Fluid mechanics of nodal flow due to embryonic primary cilia

Breaking of left–right symmetry is crucial in vertebrate development. The role of cilia-driven flow has been the subject of many recent publications, but the underlying mechanisms remain controversial. At approximately 8 days post-fertilization, after the establishment of the dorsal–ventral and anterior–posterior axes, a depressed structure is found on the ventral side of mouse embryos, termed the ventral node. Within the node, ‘whirling’ primary cilia, tilted towards the posterior, drive a flow implicated in the initial left–right signalling asymmetry. However, the underlying fluid mechanics have not been fully and correctly explained until recently and accurate characterization is required in determining how the flow triggers the downstream signalling cascades. Using the approximation of resistive force theory, we show how the flow is produced and calculate the optimal configuration to cause maximum flow, showing excellent agreement with in vitro measurements and numerical simulation, and paralleling recent analogue experiments. By calculating numerical solutions of the slender body theory equations, we present time-dependent physically based fluid dynamics simulations of particle pathlines in flows generated by large arrays of beating cilia, showing the far-field radial streamlines predicted by the theory

Mathematical modelling of cilia driven transport of biological fluids

Cilia-driven flow occurs in the airway surface liquid, in the female and male reproductive tracts and enables symmetry-breaking in the embryonic node. Viscoelastic rheology is found in healthy states in some systems, whereas in others may characterise disease, motivating the development of mathematical models that take this effect into account. We derive the fundamental solution for linear viscoelastic flow, which is subsequently used as a basis for slender-body theory. Our numerical algorithm allows efficient computation of three-dimensional time-dependent flow, bending moments, power and particle transport. We apply the model to the large-amplitude motion of a single cilium in a linear Maxwell liquid. A relatively short relaxation time of just 0.032 times the beat period significantly reduces forces, bending moments, power and particle transport, the last variable exhibiting exponential decay with relaxation time. A test particle is propelled approximately one-fifth as quickly along the direction of cilia beating for scaled relaxation time 0.032 as in the Newtonian case, and mean volume flow is abolished, emphasizing the sensitivity of cilia function to fluid rheology. These results may have implications for flow in the airways, where the transition from Newtonian to viscoelastic rheology in the peri-ciliary fluid may reduce clearance

A viscoelastic traction layer model of mucociliary flow

A new mathematical model of the transport of mucus and periciliary liquid (PCL) in the airways by cilia is presented. Mucus is represented by a linearly viscoelastic fluid, the mat of cilia is modelled as an ‘active porous medium.’ The propulsive effect of the cilia is modelled by a time-dependent force acting in a shear-thinned ‘traction layer’ between the mucus and the PCL. The effects of surface and interface tension are modelled by constraining the mucus free surface and mucus–PCL interface to be flat. It is assumed that the epithelium is impermeable to fluid. Using Fourier series, the system is converted into ODEs and solved numerically. We calculate values for mean mucus speed close to those observed by Matsui et~al. [{J. Clin. Invest.}, 102(6):1125’1131, 1998], (~40 μms−1). We obtain more detail regarding the dynamics of the flow and the nonlinear relationships between physical parameters in healthy and diseased states than in previously published models. Pressure gradients in the PCL caused by interface and surface tension are vital to ensuring efficient transport of mucus, and the role of the mucus–PCL interface appears to be to support such pressure gradients, ensuring efficient transport. Mean transport of PCL is found to be very small, consistent with previous analyses, providing insight into theories regarding the normal tonicity of PCL

