Tomaž Slivnik

TIME COURSE OF TRANSMEMBRANE VOLTAGE INDUCED BY TIME-VARYING ELECTRIC FIELDS : A METHOD FOR THEORETICAL ANALYSIS AND ITS APPLICATION

Abstract The paper describes a general method for analysis of time courses of transmembrane voltage induced by time-varying electric fields. Using this method, a response to a wide variety of time-varying fields can be studied. We apply it to different field shapes used for electroporation and electrofusion: rectangular pulses, trapezoidal pulses (approximating rectangular pulses with finite rise time), exponential pulses, and sine(RF)-modulated pulses. Using the described method, the course of induced transmembrane voltage is investigated for each selected pulse shape. All the studies are performed at different pulse durations, each for both the normal physiological and the low-conductivity medium. For all the pulse shapes investigated, it is shown that as the conductivity of extracellular medium is reduced, this slows down the process of transmembrane voltage inducement. Thus, longer pulses have to be used to attain the desired voltage amplitude, as the influence of the fast, short-lived phenomena on the induced voltage is diminished. Due to this reason, RF-modulation in such a medium is ineffective. The appendix gives a complete set of derived expressions and a discussion about possible simplifications.

Adhesion of osteoblasts to a nanorough titanium implant surface

This work considers the adhesion of cells to a nanorough titanium implant surface with sharp edges. The basic assumption was that the attraction between the negatively charged titanium surface and a negatively charged osteoblast is mediated by charged proteins with a distinctive quadrupolar internal charge distribution. Similarly, cation-mediated attraction between fibronectin molecules and the titanium surface is expected to be more efficient for a high surface charge density, resulting in facilitated integrin mediated osteoblast adhesion. We suggest that osteoblasts are most strongly bound along the sharp convex edges or spikes of nanorough titanium surfaces where the magnitude of the negative surface charge density is the highest. It is therefore plausible that nanorough regions of titanium surfaces with sharp edges and spikes promote the adhesion of osteoblasts.

Charged cylindrical surfaces: effect of finite ion size

A simple statistical mechanical approach is applied to calculate the profile of the density of the number of particles and the profile of the electrostatic potential of an electric double layer formed by a charged cylindrical surface in contact with electrolyte solution. The finite size of particles constituting the electrolyte solution is considered by including the excluded volume effect within the lattice statistics while the electrostatic interactions are considered by means of the mean electrostatic field. It is shown that the excluded volume effect decreases the density of the number of counterions and increases the electrostatic potential near the charged cylindrical surface. The effect is more pronounced for high area densities of charge of the charged surface and for larger counterions. Further, it is shown that the ratio between the density of the number of the counterions near the charged cylindrical surface and the density of the number of counterions far from the charged surface reaches a plateau at large linear charge densities for ions of finite size, while no plateau is reached for dimensionless ions. The effective thickness of the electric double layer in cylindrical geometry is introduced. It is shown that the effective thickness increases with increasing counterion size while its dependence on the area density of charge of the charged surface exhibits a minimum. The theoretical approach presented in this work can be used for description of the electrostatics of the thin cylindrical structures in biological systems such as DNA, protein macromolecules and charged micro and nano tubes.

A numerical method for the solution of two-parameter eigenvalue problems

Abstract We consider a two-parameter weakly coupled eigenvalue problem for matrix equations. Under known assumptions [4] such a problem can be reduced to a system of one-parameter problems in a tensor product space, after which it can be treated by known numerical methods. The method is illustrated by a numerical example of the simple two-parameter problem and the example of Binding and Browne [5]. It turns out that the method is especially suitable for problems of smaller orders.

