Pavel Hasal

Modeling of hydrogel immobilized enzyme reactors with mass-transport enhancement by electric field

Abstract Effects of electro-transport processes in enzymatic reactors with spatially continuous unstirred reaction media (e.g., gels or polymers) on enzyme reactions are studied by numerical simulations. Two model enzyme reactions are chosen for analysis: (i) with no ionic reaction components, and (ii) with only ionic components and with production of H+ ions. The electrophoretic migration and electro-osmotic flux are considered as mechanisms altering transport rates of reaction components in unstirred reaction medium. Mathematical models of reactor system with hydrophilic membrane (or slab) containing immobilised enzyme with the DC electric field applied in a direction perpendicular to the membrane are constructed. Remarkable increase of the immobilised enzyme productivity was observed when the electric current of proper intensity was applied to the system. This optimum current value depends on substrate concentration, the slab thickness and the rate of enzyme inactivation. Main factor limiting applicability of the electric current to the reaction slab is heating of the slab due to the Joule heat. The electrophoretic migration of H+ ions in the second reaction system prevents local over-acidification, i.e. the averaged reaction yield is higher compared to the system with no electric field applied. An example of experimental results obtained in a laboratory-scale electro-membrane reactor with immobilised penicillin G acylase is also discussed.

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.

Macro-instability: a chaotic flow component in stirred tanks

Chaotic features of the macro-instability (MI) of flow patterns in stirred tanks are studied in this paper. Datasets obtained by measuring the axial component of the fluid velocity and the tangential force affecting the baffles are used. Two geometrically identical, flat-bottomed cylindrical mixing tanks (diameter of 0.3 m) stirred with either pitched blade turbine impellers or Rushton turbine impeller are used in the experiments, and water and aqueous glycerol solutions are used as the working liquids. First, the presence of the MI component in the data is examined by spectral analysis. Then, the MI components are identified in the data using the proper orthogonal decomposition (POD) technique. The attractors of the macro-instability are reconstructed using either the POD eigenmodes or a method of delays and finally the attractor invariants are evaluated. The dependence of the correlation dimension and maximum Lyapunov exponent on the vessel operational conditions is determined together with their distribution within the tank. No significant spatial variability of the correlation dimension value is observed. Its value is strongly influenced by impeller speed and by the vessel–impeller geometry. More profound spatial distribution is displayed by the maximum Lyapunov exponent taking distinctly positive values. These two invariants, therefore, can be used to locate distinctive regions with qualitatively different MI dynamics within the stirred tank.

Mathematical modeling of wastewater decolorization in a trickle-bed bioreactor.

This work focuses on mathematical modeling of removal of organic dyes from textile industry waste waters by a white-rot fungus Irpex lacteus in a trickle-bed bioreactor. We developed a mathematical model of biomass and decolorization process dynamics. The model comprises mass balances of glucose and the dye in a fungal biofilm and a liquid film. The biofilm is modeled using a spatially two-dimensional domain. The liquid film is considered as homogeneous in the direction normal to the biofilm surface. The biomass growth, decay and the erosion of the biofilm are taken into account. Using experimental data, we identified values of key model parameters: the dye degradation rate constant, biofilm corrugation factor and liquid velocity. Considering the dye degradation rate constant 1×10⁻⁵ kg m⁻³ s⁻¹, we found optimal values of the corrugation factor 0.853 and 0.59 and values of the liquid velocity 5.23×10⁻³ m s⁻¹ and 6.2×10⁻³ m s⁻¹ at initial dye concentrations 0.09433 kg m⁻³ and 0.05284 kg m⁻³, respectively. A good agreement between the simulated and experimental data using estimated values of the model parameters was achieved. The model can be used to simulate the performance of laboratory scale trickle-bed bioreactor operated in a batch regime or to estimate values of principal parameters of the bioreactor system.

Optimization of aqueous two-phase systems for the production of 6-aminopenicillanic acid in integrated microfluidic reactors-separators

Aqueous two-phase systems (ATPSs) were screened for the production of 6-aminopenicillanic acid (6-APA) catalyzed by penicillin acylase, followed by the extractive separation of 6-APA from the reaction mixture. The key point of this study was to find an ATPS exhibiting a large difference in the partition coefficients of the biocatalyst and reaction products. Several ATPSs based on polyethylene glycol (PEG)/phosphate, PEG/citrate, and PEG/dextran were tested. We found that an ATPS consisting of 15 wt% of PEG 4000, 10 wt% of phosphates, 75 wt% of water (pH value 8.0 after dissolution) provided optimal separation of 6-APA from the enzyme. While the 6-APA was mainly found in the top PEG phase, the free enzyme favored the bottom salt-rich phase. This ATPS also fulfils other important requirements: (i) high buffering capacity, reducing an undesirable pH decrease due to the dissociation of phenylacetic acid (the side product of the reaction), (ii) a relatively low cost of the ATPS components, (iii) the possibility of electrophoretic transport of fine droplets as well as the reaction products for both the acceleration of phase separation and the enhancement of 6-APA concentration in the product stream. Extraction experiments in microcapillary and batch systems showed that the transport of 6-APA formed in the salt-rich phase to the corresponding PEG phase could occur within 30 s. The experimental results described form a base of knowledge for the development of continuously operating integrated microfluidic reactors-separators driven by an electric field for the efficient production of 6-APA.