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.This project has received funding from the EPSRC (PK) and the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement 682754 to EL)

Biophysics of Helices: Devices, Bacteria and Viruses

A prevalent morphology in the microscopic world of artificial microswimmers, bacteria and viruses is that of a helix. The intriguingly different physics at play at the small scale level make it necessary for bacteria to employ swimming strategies different from our everyday experience, such as the rotation of a helical filament. Bio-inspired microswimmers that mimic bacterial locomotion achieve propulsion at the microscale level using magnetically actuated, rotating helical filaments. A promising application of these artificial microswimmers is in non-invasive medicine, for drug delivery to tumours or microsurgery. Two crucial features need to be addressed in the design of microswimmers. First, the ability to selectively control large ensembles and second, the adaptivity to move through complex conduit geometries, such as the constrictions and curves of the tortuous tumour microvasculature. In this dissertation, a mechanics-based selective control mechanism for magnetic microswimmers is proposed, and a model and simulation of an elastic helix passing through a constricted microchannel are developed. Thereafter, a theoretical framework is developed for the propulsion by stiff elastic filaments in viscous fluids. In order to address this fluid-structure problem, a pertubative, asymptotic, elastohydrodynamic approach is used to characterise the deformation that arises from and in turn affects the motion. This framework is applied to the helical filaments of bacteria and magnetically actuated microswimmers. The dissertation then turns to the sub-bacterial scale of bacteriophage viruses, ‘phages’ for short, that infect bacteria by ejecting their genetic material and replicating inside their host. The valuable insight that phages can offer in our fight against pathogenic bacteria and the possibility of phage therapy as an alternative to antibiotics, are of paramount importance to tackle antibiotics resistance. In contrast to typical phages, flagellotropic phages first attach to bacterial flagella, and have the striking ability to reach the cell body for infection, despite their lack of independent motion. The last part of the dissertation develops the first theoretical model for the nut-and-bolt mechanism (proposed by Berg and Anderson in 1973). A nut being rotated will move along a bolt. Similarly, a phage wraps itself around a flagellum possessing helical grooves, and exploits the rotation of the flagellum in order to passively travel along and towards the cell body, according to this mechanism. The predictions from the model agree with experimental observations with respect to directionality, speed and the requirements for succesful translocation.This work was funded by the EPSRC (3 years) and the last year was funded by Prof Eric Lauga's grant from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement 682754 to Prof Eric Lauga)

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 its axis also bends, a new 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.This project has received funding from the EPSRC (PK) and the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement 682754 to EL)

Hydrodynamics of bacteriophage migration along bacterial flagella

Bacteriophage viruses, one of the most abundant entities in our planet, lack the ability to move independently. Instead, they crowd fluid environments in anticipation of a random encounter with a bacterium. Once they ‘land’ on the cell body of their victim, they are able to eject their genetic material inside the host cell. Many phage species, however, first attach to the flagellar filaments of bacteria. Being immotile, these so-called flagellotropic phages still manage to reach the cell body for infection, and the process by which they move up the flagellar filament has intrigued the scientific community for decades. In 1973, Berg and Anderson (Nature, 245, 380-382) proposed the nut-and-bolt mechanism in which, similarly to a rotated nut that is able to move along a bolt, the phage wraps itself around a flagellar filament possessing helical grooves (due to the helical rows of flagellin molecules) and exploits the rotation of the flagellar filament in order to passively travel along it. One of the main evidence for this mechanism is the fact that mutants of bacterial species such as Escherichia coli and Salmonella typhimurium that possess straight flagellar filaments with a preserved helical groove structure can still be infected by their relative phages. Using two distinct approaches to address the short-range interactions between phages and flagellar filaments, we provide here a first-principle theoretical model for the nut-and-bolt mechanism applicable to mutants possessing straight flagellar filaments. Our model is fully analytical, is able to predict the speed of translocation of a bacteriophage along a flagellar filament as a function of the geometry of both phage and bacterium, the rotation rate of the flagellar filament, and the handedness of the helical grooves, and is consistent with past experimental observations.EPSRC and ER

Selectively Controlled Magnetic Microrobots with Opposing Helices

Magnetic microrobots that swim through liquid media are of interest for minimally invasive medical procedures, bioengineering, and manufacturing. Many of the envisaged applications, such as micromanipulation and targeted cargo delivery, necessitate the use and adequate control of multiple microrobots, which will increase the velocity, robustness, and efficacy of a procedure. While various methods involving heterogeneous geometries, magnetic properties, and surface chemistries have been proposed to enhance independent control, the main challenge has been that the motion between all microwsimmers remains coupled through the global control signal of the magnetic field. Katsamba and Lauga proposed transchiral microrobots, a theoretical design with magnetized spirals of opposite handedness. The competition between the spirals can be tuned to give an intrinsic nonlinearity that each device can function only within a given band of frequencies. This allows individual microrobots to be selectively controlled by varying the frequency of the rotating magnetic field. Here we present the experimental realization and characterization of transchiral micromotors composed of independently driven magnetic helices. We show a swimming micromotor that yields negligible net motion until a critical frequency is reached and a micromotor that changes its translation direction as a function of the frequency of the rotating magnetic field. This work demonstrates a crucial step towards completely decoupled and addressable swimming magnetic microrobots