Membrane Electrostatics—A Statistical Mechanical Approach to the Functional Density Theory of Electric Double Layer

Abstract We describe physical properties of the electric double layer composed of a charged surface in contact with a solution of counter‐ions and coions representing nanoparticles. The electrostatic free energy of the electric double layer is derived using a statistical mechanical approach. The consistently related expressions for the equilibrium ion and solvent distribution functions and the differential equation for the electric potential are derived by minimization of the elctrostatic free energy of the system. The finite size of nanoparticles constituting the solution is taken into account by means of the excluded volume within the lattice model. Different geometries of the electric double layer are considered. We found that an increased size of charged nanoparticles (ions) reduces the number of counter‐ions near the charged surface, leading to an enhancement of the electrostatic surface potential. The linearized Poisson–Boltzmann theory and the influence of the finite size of ions (nanoparticles) on the thickness of the electric double layer are described. Also the intra‐ionic correlations within charged nanoparticles, which have spatially distributed (quadrupolar or dipolar) electric charge, are considered. The interaction between two charged surfaces in the solution composed of charged quadrupolar (divalent) or dipolar rod‐like nanoparticles is calculated. It is shown that for large enough dimensions of charged quadrupolar (divalent) nanoparticles and for large enough surface charge densities of the charged surfaces, two equally charged surfaces experience attractive force owing to spatially distributed charge within the nanoparticles. Also, it is shown that in the vicinity of the charged surface (wall), large rod‐like quadrupolar or dipolar nanoparticles orient in the electric field within the electric double layer. Close to the charged surfaces the orientation of the rod‐like quadrupolar or the dipolar nanoparticles is hindered because of steric restrictions (hard wall).

Flexible Membrane Inclusions and Membrane Inclusions Induced by Rigid Globular Proteins

Abstract We present a theoretical approach to the study of flexible membrane inclusions and membrane inclusions induced by rigid membrane-embedded proteins. We derive the contribution to the free energy of the membrane bilayer for both kinds of inclusions. For flexible membrane inclusions, the phenomenological interaction constants that appear in the free energy expression depend on the physical and geometrical properties of the molecules that constitute the inclusion. The cases of constrained and unconstrained local shape perturbations of the membrane around a rigid membrane inclusion are discussed. The total free energy of membrane bilayer with membrane-embedded inclusions (membrane nanodomains) is derived.

Holistic approach in developing propulsion for urban electric vehicles

In order to develop an outstanding electric vehicle (EV) we have to use all the advantages which are offered by the transition to electric propulsion system. Our concept involves direct drive (DD) propulsion system with four high specific torque inwheel electric motors, improved aerodynamics of a vehicle, weight reduction and optimized hybrid power sources involving a low power high energy primary source and a high power lower energy secondary source. Optimization of propulsion system parameters has been performed in order to obtain satisfying driving and economic performance for a standard city driving cycle.

Effect of counterion size in spherical electric double layer of concave shape

The steric effect of counterions on the electrical properties of spherical electric double layer of concave shape is discussed. In the theory, the electrostatic interaction is described by the mean field approximation, while the finite size of particles in the solution is considered by the excluded volume effect. We showed that near the spherical charged surface of concave shape, the number density of counterions decreases for large counterions compared to the dimensionless counterions while the electrostatic potential near the charged surface increases size of the counterions.

Stability of giant phospholipid vesicles at different concentrations of C/sub 12/E/sub 8/

Membrane properties of giant POPC phospholipids vesicles have been studied in the past. It has been observed that addition of the C/sub 12/E/sub 8/ surfactant may increase the speed of membrane transformation, induce the formation of vesicle protrusions and reduce the lifespan of the POPC vesicles. In this paper we studied the influence of different concentrations of the C/sub 12/E/sub 8/ surfactant on the stability of the giant phospholipids vesicles and the speed of their disintegration. We have observed that at low concentrations of C/sub 12/E/sub 8/ the vesicles eventually adopt a stable shape with the daughter endovesicle and may remain in such state unchanged for at least two hours. At higher concentrations of C/sub 12/E/sub 8/ the vesicles gradually begin to shrink and disintegrate altogether within an hour after addition of the surfactant. We propose possible molecular mechanisms underlying the reported phenomena.