Measuring Gaussian rigidity using curved substrates

The Gaussian (saddle splay) rigidity of fluid membranes controls their equilibrium topology but is notoriously difficult to measure. In lipid mixtures, typical of living cells, linear interfaces separate liquid ordered (LO) from liquid disordered (LD) bilayer phases at subcritical temperatures. Here we consider such membranes supported by curved supports that thereby control the membrane curvatures. We show how spectral analysis of the fluctuations of the LO-LD interface provides a novel way of measuring the difference in Gaussian rigidity between the two phases. We provide a number of conditions for such interface fluctuations to be both experimentally measurable and sufficiently sensitive to the value of the Gaussian rigidity, whilst remaining in the perturbative regime of our analysis.Comment: 5 pages, 3 figures. v2: version accepted for publicatio

Dynamics of lipid membrane tubes

Membrane tubes are structures ubiquitous in cells, and understanding their dynamics and morphology is of vital importance for cellular biophysics. This thesis will discuss several aspects of the dynamics of membrane tubes in situations where they are driven out of equilibrium by various biologically inspired processes. We analyse the inflation of membrane tubes and their subsequent instability due to ion pumps driving an osmotic pressure difference. This is inspired by the structure of an organelle called the contractile vacuole complex, and leads to a new instability with a much longer natural wavelength than a typical pearling instability. The stability of membrane tubes with a shear in the membrane ow is analysed and a novel helical instability which acts to amplify the fluctuations is found. We discuss the relevance of this instability in the process of dynamin-mediated tube scission. Finally we consider the dynamics and fluctuations of a membrane tube with active forces acting on it

Hydro-osmotic instabilities in active membrane tubes

We study a membrane tube with unidirectional ion pumps driving an osmotic pressure difference. A pressure driven peristaltic instability is identified, qualitatively distinct from similar tension-driven Rayleigh type instabilities on membrane tubes. We discuss how this instability could be related to the function and biogenesis of membrane bound organelles, in particular the contractile vacuole complex. The unusually long natural wavelength of this instability is in agreement with that observed in cells

Dynamics of passive and active membrane tubes

Utilising Onsager's variational formulation, we derive dynamical equations for the relaxation of a fluid membrane tube in the limit of small deformation, allowing for a contrast of solvent viscosity across the membrane and variations in surface tension due to membrane incompressibility. We compute the relaxation rates, recovering known results in the case of purely axis-symmetric perturbations and making new predictions for higher order (azimuthal) $m$-modes. We analyse the long and short wavelength limits of these modes by making use of various asymptotic arguments. We incorporate stochastic terms to our dynamical equations suitable to describe both passive thermal forces and non-equilibrium active forces. We derive expressions for the fluctuation amplitudes, an effective temperature associated with active fluctuations, and the power spectral density for both the thermal and active fluctuations. We discuss an experimental assay that might enable measurement of these fluctuations to infer the properties of the active noise. Finally we discuss our results in the context of active membranes more generally and give an overview of some open questions in the field.Comment: 14 pages, 9 figure

Chiral active membranes : odd mechanics, spontaneous flows, and shape instabilities

Living systems are chiral on multiple scales, from constituent biopolymers to large scale morphology, and their active mechanics is both driven by chiral components and serves to generate chiral morphologies. We describe the mechanics of active fluid membranes in coordinate-free form, with focus on chiral contributions to the stress. These generate geometric “odd elastic” forces in response to mean curvature gradients but directed perpendicularly. As a result, they induce tangential membrane flows that circulate around maxima and minima of membrane curvature. When the normal viscous force amplifies perturbations the membrane shape can become linearly unstable giving rise to shape instabilities controlled by an active Scriven-Love number. We describe examples for spheroids, membranes tubes, and helicoids, discussing the relevance and predictions such examples make for a variety of biological systems from the subcellular to tissue level

Mathematical Modelling of the Impact of Liquid Properties on Droplet Size from Flat Fan Nozzles

Flat fan nozzles atomize crop protection products, breaking them into droplets. Droplet size matters - smaller droplets give better perfor- mance, but very small droplets drift. We want to use mathematical models to better understand how liquid properties affect droplet size. There are three types of breakup: wavy sheet, perforation, and rim. In wavy sheet breakup, increasing viscosity or surface tension increases droplet size. To investigate further, we carry out direct numerical simulations of jet breakup, which show that suface tension has little effect, but increasing viscosity leads to fewer droplets. Decreasing the jet velocity also results in fewer droplets, with a wider size distribution. Each type of breakup involves primary breakup into cylinders of fluid, then secondary breakup into droplets. We thus consider the breakup of a cylinder of fluid. Direct numerical simulations suggest that within the tested parameter range viscosity has little impact on droplet size, however it does influence the timescale on which the instability evolves considerably. Linear stability analysis suggests that increasing viscosity increases the wavelength of the most unstable mode, which we expect leads to larger droplets, and that it reduces the rate of breakup. Perforations - holes in the sheet - also lead to breakup. We find how the length fraction of the sheet that is void changes with time. After breakup, the droplets continue to evolve. We develop a model, based on a transport equation, for this process. A key parameter is the breakup rate constant - larger values lead to more breakup, fewer large droplets, and a narrower size distribution. Together, these mathematical approaches improve our understanding of how droplets form, and can be used to guide experimental work

