Yuri A. Chizmadzhev

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.

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.

Membrane fusion: overcoming of the hydration barrier and local restructuring.

The early stages of membrane fusion have been investigated theoretically. It has been shown that the hydration repulsion, operating between apposed membranes, is overcome locally under the action of out-of-plane thermal fluctuations of the bilayers. The fluctuations lead to the formation of close (less than 0.5 nm) contact between the membranes within a small area (approximately 10 nm2). Increasing hydration repulsion between apposed polar heads of lipid molecules in this area causes the rupture of interacting monolayers. The rupture results in monolayer fusion of the membranes, i.e. in the formation of a bridge connecting the monolayers, which is usually named the monolayer stalk. The influence of degree of hydration of the monolayers and their spontaneous curvature on conditions of monolayer fusion have been analysed. The proposed mechanism of early stages of fusion process can proceed without preliminary formation of tight dehydrated contact between the membranes and even without any dehydration.

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 Lagranges 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.

Measurement of Rapid Release Kinetics for Drug Delivery

A fluorescence measurement system and methods of data analysis were developed to measure rapid kinetics of transdermal transport in vitro. Three variations on the technique were demonstrated, where the receptor compartment concentration was determined by: 1) fluorescence measurements of aliquots removed at discrete time points, 2) continuous fluorescence measurements made directly in the receptor compartment using a custom-made fluorimeter cuvette as a permeation chamber, and 3) continuous fluorescence measurements made in a flow-through cuvette containing receptor solution continuously pumped from a flow-through permeation chamber. In each case, the measured signal was a convolution of the time-dependent molecular flux (the desired information) and the characteristic response of the measurement system. Algorithms for deconvolution of the signal were derived theoretically. For the most complicated case, (3), the experimental confirmation is shown here, proving a time resolution on the order of half a minute.

Electrical Breakdown of Lipid Bilayer Membranes

It is known that in the case of a sufficiently strong polarization of cell membranes by an external electric field, processes develop in a membrane which lead to a very significant increase in conductance and permeability. When the field is switched off, the membrane can return from such a high-conducting state to the initial one. This phenomenon is called reversible electrical breakdown (Stampfli, 1958; Zimmermann, 1982). If the amplitude or duration of a pulse is sufficiently large, irreversible damage of the cell membranes occurs. Interest in the study of this phenomenon is based on the existence of important biotechnological applications, many of which have been reflected in this collective book.

Lipid Bilayer Electropermeabilization

In the majority of cells, under normal physiological conditions, there exists a transmembrane potential difference of about several tens of millivolts. This means that the electric field in biomembranes is rather high, approximately 105 V/cm. With a further increase in the electric field, biomembranes undergo changes that lead to a drastic (by 5-7 orders of magnitude) increase in their conductance and permeability (for reviews see Refs. 1-4). If this conductance increment is accompanied by mechanical rupture of the membrane, one speaks of irreversible electrical breakdown. When such an increment is temporary, the phenomenon is called reversible electrical breakdown [5,6]. Electropermeabilization of cell membranes has attracted significant attention because it has found many biomedical and biotechnological applications [1,4].

Single membrane in electric field

Biological membranes play an important role in the vital activity of a cell. It is these membranes that make it possible to maintain non-equilibrium concentrations of substances in the cytoplasm. The free energy stored in the form of ionic gradients and transmembrane potential differences is used for transmitting information, for electrosynthesis, for performing mechanical work, for reception etc. All of these varied capabilities of biomembranes are essentially based on their excellent barrier properties, combined with their ability to realize selective transport. The latter can be controlled by an electric field. If a membrane loses its barrier function, nothing will prevent the system from a transition to an equilibrium state, but for a cell, equilibrium means death. Therefore the problem of biomembrane stability is of paramount importance. An electric field holds a unique position among the various factors diminishing the membrane stability. The point is that, under normal physiological conditions, in the majority of cells there exists a transmembrane potential difference of several tens of millivolts. This means that the electric field in the membranes amounts to about 105 V/cm, i.e. it is close to the critical field which causes, for example, dielectric breakdown of liquid hydrocarbons. With a further increase in the electric field the biomembranes undergo changes that lead to a considerable (by 5-7 orders of magnitude) increase in their conductance.

Theoretical Issues in Understanding Local Transport Regions in Electroporated Stratum Corneum

A number of studies have been performed on the application of electric field pulses to human stratum in vitro. 1–12 Among other interesting results, it has been shown that molecular transport across the stratum comeum is highly localized.4,8,10 However, unlike in iontophoresis, this transport is not confined to sweat ducts or hair follicles. These “local transport regions” (LTRs) occupy perhaps 1-10% of the stratum comeum and are easily reproducible. The reason for this localization of molecular transport is poorly understood theoretically.