Cell morphology governs directional control in swimming bacteria

The ability to rapidly detect and track nutrient gradients is key to the ecological success of motile bacteria in aquatic systems. Consequently, bacteria have evolved a number of chemotactic strategies that consist of sequences of straight runs and reorientations. Theoretically, both phases are affected by fluid drag and Brownian motion, which are themselves governed by cell geometry. Here, we experimentally explore the effect of cell length on control of swimming direction. We subjected Escherichia coli to an antibiotic to obtain motile cells of different lengths, and characterized their swimming patterns in a homogeneous medium. As cells elongated, angles between runs became smaller, forcing a change from a run-and-tumble to a run-and-stop/reverse pattern. Our results show that changes in the motility pattern of microorganisms can be induced by simple morphological variation, and raise the possibility that changes in swimming pattern may be triggered by both morphological plasticity and selection on morphology

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

Statistical analysis of bacteria locomotion

Many bacteria swim by employing their helical appendages, the flagella. We studied the statistics of this locomotion. To obtain more natural and especially long trajectories compared to two-dimensional tracking strategies, we developed a measurement-setup suitable to track bacteria in three-dimensions.The main component of this setup is an electrically focus tunable lens (ETL), able to adapt it’s shape via an applied electrical current, resulting in a change of the current focal plane. This setup has no mechanical interaction with the sample to avoid adulteration of the measured trajectories. We found that for times smaller than the average running-time, the slope of the mean-squared displacement MSD of the tracked bacteria obeys a ballistic behavior, whereas for longer times we saw a clear diffusive behavior. To allow for a more efficient evaluation of the measured trajectories we introduce the Kalman-Filter. By using simulated trajectories we could show that the Kalman-Filter allows a more accurate determination of the rotational-diffusion coefficient than conventional methods. Furthermore we could show that evaluation of three-dimensional trajectories obeys slightly different statistics than the evaluation of projected two-dimensional trajectories due to missing information.Through the qualitative simulation of bacteria locomotion we could show that the flagella-positioning has a crucial impact on the tumbling dynamics.Viele Bakterien schwimmen durch Nutzung ihrer spiralförmigen Anhänge,den Flagellen. Wir untersuchten die Statistik dieser Bewegung. Um natürlichere und vor allem längere Trajektorien - verglichen mit konventionellen zweidimensionalen Trackingmethoden - zu erhalten, haben wir einen Messaufbau zum dreidimensionalen tracken von Bakterien entwickelt. Die Hauptkomponente dieses Setups ist eine elektrische, fokusanpassbare Linse (ETL),welche ihre Form durch Anlegen eines elektrischen Stroms ändern kann,was zu einer Änderung der Fokusebene führt. Dieser Messaufbau hat keine mechanischen Wechselwirkungen mit der Probe, wodurch Verfälschungender gemessenen Trajektorien verhindert werden. Wir konnten zeigen dassfür Zeiten kleiner als die durchschnittlicherunning-Zeit (dt.Renn-Zeit), die mittlere quadratische Verschiebung (MSD) der getrackten Bakterien ein ballistisches Verhalten zeigt, wohingegen für längere Zeiten ein diffusives Verhalten vorliegt. Um eine effizientere Auswertung der gemessenen Trajektorien zu erlauben, führten wir den Kalman-Filter ein. Durch Nutzung simulierterTrajektorien konnten wir zeigen dass der Kalman-Filter eine genauere Bestimmung des Rotations-Diffusionskoeffizienten - verglichen mit konventionellen Methoden - erlaubt.Weiterhin konnten wir zeigen, dass die Auswertung dreidimensionaler Trajektorien leicht andere Statistiken als die Auswertung zweidimensionaler Trajektorien liefert, was durch den Verlust an Information zu erklären ist. Durch die qualitative Simulation der Bewegung von Bakterien konnten wir zeigen, dass die Position der Flagellen einen wesentlichen Einfluss auf die Tumbling-Dynamik (dt.Taumel-Dynamik) hat

