Session A25: Biological Fluid Dynamics: Flows involving Vesicles and Micelles

Probing membrane material properties with complex and dynamic fluid environments

Membranes are composed of a variety of materials whose distribution, in combination with enclosed volume, can result in distinct and functional morphologies. It is of generic biological interest and importance to measure these material properties and many methods are used; a red blood cell's bending stiffness, for instance, may been measured by stretching it in a delicate process requiring optical tweezers. We will discuss a few new methods for probing membrane material properties like bending stiffness and spontaneous curvature using complex fluid environments, namely liquid crystals, and using fluid flows. By placing red blood cells into a liquid crystalline environment we show that the sharing of strain between the fluid and the cells can be used to rapidly characterize multiple cells in a population, and perhaps to detect problematic variants. Patches of distinct material properties along the surface, meanwhile, presents new measurement challenges, but new developments on multicomponent cell behavior in flows can also be used to infer membrane composition. Although a richness of shapes and behaviors emerge, we provide physical intuition for the roles of material properties on deformation and dynamics in both contexts.   

Stiffness of Single Apoptotic Bodies to Inform Brain Cancer Therapeutics

Treatment resistance is a major issue in glioblastoma multiform (GBM) brain cancer management. Predicting and monitoring responses to standard temozolomide (TMZ) treatment will have significant impacts in patient care. We aim to explore the TMZ response of GBM cell lines by correlating apoptotic body (AB) stiffness with TMZ treatment or resistance and protein content. ABs are large 1-5-µm extracellular vesicles shed during cellular apoptosis. ABs were isolated via centrifugation from GBM cell line supernatants (wild-type, 3-day TMZ treatment, TMZ resistance by chronic exposure). Protein concentration was measured by NanoDrop. Non-contact stiffness measurements of single ABs were performed by gently stretching ABs in extensional flow. Our microfluidic AB stiffness technique discriminated between GBM cell lines (5% sig. level) and TMZ-treated vs wild-type cells within a cell line (10% sig. level). Wild-type GBM cells with contrasting phenotypes showed different AB stiffnesses and protein content. AB stiffnesses were not significantly different between wild-type and TMZ-resistant cells, though protein content was moderately changed. Our data indicate that AB stiffness could be a sensitive indicator of short-term TMZ treatment with applications in personalized cancer treatment.   

Hydrodynamics of a permeable membrane deformed by pulling forces: a model for microtubule-mediated deformation of a nucleus membrane

The cellular nucleus is enclosed by a permeable membrane mechanically supported by a meshwork of lamin fibers.  The morphology and integrity of the nucleus are essential for the cell's function. Recent experiments show that loss of the lamin network results in nuclear deformations and rupture. To understand the mechanistic basis of this phenomenon, we developed a mathematical model that accounts for, and couples, the fluid flows around and through the permeable membrane, and the pulling on the membrane by membrane-bound, but mobile, molecular motors attached to impinging microtubules. Here the microtubules are assumed to nucleate from a cellular centrosome. We found that this model predicts the formation of a sharp corner in the vicinity of the centrosome, rather reminiscent of the Taylor cone for a surfactant-laden drop in an elongational flow.  We analyze the equilibrium shape of the membrane in terms of the total number of motors and their mobility in the nuclear membrane. Our model provides a more mechanistic understanding of nuclear deformation in cells and can give insights into the correspondence between motor forces and membrane deformation leading to nuclear rupture, which has been observed in some cancer cells.   

Hydrodynamics of a Multicomponent Vesicle Under Strong Confinement

The biophysical lipid bilayer membrane (such as a vesicle) often consists of multiple species of macromolecules such as cholesterol, surface proteins, surfactants, and different lipids. In this work I use the phase-field model for a multicomponent lipid membrane and implement the hydrodynamics with a boundary integral code. The simulations show that the multicomponent structure results in fundamentally different behaviors than a single component vesicle. I will demonstrate some of these differences by simulating multicomponent vesicles in various unbounded and strongly confined geometries.   

