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

Lipid membranes with an edge

Consider a lipid membrane with a free exposed edge. The energy describing this membrane is quadratic in the extrinsic curvature of its geometry; that describing the edge is proportional to its length. In this note we determine the boundary conditions satisfied by the equilibria of the membrane on this edge, exploiting variational principles. The derivation is free of any assumptions on the symmetry of the membrane geometry. With respect to earlier work for axially symmetric configurations, we discover the existence of an additional boundary condition which is identically satisfied in that limit. By considering the balance of the forces operating at the edge, we provide a physical interpretation for the boundary conditions. We end with a discussion of the effect of the addition of a Gaussian rigidity term for the membrane.Comment: 8 page

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

Energy Transduction of Isothermal Ratchets: Generic Aspects and Specific Examples Close to and Far from Equilibrium

We study the energetics of isothermal ratchets which are driven by a chemical reaction between two states and operate in contact with a single heat bath of constant temperature. We discuss generic aspects of energy transduction such as Onsager relations in the linear response regime as well as the efficiency and dissipation close to and far from equilibrium. In the linear response regime where the system operates reversibly the efficiency is in general nonzero. Studying the properties for specific examples of energy landscapes and transitions, we observe in the linear response regime that the efficiency can have a maximum as a function of temperature. Far from equilibrium in the fully irreversible regime, we find a maximum of the efficiency with values larger than in the linear regime for an optimal choice of the chemical driving force. We show that corresponding efficiencies can be of the order of 50%. A simple analytic argument allows us to estimate the efficiency in this irreversible regime for small external forces.Comment: 16 pages, 10 figure

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

Self-organized Beating and Swimming of Internally Driven Filaments

We study a simple two-dimensional model for motion of an elastic filament subject to internally generated stresses and show that wave-like propagating shapes which can propel the filament can be induced by a self-organized mechanism via a dynamic instability. The resulting patterns of motion do not depend on the microscopic mechanism of the instability but only of the filament rigidity and hydrodynamic friction. Our results suggest that simplified systems, consisting only of molecular motors and filaments could be able to show beating motion and self-propulsion.Comment: 8 pages, 2 figures, REVTe

Calibration of optical tweezers with positional detection in the back-focal-plane

We explain and demonstrate a new method of force- and position-calibration for optical tweezers with back-focal-plane photo detection. The method combines power spectral measurements of thermal motion and the response to a sinusoidal motion of a translation stage. It consequently does not use the drag coefficient of the trapped ob ject as an input. Thus, neither the viscosity, nor the size of the trapped ob ject, nor its distance to nearby surfaces need to be known. The method requires only a low level of instrumentation and can be applied in situ in all spatial dimensions. It is both accurate and precise: true values are returned, with small error-bars. We tested this experimentally, near and far from surfaces. Both position- and force-calibration were accurate to within 3%. To calibrate, we moved the sample with a piezo-electric translation stage, but the laser beam could be moved instead, e.g. by acousto-optic deflectors. Near surfaces, this precision requires an improved formula for the hydrodynamical interaction between an infinite plane and a micro-sphere in non-constant motion parallel to it. We give such a formula.Comment: Submitted to: Review of Scientific Instruments. 13 pages, 5 figures. Appendix added (hydrodynamically correct calibration

Force Dependence of the Michaelis Constant in a Two-State Ratchet Model for Molecular Motors

We present a quantitative analysis of recent data on the kinetics of ATP hydrolysis, which has presented a puzzle regarding the load dependence of the Michaelis constant. Within the framework of coarse grained two-state ratchet models, our analysis not only explains the puzzling data, but provides a modified Michaelis law, which could be useful as a guide for future experiments.Comment: 4 pages, 3 eps figures, accepted for publication on Physical Review Letter