Adsorption of a microtubule on a charged surface affects its disassembly dynamics.

The dynamics of disassembly of microtubules deposited on surfaces is shown to be strongly dependent on the electrostatic interaction between the microtubule and the substrate. Fluorescence microscopy of microtubules adsorbed on a Poly-L-Lysine film and immersed in pure water show a drastic decrease in disassembly velocity compared to the microtubules in bulk water solutions. While microtubules suspended in pure water disassemble in seconds, the dissociation velocity of microtubules adsorbed on a Poly-L-Lysine film ranges from 0.8 to 1.0 microm/min in pure water. Kinetic Monte Carlo simulations of the microtubule dynamics indicate that a decrease in the dissociation velocity of unstable microtubules can be achieved by reducing the heterodimer dissociation rate constant of tubulin heterodimers constituting a single protofilament, adsorbed to the Poly-L-Lysine film. This model suggests that the reduction of the dissociation velocity originates from the electrostatic interactions between the positively charged amino groups of the Poly-L-Lysine film and the negatively charged microtubule surface.

Numerical technique and computational procedure for isotachophoresis.

This paper presents a new numerical method for computation of solutions of prototypical equations of isotachophoresis. Numerical computation is complicated because the Poisson equation, which relates electrostatic potential to space charge density, contains a small parameter. This parameter is usually assumed to have the value of zero. Under this assumption the Poisson differential equation is replaced by an algebraic equation, which is often called the equation of electroneutrality, because it indeed states that the electrolyte is electrically neutral this assumption were not studied in the past. Here we propose an iterative procedure which allows for computation of solutions without the assumption of electroneutrality. The accuracy is controlled by a number of iterations and is limited by a computer round-off error only. The method is based on our previously published theory of existence and uniqueness of solutions of isotachophoretic equations. Details of the computational algorithm for prototypical equations of isotachophoresis are given. A numerical example and comparison with previously published data are also provided.

Electrophoresis: mathematical modeling and computer simulation.

A mathematical model of electrophoretic separation processes has been developed and adapted for computer simulations. The model is used to predict the characteristic behavior of a variety of electrophoretic techniques from a knowledge of chemical equilibria and physical transport phenomena. The model provides a unifying basis for a rational classification of all electrophoretic processes.

Mathematical model for transient isoelectric focusing of simple ampholytes.

A mathematical model describing transient processes in isoelectric focusing (IEF) of L biprotic ampholytes is presented. The model is a generalization of our previous research on steady slate in IEF and consists of L nonlinear partial differential equations coupled with 2L+2 algebraic equations. Constraints imposed by the mode of operation, viz., constant current. voltage or power, are described. Due to the nonlinearity of the equations, analysis of the model requires computer simulation. Model equations suitable for computer implementation are derived.

Mathematical modeling and computer simulation of isoelectric focusing with electrochemically defined ampholytes.

A mathematical model of isoelectric focusing at the steady state has been developed for an M-component system of electrochemically defined ampholytes. The model is formulated from fundamental principles describing the components' chemical equilibria, mass transfer resulting from diffusion and electromigration, and electroneutrality. The model consists of ordinary differential equations coupled with a system of algebraic equations. The model is implemented on a digital computer using FORTRAN-based simulation software. Computer simulation data are presented for several two-component systems showing the effects of varying the isoelectric points and dissociation constants of the constituents.

Application of discrete computer modeling to the dynamics of cell populations.

Computer simulation of the dynamics of cell populations is discussed in the paper. Fundamental features of CELLSIM simulation language are described. Acute leukemia cell population model was implemented on a digital computer using CELLSIM. Some of the computer outputs are shown. The results obtained so far are interesting and promissing for further research.