Dynamique des tubes à membrane lipidique

Membrane tubes are structures ubiquitous in cells, and understanding their dynamics and morphology is of vital importance for cellular biophysics. This thesis will discuss several aspects of the dynamics of membrane tubes in situations where they are driven out of equilibrium by various biologically inspired processes. We analyse the inflation of membrane tubes and their subsequent instability due to ion pumps driving an osmotic pressure difference. This is inspired by the structure of an organelle called the contractile vacuole complex, and leads to a new instability with a much longer natural wavelength than a typical Pearling instability. The stability of membrane tubes with a shear in the membrane flow is analysed and a novel helical instability which acts to amplify the fluctuations is found. We discuss the relevance of this instability in the process of Dynamin mediated tube scission. Finally we consider the dynamics and fluctuations of a membrane tube with active forces acting on it.Les tubes membranaires sont des structures omniprésentes dans les cellules, et la compréhension de leur dynamique et de leur morphologie est d'une importance cruciale pour la biophysique cellulaire. Cette thèse aborde plusieurs aspects de la dynamique des tubes membranaires dans des situations où ils sont déséquilibrés par divers processus inspirés par des phénomènes biologiques. Nous analysons le gonflement de tubes due à des pompes ioniques entraînant une différence de pression osmotique, ainsi que les instabilités qui en résultent. Ceci est inspiré par la structure d'un organelle appelé le vacuole contractile, et conduit à une nouvelle instabilité avec une longueur d'onde naturelle beaucoup plus longue que celle résultant d'une instabilité de type pearling. La stabilité des tubes membranaires présentant un écoulement de cisaillement à leur surface est également analysée. Nous avons découvert et analysé une nouvelle instabilité hélicoïdale qui conduit à l’amplification des fluctuations du tube. Nous discutons de la pertinence de cette instabilité dans le processus de scission des tubes induite par la dynamine. Enfin, nous considérons la dynamique et les fluctuations d'un tube membranaire sur lequel agissent des forces actives

Dynamique des tubes à membrane lipidique

Les tubes membranaires sont des structures omniprésentes dans les cellules, et la compréhension de leur dynamique et de leur morphologie est d'une importance cruciale pour la biophysique cellulaire. Cette thèse aborde plusieurs aspects de la dynamique des tubes membranaires dans des situations où ils sont déséquilibrés par divers processus inspirés par des phénomènes biologiques. Nous analysons le gonflement de tubes due à des pompes ioniques entraînant une différence de pression osmotique, ainsi que les instabilités qui en résultent. Ceci est inspiré par la structure d'un organelle appelé le vacuole contractile, et conduit à une nouvelle instabilité avec une longueur d'onde naturelle beaucoup plus longue que celle résultant d'une instabilité de type pearling. La stabilité des tubes membranaires présentant un écoulement de cisaillement à leur surface est également analysée. Nous avons découvert et analysé une nouvelle instabilité hélicoïdale qui conduit à l’amplification des fluctuations du tube. Nous discutons de la pertinence de cette instabilité dans le processus de scission des tubes induite par la dynamine. Enfin, nous considérons la dynamique et les fluctuations d'un tube membranaire sur lequel agissent des forces actives.Membrane tubes are structures ubiquitous in cells, and understanding their dynamics and morphology is of vital importance for cellular biophysics. This thesis will discuss several aspects of the dynamics of membrane tubes in situations where they are driven out of equilibrium by various biologically inspired processes. We analyse the inflation of membrane tubes and their subsequent instability due to ion pumps driving an osmotic pressure difference. This is inspired by the structure of an organelle called the contractile vacuole complex, and leads to a new instability with a much longer natural wavelength than a typical Pearling instability. The stability of membrane tubes with a shear in the membrane flow is analysed and a novel helical instability which acts to amplify the fluctuations is found. We discuss the relevance of this instability in the process of Dynamin mediated tube scission. Finally we consider the dynamics and fluctuations of a membrane tube with active forces acting on it

Shear-driven instabilities of membrane tubes and dynamin-induced scission

Motivated by the mechanics of dynamin-mediated membrane tube fission, we analyze the stability of fluid membrane tubes subjected to shear flow in azimuthal direction. We find a novel helical instability driven by the membrane shear flow which results in a nonequilibrium steady state for the tube fluctuations. This instability has its onset at shear rates that may be physiologically accessible under the action of dynamin and could also be probed using in vitro experiments on membrane nanotubes, e.g., using magnetic tweezers. We discuss how such an instability may play a role in the mechanism for dynamin-mediated membrane tube fission