Vortex Flows and Streamline Topology in Curved Biological Membranes

Abstract

When considering flows in biological membranes, they are usually treated as flat, though more often than not, they are curved surfaces, even extremely curved, as in the case of the endoplasmic reticulum. Here, we study the topological effects of curvature on flows in membranes. Focusing on a system of many point vortical defects, we are able to cast the viscous dynamics of the defects in terms of a geometric Hamiltonian. In contrast to the planar situation, the flows generate additional defects of positive index. For the simpler situation of two vortices, we analytically predict the location of these stagnation points. At the low curvature limit, the dynamics resemble that of vortices in an ideal fluid, but considerable deviations occur at high curvatures. The geometric formulation allows us to construct the spatio-temporal evolution of streamline topology of the flows resulting from hydrodynamic interactions between the vortices. The streamlines reveal novel dynamical bifurcations leading to spontaneous defect-pair creation and fusion. Further, we find that membrane curvature mediates defect binding and imparts a global rotation to the many-vortex system, with the individual vortices still interacting locally.

arXiv comment19+17 pages, 13 figures, v2 : References updated, typos fixed, author information updated

References in corpus (31)

• Spontaneous motion in hierarchically assembled active matter
• Swimming in circles: Motion of bacteria near solid boundaries
• Dancing Volvox: Hydrodynamic Bound States of Swimming Algae
• Defect dynamics in active nematics
• Topological structure and dynamics of three dimensional active nematics
• Self-organized dynamics and the transition to turbulence of confined active nematics
• Vortices in Superfluid Films on Curved Surfaces
• Topological Defects in Spherical Nematics
• Anomalous coupling between topological defects and curvature
• Defect unbinding in active nematics
• Hydrodynamic Collective Effects of Active Protein Machines in Solution and Lipid Bilayers
• Dynamics of viscoelastic membranes
• Topological Sound and Flocking on Curved Surfaces
• Membrane Viscosity Determined from Shear-Driven Flow in Giant Vesicles
• Correlated diffusion of membrane proteins and their effect on membrane viscosity
• Dynamics of rigid and flexible extended bodies in viscous films and membranes
• Cross-talk between topological defects in different fields revealed by nematic microfluidics
• Dynamical patterns in active nematics on a sphere
• Anomalous Topological Active Matter
• Fast crystallization of rotating membrane proteins
• Correlated dynamics of inclusions in a supported membrane
• Hydrodynamic Flows on Curved Surfaces: Spectral Numerical Methods for Radial Manifold Shapes
• Hydrodynamic Coupling of Particle Inclusions Embedded in Curved Lipid Bilayer Membranes
• Dynamics of membranes with immobile inclusions
• Shear-Driven Circulation Patterns in Lipid Membrane Vesicles
• The effect of curvature and topology on membrane hydrodynamics
• About existence of stationary points for the Arnold-Beltrami-Childress (ABC) flow
• Surface Fluctuating Hydrodynamics Methods for the Drift-Diffusion Dynamics of Particles and Microstructures within Curved Fluid Interfaces
• Driven and active colloids at fluid interfaces
• Diffusion coefficients in leaflets of bilayer membranes
• Stealthy Movements and Concealed Swarms of Swimming micro-Robots

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• Arbitrary Lagrangian--Eulerian finite element method for lipid membranes
• Co-rotating Vortices on Surfaces of Variable Negative Curvature: Hamiltonian Structure and Curvature-Induced Drift