Electrodiffusion kinetics of ionic transport in a simple membrane channel.

We employ numerical techniques for solving time-dependent full Poisson-Nernst-Planck (PNP) equations in 2D to analyze transient behavior of a simple ion channel subject to a sudden electric potential jump across the membrane (voltage clamp). Calculated spatiotemporal profiles of the ionic concentrations and electric potential show that two principal exponential processes can be distinguished in the electrodiffusion kinetics, in agreement with original Planck's predictions. The initial fast process corresponds to the dielectric relaxation, while the steady state is approached in a second slower exponential process attributed to the nonlinear ionic redistribution. Effects of the model parameters such as the channel length, height of the potential step, boundary concentrations, permittivity of the channel interior, and ionic mobilities on electrodiffusion kinetics are studied. Numerical solutions are used to determine spatiotemporal profiles of the electric field, ionic fluxes, and both the conductive and displacement currents. We demonstrate that the displacement current is a significant transient component of the total electric current through the channel. The presented results provide additional information about the classical voltage-clamp problem and offer further physical insights into the mechanism of electrodiffusion. The used numerical approach can be readily extended to multi-ionic models with a more structured domain geometry in 2D or 3D, and it is directly applicable to other systems, such as synthetic nanopores, nanofluidic channels, and nanopipettes.

Microfluidic chip for fast bioassays-evaluation of binding parameters.

A seven channel polystyrene (PS) microchip has been constructed using a micromilling machine and a high-temperature assembling. Protein A (PA) has been immobilized by a passive sorption on the microchannel walls. Two bioaffinity assays with human immunoglobulin G (hIgG) as a ligand have been carried out. (i) PA as the receptor and fluorescently labeled hIgG (FITC-hIgG) as the ligand, (ii) PA as the receptor with hIgG as the quantified ligand and fluorescently labeled goat anti-human IgG (FITC-gIgG) as the secondary ligand. One incubation step of the assays took only 5 min instead of hours typical for enzyme-linked immunosorbent assay applications. Calibration curves of the dependence of a fluorescence signal on the hIgG concentration in a sample have been obtained in one step due to a parallel arrangement of microchannels. A mathematical model of the PA-FITC-hIgG complex formation in the chip has been developed. The values of the kinetic constant of the PA-FITC-hIgG binding (k(on)=5.5 m(3) mol(-1) s(-1)) and the equilibrium dissociation constant of the formed complex (K(d)

Oscillations, period doublings, and chaos in CO oxidation and catalytic mufflers.

Early experimental observations of chaotic behavior arising via the period-doubling route for the CO catalytic oxidation both on Pt(110) and Ptgamma-Al(2)O(3) porous catalyst were reported more than 15 years ago. Recently, a detailed kinetic reaction scheme including over 20 reaction steps was proposed for the catalytic CO oxidation, NO(x) reduction, and hydrocarbon oxidation taking place in a three-way catalyst (TWC) converter, the most common reactor for detoxification of automobile exhaust gases. This reactor is typically operated with periodic variation of inlet oxygen concentration. For an unforced lumped model, we report results of the stoichiometric network analysis of a CO reaction subnetwork determining feedback loops, which cause the oscillations within certain regions of parameters in bifurcation diagrams constructed by numerical continuation techniques. For a forced system, numerical simulations of the CO oxidation reveal the existence of a period-doubling route to chaos. The dependence of the rotation number on the amplitude and period of forcing shows a typical bifurcation structure of Arnold tongues ordered according to Farey sequences, and positive Lyapunov exponents for sufficiently large forcing amplitudes indicate the presence of chaotic dynamics. Multiple periodic and aperiodic time courses of outlet concentrations were also found in simulations using the lumped model with the full TWC kinetics. Numerical solutions of the distributed model in two geometric coordinates with the CO oxidation subnetwork consisting of several tens of nonlinear partial differential equations show oscillations of the outlet reactor concentrations and, in the presence of forcing, multiple periodic and aperiodic oscillations. Spatiotemporal concentration patterns illustrate the complexity of processes within the reactor.

Mathematical modelling of adsorption and transport processes in capillary electrochromatography: open-tubular geometry.

A mathematical modelling approach for open-tubular capillary electrochromatography is presented. The spatially one-dimensional model takes into account (i) a coupling of (non)linear adsorption of positively or negatively charged analyte molecules (at a negatively charged capillary inner surface) with the equilibrium electrokinetics at this solid-liquid interface, (ii) mobile phase transport by electroosmosis and pressure-driven flow, as well as (iii) transport of species by electrophoresis and molecular diffusion. Under these conditions the local zeta-potential and electroosmotic mobility become a function of the concentration of the charged analyte. The resulting inhomogeneity of electroosmotic flow through the capillary produces a compensating pore pressure as requirement for incompressible mobile phase flow (i.e., for constant volumetric flow along the capillary). The results of the simulations are discussed in view of the surface-to-volume ratio of the capillary lumen, the analyte concentration (in combination with a Langmuir isotherm for the adsorption process), and buffer effects.

Chaotic patterns in a coupled oscillator-excitator biochemical cell system.

In this paper we examine dynamical modes resulting from diffusion-like interaction of two model biochemical cells. Kinetics in each of the cells is given by the ICC model of calcium ions in the cytosol. Constraints for one of the cells are set so that it is excitable. One of the constraints in the other cell - a fraction of activated cell surface receptors-is varied so that the dynamics in the cell is either excitable or oscillatory or a stable focus. The cells are interacting via mass transfer and dynamics of the coupled system are studied as two parameters are varied-the fraction of activated receptors and the coupling strength. We find that (i) the excitator-excitator interaction does not lead to oscillatory patterns, (ii) the oscillator-excitator interaction leads to alternating phase-locked periodic and quasiperiodic regimes, well known from oscillator-oscillator interactions; torus breaking bifurcation generates chaos when the coupling strength is in an intermediate range, (iii) the focus-excitator interaction generates compound oscillations arranged as period adding sequences alternating with chaotic windows; the transition to chaos is accompanied by period doublings and folding of branches of periodic orbits and is associated with a Shilnikov homoclinic orbit. The nature of spontaneous self-organized oscillations in the focus-excitator range is discussed. (c) 1999 American Institute of Physics.