13: Membrane tubes with active pumping: water transport, vacuole formation and osmoregulation
S.C. Al-Izzi, M.S. Turner & P. Sens, arXiv:2409.14835 (under review), (2024)
The need for organisms to regulate their volume and osmolarity when surrounded by freshwater is a basic physical challenge for many bacteria, protists and algae. Taking inspiration from the contractile vacuole complex found in many protists, we discuss how simple models of active membrane tubes can give insights into the fluid and active ionic transport properties of such systems. We show that a simple membrane tube with unidirectional ion pumps, and passive ion and water channels, forms a large vacuole due to osmotically-driven water flow and that this can be used to actively pump water out of the cell interior. We discuss the use of this system as a possible minimal method for osmoregulation.
Morphodynamic descriptions of fluid deformable surfaces are relevant for a range of biological and soft matter phenomena, spanning materials that can be passive or active, as well as ordered or topological. However, a principled, geometric formulation of the correct hydrodynamic equations has remained opaque, with objective rates proving a central, contentious issue. We argue that this is due to a conflation of several important notions that must be disambiguated when describing fluid deformable surfaces. These are the Eulerian and Lagrangian perspectives on fluid motion, and three different types of gauge freedom: in the ambient space; in the parameterisation of the surface, and; in the choice of frame field on the surface. We clarify these ideas, and show that objective rates in fluid deformable surfaces are time derivatives that are invariant under the first of these gauge freedoms, and which also preserve the structure of the ambient metric. The latter condition reduces a potentially infinite number of possible objective rates to only two: the material derivative and the Jaumann rate. The material derivative is invariant under the Galilean group, and therefore applies to velocities, whose rate captures the conservation of momentum. The Jaumann derivative is invariant under all time-dependent isometries, and therefore applies to local order parameters, or symmetry-broken variables, such as the nematic Q-tensor. We provide examples of material and Jaumann rates in two different frame fields that are pertinent to the current applications of the fluid mechanics of deformable surfaces.
The cytoskeletal component actomyosin is a canonical example of active matter since the powerstroke cycle locally converts chemical energy in the form of adenoside triphosphate (ATP) into mechanical work for remodelling. Observing myosin II minifilaments as they remodel actin in vitro, we now report that: at high concentrations of ATP, myosin minifilaments form meta-stable swirling patterns that are characterised by recurrent vortex- and spiral-like motifs, whereas; at low concentrations of ATP, such structures give way to aster-like patterns. To explain this, we construct the (quasi-)steady states of a polar active hydrodynamic theory of actomyosin whose ATP-scaling is obtained from a microscopic, stochastic description for the ATP-dependent binding of the heads of single myosin II minifilaments. The latter codifies the heuristic that, since the powerstroke cycle involves the unbinding of myosin II heads from actin, increases in the concentration of ATP reduce the likelihood that a given myosin II minifilament has more than one head bound simultaneously, reducing its ability to generate contractile forces and increasing the relative likelihood of processive motion. This reproduces several qualitative aspects of experiments, providing evidence for the theory's central phenomenon: an ATP-dependent active contractile instability. ATP therefore not only controls the rate at which work is done - i.e., the power- but also the mode by which this occurs.
10: Advecting scaffolds: controlling the remodelling of actomyosin with anillin
D. Currin-Ross, S.C. Al-Izzi, I. Noordstra, A. Yap & R.G. Morris, arXiv:2402.07430 (Accepted in Physical Review E), (2024)
We propose and analyse an active hydrodynamic theory that characterises the effects of the scaffold protein anillin. Anillin is found at major sites of cortical activity, such as adherens junctions and the cytokinetic furrow, where the canonical regulator of actomyosin remodelling is the small GTPase, RhoA. RhoA acts via intermediary ‘effectors’ to increase both the rates of activation of myosin motors and the polymerisation of actin filaments. Anillin has been shown to scaffold this action of RhoA— improving critical rates in the signalling pathway without altering the essen- tial biochemistry— but its contribution to the wider spatio-temporal organisation of the cortical cytoskeleton remains poorly understood. Here, we combine analytics and numerics to show how anillin can non-trivially regulate the cytoskeleton at hydrodynamic scales. At short times, anillin can amplify or dampen existing contractile instabilities, as well as alter the parameter ranges over which they occur. At long times, it can change both the size and speed of steady-state travelling pulses. The primary mechanism that underpins these behaviours is established to be the advection of anillin by myosin II motors, with the specifics relying on the values of two coupling parameters. These codify anillin’s effect on local signalling kinetics and can be traced back to its interaction with the acidic phospholipid phosphatidylinositol 4,5-bisphosphate (PIP2), thereby establishing a putative connection between actomyosin remodelling and membrane composition
9: Stability of a biomembrane tube covered with proteins
M. Janssen, S. Liese, S.C. Al-Izzi & A. Carlson, Physical Review E 109 044403, (2024)
Membrane tubes are essential structural features in cells that facilitate biomaterial transport and inter- and intracellular signaling. The shape of these tubes can be regulated by the proteins that surround and adhere to them. We study the stability of a biomembrane tube coated with proteins by combining linear stability analysis, out-of-equilibrium hydrodynamic calculations, and numerical solutions of a Helfrich-like membrane model. Our analysis demonstrates that both long- and short-wavelength perturbations can destabilize the tubes. Numerical simulations confirm the derived linear stability criteria and yield the nonlinearly perturbed vesicle shapes. Our study highlights the interplay between membrane shape and protein density, where the shape instability concurs with a redistribution of proteins into a banded pattern.
