Langevin dynamics deciphers the motility pattern of swimming parasites

Effect of speed fluctuations on the collective dynamics of active disks

Numerical simulations are performed on the collective dynamics of active disks, whose self-propulsion speed (U) varies in time, and whose orientation evolves according to rotational Brownian motion. Two protocols for the evolution of speed are considered: (i) a deterministic one involving a periodic change in U at a frequency ω; and (ii) a stochastic one in which the speeds are drawn from a power-law distribution at time-intervals governed by a Poissonian process of rate β. In the first case, an increase in ω causes the disks to go from a clustered state to a homogeneous one through an apparent phase-transition, provided that the direction of self-propulsion is allowed to reverse. Similarly, in the second case, for a fixed value of β, the extent of cluster-breakup is larger when reversals in the self-propulsion direction are permitted. Motility-induced phase separation of the disks may therefore be avoided in active matter suspensions in which the constituents are allowed to reverse their self-propulsion direction, immaterial of the precise temporal nature of the reversal (deterministic or stochastic). Equally, our results demonstrate that phase separation could occur even in the absence of a time-averaged motility of an individual active agent, provided that the rate of direction reversals is smaller than the orientational diffusion rate.

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.

Nuclear position relative to the Golgi body and nuclear orientation are differentially responsive indicators of cell polarized motility

Cell motility is critical to biological processes from wound healing to cancer metastasis to embryonic development. The involvement of organelles in cell motility is well established, but the role of organelle positional reorganization in cell motility remains poorly understood. Here we present an automated image analysis technique for tracking the shape and motion of Golgi bodies and cell nuclei. We quantify the relationship between nuclear orientation and the orientation of the Golgi body relative to the nucleus before, during, and after exposure of mouse fibroblasts to a controlled change in cell substrate topography, from flat to wrinkles, designed to trigger polarized motility. We find that the cells alter their mean nuclei orientation, in terms of the nuclear major axis, to increasingly align with the wrinkle direction once the wrinkles form on the substrate surface. This change in alignment occurs within 8 hours of completion of the topographical transition. In contrast, the position of the Golgi body relative to the nucleus remains aligned with the pre-programmed wrinkle direction, regardless of whether it has been fully established. These findings indicate that intracellular positioning of the Golgi body precedes nuclear reorientation during mouse fibroblast directed migration on patterned substrates. We further show that both processes are Rho-associated kinase (ROCK) mediated as they are abolished by pharmacologic ROCK inhibition whereas mouse fibroblast motility is unaffected. The automated image analysis technique introduced could be broadly employed in the study of polarization and other cellular processes in diverse cell types and micro-environments. In addition, having found that the nuclei Golgi vector may be a more sensitive indicator of substrate features than the nuclei orientation, we anticipate the nuclei Golgi vector to be a useful metric for researchers studying the dynamics of cell polarity in response to different micro-environments.

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.

Blocking Synthesis of the Variant Surface Glycoprotein Coat in Trypanosoma brucei Leads to an Increase in Macrophage Phagocytosis Due to Reduced Clearance of Surface Coat Antibodies

The extracellular bloodstream form parasite Trypanosoma brucei is supremely adapted to escape the host innate and adaptive immune system. Evasion is mediated through an antigenically variable Variant Surface Glycoprotein (VSG) coat, which is recycled at extraordinarily high rates. Blocking VSG synthesis triggers a precytokinesis arrest where stalled cells persist for days in vitro with superficially intact VSG coats, but are rapidly cleared within hours in mice. We therefore investigated the role of VSG synthesis in trypanosome phagocytosis by activated mouse macrophages. T. brucei normally effectively evades macrophages, and induction of VSG RNAi resulted in little change in phagocytosis of the arrested cells. Halting VSG synthesis resulted in stalled cells which swam directionally rather than tumbling, with a significant increase in swim velocity. This is possibly a consequence of increased rigidity of the cells due to a restricted surface coat in the absence of VSG synthesis. However if VSG RNAi was induced in the presence of anti-VSG221 antibodies, phagocytosis increased significantly. Blocking VSG synthesis resulted in reduced clearance of anti-VSG antibodies from the trypanosome surface, possibly as a consequence of the changed motility. This was particularly marked in cells in the G2/ M cell cycle stage, where the half-life of anti-VSG antibody increased from 39.3 ± 4.2 seconds to 99.2 ± 15.9 seconds after induction of VSG RNAi. The rates of internalisation of bulk surface VSG, or endocytic markers like transferrin, tomato lectin or dextran were not significantly affected by the VSG synthesis block. Efficient elimination of anti-VSG-antibody complexes from the trypanosome cell surface is therefore essential for trypanosome evasion of macrophages. These experiments highlight the essentiality of high rates of VSG recycling for the rapid removal of host opsonins from the parasite surface, and identify this process as a key parasite virulence factor during a chronic infection.

