Session K03: Biological Fluid Dynamics: Flows Involving Vesicles and Micelles (8:45am - 9:30am CST)

Vesicle Dynamics in Large Amplitude Oscillatory Extension, Simulations and Microfluidic Experiments

While the behavior of fluid vesicles in steady flows have been studied extensively, how time-dependent oscillatory flows impact the shape dynamics of vesicles is not understood. We investigate the non-linear extension and compression dynamics of vesicles in large amplitude oscillatory extensional (LAOE) flows using a combination of microfluidic experiments and boundary integral (BI) simulations. Our results characterize the transient membrane deformations, dynamical regimes, and stress response in LAOE in terms of reduced volume (vesicle's asphericity), capillary number (Ca, dimensionless flow-strength), and Deborah number (De, dimensionless flow-frequency). Single vesicle experiments are compared to BI simulations without thermal fluctuations, and agreement is found across a wide range of parameters. We establish three dynamical regimes based on the vesicle deformation: the pulsating, reorienting, and symmetrical regimes. The distinct dynamics observed in each regime result from the competition between the flow frequency, flow time scale and membrane deformation timescale. We have additionally observed the relation between average stress and strain rate is highly nonlinear. The consequences of such rheology and the dynamical regimes will be discussed in this talk.   

Pore Dynamics of Lipid Vesicles under Light-Induced Osmotic Shock

Lipid vesicles play a key role in understanding fundamental biological processes involving cell plasma membrane, and they have also been used as cargo vehicles in various biomedical applications. Therefore, resolving the non-equilibrium dynamics of lipid vesicles remains a canonical research question in modeling cell mechanics as well as designing vesicle-based delivery system. Recent experiments have shown that a light-induced osmotic shock could cause a vesicle to explode and fragment as opposed to the well-characterized swell-burst-reseal behavior, yet the explanatory mechanism is unknown. In our previous work, we developed a comprehensive model to capture the vesicle evolution in the bifurcation dynamics. In this talk, we will present the phase diagram for the pore dynamics integrating the photo-reactions. Various regimes, including no pore formation, short/long-lived pores and irreversible explosion, are identified by solving the dynamical equations numerically. We further discuss the dependence of the regime boundaries on the key parameters, including the membrane permeability, membrane bending rigidity, line tension of pore edge, vesicle size and chemical kinetics. Our work not only advances the fundamental understanding for mechanical responses of osmotically stressed vesicles, but also aides in selection of lipid substrates and appropriate chemical reactions for desired release properties in artificially constructed vesicles for drug delivery.   

Coarse-grained Modeling of Liposome Nano-extrusion Using Fluctuating Lattice Boltzmann Method

Liposome nano-extrusion is a popular technique to produce small liposomes by squeezing large lipid vesicles through an array of nanochannels. There is little understanding of such a small-scale dynamic process. An implicit solvent, coarse-grained (CG) model is utilized to study nanoscale topological changes of lipid vesicles. The CG model is coupled with a fluctuating Lattice-Boltzmann flow solver that transfers fluid velocities and thermal fluctuations between CG beads and fluid lattice points. We analyzed the effects of liposome size on the pore formation and rupture process by modeling the squeezing of lipid vesicles with the diameter of D$=$40-100nm through channels with various widths and lengths. The Reynolds number, defined by the vesicle diameter and maximum squeezing velocity, is in the range of 1-100. Results show that initial pore formation is more probable for larger vesicles, narrower constrictions, and higher Reynolds numbers. Moreover, three different regimes of passing without damage, transient hydrophilic pore formation, and complete rupture, are identified by performing a complete parametric study.   

Modeling the competition between aggregation and diffusion of proteins on curved lipid bilayers

Membrane bending is an extensively studied problem from modeling and experimental perspectives because of the wide implications of curvature generation in cell biology. Many of the curvature generating aspects in membranes can be attributed to interactions between proteins and membranes. Recently we have shown that a high membrane curvature region prevents the diffusion of proteins creating an apparent aggregation effect. Here, we focus on the role of explicit aggregation of proteins on the surface of the membrane in the presence of membrane bending and diffusion. Aggregation of proteins on the membrane surface has been implicated in many biophysical phenomena and pathological states such as Alzheimer's disease. We develop a comprehensive framework that includes lipid flow, membrane bending energy, the entropy of proteins distribution, and an explicit aggregation potential. We first derive the governing equations and compare this framework to the Cahn-Hillard formalism to find the regimes in which the proteins form patterns on the membrane. We demonstrate the utility of this model using numerical simulations of various experimental scenarios to predict how aggregation and diffusion, coupled with curvature generation can alter the energy landscape of membrane-protein interactions.   