Mammalian Sperm Motility: Observation and Theory

Mammalian spermatozoa motility is a subject of growing importance because of rising human infertility and the possibility of improving animal breeding. We highlight opportunities for fluid and continuum dynamics to provide novel insights concerning the mechanics of these specialized cells, especially during their remarkable journey to the egg. The biological structure of the motile sperm appendage, the flagellum, is described and placed in the context of the mechanics underlying the migration of mammalian sperm through the numerous environments of the female reproductive tract. This process demands certain specific changes to flagellar movement and motility for which further mechanical insight would be valuable, although this requires improved modeling capabilities, particularly to increase our understanding of sperm progression in vivo. We summarize current theoretical studies, highlighting the synergistic combination of imaging and theory in exploring sperm motility, and discuss the challenges for future observational and theoretical studies in understanding the underlying mechanics.\ud Acronyms and Definitions\ud Acrosome: the cap of the sperm head containing enzymes allowing penetration of the zona pellucida via the acrosome reaction\ud Adenosine triphosphate (ATP): the currency unit of chemical energy transfer in living cells\ud Axoneme: a phylogenetically conserved structure within the eukaryotic flagellum consisting of a ring of nine microtubule doublets and a central pair, frequently referred to as 9 + 2\ud Bending moment density: the moment per unit length associated with flagellar bending; it can be divided into a hydrodynamic moment, an elastic moment (from the flagellar bending stiffness), an active moment (generated by dyneins exerting forces between adjacent microtubule doublets), and a passive moment resisting shear\ud Capacitation: the physiological state of a sperm required for fertilization, which is accompanied by the motility patterns associated with hyperactivation, characterized in saline by high-amplitude asymmetric beating\ud Central pair: a pair of microtubules along the length of the axoneme, symmetrically and slightly offset from the axoneme centerline\ud Cumulus oophorus: the outer vestment of the mammalian egg consisting of hundreds of cells radiating out from the egg embedded within a non-Newtonian hyaluronic acid gel\ud Dynein: a molecular motor within the axoneme, attached between adjacent microtubule doublets, that exerts a shearing force to induce axonemal bending\ud Flagellum: a motile cellular appendage that drives the swimming of sperm and other cells; this article focuses on the eukaryotic flagellum\ud Microtubule doublet: a pair of proteinaceous filament structures running the length of the axoneme; dyneins drive their bending, which induces flagellar motion\ud Mid-piece: the region of a sperm flagellum with a mitochondrial sheath, where ATP is generated\ud Oocyte: the egg\ud Outer dense fibers and fibrous sheath: accessory structures reinforcing the mammalian sperm flagellum; the combined axoneme and accessory structures are referred to as 9+9+2\ud Resistive-force theory: an approximation for the local drag of a slender filament element in Stokes flow (or a viscoelastic generalization thereof)\ud Rheotaxis: directed motility in response to the influence of fluid flow\ud Shear: in the context of the flagellum, the relative movement of adjacent microtubule doublets\ud Slender-body theory: an improved approximation for the local drag on a slender filament element in Stokes flow (or a viscoelastic generalization thereof)\ud Zona pellucida: a tough glycoprotein coat between the human egg and the cumulus oophorus, which a sperm must penetrate for successful fertilizatio

Comment on "Why is the DNA denaturation transition first order?"

In this comment we argue that while the conclusions in the original paper (Y. Kafri, D. Mukamel and L. Peliti, Phys. Rev. Lett. 85, 4988 (2000)) are correct for asymptotically long DNA chains, they do not apply to the chains used in typical experiments. In the added last paragraph, we point out that for real DNA the average distance between denatured loops is not of the order of the persistence length of a single-stranded chain but much larger. This corroborates our reasoning that the double helix between loops is quite rigid, and thereby our conclusion.Comment: 1 page, REVTeX. Last paragraph adde

Self-regulation for and of learning : student insights for online success in a Bachelor of Nursing Program in regional Australia