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.

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.

Simulating the complex cell design of Trypanosoma brucei and its motility

The flagellate Trypanosoma brucei, which causes the sleeping sickness when infecting a mammalian host, goes through an intricate life cycle. It has a rather complex propulsion mechanism and swims in diverse microenvironments. These continuously exert selective pressure, to which the trypanosome adjusts with its architecture and behavior. As a result, the trypanosome assumes a diversity of complex morphotypes during its life cycle. However, although cell biology has detailed form and function of most of them, experimental data on the dynamic behavior and development of most morphotypes is lacking. Here we show that simulation science can predict intermediate cell designs by conducting specific and controlled modifications of an accurate, nature-inspired cell model, which we developed using information from live cell analyses. The cell models account for several important characteristics of the real trypanosomal morphotypes, such as the geometry and elastic properties of the cell body, and their swimming mechanism using an eukaryotic flagellum. We introduce an elastic network model for the cell body, including bending rigidity and simulate swimming in a fluid environment, using the mesoscale simulation technique called multi-particle collision dynamics. The in silico trypanosome of the bloodstream form displays the characteristic in vivo rotational and translational motility pattern that is crucial for survival and virulence in the vertebrate host. Moreover, our model accurately simulates the trypanosome's tumbling and backward motion. We show that the distinctive course of the attached flagellum around the cell body is one important aspect to produce the observed swimming behavior in a viscous fluid, and also required to reach the maximal swimming velocity. Changing details of the flagellar attachment generates less efficient swimmers. We also simulate different morphotypes that occur during the parasite's development in the tsetse fly, and predict a flagellar course we have not been able to measure in experiments so far.

Typanosoma brucei is a uni-cellular parasite that causes the sleeping sickness, a deadly disease for humans that also occurs in livestock. Injected into the mammalian host by the tsetse fly, the trypanosome travels through the blood stream, where it proliferates, and ultimately can be taken up again by a fly during a bloodmeal. In the tsetse fly, it continues its development with several morphological changes to the cell body plan. During its life cycle, the trypanosome meets different microenvironments, such as the mammalian's bloodstream and the tsetse fly's midgut, proventriculus, foregut, and salivary gland. The cell body of the trypanosome has the shape of a spindle along which an eukaryotic flagellum is attached. We have developed an accurate, in silico model trypanosome using information from live cell analyses. Performing computer simulations, we are able to reproduce all motility patterns of the blood-stream form in typical cell culture medium. Modifying the cell design, we show that the helical course of the flagellar attachment optimizes the trypanosome's swimming speed. We also design trypanosomal morphotypes that occur in the tsetse fly. Simulation science thereby provides an investigative tool to systematically explore the morphologcial diversity during the trypanosome's life cycle even beyond experimental capabilities.

Kinematic matrix theory and universalities in self-propellers and active swimmers

We describe an efficient and parsimonious matrix-based theory for studying the ensemble behavior of self-propellers and active swimmers, such as nanomotors or motile bacteria, that are typically studied by differential-equation-based Langevin or Fokker-Planck formalisms. The kinematic effects for elementary processes of motion are incorporated into a matrix, called the "kinematrix," from which we immediately obtain correlators and the mean and variance of angular and position variables (and thus effective diffusivity) by simple matrix algebra. The kinematrix formalism enables us recast the behaviors of a diverse range of self-propellers into a unified form, revealing universalities in their ensemble behavior in terms of new emergent time scales. Active fluctuations and hydrodynamic interactions can be expressed as an additive composition of separate self-propellers.