Chemically active filaments: analysis and extensions of slender phoretic theory

Autophoretic microswimmers self-propel via surface interactions with a surrounding solute fuel. Chemically-active filaments are an exciting new microswimmer design that augments traditional autophoretic microswimmers, such as spherical Janus particles, with extra functionality inherent to their slender filament geometry. Slender Phoretic Theory (SPT) was developed by Katsamba et al. to analyse the dynamics of chemically-active filaments with arbitrary three-dimensional shape and chemical patterning. SPT provides a line integral solution for the solute concentration field and slip velocity on the filament surface. In this work, we exploit the generality of SPT to calculate a number of new, non-trivial analytical solutions for slender autophoretic microswimmers, including a general series solution for phoretic filaments with arbitrary geometry and surface chemistry, a universal solution for filaments with a straight centreline, and explicit solutions for some canonical shapes useful for practical applications and benchmarking numerical code. Many common autophoretic particle designs include discrete jumps in surface chemistry; here we extend our SPT to handle such discontinuities, showing that they are regularised by a boundary layer around the jump. Since our underlying framework is linear, combinations of our results provide a library of analytic solutions that will allow researchers to probe the interplay of activity patterning and shape

Adaptive locomotion of artificial microswimmers

Bacteria can exploit mechanics to display remarkable plasticity in response to locally changing physical and chemical conditions. Compliant structures play a striking role in their taxis behavior, specifically for navigation inside complex and structured environments. Bioinspired mechanisms with rationally designed architectures capable of large, nonlinear deformation present opportunities for introducing autonomy into engineered small-scale devices. This work analyzes the effect of hydrodynamic forces and rheology of local surroundings on swimming at low Reynolds number, identifies the challenges and benefits of utilizing elastohydrodynamic coupling in locomotion, and further develops a suite of machinery for building untethered microrobots with self-regulated mobility. We demonstrate that coupling the structural and magnetic properties of artificial microswimmers with the dynamic properties of the fluid leads to adaptive locomotion in the absence of on-board sensors

Adaptive locomotion of artificial microswimmers.

Bacteria can exploit mechanics to display remarkable plasticity in response to locally changing physical and chemical conditions. Compliant structures play a notable role in their taxis behavior, specifically for navigation inside complex and structured environments. Bioinspired mechanisms with rationally designed architectures capable of large, nonlinear deformation present opportunities for introducing autonomy into engineered small-scale devices. This work analyzes the effect of hydrodynamic forces and rheology of local surroundings on swimming at low Reynolds number, identifies the challenges and benefits of using elastohydrodynamic coupling in locomotion, and further develops a suite of machinery for building untethered microrobots with self-regulated mobility. We demonstrate that coupling the structural and magnetic properties of artificial microswimmers with the dynamic properties of the fluid leads to adaptive locomotion in the absence of on-board sensors.ER

Hydrodynamics of bacteriophage migration along bacterial flagella

Bacteriophage viruses, one of the most abundant entities in our planet, lack the ability to move independently. Instead, they crowd fluid environments in anticipation of a random encounter with a bacterium. Once they ‘land’ on the cell body of their victim, they are able to eject their genetic material inside the host cell. Many phage species, however, first attach to the flagellar filaments of bacteria. Being immotile, these so-called flagellotropic phages still manage to reach the cell body for infection, and the process by which they move up the flagellar filament has intrigued the scientific community for decades. In 1973, Berg and Anderson (Nature, 245, 380-382) proposed the nut-and-bolt mechanism in which, similarly to a rotated nut that is able to move along a bolt, the phage wraps itself around a flagellar filament possessing helical grooves (due to the helical rows of flagellin molecules) and exploits the rotation of the flagellar filament in order to passively travel along it. One of the main evidence for this mechanism is the fact that mutants of bacterial species such as Escherichia coli and Salmonella typhimurium that possess straight flagellar filaments with a preserved helical groove structure can still be infected by their relative phages. Using two distinct approaches to address the short-range interactions between phages and flagellar filaments, we provide here a first-principle theoretical model for the nut-and-bolt mechanism applicable to mutants possessing straight flagellar filaments. Our model is fully analytical, is able to predict the speed of translocation of a bacteriophage along a flagellar filament as a function of the geometry of both phage and bacterium, the rotation rate of the flagellar filament, and the handedness of the helical grooves, and is consistent with past experimental observations.EPSRC and ER

Slender phoretic theory of chemically active filaments

International audienceArtificial microswimmers, or "microbots" have the potential to revolutionise non-invasive medicine and microfluidics. Microbots that are powered by self-phoretic mechanisms, such as Janus particles, often harness a solute fuel in their environment. Traditionally, selfphoretic particles are point-like, but slender phoretic rods have become an increasingly prevalent design. While there has been substantial interest in creating efficient asymptotic theories for slender phoretic rods, hitherto such theories have been restricted to straight rods with axisymmetric patterning. However, modern manufacturing methods will soon allow fabrication of slender phoretic filaments with complex three-dimensional shape. In this paper, we develop a slender body theory for the solute of self-diffusiophoretic filaments of arbitrary three-dimensional shape and patterning. We demonstrate analytically that, unlike other slender body theories, first-order azimuthal variations arising from curvature and confinement can have a leading order contribution to the swimming kinematics