The blended online digital (BOLD) approach to teaching is popular within many universities. Despite this popularity, our understanding of the experiences of students making the transition to online learning is limited, specifically an examination of those elements associated with success. The aim of this study is to explore the experiences of students transitioning from a traditional mode of delivery to a more online approach in an inaugural BOLD Bachelor of Nursing program at a regional multi-campus institution in Victoria, Australia. Fifteen students across two regional campuses participated in one of four focus groups. This qualitative exploration of students’ experience contributes to contemporary insights into how we might begin to develop programs of study that help students develop self-regulation. A modified method of thematic analysis of phenomenological data was employed to analyse the focus group interview data to identify themes that represent the meaning of the transition experience for students. This qualitative exploration of students’ experience contributes to contemporary insights into how we might begin to develop programs of study that help students develop self-regulation

Spatial Graphs with Local Knots

It is shown that for any locally knotted edge of a 3-connected graph in $S^3$, there is a ball that contains all of the local knots of that edge and is unique up to an isotopy setwise fixing the graph. This result is applied to the study of topological symmetry groups of graphs embedded in $S^3$.Comment: 20 pages, 3 figures; in v. 2 the proof of Theorem 1 has been clarified, and other minor revisions have been mad

Bacteria Monitoring in the Upper Illinois River Watershed

This project focuses on the Upper Illinois River Watershed (UIRW; HUC 11110103), which is within the Boston Mountains and Ozark Highlands ecoregions in northwest Arkansas. Headwaters of the Illinois River originate near Hogeye, Arkansas and flow north through Savoy, then west into Oklahoma near Watts. The UIRW drains an area of 1952 km2 , of which 50.3% is pasture and grassland, 35.9% is forest, 8.8% is urban and suburban, 4.3% is transitional and 0.3% is water (Arkansaswater.org, 2015). Land use throughout the watershed is also changing, with increases in residential, commercial and industrial development. The IRW has been designated a priority watershed for the Arkansas Natural Resources Commission (ANRC) 319 Nonpoint Source Program

Human sperm accumulation near surfaces: a simulation study

A hybrid boundary integral/slender body algorithm for modelling flagellar cell motility is presented. The algorithm uses the boundary element method to represent the ‘wedge-shaped’ head of the human sperm cell and a slender body theory representation of the flagellum. The head morphology is specified carefully due to its significant effect on the force and torque balance and hence movement of the free-swimming cell. The technique is used to investigate the mechanisms for the accumulation of human spermatozoa near surfaces. Sperm swimming in an infinite fluid, and near a plane boundary, with prescribed planar and three-dimensional flagellar waveforms are simulated. Both planar and ‘elliptical helicoid’ beating cells are predicted to accumulate at distances of approximately 8.5–22 μm from surfaces, for flagellar beating with angular wavenumber of 3π to 4π. Planar beating cells with wavenumber of approximately 2.4π or greater are predicted to accumulate at a finite distance, while cells with wavenumber of approximately 2π or less are predicted to escape from the surface, likely due to the breakdown of the stable swimming configuration. In the stable swimming trajectory the cell has a small angle of inclination away from the surface, no greater than approximately 0.5°. The trapping effect need not depend on specialized non-planar components of the flagellar beat but rather is a consequence of force and torque balance and the physical effect of the image systems in a no-slip plane boundary. The effect is relatively weak, so that a cell initially one body length from the surface and inclined at an angle of 4°–6° towards the surface will not be trapped but will rather be deflected from the surface. Cells performing rolling motility, where the flagellum sweeps out a ‘conical envelope’, are predicted to align with the surface provided that they approach with sufficiently steep angle. However simulation of cells swimming against a surface in such a configuration is not possible in the present framework. Simulated human sperm cells performing a planar beat with inclination between the beat plane and the plane-of-flattening of the head were not predicted to glide along surfaces, as has been observed in mouse sperm. Instead, cells initially with the head approximately 1.5–3 μm from the surface were predicted to turn away and escape. The simulation model was also used to examine rolling motility due to elliptical helicoid flagellar beating. The head was found to rotate by approximately 240° over one beat cycle and due to the time-varying torques associated with the flagellar beat was found to exhibit ‘looping’ as has been observed in cells swimming against coverslips