Intrinsic fluctuations of cell migration under different cellular densities

The motility of the Dictyostelium discoideum (DD) cell is studied by video microscopy when the cells are plated on top of an agar plate at different densities, n. It is found that the fluctuating kinetics of the cells can be divided into two normal directions: the cell's forward-moving direction and its normal direction. Along the forward-moving direction, the slope of the amplitude of fluctuation vs. velocity (R||(v)) increases with n, while along the normal direction the slope of R⊥ is independent of n. Both R|| and R⊥ are functions of the cell speed v. The observed linearity in R⊥(v) indicated that the amplitude of orientational fluctuation (κ) of DD cells is a constant independent of v. The independence of the slope of R⊥(v) on n indicated that κ is also not affected by cellular interactions. The independence of κ on both v and n suggests that orientational fluctuation originates from the intrinsic property of motion fluctuations in DD.

Trypanosome motion represents an adaptation to the crowded environment of the vertebrate bloodstream

Blood is a remarkable habitat: it is highly viscous, contains a dense packaging of cells and perpetually flows at velocities varying over three orders of magnitude. Only few pathogens endure the harsh physical conditions within the vertebrate bloodstream and prosper despite being constantly attacked by host antibodies. African trypanosomes are strictly extracellular blood parasites, which evade the immune response through a system of antigenic variation and incessant motility. How the flagellates actually swim in blood remains to be elucidated. Here, we show that the mode and dynamics of trypanosome locomotion are a trait of life within a crowded environment. Using high-speed fluorescence microscopy and ordered micro-pillar arrays we show that the parasites mode of motility is adapted to the density of cells in blood. Trypanosomes are pulled forward by the planar beat of the single flagellum. Hydrodynamic flow across the asymmetrically shaped cell body translates into its rotational movement. Importantly, the presence of particles with the shape, size and spacing of blood cells is required and sufficient for trypanosomes to reach maximum forward velocity. If the density of obstacles, however, is further increased to resemble collagen networks or tissue spaces, the parasites reverse their flagellar beat and consequently swim backwards, in this way avoiding getting trapped. In the absence of obstacles, this flagellar beat reversal occurs randomly resulting in irregular waveforms and apparent cell tumbling. Thus, the swimming behavior of trypanosomes is a surprising example of micro-adaptation to life at low Reynolds numbers. For a precise physical interpretation, we compare our high-resolution microscopic data to results from a simulation technique that combines the method of multi-particle collision dynamics with a triangulated surface model. The simulation produces a rotating cell body and a helical swimming path, providing a functioning simulation method for a microorganism with a complex swimming strategy.

Langevin description of superdiffusive Lévy processes

The description of diffusion processes is possible in different frameworks such as random walks or Fokker-Planck or Langevin equations. Whereas for classical diffusion the equivalence of these methods is well established, in the case of anomalous diffusion it often remains an open problem. In this paper we aim to bring three approaches describing anomalous superdiffusive behavior to a common footing. While each method clearly has its advantages it is crucial to understand how those methods relate and complement each other. In particular, by using the method of subordination, we show how the Langevin equation can describe anomalous diffusion exhibited by Lévy-walk-type models and further show the equivalence of the random walk models and the generalized Kramers-Fokker-Planck equation. As a result a synergetic and complementary description of anomalous diffusion is obtained which provides a much more flexible tool for applications in real-world systems.

Flow loading induces oscillatory trajectories in a bloodstream parasite

The dynamics of isolated microswimmers are studied in bounded flow using the African trypanosome, a unicellular parasite, as the model organism. With the help of a microfluidics platform, cells are subjected to flow and found to follow an oscillatory path that is well fit by a sine wave. The frequency and amplitudes of the oscillatory trajectories are dependent on the flow velocity and cell orientation. When traveling in such a manner, trypanosomes orient upstream while downstream-facing cells tumble within the same streamline. A comparison with immotile trypanosomes demonstrates that self-propulsion is essential to the trajectories of trypanosomes even at flow velocities up to ∼40 times higher than their own swimming speed. These studies reveal important swimming dynamics that may be generally pertinent to the transport of microswimmers in flow and may be relevant to microbial pathogenesis.