Nonlinear material and ionic transport through membrane nanotubes.

Membrane nanotubes (NTs) and their networks play an important role in intracellular membrane transport and intercellular communications. The transport characteristics of the NT lumen resemble those of conventional solid-state nanopores. However, unlike the rigid pores, the soft membrane wall of the NT can be deformed by forces driving the transport through the NT lumen. This intrinsic coupling between the NT geometry and transport properties remains poorly explored. Using synchronized fluorescence microscopy and conductance measurements, we revealed that the NT shape was changed by both electric and hydrostatic forces driving the ionic and solute fluxes through the NT lumen. Far from the shape instability, the strength of the force effect is determined by the lateral membrane tension and is scaled with membrane elasticity so that the NT can be operated as a linear elastic sensor. Near shape instabilities, the transport forces triggered large-scale shape transformations, both stochastic and periodic. The periodic oscillations were coupled to a vesicle passage along the NT axis, resembling peristaltic transport. The oscillations were parametrically controlled by the electric field, making NT a highly nonlinear nanofluidic circuitry element with biological and technological implications.

A quantitative model for membrane fusion based on low-energy intermediates.

The energetics of a fusion pathway is considered, starting from the contact site where two apposed membranes each locally protrude (as "nipples") toward each other. The equilibrium distance between the tips of the two nipples is determined by a balance of physical forces: repulsion caused by hydration and attraction generated by fusion proteins. The energy to create the initial stalk, caused by bending of cis monolayer leaflets, is much less when the stalk forms between nipples rather than parallel flat membranes. The stalk cannot, however, expand by bending deformations alone, because this would necessitate the creation of a hydrophobic void of prohibitively high energy. But small movements of the lipids out of the plane of their monolayers allow transformation of the stalk into a modified stalk. This intermediate, not previously considered, is a low-energy structure that can reconfigure into a fusion pore via an additional intermediate, the prepore. The lipids of this latter structure are oriented as in a fusion pore, but the bilayer is locally compressed. All membrane rearrangements occur in a discrete local region without creation of an extended hemifusion diaphragm. Importantly, all steps of the proposed pathway are energetically feasible.

Stalk dynamics and lipid flow upon membrane hemifusion.

A hydrodynamic theory describing the stalk dynamics and lipid flows upon BLM hemifusion was developed. The value of intermonolayer viscosity, etar, for membranes formed from azolectin mixed with lysophosphatidylcholine (7.10(-4) mg/ml) in n-decane, etar approximately 10(-9) g/s, was determined from comparison of the theoretical calculations and literature data. For membranes formed in squalene, the values etar approximately 10(-7) g/s for phosphatidylethanolamine and etar approximately 2-10(-7) g/s for azolectin were obtained. The calculated values are close to the published results of independent experiments which shows that the developed theory describes well the stalk growth and lipid flow.

Dynamics of fusion pores connecting membranes of different tensions.

The energetics underlying the expansion of fusion pores connecting biological or lipid bilayer membranes is elucidated. The energetics necessary to deform membranes as the pore enlarges, in some combination with the action of the fusion proteins, must determine pore growth. The dynamics of pore growth is considered for the case of two homogeneous fusing membranes under different tensions. It is rigorously shown that pore growth can be quantitatively described by treating the pore as a quasiparticle that moves in a medium with a viscosity determined by that of the membranes. Motion is subject to tension, bending, and viscous forces. Pore dynamics and lipid flow through the pore were calculated using Lagrange's equations, with dissipation caused by intra- and intermonolayer friction. These calculations show that the energy barrier that restrains pore enlargement depends only on the sum of the tensions; a difference in tension between the fusing membranes is irrelevant. In contrast, lipid flux through the fusion pore depends on the tension difference but is independent of the sum. Thus pore growth is not affected by tension-driven lipid flux from one membrane to the other. The calculations of the present study explain how increases in tension through osmotic swelling of vesicles cause enlargement of pores between the vesicles and planar bilayer membranes. In a similar fashion, swelling of secretory granules after fusion in biological systems could promote pore enlargement during exocytosis. The calculations also show that pore expansion can be caused by pore lengthening; lengthening may be facilitated by fusion proteins.

