Formula: see text] in thin-layered fluid collectives

We describe a system for the analysis of an important unicellular eukaryotic flagellate in a confining and crowded environment. The parasite Trypanosoma brucei is arguably one of the most versatile microswimmers known. It has unique properties as a single microswimmer and shows remarkable adaptations (not only in motility, but prominently so), to its environment during a complex developmental cycle involving two different hosts. Specific life cycle stages show fascinating collective behaviour, as millions of cells can be forced to move together in extreme confinement. Our goal is to examine such motile behaviour directly in the context of the relevant environments. Therefore, for the first time, we analyse the motility behaviour of trypanosomes directly in a widely used assay, which aims to evaluate the parasites behaviour in collectives, in response to as yet unknown parameters. In a step towards understanding whether, or what type of, swarming behaviour of trypanosomes exists, we customised the assay for quantitative tracking analysis of motile behaviour on the single-cell level. We show that the migration speed of cell groups does not directly depend on single-cell velocity and that the system remains to be simplified further, before hypotheses about collective motility can be advanced.

Multi-particle collision dynamics with a non-ideal equation of state. I

The method of multi-particle collision dynamics (MPCD) and its different implementations are commonly used in the field of soft matter physics to simulate fluid flow at the micron scale. Typically, the coarse-grained fluid particles are described by the equation of state of an ideal gas, and the fluid is rather compressible. This is in contrast to conventional fluids, which are incompressible for velocities much below the speed of sound, and can cause inhomogeneities in density. We propose an algorithm for MPCD with a modified collision rule that results in a non-ideal equation of state and a significantly decreased compressibility. It allows simulations at less computational costs compared to conventional MPCD algorithms. We derive analytic expressions for the equation of state and the corresponding compressibility as well as shear viscosity. They show overall very good agreement with simulations, where we determine the pressure by simulating a quiet bulk fluid and the shear viscosity by simulating a linear shear flow and a Poiseuille flow.

Microtubule polyglutamylation is important for regulating cytoskeletal architecture and motility in Trypanosoma brucei

The shape of kinetoplastids, such as Trypanosoma brucei, is precisely defined during the stages of the life cycle and governed by a stable subpellicular microtubule cytoskeleton. During the cell cycle and transitions between life cycle stages, this stability has to transiently give way to a dynamic behaviour to enable cell division and morphological rearrangements. How these opposing requirements of the cytoskeleton are regulated is poorly understood. Two possible levels of regulation are activities of cytoskeleton-associated proteins and microtubule post-translational modifications (PTMs). Here, we investigate the functions of two putative tubulin polyglutamylases in T. brucei, TTLL6A and TTLL12B. Depletion of both proteins leads to a reduction in tubulin polyglutamylation in situ and is associated with disintegration of the posterior cell pole, loss of the microtubule plus-end-binding protein EB1 and alterations of microtubule dynamics. We also observe a reduced polyglutamylation of the flagellar axoneme. Quantitative motility analysis reveals that the PTM imbalance correlates with a transition from directional to diffusive cell movement. These data show that microtubule polyglutamylation has an important role in regulating cytoskeletal architecture and motility in the parasite T. bruceiThis article has an associated First Person interview with the first author of the paper.

The 2020 motile active matter roadmap

Activity and autonomous motion are fundamental in living and engineering systems. This has stimulated the new field of 'active matter' in recent years, which focuses on the physical aspects of propulsion mechanisms, and on motility-induced emergent collective behavior of a larger number of identical agents. The scale of agents ranges from nanomotors and microswimmers, to cells, fish, birds, and people. Inspired by biological microswimmers, various designs of autonomous synthetic nano- and micromachines have been proposed. Such machines provide the basis for multifunctional, highly responsive, intelligent (artificial) active materials, which exhibit emergent behavior and the ability to perform tasks in response to external stimuli. A major challenge for understanding and designing active matter is their inherent nonequilibrium nature due to persistent energy consumption, which invalidates equilibrium concepts such as free energy, detailed balance, and time-reversal symmetry. Unraveling, predicting, and controlling the behavior of active matter is a truly interdisciplinary endeavor at the interface of biology, chemistry, ecology, engineering, mathematics, and physics. The vast complexity of phenomena and mechanisms involved in the self-organization and dynamics of motile active matter comprises a major challenge. Hence, to advance, and eventually reach a comprehensive understanding, this important research area requires a concerted, synergetic approach of the various disciplines. The 2020 motile active matter roadmap of Journal of Physics: Condensed Matter addresses the current state of the art of the field and provides guidance for both students as well as established scientists in their efforts to advance this fascinating area.

