Transitions in synchronization states of model cilia through basal-connection coupling

Despite evidence for a hydrodynamic origin of flagellar synchronization between different eukaryotic cells, recent experiments have shown that in single multi-flagellated organisms, coordination hinges instead on direct basal body connections. The mechanism by which these connections leads to coordination, however, is currently not understood. Here we focus on the model biflagellate {\it Chlamydomonas reinhardtii}, and propose a minimal model for the synchronization of its two flagella as a result of both hydrodynamic and direct mechanical coupling. A spectrum of different types of coordination can be selected, depending on small changes in the stiffness of intracellular couplings. These include prolonged in-phase and anti-phase synchronization, as well as a range of multistable states induced by spontaneous symmetry breaking of the system. Linking synchrony to intracellular stiffness could lead to the use of flagellar dynamics as a probe for the mechanical state of the cell.Comment: 14 pages, 9 figure

Metachronal waves in the flagellar beating of Volvox and their hydrodynamic origin.

Groups of eukaryotic cilia and flagella are capable of coordinating their beating over large scales, routinely exhibiting collective dynamics in the form of metachronal waves. The origin of this behavior--possibly influenced by both mechanical interactions and direct biological regulation--is poorly understood, in large part due to a lack of quantitative experimental studies. Here we characterize in detail flagellar coordination on the surface of the multicellular alga Volvox carteri, an emerging model organism for flagellar dynamics. Our studies reveal for the first time that the average metachronal coordination observed is punctuated by periodic phase defects during which synchrony is partial and limited to specific groups of cells. A minimal model of hydrodynamically coupled oscillators can reproduce semi-quantitatively the characteristics of the average metachronal dynamics, and the emergence of defects. We systematically study the model's behaviour by assessing the effect of changing intrinsic rotor characteristics, including oscillator stiffness and the nature of their internal driving force, as well as their geometric properties and spatial arrangement. Our results suggest that metachronal coordination follows from deformations in the oscillators' limit cycles induced by hydrodynamic stresses, and that defects result from sufficiently steep local biases in the oscillators' intrinsic frequencies. Additionally, we find that random variations in the intrinsic rotor frequencies increase the robustness of the average properties of the emergent metachronal waves.This work was supported in part by the EPSRC (M.P.), ERC Advanced Investigator grant 247333 and a Senior Investigator Award from the Wellcome Trust.This is the final version. It was first published by Royal Society Publishing at http://rsif.royalsocietypublishing.org/content/12/108/20141358

Point torque representations of ciliary flows

Ciliary flows are generated by a vast array of eukaryotic organisms, from unicellular algae to mammals, and occur in a range of different geometrical configurations. We employ a point torque -- or `rotlet' -- model to capture the time-averaged ciliary flow above a planar rigid wall. We demonstrate the advantages (i.e. accuracy and computational efficiency) of using this, arguably simpler approach compared to other singularity-based models in Stokes flows. Then, in order to model ciliary flows in confined spaces, we extend the point torque solution to a bounded domain between two plane parallel no-slip walls. The flow field is resolved using the method of images and Fourier transforms, and we analyze the role of confinement by comparing the resultant fluid velocity to that of a rotlet near a single wall. Our results suggest that the flow field of a single cilium is not changed significantly by the confinement, even when the distance between the walls is commensurate with the cilium's length.Comment: 20 pages, 13 figure

Long-range interactions, wobbles, and phase defects in chains of model cilia

Eukaryotic cilia and flagella are chemo-mechanical oscillators capable of generating long-range coordinated motions known as metachronal waves. Pair synchronization is a fundamental requirement for these collective dynamics, but it is generally not sufficient for collective phase-locking, chiefly due to the effect of long-range interactions. Here we explore experimentally and numerically a minimal model for a ciliated surface: hydrodynamically coupled oscillators rotating above a no-slip plane. Increasing their distance from the wall profoundly affects the global dynamics, due to variations in hydrodynamic interaction range. The array undergoes a transition from a traveling wave to either a steady chevron pattern or one punctuated by periodic phase defects. Within the transition between these regimes the system displays behavior reminiscent of chimera states

Simultaneous visualization of flow fields and oxygen concentrations to unravel transport and metabolic processes in biological systems

From individual cells to whole organisms, O2 transport unfolds across micrometer- tomillimeter-length scales and can change within milliseconds in response to fluid flows and organismal behavior. The spatiotemporal complexity of these processes makes the accurate assessment ofO2 dynamics via currently availablemethods difficult or unreliable. Here, we present ‘‘sensPIV,’’ a method to simultaneously measure O2 concentrations and flow fields. By tracking O2-sensitive microparticles in flow using imaging technologies that allow for instantaneous referencing,we measuredO2 transport within (1) microfluidic devices, (2) sinking model aggregates, and (3) complex colony-forming corals. Through the use of sensPIV, we find that corals use ciliary movement to link zones of photosynthetic O2 production to zones of O2 consumption. SensPIV can potentially be extendable to study flow-organism interactions across many life-science and engineering applications

Hydrodynamic synchronization and metachronal waves on the surface of the colonial alga Volvox carteri

From unicellular ciliates to the respiratory epithelium, carpets of cilia display metachronal waves, long-wavelength phase modulations of the beating cycles, which theory suggests may arise from hydrodynamic coupling. Experiments have been limited by a lack of organisms suitable for systematic study of flagella and the flows they create. Using time-resolved particle image velocimetry, we report the discovery of metachronal waves on the surface of the colonial alga Volvox carteri, whose large size and ease of visualization make it an ideal model organism for these studies. An elastohydrodynamic model of weakly coupled compliant oscillators, recast as interacting phase oscillators, reveals that orbit compliance can produce fast, robust synchronization in a manner essentially independent of boundary conditions, and offers an intuitive understanding of a possible mechanism leading to the emergence of metachronal waves

Flagella, flexibility and flow: Physical processes in microbial ecology

How microorganisms interact with their environment and with their conspecifics depends strongly on their mechanical properties, on the hydrodynamic signatures they generate while swimming and on fluid flows in their environment. The rich fluid-structure interaction between flagella – the appendages microorganisms use for propulsion – and the surrounding flow, has broad reaching effects for both eukaryotic and prokaryotic microorganisms. Here, we discuss selected recent advances in our understanding of the physical ecology of microorganisms, which have hinged on the ability to directly interrogate the movement of individual cells and their swimming appendages, in precisely controlled fluid environments, and to image them at appropriately fast timescales. We review how a flagellar buckling instability can unexpectedly serve a fundamental function in the motility of bacteria, we elucidate the role of hydrodynamics and flexibility in the emergent properties of groups of eukaryotic flagella, and we show how fluid flows characteristic of microbial habitats can strongly bias the migration and spatial distribution of bacteria. The topics covered here are illustrative of the potential inherent in the adoption of experimental methods and conceptual frameworks from physics in understanding the lives of microorganisms.ISSN:1951-6355ISSN:1951-640