Confinement by biased velocity jumps: aggregation of Escherichia coli

We investigate a linear kinetic equation derived from a velocity jump process modelling bacterial chemotaxis in the presence of an external chemical signal centered at the origin. We prove the existence of a positive equilibrium distribution with an exponential decay at infinity. We deduce a hypocoercivity result, namely: the solution of the Cauchy problem converges exponentially fast towards the stationary state. The strategy follows [J. Dolbeault, C. Mouhot, and C. Schmeiser, Hypocoercivity for linear kinetic equations conserving mass, Trans. AMS 2014]. The novelty here is that the equilibrium does not belong to the null spaces of the collision operator and of the transport operator. From a modelling viewpoint it is related to the observation that exponential confinement is generated by a spatially inhomogeneous bias in the velocity jump process.Comment: 15 page

Limits of feedback control in bacterial chemotaxis

Inputs to signaling pathways can have complex statistics that depend on the environment and on the behavioral response to previous stimuli. Such behavioral feedback is particularly important in navigation. Successful navigation relies on proper coupling between sensors, which gather information during motion, and actuators, which control behavior. Because reorientation conditions future inputs, behavioral feedback can place sensors and actuators in an operational regime different from the resting state. How then can organisms maintain proper information transfer through the pathway while navigating diverse environments? In bacterial chemotaxis, robust performance is often attributed to the zero integral feedback control of the sensor, which guarantees that activity returns to resting state when the input remains constant. While this property provides sensitivity over a wide range of signal intensities, it remains unclear how other parameters affect chemotactic performance, especially when considering that the swimming behavior of the cell determines the input signal. Using analytical models and simulations that incorporate recent experimental evidences about behavioral feedback and flagellar motor adaptation we identify an operational regime of the pathway that maximizes drift velocity for various environments and sensor adaptation rates. This optimal regime is outside the dynamic range of the motor response, but maximizes the contrast between run duration up and down gradients. In steep gradients, the feedback from chemotactic drift can push the system through a bifurcation. This creates a non-chemotactic state that traps cells unless the motor is allowed to adapt. Although motor adaptation helps, we find that as the strength of the feedback increases individual phenotypes cannot maintain the optimal operational regime in all environments, suggesting that diversity could be beneficial.Comment: Corrected one typo. First two authors contributed equally. Notably, there were various typos in the values of the parameters in the model of motor adaptation. The results remain unchange

Movement of zoospores of Phytophthora citricola in saturated porous media

The genus Phytophthora comprises numerous plant pathogens in both natural and managed ecosystems. For Phytophthora spp. that infect roots, dispersal occurs in soil water through a combination of advection and swimming of specialized motile propagules (zoospores). Specific biological and physico-chemical processes, however, remain poorly understood, due to difficulties in studying phenomena in opaque media and lack of a theoretical framework for analyzing transport of motile microorganisms. The goal of this research was to elucidate the impacts of advection and swimming on zoospore movement in a saturated, ideal soil. The work was accomplished in two stages, (i) conceptualization of 3-dimensional topography and flow field heterogeneity at the subpore-scale, and (ii) observation of behavior of zoospore suspensions infiltrated into saturated media. Chapter 2 introduces a 3-dimensional particle tracking method and presents two studies investigating particle transport in simplified 'ideal pores'. The first study describes 'avoidance' by latex microspheres of a volume surrounding orthogonal grain contacts and the second describes 'capture', translation, and retention of microspheres under conditions unfavorable to deposition. Chapter 3 expands on the first study and demonstrates, with the aid of computational fluid dynamics, that low flow zones associated with orthogonal grain contacts are minimally connected to the main flow. Thus, probability of entry into these regions for large, non-Brownian particles by advection alone is low. In zoospore infiltration experiments, zoospore plumes 'converged' rather than dispersing as expected. To assess the possibility of zoospore auto-aggregation driving this 'convergence', Chapter 4 delves into the 'pattern swimming' observed in free-swimming zoospore suspensions, concluding that the concentrating is an example of bioconvection. Chapter 5 introduces a conceptual model to explain the anomalous zoospore plume behavior. Random walk simulations replicated plume convergence but were less successful at modeling anisotropic dispersion. At low infiltration rates (<100 μm s⁻¹), simulations predict that zoospores will remain at or near the soil surface, resulting in greater opportunity to find host tissues or to be transported with surface water. Further investigation is necessary to develop a robust theoretical framework with appropriate conceptualization of the subpore hydrodynamic environment for predicting transport of zoospores and other motile microorganisms in porous media