Lab-on-a-Chip Technologies for the Single Cell Level: Separation, Analysis, and Diagnostics

In the last three decades, microfluidics and its applications have been on an exponential rise, including approaches to isolate rare cells and diagnose diseases on the single-cell level. The techniques mentioned herein have already had significant impacts in our lives, from in-the-field diagnosis of disease and parasitic infections, through home fertility tests, to uncovering the interactions between SARS-CoV-2 and their host cells. This review gives an overview of the field in general and the most notable developments of the last five years, in three parts: 1. What can we detect? 2. Which detection technologies are used in which setting? 3. How do these techniques work? Finally, this review discusses potentials, shortfalls, and an outlook on future developments, especially in respect to the funding landscape and the field-application of these chips.

Motility Analysis of Trypanosomatids

Motility analysis of microswimmers has long been limited to a few model cell types and broadly restricted by technical challenges of high-resolution in vivo microscopy. Recently, interdisciplinary interest in detailed analysis of the motile behavior of various species has gained momentum. Here we describe a basic protocol for motility analysis of an important, highly diverse group of eukaryotic flagellate microswimmers, using high spatiotemporal resolution videomicroscopy. Further, we provide a special, time-dependent tomographic approach for the proof of rotational locomotion of periodically oscillating microswimmers, using the same data. Taken together, the methods describe part of an integrative approach to generate decisive information on three-dimensional in vivo motility from standard two-dimensional videomicroscopy data.

Diffusiophoresis of active colloids in viscoelastic media

Self-diffusiophoresis of synthetic Janus (Si/Pt) microspheres in the presence of hydrogen peroxide in complex environments is here investigated. We aim to address the single particle dynamics of these active colloids in different viscoelastic fluids. Experimentally, the Janus colloids were dispersed in a dilute polyvinylpyrrolidone (PVP) solution and in a polyacrylamide (PAM) solution in semi-dilute and semi-dilute entangled regime to analyze their Brownian and active motion. These two systems were chosen to probe different relaxation times from relatively short (∼5 ms) for PVP to large (∼14.5 s) for PAM but always smaller than the rotary Brownian motion time scale. Within this regime, we investigate the coupling between the self-propulsion velocity and the medium rheology. Janus particles are found to get physically confined by polymeric entanglements but surprisingly they are able to escape the physical cage in a time scale much shorter than the relaxation time of the polymer solution. This is particularly relevant for application of self-propelling particles in biomedicine, water and soil remediation where complex environments are naturally present.

Visualizing trypanosomes in a vertebrate host reveals novel swimming behaviours, adaptations and attachment mechanisms

Trypanosomes are important disease agents of humans, livestock and cold-blooded species, including fish. The cellular morphology of trypanosomes is central to their motility, adaptation to the host’s environments and pathogenesis. However, visualizing the behaviour of trypanosomes resident in a live vertebrate host has remained unexplored. In this study, we describe an infection model of zebrafish (Danio rerio) with Trypanosoma carassii. By combining high spatio-temporal resolution microscopy with the transparency of live zebrafish, we describe in detail the swimming behaviour of trypanosomes in blood and tissues of a vertebrate host. Besides the conventional tumbling and directional swimming, T. carassii can change direction through a ‘whip-like’ motion or by swimming backward. Further, the posterior end can act as an anchoring site in vivo. To our knowledge, this is the first report of a vertebrate infection model that allows detailed imaging of trypanosome swimming behaviour in vivo in a natural host environment.

