Filament mechanics in a half-space via regularised Stokeslet segments

We present a generalisation of efficient numerical frameworks for modelling fluid-filament interactions via the discretisation of a recently-developed, non-local integral equation formulation to incorporate regularised Stokeslets with half-space boundary conditions, as motivated by the importance of confining geometries in many applications. We proceed to utilise this framework to examine the drag on slender inextensible filaments moving near a boundary, firstly with a relatively-simple example, evaluating the accuracy of resistive force theories near boundaries using regularised Stokeslet segments. This highlights that resistive force theories do not accurately quantify filament dynamics in a range of circumstances, even with analytical corrections for the boundary. However, there is the notable and important exception of movement in a plane parallel to the boundary, where accuracy is maintained. In particular, this justifies the judicious use of resistive force theories in examining the mechanics of filaments and monoflagellate microswimmers with planar flagellar patterns moving parallel to boundaries. We proceed to apply the numerical framework developed here to consider how filament elastohydrodynamics can impact drag near a boundary, analysing in detail the complex responses of a passive cantilevered filament to an oscillatory flow. In particular, we document the emergence of an asymmetric periodic beating in passive filaments in particular parameter regimes, which are remarkably similar to the power and reverse strokes exhibited by motile 9+2 cilia. Furthermore, these changes in the morphology of the filament beating, arising from the fluid-structure interactions, also induce a significant increase in the hydrodynamic drag of the filament.Comment: 21 pages, 9 figures. Supplementary Material available upon reques

Regularised non-uniform segments and efficient no-slip elastohydrodynamics

The elastohydrodynamics of slender bodies in a viscous fluid have long been the source of theoretical investigation, being pertinent to the microscale world of ciliates and flagellates as well as to biological and engineered active matter more generally. Though recent works have overcome the severe numerical stiffness typically associated with slender elastohydrodynamics, employing both local and non-local couplings to the surrounding fluid, there is no framework of comparable efficiency that rigorously justifies its hydrodynamic accuracy. In this study, we combine developments in filament elastohydrodynamics with a recent slender-body theory, affording algebraic asymptotic accuracy to the commonly imposed no-slip condition on the surface of a slender filament of potentially non-uniform cross-sectional radius. Further, we do this whilst retaining the remarkable practical efficiency of contemporary elastohydrodynamic approaches, having drawn inspiration from the method of regularised Stokeslet segments to yield an efficient and flexible slender-body theory of regularised non-uniform segments

Modelling mechanically dominated vasculature development

Vascular networks play a key role in the development, function, and survival of many organisms, facilitating transport of nutrients and other critical factors within and between systems. The development of these vessel networks has been thoroughly explored in a variety of in vivo, in vitro and in silico contexts. However, the role of interactions between the growing vasculature and its environment remains largely unresolved, particularly concerning mechanical effects. Motivated by this gap in understanding, we develop a computational framework that is tailored to exploring the role of the mechanical environment on the formation of vascular networks. Here, we describe, document, implement, and explore an agent-based modelling framework, resolving the growth of individual vessels and seeking to capture phenomenology and intuitive qualitative mechanisms. In our explorations, we demonstrate that such a model can successfully reproduce familiar network structures, whilst highlighting the roles that mechanical influences could play in vascular development. For instance, we illustrate how an external substrate could act as an effective shared memory for the periodic regrowth of vasculature. We also observe the emergence of a nuanced collective behaviour and clustered vessel growth, which results from mechanical characteristics of the external environment

Automated identification of flagella from videomicroscopy via the medial axis transform

Ubiquitous in eukaryotic organisms, the flagellum is a well-studied organelle that is well-known to be responsible for motility in a variety of organisms. Commonly necessitated in their study is the capability to image and subsequently track the movement of one or more flagella using videomicroscopy, requiring digital isolation and location of the flagellum within a sequence of frames. Such a process in general currently requires some researcher input, providing some manual estimate or reliance on an experiment-specific heuristic to correctly identify and track the motion of a flagellum. Here we present a fully-automated method of flagellum identification from videomicroscopy based on the fact that the flagella are of approximately constant width when viewed by microscopy. We demonstrate the effectiveness of the algorithm by application to captured videomicroscopy of Leishmania mexicana, a parasitic monoflagellate of the family Trypanosomatidae. ImageJ Macros for flagellar identification are provided, and high accuracy and remarkable throughput are achieved via this unsupervised method, obtaining results comparable in quality to previous studies of closely-related species but achieved without the need for precursory measurements or the development of a specialised heuristic, enabling in general the automated generation of digitised kinematic descriptions of flagellar beating from videomicroscopy.Comment: 10 pages, 5 figures. Author accepted manuscript. Supplementary Material available at https://doi.org/10.1038/s41598-019-41459-

Altered chemomechanical coupling causes impaired motility of the kinesin-4 motors KIF27 and KIF7.

