Active phase and amplitude fluctuations of flagellar beating

The eukaryotic flagellum beats periodically, driven by the oscillatory dynamics of molecular motors, to propel cells and pump fluids. Small, but perceivable fluctuations in the beat of individual flagella have physiological implications for synchronization in collections of flagella as well as for hydrodynamic interactions between flagellated swimmers. Here, we characterize phase and amplitude fluctuations of flagellar bending waves using shape mode analysis and limit cycle reconstruction. We report a quality factor of flagellar oscillations, $Q=38.0\pm 16.7$ (mean$\pm$s.e.). Our analysis shows that flagellar fluctuations are dominantly of active origin. Using a minimal model of collective motor oscillations, we demonstrate how the stochastic dynamics of individual motors can give rise to active small-number fluctuations in motor-cytoskeleton systems.Comment: accepted for publication in Physical Review Letter

Determining physical properties of the cell cortex

Actin and myosin assemble into a thin layer of a highly dynamic network underneath the membrane of eukaryotic cells. This network generates the forces that drive cell and tissue-scale morphogenetic processes. The effective material properties of this active network determine large-scale deformations and other morphogenetic events. For example,the characteristic time of stress relaxation (the Maxwell time)in the actomyosin sets the time scale of large-scale deformation of the cortex. Similarly, the characteristic length of stress propagation (the hydrodynamic length) sets the length scale of slow deformations, and a large hydrodynamic length is a prerequisite for long-ranged cortical flows. Here we introduce a method to determine physical parameters of the actomyosin cortical layer (in vivo). For this we investigate the relaxation dynamics of the cortex in response to laser ablation in the one-cell-stage {\it C. elegans} embryo and in the gastrulating zebrafish embryo. These responses can be interpreted using a coarse grained physical description of the cortex in terms of a two dimensional thin film of an active viscoelastic gel. To determine the Maxwell time, the hydrodynamic length and the ratio of active stress and per-area friction, we evaluated the response to laser ablation in two different ways: by quantifying flow and density fields as a function of space and time, and by determining the time evolution of the shape of the ablated region. Importantly, both methods provide best fit physical parameters that are in close agreement with each other and that are similar to previous estimates in the two systems. We provide an accurate and robust means for measuring physical parameters of the actomyosin cortical layer.It can be useful for investigations of actomyosin mechanics at the cellular-scale, but also for providing insights in the active mechanics processes that govern tissue-scale morphogenesis.Comment: 17 pages, 4 figure

Length control of long cell protrusions: Rulers, timers and transport

Living cells use long tubular appendages for locomotion and sensory purposes. Hence, assembling and maintaining a protrusion of correct length is crucial for survival and overall performance. Usually the protrusions lack the machinery for the synthesis of building blocks and imports them from the cell body. What are the unique features of the transport logistics which facilitate the exchange of these building blocks between the cell and the protrusion? What kind of 'rulers' and 'timers' does the cell use for constructing its appendages of correct length on time? How do the multiple appendages coordinate and communicate among themselves during different stages of their existence? How frequently do the fluctuations drive the length of these dynamic protrusions out of the acceptable bounds? These questions are addressed from a broad perspective in this review which is organized in three parts. In part-I the list of all known cell protrusions is followed by a comprehensive list of the mechanisms of length control of cell protrusions reported in the literature. We review not only the dynamics of the genesis of the protrusions, but also their resorption and regrowth as well as regeneration after amputation. As a case study in part-II, the specific cell protrusion that has been discussed in detail is eukaryotic flagellum (also known as cilium); this choice was dictated by the fact that flagellar length control mechanisms have been studied most extensively over more than half a century in cells with two or more flagella. Although limited in scope, brief discussions on a few non-flagellar cell protrusions in part-III of this review is intended to provide a glimpse of the uncharted territories and challenging frontiers of research on subcellular length control phenomena that awaits rigorous investigations.(c) 2022 Elsevier B.V. All rights reserved