Trypanosomes are one-celled parasites that cause the disease trypanosomiasis, which is also known as sleeping sickness. Trypanosomiasis is transmitted to humans and animals by a type of fly, known as tse-tse, which is commonly found in sub-Saharan Africa. A bite from the tse-tse fly transfers the trypanosome cells into the host’s bloodstream, where they spread from the blood to the internal organs and brain. This leads to a long-term illness, which can sometimes result in a coma and eventually death.

Once in the blood trypanosomes move around using a structure similar to an underwater propeller called the flagellum. How the trypanosomes move and behave in the blood determines how the infection will progress. Until now it has only been possible to observe trypanosomes in plastic dishes or in blood drawn from infected patients. However, neither of these settings mimic the conditions of the bloodstream, and it is currently impossible to look inside human hosts to watch how trypanosomes move.

To overcome this hurdle, Doro et al. infected zebrafish with Trypanosoma carassii, a close relative of the sub-Saharan trypanosomes that specifically infects fish. Zebrafish are transparent when young, making it possible to observe the parasite in the blood and tissues of live fish using a microscope.

Doro et al. noticed that Trypanosoma carassii cells adapt to different environments in the host by using different swimming techniques. For example, in small capillaries trypanosomes were dragged along with the blood flow, whilst in larger vessels, when blood flow was slow or there were fewer red blood cells, trypanosomes actively swam against the current. The parasites were also able to change direction by using their flagella in a ‘whip-like’ motion. Lastly, it was discovered that Trypanosoma carassii could rapidly attach to blood vessel walls using one end of its cell body, even when blood flow was strong. This behaviour may help the parasites escape from the bloodstream into the surrounding tissues, making the infection more dangerous.

Studying how trypanosomes infect zebrafish at this high level of detail provides new insights into how these parasites move and behave inside a host. An important question that remains to be answered, is how exactly the trypanosomes leave the bloodstream. A better understanding of the whole infection process may hint at new ways of fighting these deadly infections in future.

Propulsion by stiff elastic filaments in viscous fluids

Flexible filaments moving in viscous fluids are ubiquitous in the natural microscopic world. For example, the swimming of bacteria and spermatozoa as well as important physiological functions at organ level, such as the cilia-induced motion of mucus in the lungs, or individual cell level, such as actin filaments or microtubules, all employ flexible filaments moving in viscous fluids. As a result of fluid-structure interactions, a variety of nonlinear phenomena may arise in the dynamics of such moving flexible filaments. In this paper we derive the mathematical tools required to study filament-driven propulsion in the asymptotic limit of stiff filaments. Motion in the rigid limit leads to hydrodynamic loads which deform the filament and impact the filament propulsion. We first derive the general mathematical formulation and then apply it to the case of a helical filament, a situation relevant for the swimming of flagellated bacteria and for the transport of artificial, magnetically actuated motors. We find that, as a result of flexibility, the helical filament is either stretched or compressed (conforming previous studies) and additionally its axis also bends, a result which we interpret physically. We then explore and interpret the dependence of the perturbed propulsion speed due to the deformation on the relevant dimensionless dynamic and geometric parameters.

Flagellum couples cell shape to motility in Trypanosoma brucei

Trypanosoma brucei is a highly invasive pathogen capable of penetrating deeply into host tissues. To understand how flagellar motility facilitates cell penetration, we used cryo-electron tomography (cryo-ET) to visualize two genetically anucleate mutants with different flagellar motility behaviors. We found that the T. brucei cell body is highly deformable as defined by changes in cytoskeletal twist and spacing, in response to flagellar beating and environmental conditions. Based on the cryo-ET models, we proposed a mechanism of how flagellum motility is coupled to cell shape changes, which may facilitate penetration through size-limiting barriers.

In the unicellular parasite Trypanosoma brucei, the causative agent of human African sleeping sickness, complex swimming behavior is driven by a flagellum laterally attached to the long and slender cell body. Using microfluidic assays, we demonstrated that T. brucei can penetrate through an orifice smaller than its maximum diameter. Efficient motility and penetration depend on active flagellar beating. To understand how active beating of the flagellum affects the cell body, we genetically engineered T. brucei to produce anucleate cytoplasts (zoids and minis) with different flagellar attachment configurations and different swimming behaviors. We used cryo-electron tomography (cryo-ET) to visualize zoids and minis vitrified in different motility states. We showed that flagellar wave patterns reflective of their motility states are coupled to cytoskeleton deformation. Based on these observations, we propose a mechanism for how flagellum beating can deform the cell body via a flexible connection between the flagellar axoneme and the cell body. This mechanism may be critical for T. brucei to disseminate in its host through size-limiting barriers.