Lipid flow through fusion pores connecting membranes of different tensions.

When two membranes fuse, their components mix; this is usually described as a purely diffusional process. However, if the membranes are under different tensions, the material will spread predominantly by convection. We use standard fluid mechanics to rigorously calculate the steady-state convective flux of lipids. A fusion pore is modeled as a toroid shape, connecting two planar membranes. Each of the membrane monolayers is considered separately as incompressible viscous media with the same shear viscosity, etas. The two monolayers interact by sliding past each other, described by an intermonolayer viscosity, etar. Combining a continuity equation with an equation that balances the work provided by the tension difference, Deltasigma, against the energy dissipated by flow in the viscous membrane, yields expressions for lipid velocity, upsilon, and area of lipid flux, Phi. These expressions for upsilon and Phi depend on Deltasigma, etas, etar, and geometrical aspects of a toroidal pore, but the general features of the theory hold for any fusion pore that has a roughly hourglass shape. These expressions are readily applicable to data from any experiments that monitor movement of lipid dye between fused membranes under different tensions. Lipid velocity increases nonlinearly from a small value for small pore radii, rp, to a saturating value at large rp. As a result of velocity saturation, the flux increases linearly with pore radius for large pores. The calculated lipid flux is in agreement with available experimental data for both large and transient fusion pores.

Skin appendageal macropores as a possible pathway for electrical current.

The electrical properties of the outermost layer of skin are described by lipid-corneocyte (Zm) and appendageal (Za) impedance, which are connected in parallel. Appendageal macropores are considered as long tubes with distributed electrical parameters. It has been shown that not only Za, but also the macropore resistance Ra and capacitance Ca are frequency dependent. The input of Za in the overall impedance (Z) depends on the space density of active (conductive) macropores n(i), which increase with current density (i) and the duration of iontophoresis. Skin impedance has been demonstrated to decrease under the influence of iontophoretic treatment. Application of the theoretical model to these data provides an estimate of the increase in macropore density during iontophoresis. A comparison of these results with n(i), which was measured directly, shows a strong correlation supporting this unique model.

Electrical properties of skin at moderate voltages: contribution of appendageal macropores.

The electrical properties of human skin in the range of the applied voltages between 0.2 and 60 V are modeled theoretically and measured experimentally. Two parallel electric current pathways are considered: one crossing lipid-corneocyte matrix and the other going through skin appendages. The appendageal ducts are modeled as long tubes with distributed electrical parameters. For both transport systems, equations taking into account the electroporation of lipid lamella in the case the lipid-corneocyte matrix or the walls of the appendageal ducts in the case of the skin appendages are derived. Numerical solutions of these nonlinear equations are compared with published data and the results of our own experiments. The current-time response of the skin during the application of rectangular pulses of different voltage amplitudes show a profound similarity with the same characteristics in model and plasma membrane electroporation. A comparison of the theory and the experiment shows that a significant (up to three orders of magnitude) drop of skin resistance due to electrotreatment can be explained by electroporation of different substructures of stratum corneum. At relatively low voltages (U < 30 V) this drop of skin resistance can be attributed to electroporation of the appendageal ducts. At higher voltages (U > 30 V), electroporation of the lipid-corneocyte matrix leads to an additional drop of skin resistance. These theoretical findings are in a good agreement with the experimental results and literature data.

A theoretical study of outermost skin layer electroporation.

Two models of electrohydration of stratum corneum (SC) have been developed. In the first model, the hydration of one interbilayer region is considered on the assumption that water molecules are adsorbed on the inhomogeneous surface of a bilayer and can interact, thereby lowering their energy on the surface. The dependence of the hydration degree on the voltage across the skin had been found. At certain parameter values the degree of hydration rapidly grows at certain voltage up to the magnitudes at which continuous water pathways appear. The second model has used the macroscopic approach which presumes water to be present in the interbilayer region as microdrops. The dependence of the hydration degree on voltage has been also found. At voltages of the order of tens of volts the obtained hydrations of interbilayer regions are sufficient to generate electroinduced hydrophilic pores in the SC lipid phase. Formation of tortuous continuous pathways for the transport of small ions is little probable because it requires voltages much higher than 100 V. We suggest that small ions pass the skin by the straight way through corneocytes and lipid bilayers at voltages of the order of tens of volts and higher.

