Design of Electroporation Process in Irregularly Shaped Multicellular Systems

Electroporation technique is widely used in biotechnology and medicine for the transport of various molecules through the membranes of biological cells. Different mathematical models of electroporation have been proposed in the literature to study pore formation in plasma and nuclear membranes. These studies are mainly based on models using a single isolated cell with a canonical shape. In this work, a space–time (x,y,t) multiphysics model based on quasi-static Maxwell’s equations and nonlinear Smoluchowski’s equation has been developed to investigate the electroporation phenomenon induced by pulsed electric field in multicellular systems having irregularly shape. The dielectric dispersion of the cell compartments such as nuclear and plasmatic membranes, cytoplasm, nucleoplasm and external medium have been incorporated into the numerical algorithm, too. Moreover, the irregular cell shapes have been modeled by using the Gielis transformations.

Analytical Solutions for Composition-Dependent Coagulation

Exact solutions of the bicomponent Smoluchowski’s equation with a composition-dependent additive kernelK(va,vb;va′,vb′)=α(va+va′)+(vb+vb′)are derived by using the Laplace transform for any initial particle size distribution. The exact solution for an exponential initial distribution is then used to analyse the effects of parameterαon mixing degree of such bicomponent mixtures and the conditional distribution of the first component for particles with given mass. The main finding is that the conditional distribution of large particles at larger time is a Gaussian function which is independent of the parameterα.

Kinetics of the renneting reaction followed by measurement of turbidity as a function of wavelength

In order to describe the kinetics of rennet coagulation, measurements of turbidity as a function of wavelength were used to determine the weight-average degree of polymerization, x¯w, during renneting of milk at three different concentrations of enzyme and three concentrations of casein, including the normal casein concentration of milk. The change of x¯w as a function of time was described using Von Smoluchowski's equation, testing a number of expressions for the aggregation rate constant, kij. The best description was achieved when kij was taken as a function of an energy barrier against aggregation that was diminished by the proteolysis of κ-casein. The initial value of the energy barrier partly depended on the casein concentration, and had a value >25 kBT at normal casein concentration, where kB is Boltzmann's constant and T the absolute temperature. When the proteolysis of κ-casein was complete, the energy barrier was reduced to 11 kBT and was independent of casein concentration.

Boundary effects on electrophoresis of colloidal cylinders

An exact analytical study is presented for the electrophoresis of an infinite insulating cylinder in the proximity of an infinite plane wall parallel to its axis. The electric field is exerted perpendicular to the particle axis in two fundamental cases: normal to a conducting plane and parallel to a non-conducting wall. The electrical double layers adjacent to solid surfaces are assumed to be thin with respect to the particle radius and the gap thickness between surfaces. The two-dimensional electrostatic and hydrodynamic governing equations are solved in the quasi-steady limit using bipolar coordinates and the typical electric-field-line, equipotential-line and streamline patterns are exhibited. Corrections to Smoluchowski's equation for the electrophoretic velocities of the particle are determined in simple closed forms as a function of λ, the ratio of particle radius to distance of the particle axis from the wall. Interestingly, the electrophoretic mobility of the cylinder in the direction parallel to a dielectric plane increases monotonically as the particle approaches the wall and becomes infinity when the particle touches the wall. For the motion of a cylinder normal to a conducting plane, the presence of the wall causes a reduction in the electrophoretic velocity, which goes to zero as λ → 1. It is found that boundary effects on the electrophoresis of a cylinder are much stronger than for a sphere at the same value of λ. The boundary effects on the particle mobility and on the fluid flow pattern in electrophoresis differ significantly from those of the corresponding sedimentation problem with which comparisons are made.