Simulating squirmers with multiparticle collision dynamics

Multiparticle collision dynamics is a modern coarse-grained simulation technique to treat the hydrodynamics of Newtonian fluids by solving the Navier-Stokes equations. Naturally, it also includes thermal noise. Initially it has been applied extensively to spherical colloids or bead-spring polymers immersed in a fluid. Here, we review and discuss the use of multiparticle collision dynamics for studying the motion of spherical model microswimmers called squirmers moving in viscous fluids.

The Fantastic Voyage of the Trypanosome: A Protean Micromachine Perfected during 500 Million Years of Engineering

The human body is constantly attacked by pathogens. Various lines of defence have evolved, among which the immune system is principal. In contrast to most pathogens, the African trypanosomes thrive freely in the blood circulation, where they escape immune destruction by antigenic variation and incessant motility. These unicellular parasites are flagellate microswimmers that also withstand the harsh mechanical forces prevailing in the bloodstream. They undergo complex developmental cycles in the bloodstream and organs of the mammalian host, as well as the disease-transmitting tsetse fly. Each life cycle stage has been shaped by evolution for manoeuvring in distinct microenvironments. Here, we introduce trypanosomes as blueprints for nature-inspired design of trypanobots, micromachines that, in the future, could explore the human body without affecting its physiology. We review cell biological and biophysical aspects of trypanosome motion. While this could provide a basis for the engineering of microbots, their actuation and control still appear more like fiction than science. Here, we discuss potentials and challenges of trypanosome-inspired microswimmer robots.

Flow properties and hydrodynamic interactions of rigid spherical microswimmers

We analyze a minimal model for a rigid spherical microswimmer and explore the consequences of its extended surface on the interplay between its self-propulsion and flow properties. The model is the first order representation of microswimmers, such as bacteria and algae, with rigid bodies and flexible propelling appendages. The flow field of such a microswimmer at finite distances significantly differs from that of a point-force (Stokeslet) dipole. For a suspension of microswimmers, we derive the grand mobility matrix that connects the motion of an individual swimmer to the active and passive forces and torques acting on all the swimmers. Our investigation of the mobility tensors reveals that hydrodynamic interactions among rigid-bodied microswimmers differ considerably from those among the corresponding point-force dipoles. Our results are relevant for the study of collective behavior of hydrodynamically interacting microswimmers by means of Stokesian dynamics simulations at moderate concentrations.

Developmental adaptations of trypanosome motility to the tsetse fly host environments unravel a multifaceted in vivo microswimmer system

The highly motile and versatile protozoan pathogen Trypanosoma brucei undergoes a complex life cycle in the tsetse fly. Here we introduce the host insect as an expedient model environment for microswimmer research, as it allows examination of microbial motion within a diversified, secluded and yet microscopically tractable space. During their week-long journey through the different microenvironments of the fly´s interior organs, the incessantly swimming trypanosomes cross various barriers and confined surroundings, with concurrently occurring major changes of parasite cell architecture. Multicolour light sheet fluorescence microscopy provided information about tsetse tissue topology with unprecedented resolution and allowed the first 3D analysis of the infection process. High-speed fluorescence microscopy illuminated the versatile behaviour of trypanosome developmental stages, ranging from solitary motion and near-wall swimming to collective motility in synchronised swarms and in confinement. We correlate the microenvironments and trypanosome morphologies to high-speed motility data, which paves the way for cross-disciplinary microswimmer research in a naturally evolved environment.