Changes in the electrical properties of the skin outermost layer during pulse electrotreatment.

The kinetics of changes in the electric current I(t) passing through human skin samples of full thickness in vitro during rectangular voltage pulses (amplitude, 10-60 V; duration, 5-8 ms) was investigated. The function I(t) was shown to rapidly decrease, to pass through its minimum, and then to increase slowly. With the increase in voltage, the minimal current grew; the dropping branch became less pronounced (up to its complete disappearance at 40 V); and the position of the minimum shifted to short times. All these features of the current response were explained in the assumption that the electrical properties of the skin at a voltage less than 30 V are determined by macropores of skin appendages (hair follicles, sweat glands, etc.). The dropping branch of the current was a superposition of the charging current of the macropore wall capacity and the conductive current through the electroporated walls. At voltages over 30 V, increases in current and conductivity are determined by electroporation of the lipid-corneocyte matrix of the skin outermost layer (stratum corneum). The kinetics of skin resistance restoration after pulse electrotreatment was also investigated. The characteristic time of restoration, which did not exceed 1 min at 10 V, increased up to dozens of minutes at voltages above 30 V. The investigated phenomena were found to be very much similar to the electroporation of plane lipid bilayers and plasma membranes of isolated cells.

A mechanism of skin appendage macropores electroactivation during iontophoresis.

A physical mechanism of activation of skin appendage macropores under the influence of an electric field is considered theoretically. The macropore is considered as a long cylinder tube which is closed and flattened out before the electric field is applied. The charging of the capacitance of the macropore walls is the driving force of electroactivation. During this process the free energy of the system decreases, which is energetically favourable and results in water pulled into the tube and to a gradual opening of the tube. It is shown that consideration of the macropore wall conductance leads to a considerable slowdown of electroactivation. The opening time of a separate macropore is estimated. It is equal to 30 min for a macropore 4 mm in length. The dependence of the surface density of activated macropores on time is calculated theoretically. The obtained theoretical results are in a good agreement with the literature data.

Formation of cell protrusions by an electric field: a thermodynamic analysis.

This work gives a thermodynamic analysis of outgrowth extraction from the cell body by a pulling force. The results are applied for a case when the pulling force is generated by an external high-frequency electric field. Two equilibrium conditions are analyzed: internal equilibrium of an outgrowth and equilibrium between the outgrowth and the cell body. In both cases the stability of feasible equilibrium states was studied. The work shows that the curvature of an outgrowth equilibrated with a pulling electric force depends on the squared amplitude of the electric field E0(2), on the outgrowth length l and on the transmembrane pressure differential delta P, and that at a sufficiently large transmembrane pressure differential the cylindrical form of the outgrowth loses its stability. Long outgrowths are more stable than short ones. The minimal value of critical pressure differential was estimated. The work also shows that outgrowth extraction from the cell body requires that the applied force exceeds a critical value below which no outgrowth is formed. The value of the electric field at which outgrowth formation is feasible was estimated.

Behavior of cells in rotating electric fields with account to surface charges and cell structures.

The behavior of a single biological cell in a rotating electric field is investigated both theoretically and experimentally. The torque acting on the cell is calculated. The dependence of the torque on electric cell properties (the dielectric constants, the conductivities, and the surface charges of the cell components) and the field frequency is discussed. The dependence of the rotation velocity on the field frequency shows a typical resonance behavior. It is discussed in which manner the single rotation extrema are related to the different homogeneous cell compartments (cytoplasm, cell membrane, and cell wall). It is shown that the cell surface charge shifts the resonance frequency and influences the absolute value of rotation velocity.