Hydromechanics of low-Reynolds-number flow. Part 1. Rotation of axisymmetric prolate bodies

The present series of studies is concerned with low-Reynolds-number flow in general; the main objective is to develop an effective method of solution for arbitrary body shapes. In this first part, consideration is given to the viscous flow generated by pure rotation of an axisymmetric body having an arbitrary prolate form, the inertia forces being assumed to have a negligible effect on the flow. The method of solution explored here is based on a spatial distribution of singular torques, called rotlets, by which the rotational motion of a given body can be represented. Exact solutions are determined in closed form for a number of body shapes, including the dumbbell profile, elongated rods and some prolate forms. In the special case of prolate spheroids, the present exact solution agrees with that of Jeffery (1922), this being one of very few cases where previous exact solutions are available for comparison. The velocity field and the total torque are derived, and their salient features discussed for several representative and limiting cases. The moment coefficient C[sub]M = M/(8[pi][mu][omega sub 0]ab^2) (M being the torque of an axisymmetric body of length 2a and maximum radius b rotating at angular velocity [omega], about its axis in a fluid of viscosity [mu]) of various body shapes so far investigated is found to lie between 2/3 and 1, usually very near unity for not extremely slender bodies. For slender bodies, an asymptotic relationship is found between the nose curvature and the rotlet strength near the end of its axial distribution. It is also found that the theory, when applied to slender bodies, remains valid at higher Reynolds numbers than was originally intended, so long as they are small compared with the (large) aspect ratio of the body, before the inertia effects become significant

Kinematics of the swimming of Spiroplasma

\emph{Spiroplasma} swimming is studied with a simple model based on resistive-force theory. Specifically, we consider a bacterium shaped in the form of a helix that propagates traveling-wave distortions which flip the handedness of the helical cell body. We treat cell length, pitch angle, kink velocity, and distance between kinks as parameters and calculate the swimming velocity that arises due to the distortions. We find that, for a fixed pitch angle, scaling collapses the swimming velocity (and the swimming efficiency) to a universal curve that depends only on the ratio of the distance between kinks to the cell length. Simultaneously optimizing the swimming efficiency with respect to inter-kink length and pitch angle, we find that the optimal pitch angle is 35.5$^\circ$ and the optimal inter-kink length ratio is 0.338, values in good agreement with experimental observations.Comment: 4 pages, 5 figure

Floppy swimming: Viscous locomotion of actuated elastica

Actuating periodically an elastic filament in a viscous liquid generally breaks the constraints of Purcell's scallop theorem, resulting in the generation of a net propulsive force. This observation suggests a method to design simple swimming devices - which we call "elastic swimmers" - where the actuation mechanism is embedded in a solid body and the resulting swimmer is free to move. In this paper, we study theoretically the kinematics of elastic swimming. After discussing the basic physical picture of the phenomenon and the expected scaling relationships, we derive analytically the elastic swimming velocities in the limit of small actuation amplitude. The emphasis is on the coupling between the two unknowns of the problems - namely the shape of the elastic filament and the swimming kinematics - which have to be solved simultaneously. We then compute the performance of the resulting swimming device, and its dependance on geometry. The optimal actuation frequency and body shapes are derived and a discussion of filament shapes and internal torques is presented. Swimming using multiple elastic filaments is discussed, and simple strategies are presented which result in straight swimming trajectories. Finally, we compare the performance of elastic swimming with that of swimming microorganisms.Comment: 23 pages, 6 figure

Swimming in circles: Motion of bacteria near solid boundaries

Near a solid boundary, E. coli swims in clockwise circular motion. We provide a hydrodynamic model for this behavior. We show that circular trajectories are natural consequences of force-free and torque-free swimming, and the hydrodynamic interactions with the boundary, which also leads to a hydrodynamic trapping of the cells close to the surface. We compare the results of the model with experimental data and obtain reasonable agreement. In particular, we show that the radius of curvature of the trajectory increases with the length of the bacterium body.Comment: Also available at http://people.deas.harvard.edu/~lauga

Discrete cilia modelling with singularity distributions

We discuss in detail techniques for modelling flows due to finite and infinite arrays of beating cilia. An efficient technique, based on concepts from previous ‘singularity models’ is described, that is accurate in both near and far-fields. Cilia are modelled as curved slender ellipsoidal bodies by distributing Stokeslet and potential source dipole singularities along their centrelines, leading to an integral equation that can be solved using a simple and efficient discretisation. The computed velocity on the cilium surface is found to compare favourably with the boundary condition. We then present results for two topics of current interest in biology. 1) We present the first theoretical results showing the mechanism by which rotating embryonic nodal cilia produce a leftward flow by a ‘posterior tilt,’ and track particle motion in an array of three simulated nodal cilia. We find that, contrary to recent suggestions, there is no continuous layer of negative fluid transport close to the ciliated boundary. The mean leftward particle transport is found to be just over 1 μm/s, within experimentally measured ranges. We also discuss the accuracy of models that represent the action of cilia by steady rotlet arrays, in particular, confirming the importance of image systems in the boundary in establishing the far-field fluid transport. Future modelling may lead to understanding of the mechanisms by which morphogen gradients or mechanosensing cilia convert a directional flow to asymmetric gene expression. 2) We develop a more complex and detailed model of flow patterns in the periciliary layer of the airway surface liquid. Our results confirm that shear flow of the mucous layer drives a significant volume of periciliary liquid in the direction of mucus transport even during the recovery stroke of the cilia. Finally, we discuss the advantages and disadvantages of the singularity technique and outline future theoretical and experimental developments required to apply this technique to various other biological problems, particularly in the reproductive system