Self-Organized Velocity Pulses of Dense Colloidal Suspensions in Microchannel Flow

We present a numerical study of dense colloidal suspensions in a pressure-driven microchannel flow in two dimensions. The colloids are modeled as elastic and frictional spheres suspended in a Newtonian fluid, which we simulate using the method of multiparticle collision dynamics. The model reproduces periodic velocity and density pulse trains, traveling upstream in the microchannel, which are found in experiments conducted by Isa et al. [Phys. Rev. Lett. 102, 058302 (2009)PRLTAO0031-900710.1103/PhysRevLett.102.058302]. We show that colloid-wall friction and the resultant force chains are crucial for the formation of these pulses. With an increasing colloid density, first solitary jams occur, which become periodic pulse trains at intermediate densities and unstable solitary pulses at high densities. We formulate a phenomenological continuum model and show how these spatiotemporal flow and density profiles can be understood as homoclinic and periodic orbits in traveling-wave equations.

Active Brownian particles moving in a random Lorentz gas

Biological microswimmers often inhabit a porous or crowded environment such as soil. In order to understand how such a complex environment influences their spreading, we numerically study non-interacting active Brownian particles (ABPs) in a two-dimensional random Lorentz gas. Close to the percolation transition in the Lorentz gas, they perform the same subdiffusive motion as ballistic and diffusive particles. However, due to their persistent motion they reach their long-time dynamics faster than passive particles and also show superdiffusive motion at intermediate times. While above the critical obstacle density [Formula: see text] the ABPs are trapped, their long-time diffusion below [Formula: see text] is strongly influenced by the propulsion speed v₀. With increasing v₀, ABPs are stuck at the obstacles for longer times. Thus, for large propulsion speed, the long-time diffusion constant decreases more strongly in a denser obstacle environment than for passive particles. This agrees with the behavior of an effective swimming velocity and persistence time, which we extract from the velocity autocorrelation function.

Use of chiral cell shape to ensure highly directional swimming in trypanosomes

Swimming cells typically move along a helical path or undergo longitudinal rotation as they swim, arising from chiral asymmetry in hydrodynamic drag or propulsion bending the swimming path into a helix. Helical paths are beneficial for some forms of chemotaxis, but why asymmetric shape is so prevalent when a symmetric shape would also allow highly directional swimming is unclear. Here, I analyse the swimming of the insect life cycle stages of two human parasites; Trypanosoma brucei and Leishmania mexicana. This showed quantitatively how chirality in T. brucei cell shape confers highly directional swimming. High speed videomicrographs showed that T. brucei, L. mexicana and a T. brucei RNAi morphology mutant have a range of shape asymmetries, from wild-type T. brucei (highly chiral) to L. mexicana (near-axial symmetry). The chiral cells underwent longitudinal rotation while swimming, with more rapid longitudinal rotation correlating with swimming path directionality. Simulation indicated hydrodynamic drag on the chiral cell shape caused rotation, and the predicted geometry of the resulting swimming path matched the directionality of the observed swimming paths. This simulation of swimming path geometry showed that highly chiral cell shape is a robust mechanism through which microscale swimmers can achieve highly directional swimming at low Reynolds number. It is insensitive to random variation in shape or propulsion (biological noise). Highly symmetric cell shape can give highly directional swimming but is at risk of giving futile circular swimming paths in the presence of biological noise. This suggests the chiral T. brucei cell shape (associated with the lateral attachment of the flagellum) may be an adaptation associated with the bloodstream-inhabiting lifestyle of this parasite for robust highly directional swimming. It also provides a plausible general explanation for why swimming cells tend to have strong asymmetries in cell shape or propulsion.

Swimming cells often follow a helical swimming path, however the advantage of helical paths over a simple straight line path is not clear. To analyse this phenomenon, I analysed the swimming of the human parasites Trypanosoma brucei (which causes sleeping sickness/trypanosomiasis) and Leishmania mexicana (which causes leishmaniasis). Using new computational methods to determine the three dimensional shape of swimming cells I showed that T. brucei have a helical shape which causes rotation as the cell swims, and the geometry of the resulting swimming path makes the cell movement highly directional. In contrast, L. mexicana are symmetrical, do not rotate, and their swimming paths are curved and have low directionality. Using a T. brucei mutant I showed that the cell structure responsible for the helical shape while swimming is the flagellum attachment zone. This explains a key function of this structure. Finally, simulations showed the phenomenon of rotation while swimming is a way cells can ensure highly directional swimming along a controlled helical path, overcoming random variation in cell shape or propulsion. This provides a general explanation for why swimming cells are often asymmetric and tend to follow helical paths.