Quantitative Untersuchung der Motilität des Blutparasiten Trypanosoma brucei brucei durch 4D-Tracking mittels digitaler In-line Holographie

In der vorliegenden Arbeit wurde die Motilität des Blutparasiten Trypanosoma brucei brucei untersucht. Dieser vor allem in Subsahara-Afrika verbreitete Organismus wird von der Tsetse-Fliege auf Menschen und Tiere übertragen und löst die unbehandelt tödlich verlaufende Afrikanische Schlafkrankheit aus. Nur wenige Medikamente sind bekannt, diese zeichnen sich jedoch meistens durch das Auftreten schwerer Nebenwirkungen aus. Der Organismus ist lange bekannt und seine Eigenmotilität wird seit langem mit seiner Pathogenität in Verbindung gebracht, trotzdem fehlen bislang weitgehend quantitative Untersuchungen zur Fortbewegung, vor allem der im infizierten Organismus vorkommenden Blutstromformen. Eine Strategie des Parasiten um die Immunantwort des Wirtes zu umgehen ist das „Abwaschen“ an der Zelloberfläche gebundener Antikörper durch gerichtetes Schwimmen. Desweiteren ist die Eigenbewegung von großer Bedeutung für die Zellteilung und damit erfolgreiche Vermehrung des Organismus sowie für die Verteilung im Wirt, da im Endstadium der Krankheit durch den Parasiten aktiv die Blut-Hirn-Schranke passiert wird. Die Kenntnis des zugrundeliegenden Fortbewegungsmechanismus ist also von grundlegender Bedeutung zum Verständnis der Pathogenese und damit zur Entwicklung von Strategien zur medikamentösen Bekämpfung des Erregers im infizierten Wirt. Im Rahmen dieser Arbeit wurde das Motilitätsverhalten von Trypanosomen unterschiedlicher Lebenszyklusstadien bei verschiedenen Temperaturen mikroskopisch untersucht. Dazu wurde ein portables, holographisches Mikroskop entwickelt, dass die Vermessung von Trypanosomen bei physiologischen Temperaturen mit hoher Auflösung und Stabilität erlaubt. Die erhaltenen 3D-Daten erlauben erstmals eine quantitative Analyse frei schwimmender Trypanosomen über große Volumina und Zeiträume. Aus den Daten wurden zwei deutlich unterscheidbare Schwimmzustände abgeleitet, für die charakteristische Schwimmparameter, wie mittlere Schwimmgeschwindigkeiten und –winkel sowie typische Ausbreitungsverhalten abgeleitet werden konnten. Die Schwimmzustände konnten durch Referenzmessungen mit Motilitätsmutanten und unter Verwendung spezieller Probenkammern erfolgreich zwei unterschiedlichen Bewegungsmodi der die Trypanosomen antreibenden Struktur, dem Flagellum, zugeordnet werden. Die erhaltenen Daten zeigen deutlich die Adaption der Lebenszyklusstadien an ihre jeweils physiologische Temperatur und stützen eines der postulierten Modelle für die Trypanosomenbewegung, das run-and-tumble-Modell. Sie stellen somit einen wichtigen Beitrag zur Diskussion des Fortbewegungsmechanismus von Trypanosomen dar

Mathematical modelling and analysis of aspects of bacterial motility

The motile behaviour of bacteria underlies many important aspects of their actions, including pathogenicity, foraging efficiency, and ability to form biofilms. In this thesis, we apply mathematical modelling and analysis to various aspects of the planktonic motility of flagellated bacteria, guided by experimental observations. We use data obtained by tracking free-swimming Rhodobacter sphaeroides under a microscope, taking advantage of the availability of a large dataset acquired using a recently developed, high-throughput protocol. A novel analysis method using a hidden Markov model for the identification of reorientation phases in the tracks is described. This is assessed and compared with an established method using a computational simulation study, which shows that the new method has a reduced error rate and less systematic bias. We proceed to apply the novel analysis method to experimental tracks, demonstrating that we are able to successfully identify reorientations and record the angle changes of each reorientation phase. The analysis pipeline developed here is an important proof of concept, demonstrating a rapid and cost-effective protocol for the investigation of myriad aspects of the motility of microorganisms. In addition, we use mathematical modelling and computational simulations to investigate the effect that the microscope sampling rate has on the observed tracking data. This is an important, but often overlooked aspect of experimental design, which affects the observed data in a complex manner. Finally, we examine the role of rotational diffusion in bacterial motility, testing various models against the analysed data. This provides strong evidence that R. sphaeroides undergoes some form of active reorientation, in contrast to the mainstream belief that the process is passive