Finite element approximation for the dynamics of asymmetric fluidic biomembranes

We present a parametric finite element approximation of a fluidic membrane, whose evolution is governed by a surface Navier–Stokes equation coupled to bulk Navier–Stokes equations. The elastic properties of the membrane are modelled with the help of curvature energies of Willmore and Helfrich type. Forces stemming from these energies act on the surface fluid, together with a forcing from the bulk fluid. Using ideas from PDE constrained optimization, a weak formulation is derived, which allows for a stable semi-discretization. An important new feature of the present work is that we are able to also deal with spontaneous curvature and an area-difference elasticity contribution in the curvature energy. This allows for the modelling of asymmetric membranes, which compared to the symmetric case lead to quite different shapes. This is demonstrated in the numerical computations presented

Geometric partial differential equations: Surface and bulk processes

The workshop brought together experts representing a wide range of topics in geometric partial differential equations ranging from analyis over numerical simulation to real-life applications. The main themes of the conference were the analysis of curvature energies, new developments in pdes on surfaces and the treatment of coupled bulk/surface problems

Finite Element Approximation for the Dynamics of Fluidic Two-Phase Biomembranes

Biomembranes and vesicles consisting of multiple phases can attain a multitude of shapes, undergoing complex shape transitions. We study a Cahn--Hilliard model on an evolving hypersurface coupled to Navier--Stokes equations on the surface and in the surrounding medium to model these phenomena. The evolution is driven by a curvature energy, modelling the elasticity of the membrane, and by a Cahn--Hilliard type energy, modelling line energy effects. A stable semidiscrete finite element approximation is introduced and, with the help of a fully discrete method, several phenomena occurring for two-phase membranes are computed

The interplay of geometry and coarsening in multicomponent lipid vesicles under the influence of hydrodynamics

We consider the impact of surface hydrodynamics on the interplay between curvature and composition in coarsening processes on model systems for biomembranes. This includes scaling laws and equilibrium configurations, which are investigated by computational studies of a surface two-phase flow problem with additional phase-depending bending terms. These additional terms geometrically favor specific configurations. We find that as in 2D the effect of hydrodynamics strongly depends on the composition. In situations where the composition allows a realization of a geometrically favored configuration, the hydrodynamics enhances the evolution into this configuration. We restrict our model and numerics to stationary surfaces and validate the numerical approach with various benchmark problems and convergence studies

Coarsening dynamics of ternary amphiphilic fluids and the self-assembly of the gyroid and sponge mesophases: lattice-Boltzmann simulations

By means of a three-dimensional amphiphilic lattice-Boltzmann model with short-range interactions for the description of ternary amphiphilic fluids, we study how the phase separation kinetics of a symmetric binary immiscible fluid is altered by the presence of the amphiphilic species. We find that a gradual increase in amphiphile concentration slows down domain growth, initially from algebraic, to logarithmic temporal dependence, and, at higher concentrations, from logarithmic to stretched-exponential form. In growth-arrested stretched-exponential regimes, at late times we observe the self-assembly of sponge mesophases and gyroid liquid crystalline cubic mesophases, hence confirming that (a) amphiphile-amphiphile interactions need not be long-ranged in order for periodically modulated structures to arise in a dynamics of competing interactions, and (b) a chemically-specific model of the amphiphile is not required for the self-assembly of cubic mesophases, contradicting claims in the literature. We also observe a structural order-disorder transition between sponge and gyroid phases driven by amphiphile concentration alone or, independently, by the amphiphile-amphiphile and the amphiphile-binary fluid coupling parameters. For the growth-arrested mesophases, we also observe temporal oscillations in the structure function at all length scales; most of the wavenumbers show slow decay, and long-term stationarity or growth for the others. We ascribe this behaviour to a combination of complex amphiphile dynamics leading to Marangoni flows.Comment: 16 pages, 13 figures. Accepted for publication in Phys. Rev. E. (Replaced for the latest version, in press.) Higher-quality figures can be sent upon reques

Microfluidic Planar Phospholipids Membrane System Advancing Dynamics Studies of Ion Channels and Membrane Physics