Active Brownian particles and run-and-tumble particles separate inside a maze

A diverse range of natural and artificial self-propelled particles are known and are used nowadays. Among them, active Brownian particles (ABPs) and run-and-tumble particles (RTPs) are two important classes. We numerically study non-interacting ABPs and RTPs strongly confined to different maze geometries in two dimensions. We demonstrate that by means of geometrical confinement alone, ABPs are separable from RTPs. By investigating Matryoshka-like mazes with nested shells, we show that a circular maze has the best filtration efficiency. Results on the mean first-passage time reveal that ABPs escape faster from the center of the maze, while RTPs reach the center from the rim more easily. According to our simulations and a rate theory, which we developed, ABPs in steady state accumulate in the outermost region of the Matryoshka-like mazes, while RTPs occupy all locations within the maze with nearly equal probability. These results suggest a novel technique for separating different types of self-propelled particles by designing appropriate confining geometries without using chemical or biological agents.

Structural mechanics and helical geometry of thin elastic composites

Helices are ubiquitous in nature, and helical shape transition is often observed in residually stressed bodies, such as composites, wherein materials with different mechanical properties are glued firmly together to form a whole body. Inspired by a variety of biological examples, the basic physical mechanism responsible for the emergence of twisting and bending in such thin composite structures has been extensively studied. Here, we propose a simplified analytical model wherein a slender membrane tube undergoes a helical transition driven by the contraction of an elastic ribbon bound to the membrane surface. We analytically predict the curvature and twist of an emergent helix as functions of differential strains and elastic moduli, which are confirmed by our numerical simulations. Our results may help understand shapes observed in different biological systems, such as spiral bacteria, and could be applied to novel designs of soft machines and robots.

Taylor line swimming in microchannels and cubic lattices of obstacles

Microorganisms naturally move in microstructured fluids. Using the simulation method of multi-particle collision dynamics, we study in two dimensions an undulatory Taylor line swimming in a microchannel and in a cubic lattice of obstacles, which represent simple forms of a microstructured environment. In the microchannel the Taylor line swims at an acute angle along a channel wall with a clearly enhanced swimming speed due to hydrodynamic interactions with the bounding wall. While in a dilute obstacle lattice swimming speed is also enhanced, a dense obstacle lattice gives rise to geometric swimming. This new type of swimming is characterized by a drastically increased swimming speed. Since the Taylor line has to fit into the free space of the obstacle lattice, the swimming speed is close to the phase velocity of the bending wave traveling along the Taylor line. While adjusting its swimming motion within the lattice, the Taylor line chooses a specific swimming direction, which we classify by a lattice vector. When plotting the swimming velocity versus the magnitude of the lattice vector, all our data collapse on a single master curve. Finally, we also report more complex trajectories within the obstacle lattice.

Active Brownian motion of emulsion droplets: Coarsening dynamics at the interface and rotational diffusion

A micron-sized droplet of bromine water immersed in a surfactant-laden oil phase can swim (S. Thutupalli, R. Seemann, S. Herminghaus, New J. Phys. 13 073021 (2011). The bromine reacts with the surfactant at the droplet interface and generates a surfactant mixture. It can spontaneously phase-separate due to solutocapillary Marangoni flow, which propels the droplet. We model the system by a diffusion-advection-reaction equation for the mixture order parameter at the interface including thermal noise and couple it to fluid flow. Going beyond previous work, we illustrate the coarsening dynamics of the surfactant mixture towards phase separation in the axisymmetric swimming state. Coarsening proceeds in two steps: an initially slow growth of domain size followed by a nearly ballistic regime. On larger time scales thermal fluctuations in the local surfactant composition initiates random changes in the swimming direction and the droplet performs a persistent random walk, as observed in experiments. Numerical solutions show that the rotational correlation time scales with the square of the inverse noise strength. We confirm this scaling by a perturbation theory for the fluctuations in the mixture order parameter and thereby identify the active emulsion droplet as an active Brownian particle.