Swinging, tumbling, and phase-lagging of multicomponent membranes in a shear flow

Biological membranes are host to proteins and molecules which can form domain-like structures, resulting in spatially-varying material properties such as bending rigidity and spontaneous curvature. Such membranes can exhibit intricate shapes at equilibrium, suggesting the possibility of rich dynamics when such a body is placed into a flow. Under the assumption of small deformations we develop a reduced order model to describe the full fluid-structure interaction between a viscous background shear flow and a vesicle with spatially varying bending stiffness and curvature, which is solved exactly to predict the membrane's time-dependent deformation and inclination angles. A critical ratio which links the flow rate, internal viscosity, and the gradient in material properties is derived, which identifies a rapid transition in the membrane dynamics: from a swinging motion (which includes tangential tank-treading) to a rigid body tumbling behavior, passing through a transition regime which features tumbling and periodic phase-lagging of the membrane material relative to the body's long axis. Full numerical simulations are used to probe the theoretical predictions, which appear valid even when studying substantially deformed membranes.   

An elastohydrodynamic thin film theory for the onset of compartmentalization of lipid bilayer based model protocells

Vesicles of charged lipid bilayers attached to like-charged surfaces via divalent ions autonomously form daughter vesicles upon removal of the ions from the interface. We hypothesized that the onset of the subcompartment formation may be governed by an elastohydrodynamic instability caused by (1) electrostatic repulsion, (2) attractive van der Waals interactions between the surface and the bilayer, and/or (3) membrane spontaneous curvature, penalized solely by the bending energy of the membrane. To test the three candidates, we have developed an elastohydrodynamic thin film theory that relates the coupling between membrane bending and each of the three mechanisms to the pressure gradients that drive fluid flow underneath the membrane. Our stability analysis rules out the electrostatic effects in the presence of ionic screening and shows that the spontaneous curvature stabilizes a flat interface at the linear order. On the other hand, attractive van der Waals interactions give rise to an instability above a critical wavelength of 250 nm, in agreement with experiments. Our results suggest that molecular van der Waals forces at a range of membrane thickness scale may have played an important role in the formation of lipid membrane based molecular compartments on the early Earth.   

Giant unilamellar vesicle dynamics in large amplitude oscillatory extension

The dynamics of vesicles in simple shear and extensional flows have been thoroughly studied. However, the flow types present in microfluidic devices or biological systems are not always described by those flows alone. We present our work on the nonlinear dynamics of vesicles in large amplitude oscillatory extensional (LAOE) flows using both experiments and boundary integral (BI) simulations. Our results characterize the transient membrane deformations, dynamical regimes, and stress response of vesicles in LAOE in terms of reduced volume (vesicle asphericity), capillary number (dimensionless flow strength), and Deborah number (dimensionless flow frequency). We find the results from single vesicle experiments to be in good agreement with BI simulations across a wide range of parameters. Our results reveal three dynamical regimes based on vesicle deformation: pulsating, reorienting, and symmetrical regimes. The dynamics observed in each regime result from a competition between the flow frequency, flow time scale, and membrane deformation timescale. Broadly, this work provides new information regarding the transient dynamics of vesicles in time-dependent flows that informs bulk suspension rheology. We will also present some preliminary work on the dynamics of multicomponent vesicles.   

Hydrodynamics of a semipermeable inextensible membrane under flow and confinement

Lipid bilayer membranes have a native permeability for water molecules. In the absence of osmolarity, the water flux is often assumed to be negligible. However, we demonstrate that semipermeability can cause large amounts of fluid exchange, even in the absence of osmolarity. We investigate the effects of semipermeability on the hydrodynamics of an inextensible vesicle under mechanical loads caused by an external flow and extreme confinement. Several comparisons are made between impermeable and semipermeable vesicles.   

Braiding Dynamics in Active Nematic Flows

In active matter systems, energy consumed at the small scale by individual agents gives rise to emergent flows at large scales.  For 2D active nematic microtubule systems, these flows are largely characterized by the dynamics of mobile defects in the nematic director field.  As these defects wind about each other, their trajectories trace out braids, and the topological properties of these braids encode the most important global features of the flow.  In particular, the topological entropy of a braid quantifies how chaotic the associated flow is.  Since microtubule bundles, an extensile system, stretch out exponentially in time, the resultant defect movement must correspond to braids with positive topological entropy.  Indeed, we conjecture that the emergent defect dynamics are often optimal in that they give braids which maximize the, suitably normalized, topological entropy.  We will look at the dynamics of four +1/2 defects on a sphere as a case study, using both experimental data and simulations.  Additionally, we will share some predictions for the behavior of microtubules confined to the region between a lattice of pillars, based on recent advances in braid theory.