Untethered bio-inspired helical swimmer in channels

This study focuses on analyzing the effects of parameters such as helical pitch, helical wavelength, and frequency of rotations and diameter of channels on the measured velocity of helix and rotation rate of the body. The first stage of this study is macro design of robots with helical tails. The fundamentals of the design are mainly based on the criteria that affect the robots' motion. The second purpose of the thesis is applying the resistive force theory (RFT) to analyze the effects of swimming parameters and diameter of channels on the velocity of helix and rotation rate of body, analytically. This theoretical model is developed for six degree-of-freedom motion of the helix but two degree-of-freedom motion results are considered because only forward speed and body rotation rates are observable from experiments. The third stage of this study is analyzing the effect of swimming parameters and the diameter of channel on the swimming motion of the swimmer with helical tail by means of CFD (computational fluid dynamics) models. In the last stage, the experimental results are compared with RFT and CFD models

Active Brownian Particles. From Individual to Collective Stochastic Dynamics

We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of such self-propelled entities in the framework of statistical mechanics. Examples of such active units in complex physico-chemical and biological systems are chemically powered nano-rods, localized patterns in reaction-diffusion system, motile cells or macroscopic animals. Based on the description of individual motion of point-like active particles by stochastic differential equations, we discuss different velocity-dependent friction functions, the impact of various types of fluctuations and calculate characteristic observables such as stationary velocity distributions or diffusion coefficients. Finally, we consider not only the free and confined individual active dynamics but also different types of interaction between active particles. The resulting collective dynamical behavior of large assemblies and aggregates of active units is discussed and an overview over some recent results on spatiotemporal pattern formation in such systems is given.Comment: 161 pages, Review, Eur Phys J Special-Topics, accepte

Bio-inspired Magnetic Systems: Controlled Swimming, Fluid Pumps, and Collective Behaviour

This thesis details the original experimental investigations of magnetically actuated and controlled microscopic systems enabling a range of actions at low Reynolds number. From millimetre-robots and self-propelled swimmers to microfluidic and lab-on-a-chip technology applications. The main theme throughout the thesis is that the systems reply on the interactions between magnetic and elastic components. Scientists often take inspiration from nature for many aspects of science. Millimetre to micrometre machines are no exception to this. Nature demonstrates how soft materials can be used to deform in a manner to create actuation at the microscale in biological environments. Nature also shows the effectiveness of using beating tails known as flagella and the apparent enhancements in flow speeds of collective motion. To begin with, a swimmer comprised of two ferromagnetic particles coupled together with an elastic link (the two-ferromagnetic particle swimmer), was fabricated. The system was created to mimic the swimming mechanism seen by eukaryotic cells, in which these cells rely on morphological changes which allows them to propel resulting in approximate speeds of up to 2 body lengths per second. The aim of this system was to create a net motion and control the direction of propagation by manipulating the external magnetic field parameters. It was shown that the direction of swimming has a dependence on both the frequency and amplitude of the applied external magnetic field. A key factor discovered was that the influence of a small bias field, in this case, the Earth’s magnetic field (100 orders of magnitude smaller than the external magnetic field) resulted in robust control over the speed (resulting in typical swimming speeds of 4 body lengths per second) and direction of propulsion. Following this work, swimmers with a hard ferromagnetic head attached to an elastic tail (the torque driven ferromagnetic swimmer) were investigated. These systems were created to be analogous to the beating flagella of many natural microscopic swimmers, two examples would be sperm cells and chlamydomonas cells. These biological cells have typical speeds of 10s of body lengths per second. The main focus of this investigation was to understand how the tail length affects the swimming performance. An important observation was that there is an obvious length tail (5.7 times the head length) at which the swimming speed is maximised (approximately 13 body lengths per second). The experimental results were compared to a theoretical model based on three beads, one of which having a fixed magnetic moment and the other two non-magnetic, connected via elastic filaments. The model shows sufficient complexity to break time symmetry and create a net motion, giving good agreement with experiment. Portable point-of-care systems have the potential to revolutionise medical diagnostics. Such systems require active pumps with low power (USB powered devices) external triggers. Due to the wireless and localisation of magnetic fields could possibly allow these portable point-of-care devices to come to life. The main focus of this investigation was to create fluid pump systems comprising from the previously investigated two-ferromagnetic particle swimmer and the torque driven ferromagnetic swimmer. Building on the fact that if a system can generate a net motion it would also be able to create a net flow. Utilising the geometry of the systems, it has been demonstrated that a swimmer-based system can become a fluid pump by restricting the translational motion. The flow structure generated by a pinned swimmer in different scenarios, such as unrestricted flow around it as well as flow generated in straight, cross-shaped, Y-shaped and circular channels were investigated. This investigation demonstrated the feasibility of incorporating the device into a channel and its capability of acting as a pump, valve and flow splitter. As well as a single pump system, networks of the previously mentioned pump systems were fabricated and experimentally investigated. The purpose of this investigation was to utilise the behaviour of the collective motion. Such networks could also be attached to the walls or top of the channel to create a less invasive system compared to pump based within the channel system. The final investigation involved creating collective motion systems which could mimic the beating of cilia - known as a metachronal wave. Two methods were used to create an analogous behaviour. The first was using arrays of identical magnetic rotors, which under the influence of an external magnetic field created two main rotational patterns. The rotational patterns were shown to be controllable producing useful flow fields at low Reynolds numbers. The second system relied on the magnetic components having different fixed magnetisation to create a phase lag between oscillations. The magnetic components were investigated within a channel and the separation between the components was shown to be a key parameter for controlling the induced flow. In both cases, a simple model was produced to help understand the behaviour. Finally, a selection of preliminary investigations into possible applications were conducted experimentally. These investigations included, measuring the effective surface viscosity of lipid monolayers, created cell growth microchannels, as well as systems which could be used for blood plasma separation. The properties of lipid monolayers vary with the surface density, resulting on distinct phase transitions. Slight differences in the molecular lattice are often accompanied by significant changes in the surface viscosity and elasticity. The idea was to use a swimmer as a reporter of the monolayer viscosity, resulting in a less invasive method compared to current techniques to monitor monolayer viscosity, for example torsion pendulums and channel viscometers. The reported effective surface viscosity closely matched the typical Langmuir trough measurements (with a systematic shift of approximately 17 Ų/molecule). The blood plasma separation preliminary work shows the previously investigated two-ferromagnetic particle swimmer mixing a typical volume (100 μm) blood sample with a buffer solution in 21 seconds. The system was also able to create locations with a high population of red blood cells. This resulted in a separation between the blood plasma and red blood cells. Two other preliminary results of future investigations were presented; the collective motion of free swimmers, and the fabrication of ribbon-like structures with fixed magnetic moment patterns.European CommissionEngineering and Physical Sciences Research Council (EPSRC

