Enhancement of Cell Membrane Invaginations, Vesiculation and Uptake of Macromolecules by Protonation of the Cell Surface

The different pathways of endocytosis share an initial step involving local inward curvature of the cell’s lipid bilayer. It has been shown that to generate membrane curvature, proteins or lipids enforce transversal asymmetry of the plasma membrane. Thus it emerges as a general phenomenon that transversal membrane asymmetry is the common required element for the formation of membrane curvature. The present study demonstrates that elevating proton concentration at the cell surface stimulates the formation of membrane invaginations and vesiculation accompanied by efficient uptake of macromolecules (Dextran-FITC, 70 kD), relative to the constitutive one. The insensitivity of proton induced uptake to inhibiting treatments and agents of the known endocytic pathways suggests the entry of macromolecules to proceeds via a yet undefined route. This is in line with the fact that neither ATP depletion, nor the lowering of temperature, abolishes the uptake process. In addition, fusion mechanism such as associated with low pH uptake of toxins and viral proteins can be disregarded by employing the polysaccharide dextran as the uptake molecule. The proton induced uptake increases linearly in the extracellular pH range of 6.5 to 4.5, and possesses a steep increase at the range of 4> pH>3, reaching a plateau at pH≤3. The kinetics of the uptake implies that the induced vesicles release their content to the cytosol and undergo rapid recycling to the plasma membrane. We suggest that protonation of the cell’s surface induces local charge asymmetries across the cell membrane bilayer, inducing inward curvature of the cell membrane and consequent vesiculation and uptake

Oscillatory and electrohydrodynamic instabilities in flow over a viscoelastic gel

The stability of oscillatory flows over compliant surfaces is studied analytically and numerically. The type of compliant surfaces studied is the incompressible viscoelastic gel model. The stability is determined using the Floquet analysis, where amplitude of perturbations at time intervals separated by one time period is examined to determine whether perturbations grow or decay. Oscillatory flows pas viscoelastic gels exhibit an instability in the limit of zero Reynolds number, and the transition amplitude of the oscillatory velocity increases with the frequency of oscillations. The transition amplitude has a minimum at a finite wavenumber for the viscoelastic gel model. The instability is found to depend strongly on the gel viscosity eta (g) , and the effect of oscillations on the continuation of viscous modes at intermediate Reynolds number shows a complicated dependence on the oscillation frequency. Experimental studies are carried out on the stability of an oscillatory flow past a viscoelastic gel at zero Reynolds number, and these confirm the theoretical predictions

Dielectrophoresis and deformation of a liquid drop in a non-uniform, axisymmetric AC electric field

Analytical theory for the dielectrophoresis and deformation of a leaky dielectric drop, suspended in a leaky dielectric medium, subjected to non-uniform, axisymmetric Alternating Current (AC) fields is presented in the small deformation limit. The applied field is assumed to be a combination of a uniform part and a quadrupole component. The analysis shows that the magnitude and the sign of the steady and time-periodic dielectrophoretic velocity depend upon the frequency of the applied voltage. The frequency of oscillatory motion is twice that of the applied frequency and the phase lag is a consequence of charge dynamics. A deformed drop under non-uniform axisymmetric AC fields admits Legendre modes l = 2, 3, 4. The deformation has a frequency-dependent steady and time-periodic parts due to charge and interface dynamics. The steady deformation can be zero at a certain critical frequency in leaky dielectric systems. The time-periodic deformation also has a frequency which is twice the frequency of the applied voltage. In perfect dielectric systems, unlike the steady state deformation which is a balance of Maxwell and curvature stresses, the time-periodic deformation additionally includes viscous stresses associated with the oscillatory shape changes of the drop. A consequence of this effect is a phase lag that is dependent on the charge and interface hydrodynamics and a lag of pi/2 at high frequencies. It also results in vanishing amplitude of the oscillatory deformation at high frequencies. The study should lead to a better understanding of dielectrophoresis under non-uniform axisymmetric AC fields and better electrode design to affect drop breakup

Weakly nonlinear analysis of the electrohydrodynamic instability of a charged membrane

The effect of nonlinear interactions on the linear instability of shape fluctuations of a flat charged membrane immersed in a fluid is analyzed using a weakly nonlinear stability analysis. There is a linear instability when the surface tension reduces below a critical value for a given charge density, because a displacement of the membrane surface causes a fluctuation in the counterion density at the surface, resulting in an additional Maxwell normal stress at the surface which is opposite in direction to the stress caused by surface tension. The nonlinear analysis shows that at low surface charge densities, the nonlinear interactions saturate the growth of perturbations resulting in a new steady state with a fluctuation amplitude determined by the balance between the destabilizing electrodynamic force and surface tension. As the surface charge density is increased, the nonlinear terms destabilize the perturbations, and the bifurcation is subcritical. There is also a significant difference in the predictions of the approximate Debye-Huckel and more exact Poisson-Boltzmann equations at high charge densities, with the former erroneously predicting that the bifurcation is supercritical at all charge densities