Dynamics of a bacterial flagellum under reverse rotation

To initiate tumbling of an E. coli, one of the helical flagella reverses its sense of rotation. It then transforms from its normal form first to the transient semicoiled state and subsequently to the curly-I state. The dynamics of polymorphism is effectively modeled by describing flagellar elasticity through an extended Kirchhoff free energy. However, the complete landscape of the free energy remains undetermined because the ground state energies of the polymorphic forms are not known. We investigate how variations in these ground state energies affect the dynamics of a reversely rotated flagellum of a swimming bacterium. We find that the flagellum exhibits a number of distinct dynamical states and comprehensively summarize them in a state diagram. As a result, we conclude that tuning the landscape of the extended Kirchhoff free energy alone cannot generate the intermediate full-length semicoiled state. However, our model suggests an ad hoc method to realize the sequence of polymorphic states as observed for a real bacterium. Since the elastic properties of bacterial flagella are similar, our findings can easily be extended to other peritrichous bacteria.

Motility, Force Generation, and Energy Consumption of Unicellular Parasites

Motility is a key factor for pathogenicity of unicellular parasites, enabling them to infiltrate and evade host cells, and perform several of their life-cycle events. State-of-the-art methods of motility analysis rely on a combination of optical tweezers with high-resolution microscopy and microfluidics. With this technology, propulsion forces, energies, and power generation can be determined so as to shed light on the motion mechanisms, chemotactic behavior, and specific survival strategies of unicellular parasites. With these new tools in hand, we can elucidate the mechanisms of motility and force generation of unicellular parasites, and identify ways to manipulate and eventually inhibit them.

Mode instabilities and dynamic patterns in a colony of self-propelled surfactant particles covering a thin liquid layer

We consider a colony of point-like self-propelled surfactant particles (swimmers) without direct interactions that cover a thin liquid layer on a solid support. The particles predominantly swim normal to the free film surface with only a small component parallel to the film surface. The coupled dynamics of the swimmer density and film height profile is captured in a long-wave model allowing for diffusive and convective transport of the swimmers (including rotational diffusion). The dynamics of the film height profile is determined by i) the upward pushing force of the swimmers onto the liquid-gas interface, ii) the solutal Marangoni force due to gradients in the swimmer concentration, and iii) the rotational diffusion of the swimmers together with the in-plane active motion. After reviewing and extending the analysis of the linear stability of the uniform state, we analyse the fully nonlinear dynamic equations and show that point-like swimmers, which only interact via long-wave deformations of the liquid film, self-organise in highly regular (standing, travelling, and modulated waves) and various irregular patterns.

Transient Superdiffusion and Long-Range Correlations in the Motility Patterns of Trypanosomatid Flagellate Protozoa

We report on a diffusive analysis of the motion of flagellate protozoa species. These parasites are the etiological agents of neglected tropical diseases: leishmaniasis caused by Leishmania amazonensis and Leishmania braziliensis, African sleeping sickness caused by Trypanosoma brucei, and Chagas disease caused by Trypanosoma cruzi. By tracking the positions of these parasites and evaluating the variance related to the radial positions, we find that their motions are characterized by a short-time transient superdiffusive behavior. Also, the probability distributions of the radial positions are self-similar and can be approximated by a stretched Gaussian distribution. We further investigate the probability distributions of the radial velocities of individual trajectories. Among several candidates, we find that the generalized gamma distribution shows a good agreement with these distributions. The velocity time series have long-range correlations, displaying a strong persistent behavior (Hurst exponents close to one). The prevalence of “universal” patterns across all analyzed species indicates that similar mechanisms may be ruling the motion of these parasites, despite their differences in morphological traits. In addition, further analysis of these patterns could become a useful tool for investigating the activity of new candidate drugs against these and others neglected tropical diseases.

