Role of spatial heterogeneity in the collective dynamics of cilia beating in a minimal one-dimensional model

Abstract

§Cilia are elastic hairlike protuberances of the cell membrane found in various unicellular organisms and in several tissues of most living organisms. In some tissues such as the airway tissues of the lung, the coordinated beating of cilia induce a fluid flow of crucial importance as it allows the continuous cleaning of our bronchia, known as mucociliary clearance. While most of the models addressing the question of collective dynamics and metachronal wave consider homogeneous carpets of cilia, experimental observations rather show that cilia clusters are heterogeneously distributed over the tissue surface. The purpose of this paper is to investigate the role of spatial heterogeneity on the coherent beating of cilia using a very simple one dimensional model for cilia known as the rower model. We systematically study systems consisting of a few rowers to hundreds of rowers and we investigate the conditions for the emergence of collective beating. When considering a small number of rowers, a phase drift occurs, hence a bifurcation in beating frequency is observed as the distance between rowers clusters is changed. In the case of many rowers, a distribution of frequencies is observed. We found in particular the pattern of the patchy structure that shows the best robustness in collective beating behavior, as the density of cilia is varied over a wide range.

Self-organization of self-clearing beating patterns in an array of locally interacting ciliated cells formulated as an adaptive Boolean network

“…As very recently pointed out in [47], theoretical studies investigating the collective dynamics of hydrodynamically interacting cilia have, so far, usually considered homogeneous carpets of cilia. In [47] the role of a spatial heterogeneous ciliary distribution on coherent ciliary beating using one dimensional arrays of cilia represented by rowers has been investigated.…”

“…As very recently pointed out in [47], theoretical studies investigating the collective dynamics of hydrodynamically interacting cilia have, so far, usually considered homogeneous carpets of cilia. In [47] the role of a spatial heterogeneous ciliary distribution on coherent ciliary beating using one dimensional arrays of cilia represented by rowers has been investigated. It is particularly shown that the phase coherence of random clustered distributions of rowers are less sensitive to variations of the number density than (homogeneously) random distributions of rowers.…”

Thermodynamic cost of synchronizing a population of beating cilia

“…, N. The phase variable φ i represents the beating motion of the i-th cilium characterized with its own natural driving frequency ω i . With an assumption of cilium-to-cilium heterogeneity, which is supported by experimental observations [17,18], the natural frequency ω i in the first term could be chosen from a distribution function, g(ω). In this study, we consider a Gaussian function, g(ω i ) = N(ω m , σ 2 ), with the mean ω m and variance σ 2 , as a model of heterogeneous cilia population.…”

Role of intercellular coupling and delay on the synchronization of genetic oscillators

“…Sustained oscillations are ubiquitous in biological systems from oscillating gene products inside cells to spontaneous beating of cilia and flagella on the cell surface microorganisms and airway epithelium [1]- [3]. Diverse cell types are known to encode genetic oscillators or clocks that function in circadian timekeeping [4], [5], cell cycle regulation [6], [7] and rhythmic structure formations across organisms during development [8]- [10].…”