Kinesin-4 motors play important roles in cell division, microtubule organization, and signaling. Understanding how motors perform their functions requires an understanding of their mechanochemical and motility properties. We demonstrate that KIF27 can influence microtubule dynamics, suggesting a conserved function in microtubule organization across the kinesin-4 family. However, kinesin-4 motors display dramatically different motility characteristics: KIF4 and KIF21 motors are fast and processive, KIF7 and its Drosophila melanogaster homologue Costal2 (Cos2) are immotile, and KIF27 is slow and processive. Neither KIF7 nor KIF27 can cooperate for fast processive transport when working in teams. The mechanistic basis of immotile KIF7 behavior arises from an inability to release adenosine diphosphate in response to microtubule binding, whereas slow processive KIF27 behavior arises from a slow adenosine triphosphatase rate and a high affinity for both adenosine triphosphate and microtubules. We suggest that evolutionarily selected sequence differences enable immotile KIF7 and Cos2 motors to function not as transporters but as microtubule-based tethers of signaling complexes

Systematic parameterisations of minimal models of microswimming

Simple models are used throughout the physical sciences as a means of developing intuition, capturing phenomenology, and qualitatively reproducing observations. In studies of microswimming, simple force-dipole models are commonplace, arising generically as the leading-order, far-field descriptions of a range of complex biological and artificial swimmers. Though many of these swimmers are associated with intricate, time varying flow fields and changing shapes, we often turn to models with constant, averaged parameters for intuition, basic understanding, and back-of-the-envelope prediction. In this brief study, via an elementary multi-timescale analysis, we examine whether the standard use of a priori-averaged parameters in minimal microswimmer models is justified, asking if their behavioural predictions qualitatively align with those of models that incorporate rapid temporal variation through simple extensions. In doing so, we highlight and exemplify how a straightforward asymptotic analysis of these non-autonomous models can result in effective, systematic parameterisations of minimal models of microswimming

Are Small Urban Centers Magnets for Economic Growth?

This report estimates a model of county-level job growth and finds an effect of small urban centers on their regional economies

Systematic parameterizations of minimal models of microswimming

Simple models are used throughout the physical sciences as a means of developing intuition, capturing phenomenology, and qualitatively reproducing observations. In studies of microswimming, simple force-dipole models are commonplace, arising generically as the leading-order, far-field descriptions of a range of complex biological and artificial swimmers. Though many of these swimmers are associated with intricate, time varying flow fields and changing shapes, we often turn to models with constant, averaged parameters for intuition, basic understanding, and back-of-the-envelope prediction. In this brief study, via an elementary multitimescale analysis, we examine whether the standard use of a priori-averaged parameters in minimal microswimmer models is justified, asking if their behavioural predictions qualitatively align with those of models that incorporate rapid temporal variation through simple extensions. In doing so, we find that widespread, seemingly innocuous choices of parameters can give rise to qualitatively incorrect conclusions from simple models, with the potential to alter our intuition for swimming on the microscale. Further, we highlight and exemplify how a straightforward asymptotic analysis of the non-autonomous models can result in effective, systematic parametrizations of minimal models of microswimming

A hydrodynamic slender-body theory for local rotation at zero Reynolds number

Slender objects are commonplace in microscale flow problems, from soft deformable sensors to biological filaments such as flagella and cilia. While much research has focused on the local translational motion of these slender bodies, relatively little attention has been given to local rotation, even though it can be the dominant component of motion. In this study, we explore a classically motivated ansatz for the Stokes flow around a rotating slender body via superposed rotlet singularities, which leads us to pose an alternative ansatz that accounts for both translation and rotation. Through an asymptotic analysis that is supported by numerical examples, we determine the suitability of these flow ansatzes for capturing the fluid velocity at the surface of a slender body, assuming local axisymmetry of the object but allowing the cross-sectional radius to vary with arclength. In addition to formally justifying the presented slender-body ansatzes, this analysis reveals a markedly simple relation between the local angular velocity and the torque exerted on the body, which we term resistive torque theory. Though reminiscent of classical resistive force theories, this local relation is found to be algebraically accurate in the slender-body aspect ratio, even when translation is present, and is valid and required whenever local rotation contributes to the surface velocity at leading asymptotic order