8: The HIV capsid mimics karyopherin engagement of FG-nucleoporins
C.F. Dickson, S. Hertel, N. Li, A. Tuckwell, J. Ruan, S.C. Al-Izzi, N. Ariotti, E. Sierecki, Y. Gambin, R.G. Morris, G.J. Towers, T. Böcking & D.A. Jacques, Nature 626 836–842, (2024)
HIV can infect non-dividing cells because the viral capsid can overcome the selective barrier of the nuclear pore complex and deliver the genome directly into the nucleus. Remarkably, the intact HIV capsid is more than 1,000 times larger than the size limit prescribed by the diffusion barrier of the nuclear pore. This barrier in the central channel of the nuclear pore is composed of intrinsically disordered nucleoporin domains enriched in phenylalanine–glycine (FG) dipeptides. Through multivalent FG interactions, cellular karyopherins and their bound cargoes solubilize in this phase to drive nucleocytoplasmic transport. By performing an in vitro dissection of the nuclear pore complex, we show that a pocket on the surface of the HIV capsid similarly interacts with FG motifs from multiple nucleoporins and that this interaction licences capsids to penetrate FG-nucleoporin condensates. This karyopherin mimicry model addresses a key conceptual challenge for the role of the HIV capsid in nuclear entry and offers an explanation as to how an exogenous entity much larger than any known cellular cargo may be able to non-destructively breach the nuclear envelope.
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.
Morphodynamic equations governing the behaviour of active nematic fluids on deformable curved surfaces are constructed in the large deformation limit. Emphasis is placed on the formulation of objective rates that account for normal deformations whilst ensuring that tangential flows are Eulerian, and the use of the surface derivative (rather than the covariant derivative) in the nematic free energy, which elastically couples local order to out-of-plane bending of the surface. Focusing on surface geometry and its dynamical interplay with the hydrodynamics, several illustrative instabilities are then characterised. These include cases where the role of the Scriven–Love number and its nematic analogue are non-negligible, and where the active nematic forcing can be characterised by an analogue of the Föppl–von Kármán number. For the former, flows and changes to the nematic texture are coupled to surface geometry by viscous dissipation. This is shown to result in non-trivial relaxation dynamics for a nematic tube. For the latter, the nematic active forcing couples to the surface bending terms of the nematic free energy, resulting in extensile (active ruffling) and contractile (active pearling) instabilities in the tube shape, as well as active bend instabilities in the nematic texture. In comparison to the flat case, such bend instabilities now have a threshold set by the extrinsic curvature of the tube. Finally, we examine a topological defect located on an almost flat surface, and show that there exists a steady state where a combination of defect elasticity, activity and non-negligible spin connection drive a shape change in the surface.
5: Active flows and deformable surfaces in development
S.C. Al-Izzi & R.G. Morris, Seminars in Cell and Developmental Biology 120 44-52, (2021)
We review progress in active hydrodynamic descriptions of flowing media on curved and deformable manifolds: the state-of-the-art in continuum descriptions of single-layers of epithelial and/or other tissues during development. First, after a brief overview of activity, flows and hydrodynamic descriptions, we highlight the generic challenge of identifying the dependence on dynamical variables of so-called active kinetic coefficients— active counterparts to dissipative Onsager coefficients. We go on to describe some of the subtleties concerning how curvature and active flows interact, and the issues that arise when surfaces are deformable. We finish with a broad discussion around the utility of such theories in developmental biology. This includes limitations to analytical techniques, challenges associated with numerical integration, fitting-to-data and inference, and potential tools for the future, such as discrete differential geometry.
S.C. Al-Izzi, P. Sens, M.S. Turner & S. Komura, Soft Matter 16 9319, (2020)
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.
3: Measuring Gaussian rigidity using curved substrates
P. Fonda, S.C. Al-Izzi, L. Giomi & M.S. Turner, Physical Review Letters 125 188002, (2020)
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 substrates 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, while remaining in the perturbative regime of our analysis.
2: Shear-driven instabilities of membrane tubes and dynamin-induced scission
S.C. Al-Izzi, P. Sens & M.S. Turner, Physical Review Letters 125 018101, (2020)
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.
1: Hydro-osmotic instabilities in active membrane tubes
S.C. Al-Izzi, G. Rowlands, P. Sens & M.S. Turner, Physical Review Letters 120 138102, (2018)
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.