Transformation of dynamical fluctuation into coherent energy

Studies of noise-induced motions are showing that coherent energy can be extracted from some kinds of noise in a periodic ratchet. Recently, energetics of Langevin dynamics is formulated by Sekimoto [J.Phys.Soc.Jpn, 66 1234 (1997)], which can be applied to ratchet systems described by Fokker-Planck equation. In this paper, we derive an energetics of ratchet systems that can be applied to dynamical-noise-induced motion in a static potential. Analytical efficiency of the energy transformation is derived for the dynamical noise in an overdumping limit of the system. Comparison between analytical and numerical studies is performed for chaotic noise.Comment: 3 pages, 2 figures; submitted to Phys. Rev. Let

Morphogen Transport in Epithelia

We present a general theoretical framework to discuss mechanisms of morphogen transport and gradient formation in a cell layer. Trafficking events on the cellular scale lead to transport on larger scales. We discuss in particular the case of transcytosis where morphogens undergo repeated rounds of internalization into cells and recycling. Based on a description on the cellular scale, we derive effective nonlinear transport equations in one and two dimensions which are valid on larger scales. We derive analytic expressions for the concentration dependence of the effective diffusion coefficient and the effective degradation rate. We discuss the effects of a directional bias on morphogen transport and those of the coupling of the morphogen and receptor kinetics. Furthermore, we discuss general properties of cellular transport processes such as the robustness of gradients and relate our results to recent experiments on the morphogen Decapentaplegic (Dpp) that acts in the fruit fly Drosophila

Hydrodynamic flow patterns and synchronization of beating cilia

We calculate the hydrodynamic flow field generated far from a cilium which is attached to a surface and beats periodically. In the case of two beating cilia, hydrodynamic interactions can lead to synchronization of the cilia, which are nonlinear oscillators. We present a state diagram where synchronized states occur as a function of distance of cilia and the relative orientation of their beat. Synchronized states occur with different relative phases. In addition, asynchronous solutions exist. Our work could be relevant for the synchronized motion of cilia generating hydrodynamic flows on the surface of cells.Comment: 5 pages, 4 figures, v2: minor correction

Energetics of Open Systems and Chemical Potential From Micro-Dynamics Viewpoints

We present the energetic aspect of open systems which may exchange particles with their environments. Our attention shall be paid to the scale that the motion of the particles is described by the classical Langevin dynamics. Along a particular realization of the stochastic process, we study the energy transfer into the open system from the environments. We are able to clarify how much energy each particle carries when it enters or leaves the system. On the other hand, the chemical potential should be considered as the concept in macro scale, which is relevant to the free energy potential with respect to the number of particles. Keywords: open systems, stochastic energetics, chemical potentialComment: 7 pages, 1 figur

Power-law population heterogeneity governs epidemic waves

We generalize the Susceptible-Infected-Removed (SIR) model for epidemics to take into account generic effects of heterogeneity in the degree of susceptibility to infection in the population. We introduce a single new parameter corresponding to a power-law exponent of the susceptibility distribution at small susceptibilities. We find that for this class of distributions the gamma distribution is the attractor of the dynamics. This allows us to identify generic effects of population heterogeneity in a model as simple as the original SIR model which is contained as a limiting case. Because of this simplicity, numerical solutions can be generated easily and key properties of the epidemic wave can still be obtained exactly. In particular, we present exact expressions for the herd immunity level, the final size of the epidemic, as well as for the shape of the wave and for observables that can be quantified during an epidemic. In strongly heterogeneous populations, the herd immunity level can be much lower than in models with homogeneous populations as commonly used for example to discuss effects of mitigation. Using our model to analyze data for the SARS-CoV-2 epidemic in Germany shows that the reported time course is consistent with several scenarios characterized by different levels of immunity. These scenarios differ in population heterogeneity and in the time course of the infection rate, for example due to mitigation efforts or seasonality. Our analysis reveals that quantifying the effects of mitigation requires knowledge on the degree of heterogeneity in the population. Our work shows that key effects of population heterogeneity can be captured without increasing the complexity of the model. We show that information about population heterogeneity will be key to understand how far an epidemic has progressed and what can be expected for its future course