The interrogation of lipid membrane and biological ion channels supported within bilayer phospholipid membranes has greatly expanded our understanding of the roles membrane and ion channels play in a host of biological functions. Several key drawbacks of traditional electrophysiology systems used in these studies have long limited our effort to study the ion channels. Firstly, the large volume buffer in this system typically only allows single or multiple additions of reagents, while complete removal either is impossible or requires tedious effort to ensure the stability of membrane. Thus, it has been highly desirable to be able to rapidly and dynamically modulate the (bio)chemical conditions at the membrane site. Second, it is difficult to change temperature effectively with large thermal mass in macro device. Third, traditional PPM device host vertical membranes, therefore incompatible with confocal microscopy techniques. The miniaturization of bilayer phospholipid membrane has shown potential solution to the drawbacks stated above. A simple microfluidic design is developed to enable effective and robust dynamic perfusion of reagents directly to an on-chip planar phospholipid membrane (PPM). It allows ion channel conductance to be readily monitored under different dynamic reagent conditions, with perfusion rates up to 20 µL/min feasible without compromising the membrane integrity. It is estimated that the lower limit of time constant of kinetics that can be resolved by our system is 1 minute. Using this platform, the time-dependent responses of membrane-bound ceramide ion channels to treatments with La3+ and a Bcl-xL mutant were studied and the results were interpreted with a novel elastic biconcave distortion model. Another engineering challenge this dissertation takes on is the integration of fluorescence studies to micro-PPM system. The resulting novel microfluidic system enables high resolution, high magnification and real-time confocal microscope imaging with precise top and bottom (bio)chemical boundary conditions defined by perfusion, by integrating in situ PPM formation method, perfusion capability and microscopy compatibility. To demonstrate such electro-optical chip, lipid micro domains were imaged and quantitatively studied for their movements and responses to different physical parameters. As an extension to this platform, a double PPM system has been developed with the aim to study interactions between two membranes. Potential application in biophysics and biochemistry using those two platforms were discussed. Another important advantage of microfluidics is its lower thermal mass and compatibility with various microfabrication methods which enables potential integration of local temperature controller and sensor. A prototype thermal PPM chip is also discussed together with some preliminary results and their implication on ceramide channel assembly and disassembly mechanism

Fluid Vesicles in Flow

We review the dynamical behavior of giant fluid vesicles in various types of external hydrodynamic flow. The interplay between stresses arising from membrane elasticity, hydrodynamic flows, and the ever present thermal fluctuations leads to a rich phenomenology. In linear flows with both rotational and elongational components, the properties of the tank-treading and tumbling motions are now well described by theoretical and numerical models. At the transition between these two regimes, strong shape deformations and amplification of thermal fluctuations generate a new regime called trembling. In this regime, the vesicle orientation oscillates quasi-periodically around the flow direction while asymmetric deformations occur. For strong enough flows, small-wavelength deformations like wrinkles are observed, similar to what happens in a suddenly reversed elongational flow. In steady elongational flow, vesicles with large excess areas deform into dumbbells at large flow rates and pearling occurs for even stronger flows. In capillary flows with parabolic flow profile, single vesicles migrate towards the center of the channel, where they adopt symmetric shapes, for two reasons. First, walls exert a hydrodynamic lift force which pushes them away. Second, shear stresses are minimal at the tip of the flow. However, symmetry is broken for vesicles with large excess areas, which flow off-center and deform asymmetrically. In suspensions, hydrodynamic interactions between vesicles add up to these two effects, making it challenging to deduce rheological properties from the dynamics of individual vesicles. Further investigations of vesicles and similar objects and their suspensions in steady or time-dependent flow will shed light on phenomena such as blood flow.Comment: 13 pages, 13 figures. Adv. Colloid Interface Sci., 201

Multiscale analysis of the effect of surface charge pattern on a nanopore’s rectification and selectivity properties: From all-atom model to Poisson-Nernst-Planck

We report a multiscale modeling study for charged cylindrical nanopores using three modeling levels that include (1) an all-atom explicit-water model studied with molecular dynamics, and reduced models with implicit water containing (2) hard-sphere ions studied with the Local Equilibrium Monte Carlo simulation method (computing ionic correlations accurately), and (3) point ions studied with Poisson-Nernst-Planck theory (mean-field approximation). We show that reduced models are able to reproduce device functions (rectification and selectivity) for a wide variety of charge patterns, that is, reduced models are useful in understanding the mesoscale physics of the device (i.e., how the current is produced). We also analyze the relationship of the reduced implicit-water models with the explicit-water model and show that diffusion coefficients in the reduced models can be used as adjustable parameters with which the results of the explicit- and implicit-water models can be related. We find that the values of the diffusion coefficients are sensitive to the net charge of the pore but are relatively transferable to different voltages and charge patterns with the same total charge