The Trypanosome Flagellar Pocket Collar and Its Ring Forming Protein-TbBILBO1

Sub-species of Trypanosoma brucei are the causal agents of human African sleeping sickness and Nagana in domesticated livestock. These pathogens have developed an organelle-like compartment called the flagellar pocket (FP). The FP carries out endo- and exocytosis and is the only structure this parasite has evolved to do so. The FP is essential for parasite viability, making it an interesting structure to evaluate as a drug target, especially since it has an indispensible cytoskeleton component called the flagellar pocket collar (FPC). The FPC is located at the neck of the FP where the flagellum exits the cell. The FPC has a complex architecture and division cycle, but little is known concerning its organization. Recent work has focused on understanding how the FP and the FPC are formed and as a result of these studies an important calcium-binding, polymer-forming protein named TbBILBO1 was identified. Cellular biology analysis of TbBILBO1 has demonstrated its uniqueness as a FPC component and until recently, it was unknown what structural role it played in forming the FPC. This review summarizes the recent data on the polymer forming properties of TbBILBO1 and how these are correlated to the FP cytoskeleton.

Species-Specific Adaptations of Trypanosome Morphology and Motility to the Mammalian Host

African trypanosomes thrive in the bloodstream and tissue spaces of a wide range of mammalian hosts. Infections of cattle cause an enormous socio-economic burden in sub-Saharan Africa. A hallmark of the trypanosome lifestyle is the flagellate's incessant motion. This work details the cell motility behavior of the four livestock-parasites Trypanosoma vivax, T. brucei, T. evansi and T. congolense. The trypanosomes feature distinct swimming patterns, speeds and flagellar wave frequencies, although the basic mechanism of flagellar propulsion is conserved, as is shown by extended single flagellar beat analyses. Three-dimensional analyses of the trypanosomes expose a high degree of dynamic pleomorphism, typified by the 'cellular waveform'. This is a product of the flagellar oscillation, the chirality of the flagellum attachment and the stiffness of the trypanosome cell body. The waveforms are characteristic for each trypanosome species and are influenced by changes of the microenvironment, such as differences in viscosity and the presence of confining obstacles. The distinct cellular waveforms may be reflective of the actual anatomical niches the parasites populate within their mammalian host. T. vivax displays waveforms optimally aligned to the topology of the bloodstream, while the two subspecies T. brucei and T. evansi feature distinct cellular waveforms, both additionally adapted to motion in more confined environments such as tissue spaces. T. congolense reveals a small and stiff waveform, which makes these parasites weak swimmers and destined for cell adherence in low flow areas of the circulation. Thus, our experiments show that the differential dissemination and annidation of trypanosomes in their mammalian hosts may depend on the distinct swimming capabilities of the parasites.

Zipping and entanglement in flagellar bundle of E. coli: Role of motile cell body

The course of a peritrichous bacterium, such as E. coli, crucially depends on the level of synchronization and self-organization of several rotating flagella. However, the rotation of each flagellum generates countermovements of the body which in turn affect the flagellar dynamics. Using a detailed numerical model of an E. coli, we demonstrate that flagellar entanglement, besides fluid flow relative to the moving body, dramatically changes the dynamics of flagella from that compared to anchored flagella. In particular, bundle formation occurs through a zipping motion in a remarkably rapid time, affected little by initial flagellar orientation. A simplified analytical model supports our observations. Finally, we illustrate how entanglement, hydrodynamic interactions, and body movement contribute to zipping and bundling.

Hydrodynamic segregation in a bidisperse colloidal suspension in microchannel flow: A theoretical study

Colloids in suspension exhibit shear-induced migration towards regions of low viscous shear. In dense bidisperse colloidal suspensions under pressure driven flow large particles can segregate in the center of a microchannel and the suspension partially demixes. To develop a theoretical understanding of these effects, we formulate a phenomenological model for the particle currents based on the work of Phillips et al. [Phys. Fluids 4, 30 (1992)]. We also simulate hard spheres under pressure-driven flow in two and three dimensions using the mesoscale simulation technique of multi-particle collision dynamics. Using a single fit parameter for the intrinsic diffusivity, our theory accurately reproduces the simulated density profiles across the channel. We present a detailed parameter study on how a monodisperse suspension enriches the channel center and quantitatively confirm the experimental observation that a binary colloidal mixture partially segregates into its two species. In particular, we always find a strong accumulation of large particles in the center. Qualitative differences between two and three dimensions reveal that collective diffusion is more relevant in two dimensions.