Semipermeable Vesicle in Stokes Flows

I will describe our recent work on multicomponent vesicles in various Stokes flows. Our multicomponent vesicles are representative of cell membranes containing aquaporins and are only permeable to water, and our model depends on the membrane forces and the lipid species. I will discuss our results for vesicles in unbounded quiescent flow, shear flow, Poiseuille flow, and finally a vesicle moving through a constriction.   

Hydrodynamic shear dissipation and transmission in lipid bilayers

Vital biological processes, such as trafficking, sensing, and motility, are facilitated by cellular lipid membranes and often involve mechanical interactions, especially with the surrounding fluid. Such lipid membranes are comprised of a nanometer-thick, liquid crystalline structure known as the lipid bilayer. In this study, we use optical tweezers to both apply and measure local forces on free-standing lipid bilayers within microfluidic channels. This technique is the first to combine multiple optical~tweezers~probes with planar free-standing lipid bilayers~accessible on both sides. We quantify fluid slip close to the bilayer surface and transmission of shear forces across the structure. Through numerical simulations of the hydrodynamics, we determine monolayer viscosity and intermonolayer friction, and find these properties are highly dependent on lipid composition. Our study sheds light on the physical principles~governing the transfer of shear forces by and through lipid membranes, which underpin cell behavior and homeostasis.   

Hydrodynamics of small unilamellar vesicles (sUVs) simulated using a hybrid approach

In this talk we simulate the hydrodynamics of small unilamellar vesicles (sUVs) using a hybrid approach that is shown to capture the formation of sUVs in a solvent (SIAM J Multiscale Model. Simul., vol 18, pp. 79-103). In this hybrid formulation, the non-local interactions between the coarse-grained lipid molecules are described by a hydrophobicity functional, giving rise to forces and torques (between lipid particles) that dictate the motion of both particles and the fluid flow in the viscous solvent. Both the hydrophobic and hydrodynamic interactions between the coarse-grained amphiphilic particles are formulated into integral equations, which allow for accurate and efficient numerical simulations in both two- and three-dimensions. We validate our hybrid coarse-grained model by reproducing various physical properties of a lipid bilayer membrane, and use this simulation tool to examine how a small unilamellar vesicle behaves under a planar shear flow, and investigate the collective dynamics of sUVs under a shear flow. Finally we also examine the possibility of membrane rupture by extreme flowing conditions.   

Effects of surface shear viscosity on the dynamics of bilayer membranes

Membrane viscosity is a key mechanical property of cell membranes that controls time-dependent processes such as membrane deformations and the diffusion of embedded proteins. Yet, it has proven to be an elusive property to quantify. Here we present two methods to measure shear surface viscosity of bilayer membranes. The first one analyzes the transient deformation of a giant unilamellar vesicle (GUV) induced by AC uniform electric field. The second approach analyzes the thermally driven membrane undulations of a GUV. The two methods are non-invasive, easy to implement, and probe-independent.   

Curvature affected flow in surfactant films

Free surface surfactant films are comprised of two organized surfactant molecule monolayers surrounding an interstitial fluid region. Thin soap films have been an important experimental tool for modeling two dimensional fluid flow. The relationship between the bulk flow regime in the interstitial fluid and the chemical behavior of the monolayers has been well established for flat films. Surfactant films with non-zero curvature have the potential to exhibit different fluid flow patterns than flat films due to surface tension and curvature effects. We provide a rigorous asymptotic study of the equations governing the motion and composition of a spherical fluid surfactant film, investigating the effects of dimensionless parameters on the resulting leading-order dynamical equations. Our findings indicate that the interstitial fluid flow is affected by film curvature especially in surfactant solutions of concentration above the critical micelle concentration, at which point the bending effects of the monolayer films contribute to the governing equations.   

Breathing and tumbling of multicomponent vesicles in a shear flow

Biological membranes are composed of numerous proteins and molecules which can form domain-like structures, resulting in variable material properties such as bending rigidity and spontaneous curvature of the membrane. In this talk we will focus on a two dimensional multicomponent vesicle in shear flow. Using small amplitude perturbation analysis a reduced order model is developed, revealing tank-treading and tumbling modes, and a new breathing mode which depends on membrane inhomogeneity. The theoretically derived dynamics are compared to the results of full numerical simulations. The utility of this model to predict spatially-varying membrane bending rigidity or spontaneous curvature in the lab setting will also be discussed.