Vesicles consisting of a bilayer membrane of amphiphilic lipid molecules are remarkably flexible surfaces that show an amazing variety of shapes of different symmetry and topology. Owing to the fluidity of the membrane, shape transitions such as budding can be induced by temperature changes or the action of optical tweezers. Thermally excited shape fluctuations are both strong and slow enough to be visible by video microscopy. Depending on the physical conditions, vesicles adhere to and unbind from each other or a substrate. This article describes the systematic physical theory developed to understand the static and dynamic aspects of membrane and vesicle configurations. The preferred shapes arise from a competition between curvature energy, which derives from the bending elasticity of the membrane, geometrical constraints such as fixed surface area and fixed enclosed volume, and a signature of the bilayer aspect. These shapes of lowest energy are arranged into phase diagrams, which separate regi...

Configurations of fluid membranes and vesicles

1. Introduction to the cell Part I. Rods and Ropes: 2. Polymers 3. Two-dimensional networks 4. Three-dimensional networks Part II. Membranes: 5. Biomembranes 6. Membrane undulations Part III. The Whole Cell: 7. The simplest cells 8. Intermembrane forces 9. Dynamic filaments 10. Mechanical designs Appendix A. Animal cells and tissues Appendix B. The cell's molecular building blocks Appendix C. Elementary statistical mechanics Appendix D. Elasticity References Index.

/pdf/mechanics-of-the-cell-5g5c71kjw2.pdf

Mechanics of the cell

In this review, we describe and analyze a mesoscale simulation method for fluid flow, which was introduced by Malevanets and Kapral in 1999, and is now called multi-particle collision dynamics (MPC) or stochastic rotation dynamics (SRD). The method consists of alternating streaming and collision steps in an ensemble of point particles. The multi-particle collisions are performed by grouping particles in collision cells, and mass, momentum, and energy are locally conserved. This simulation technique captures both full hydrodynamic interactions and thermal fluctuations. The first part of the review begins with a description of several widely used MPC algorithms and then discusses important features of the original SRD algorithm and frequently used variations. Two complementary approaches for deriving the hydrodynamic equations and evaluating the transport coefficients are reviewed. It is then shown how MPC algorithms can be generalized to model non-ideal fluids, and binary mixtures with a consolute point. The importance of angular-momentum conservation for systems like phase-separated liquids with different viscosities is discussed. The second part of the review describes a number of recent applications of MPC algorithms to study colloid and polymer dynamics, the behavior of vesicles and cells in hydrodynamic flows, and the dynamics of viscoelastic fluids.

Multi-Particle Collision Dynamics -- a Particle-Based Mesoscale Simulation Approach to the Hydrodynamics of Complex Fluids

Strength of a Weak Bond Connecting Flexible Polymer Chains

https://www.sfu.ca/%7Eboal/papers/paper94.pdf

Simulations of the Erythrocyte Cytoskeleton at Large Deformation. II. Micropipette Aspiration

The shape dynamics of fluid vesicles is governed by the coupling of the flow within the two-dimensional membrane to the hydrodynamics of the surrounding bulk fluid. We present a numerical scheme which is capable of solving this flow problem for arbitrarily shaped vesicles using the Oseen tensor formalism. For the particular problem of simple shear flow, stationary shapes are found for a large range of parameters. The dependence of the orientation of the vesicle and the membrane velocity on shear rate and vesicle volume can be understood from a simplified model.

/pdf/fluid-vesicles-in-shear-flow-1wuuf4unj0.pdf

Fluid vesicles in shear flow

The equilibrium shapes of fluid-phase phospholipid vesicles in an aqueous solution are controlled by bending elasticity. The regime of nonvesiculated shapes at reduced volume v\ensuremath{\ge}1/ \ensuremath{\surd}2 involves the interplay of five branches of distinct stationary shapes: pears, prolates, oblates, stomatocytes, plus a branch of nonaxisymmetric shapes with the symmetry ${\mathit{D}}_{2\mathit{h}}$. We exploit a method for calculating explicitly the stability of arbitrary axisymmetric shapes to map out in a numerically exact way both the stable phases and the metastability of the low-lying shape branches. To obtain additional required information about nonaxisymmetric shapes, we calculate these by numerical minimization of the curvature energy on a triangulated surface. Combining these two methods allows us to construct the full (shape) phase diagram and the full stability diagram in this region. We provide explicit results for values of the bending constants appropriate to stearoyl-oleoyl-phosphatidylcholine; generalization to other values is straightforward. (c) 1995 The American Physical Society

Vesicular instabilities: The prolate-to-oblate transition and other shape instabilities of fluid bilayer membranes

We investigate the propagation of a suddenly applied tension along a thermally excited semiflexible polymer using analytical approximations, scaling arguments, and numerical simulation. This problem is inherently nonlinear. We find subdiffusive propagation with a dynamical exponent of 1/4. By generalizing the internal elasticity, we show that tense strings exhibit qualitatively different tension profiles and propagation with an exponent of 1/2.

/pdf/straightening-of-thermal-fluctuations-in-semiflexible-2adrtyj7n9.pdf

Straightening of Thermal Fluctuations in Semiflexible Polymers by Applied Tension.

We consider two-dimensional triangular networks of beads connected by Hookean tethers under isotropic compression. We determine both the compression and the shear modulus as a function of temperature and compression within simple approximations and by a Monte Carlo simulation. At low temperature, this network undergoes a collapse transition with increasing compression. In the two phase region, collapsed and non-collapsed triangles coexist. While the compression modulus vanishes in the two phase region, the shear modulus shows only a small anomaly at the transition. With increasing temperature, this transition disappears in our simulation. Anharmonic shear fluctuations invalidate a harmonic analysis in large regions of the phase space. In application to the red blood cell membrane, we obtain good agreement with more microscopic models for the shear modulus. Our results also indicate that strong compression will lead to non-trivial elastic behavior of the cell membrane.

https://hal.archives-ouvertes.fr/jpa-00247384/document

Wolfgang Wintz

Papers

Fluid vesicles in shear flow

Vesicular instabilities: The prolate-to-oblate transition and other shape instabilities of fluid bilayer membranes

Straightening of Thermal Fluctuations in Semiflexible Polymers by Applied Tension.

Mesh Collapse in Two-Dimensional Elastic Networks under Compression