Genetic Modulation of Rpd3 Expression Impairs Long-Term Courtship Memory in Drosophila

There is increasing evidence that regulation of local chromatin structure is a critical mechanism underlying the consolidation of long-term memory (LTM), however considerably less is understood about the specific mechanisms by which these epigenetic effects are mediated. Furthermore, the importance of histone acetylation in Drosophila memory has not been reported. The histone deacetylase (HDAC) Rpd3 is abundant in the adult fly brain, suggesting a post-mitotic function. Here, we investigated the role of Rpd3 in long-term courtship memory in Drosophila. We found that while modulation of Rpd3 levels predominantly in the adult mushroom body had no observed impact on immediate recall or one-hour memory, 24-hour LTM was severely impaired. Surprisingly, both overexpression as well as RNAi-mediated knockdown of Rpd3 resulted in impairment of long-term courtship memory, suggesting that the dose of Rpd3 is critical for normal LTM

A separated vortex ring underlies the flight of the dandelion

Wind-dispersed plants have evolved ingenious ways to lift their seeds1,2. The common dandelion uses a bundle of drag-enhancing bristles (the pappus) that helps to keep their seeds aloft. This passive flight mechanism is highly effective, enabling seed dispersal over formidable distances3,4; however, the physics underpinning pappus-mediated flight remains unresolved. Here we visualized the flow around dandelion seeds, uncovering an extraordinary type of vortex. This vortex is a ring of recirculating fluid, which is detached owing to the flow passing through the pappus. We hypothesized that the circular disk-like geometry and the porosity of the pappus are the key design features that enable the formation of the separated vortex ring. The porosity gradient was surveyed using microfabricated disks, and a disk with a similar porosity was found to be able to recapitulate the flow behaviour of the pappus. The porosity of the dandelion pappus appears to be tuned precisely to stabilize the vortex, while maximizing aerodynamic loading and minimizing material requirements. The discovery of the separated vortex ring provides evidence of the existence of a new class of fluid behaviour around fluid-immersed bodies that may underlie locomotion, weight reduction and particle retention in biological and manmade structures

Age-Related Memory Impairment Is Associated with Disrupted Multivariate Epigenetic Coordination in the Hippocampus

Mounting evidence linking epigenetic regulation to memory-related synaptic plasticity raises the possibility that altered chromatin modification dynamics might contribute to age-dependent cognitive decline. Here we show that the coordinated orchestration of both baseline and experience-dependent epigenetic regulation seen in the young adult hippocampus is lost in association with cognitive aging. Using a well-characterized rat model that reliably distinguishes aged individuals with significant memory impairment from others with normal memory, no single epigenetic mark or experience-dependent modification in the hippocampus uniquely predicted differences in the cognitive outcome of aging. The results instead point to a multivariate pattern in which modification-specific, bidirectional chromatin regulation is dependent on recent behavioral experience, chronological age, cognitive status, and hippocampal region. Whereas many epigenetic signatures were coupled with memory capacity among young adults and aged rats with preserved cognitive function, such associations were absent among aged rats with deficits in hippocampal memory. By comparison with the emphasis in current preclinical translational research on promoting chromatin modifications permissive for gene expression, our findings suggest that optimally successful hippocampal aging may hinge instead on enabling coordinated control across the epigenetic landscape

Stress-induced lipocalin-2 controls dendritic spine formation and neuronal activity in the amygdala.

This is a freely-available open access publication. Please cite the published version which is available via the DOI link in this record.Behavioural adaptation to psychological stress is dependent on neuronal plasticity and dysfunction at this cellular level may underlie the pathogenesis of affective disorders such as depression and post-traumatic stress disorder. Taking advantage of genome-wide microarray assay, we performed detailed studies of stress-affected transcripts in the amygdala - an area which forms part of the innate fear circuit in mammals. Having previously demonstrated the role of lipocalin-2 (Lcn-2) in promoting stress-induced changes in dendritic spine morphology/function and neuronal excitability in the mouse hippocampus, we show here that the Lcn-2 gene is one of the most highly upregulated transcripts detected by microarray analysis in the amygdala after acute restraint-induced psychological stress. This is associated with increased Lcn-2 protein synthesis, which is found on immunohistochemistry to be predominantly localised to neurons. Stress-naïve Lcn-2(-/-) mice show a higher spine density in the basolateral amygdala and a 2-fold higher rate of neuronal firing rate compared to wild-type mice. Unlike their wild-type counterparts, Lcn-2(-/-) mice did not show an increase in dendritic spine density in response to stress but did show a distinct pattern of spine morphology. Thus, amygdala-specific neuronal responses to Lcn-2 may represent a mechanism for behavioural adaptation to psychological stress.Marie Curie Excellence Grant from the European Commission.Medical Research Council Project GrantCOST Action ECMNe