Electrohydrodynamics of a compound vesicle under an AC electric field

Compound vesicles are relevant as simplified models for biological cells as well as in technological applications such as drug delivery. Characterization of these compound vesicles, especially the inner vesicle, remains a challenge. Similarly their response to electric field assumes importance in light of biomedical applications such as electroporation. Fields lower than that required for electroporation cause electrodeformation in vesicles and can be used to characterize their mechanical and electrical properties. A theoretical analysis of the electrohydrodynamics of a compound vesicle with outer vesicle of radius R-0 and an inner vesicle of radius lambda R-0, is presented. A phase diagram for the compound vesicle is presented and elucidated using detailed plots of electric fields, free charges and electric stresses. The electrohydrodynamics of the outer vesicle in a compound vesicle shows a prolate-sphere and prolate-oblate-sphere shape transitions when the conductivity of the annular fluid is greater than the outer fluid, and vice-versa respectively, akin to single vesicle electrohydrodynamics reported in the literature. The inner vesicle in contrast shows sphere-prolate-sphere and sphere-prolate-oblate-sphere transitions when the inner fluid conductivity is greater and smaller than the annular fluid, respectively. Equations and methodology are provided to determine the bending modulus and capacitance of the outer as well as the inner membrane, thereby providing an easy way to characterize compound vesicles and possibly biological cells

Role of conductivity in the electrohydrodynamic patterning of air-liquid interfaces

The effect of electrical conductivity on the wavelength of an electrohydrodynamic instability of a leaky dielectric-perfect dielectric (LD-PD) fluid interface is investigated. For instabilities induced by dc fields, two models, namely the PD-PD model, which is independent of the conductivity, and the LD-PD model, which shows very weak dependence on the conductivity of the LD fluid, have been previously suggested. In the past, experiments have been compared with either of these two models. In the present work, experiments, analytical theory, and simulations are used to elucidate the dependence of the wavelength obtained under dc fields on the ratio of the instability time (tau(s) = 1/s(max)) and the charge relaxation time (tau(c) = epsilon epsilon(0)/sigma, where epsilon(0) is the permittivity of vacuum, epsilon is the dielectric constant, and sigma is the electrical conductivity). Sensitive dependence of the wavelength on the nondimensional conductivity S-2 = sigma(2)mu(2)h(0)(2)/(epsilon(2)(0)f(0)(2)delta(2)) (where sigma(2) is the electrical conductivity, mu(2) is the viscosity, h(0) is the thickness of the thin liquid film, phi(0) is the rms value of the applied field, and delta is a small parameter) is observed and the PD-PD and the LD-PD cases are observed only as limiting behaviors at very low and very high values of S-2, respectively. Under an alternating field, the frequency of the applied voltage can be altered to realize several regimes of relative magnitudes of the three time scales inherent to the system, namely tau(c), tau(s), and the time period of the applied field, tau(f). The wavelength in the various regimes that result from a systematic variation of these three time scales is studied. It is observed that the linear Floquet theory is invalid in most of these regimes and nonlinear analysis is used to complement it. Systematic dependence of the wavelength of the instability on the frequency of the applied field is presented and it is demonstrated that nonlinear simulations are necessary to explain the experimental results

Large-deformation electrohydrodynamics of an elastic capsule in a DC electric field

The dynamics of a spherical elastic capsule, containing a Newtonian fluid bounded by an elastic membrane and immersed in another Newtonian fluid, in a uniform DC electric field is investigated. Discontinuity of electrical properties, such as the conductivities of the internal and external fluid media as well as the capacitance and conductance of the membrane, leads to a net interfacial Maxwell stress which can cause the deformation of such an elastic capsule. We investigate this problem considering well-established membrane laws for a thin elastic membrane, with fully resolved hydrodynamics in the Stokes flow limit, and describe the electrostatics using the capacitor model. In the limit of small deformation, the analytical theory predicts the dynamics fairly satisfactorily. Large deformations at high capillary number, though, necessitate a numerical approach (axisymmetric boundary element method in the present case) to solve this highly nonlinear problem. Akin to vesicles, at intermediate times, highly nonlinear biconcave shapes along with squaring and hexagon-like shapes are observed when the outer medium is more conducting. The study identifies the essentiality of parameters such as high membrane capacitance, low membrane conductance, low hydrodynamic time scales and high capillary number (the ratio of the destabilizing electric force to the stabilizing elastic force) for observation of these shape transitions. The transition is due to large compressive Maxwell stress at the poles at intermediate times. Thus such shape transition can be seen in spherical globules admitting electrical capacitance, possibly irrespective of the nature of the interfacial restoring force

Weakly nonlinear analysis of the electrohydrodynamic instability of a charged membrane

The effect of nonlinear interactions on the linear instability of shape fluctuations of a flat charged membrane immersed in a fluid is analyzed using a weakly nonlinear stability analysis. There is a linear instability when the surface tension reduces below a critical value for a given charge density, because a displacement of the membrane surface causes a fluctuation in the counterion density at the surface, resulting in an additional Maxwell normal stress at the surface which is opposite in direction to the stress caused by surface tension. The nonlinear analysis shows that at low surface charge densities, the nonlinear interactions saturate the growth of perturbations resulting in a new steady state with a fluctuation amplitude determined by the balance between the destabilizing electrodynamic force and surface tension. As the surface charge density is increased, the nonlinear terms destabilize the perturbations, and the bifurcation is subcritical. There is also a significant difference in the predictions of the approximate Debye-Huckel and more exact Poisson-Boltzmann equations at high charge densities, with the former erroneously predicting that the bifurcation is supercritical at all charge densities