Microfluidics and Bio-MEMS for Next Generation Healthcare.

Ph.D. Thesis. University of Hawaiʻi at Mānoa 2018

Gait optimality for undulatory locomotion with applications to C. elegans phenotyping

This thesis focuses on the optimality and efficiency of organism locomotion strategies, specifically of microscopic undulators, in two distinct parts. Undulators loco- mote by propagating waves of bending deformation along their bodies, and at the microscale (ie low Reynolds number) interactions between undulators and their surroundings are well-described by biomechanical models due to high viscosity and negligible inertia. Frameworks such as resistive force theory enable the determination of optimal gaits for micro-undulators, often defined as the waveform maximising the ratio of swimming speed to energetic cost. Part I explores this avenue of research in a theoretical setting. Primary mathematical focus has been on finding optimal waveforms for straight-path forwards locomotion, but organisms do not move exclusively this way: turning and manoeuvring is key to survival. Here we establish a mathematical model, extend- ing previous approaches to modelling swimming micro-undulators, now introducing path curvature, to obtain optimal turning gaits. We obtain an analytical result demonstrating that high-curvature shapes minimise energetic cost when the penalty for bending is reduced. Imposing limitations on the curvature, and investigating multiple high-dimensional shape-spaces, we show that optimal turning results can be closely approximated as constant-curvature travelling waves. Part II adopts an experimental approach. Quantitative phenotyping tools can be used in behavioural screens of the model organism C. elegans to detect differences between wildtype and mutant strains. Expanding the current set of tools to include more orthogonal features could enable increased detection of deficiencies. Here we develop efficiency as a phenotyping lens for C. elegans, quantifying the gait optimality of rare human genetic disease model strains. Genetic diseases in humans are modelled in C. elegans with disease-associated orthologs. We find worm gait efficiency is found to correlate highly with percentage time paused. High efficiencies are exhibited during reversals and backing motions, due to suppressed head-swinging and increase in speed.Open Acces