A theoretical model for enzymatic catalysis using asymmetric hollow fiber membranes
TL;DR: A numerical finite difference solution for nonlinear Michaelis-Menten reaction kinetics is shown to agree with the analytic solution, as Km/C0, the ratio of the Michaelis constant to the initial substrate concentration, becomes large (> 100).
Abstract: The behavior of an immobilized enzyme reactor utilizing asymmetric hollow fibers is simulated using a theoretical model. In this reactor, an enzyme solution contained within the annular open-cell porous support structure of the fiber is separated from a substrate flowing through the fiber lumen by an ultrathin dense membrane impermeable to enzyme but permeable to substrate and product. The coupled set of model equations describing the behavior of this reactor represents an extended Graetz problem in the fiber lumen, with diffusion through the ultrathin fiber skin and reaction in the microporous sponge region. Exact analytic expressions for substrate concentration profiles throughout an idealized fiber which incorporate the membrane and hydrodynamic mass transfer resistances are obtained for a first-order enzyme reaction, and numerical techniques for their evaluation are given. This analysis is extended to yield a numerical finite difference solution for nonlinear Michaelis-Menten reaction kinetics, which is shown to agree with the analytic solution, as Km/C0, the ratio of the Michaelis constant to the initial substrate concentration, becomes large (> 100).
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TL;DR: Any comprehensive review of the membrane technology field written today would have to contain even more references than this one does; it is partly an overview, giving my opinions of what, among all the work done in this field over the past two centuries or so, is most relevant.
537 citations
TL;DR: Techniques which have been used to immobilize whole cells include adsorption, aggregation, confinement and entrapment, and many more have been proposed.
432 citations
TL;DR: This chapter discusses the kinetic behavior of immobilized enzyme systems, which can be controlled by both microenvironmental and mass-transfer effects.
Abstract: Publisher Summary This chapter discusses the kinetic behavior of immobilized enzyme systems. In the case of immobilized enzymes, the kinetic behavior can be controlled by both microenvironmental and mass-transfer effects. It is useful to distinguish between intrinsic rate parameters of the enzymic reaction—that is, the kinetic parameters characteristic of the native enzyme in solution. The techniques commonly employed for the characterization of diffusional resistances and the evaluation of the intrinsic or inherent kinetic parameters of immobilized enzyme systems are classified in three main groups: direct determination of kinetic and transport parameters, variation of substrate concentration, and variation of characteristic support dimensions.
189 citations
TL;DR: Despite considerable uncertainty in parameters and nonidealities in hollow fiber geometry, the cell distribution correlated well with the modeling results, and design criteria such as fiber dimensions and spacing, reactor lengths, and recycle flow rates can be selected using these plots.
Abstract: Axial and radial oxygen depletion are believed to be critical scale-limiting factors in the design of cell culture hollow fiber bioreactors. A mathematical analysis of oxygen depletion has been performed in order to develop effectiveness factor plots to aid in the scaling of hollow fiber bioreactors with cells immobilized in the shell-side. Considerations of the lumen mass transport resistances and the axial gradients were added to previous analyses of this immobilization geometry. An order of magnitude analysis was used to evaluate the impact of the shell-side convective fluxes on the oxygen transport. A modified Thiele modulus and a lumen and membrane resistance factor have been derived from the model. Use of these terms in the effectiveness factor plots results in a considerable simplification of the presentation and use of the model. Design criteria such as fiber dimensions and spacing, reactor lengths, and recycle flow rates can be selected using these plots. Model predictions of the oxygen limitations were compared to experimental measurements of the axial cell distributions in a severely oxygen limited hollow fiber bioreactor. Despite considerable uncertainty in our parameters and nonidealities in hollow fiber geometry, the cell distribution correlated well with the modeling results.
117 citations
TL;DR: A radial flow hollow fiber bioreactor has been developed that maximizes the utilization of fiber surface for cell growth while eliminating nutrient and metabolic gradients inherent in conventional hollow fiber cartridges.
Abstract: A radial flow hollow fiber bioreactor has been developed that maximizes the utilization of fiber surface for cell growth while eliminating nutrient and metabolic gradients inherent in conventional hollow fiber cartridges. The reactor consists of a central flow distributor tube surrounded by an annular bed of hollow fibers. The central flow distributor tube ensures an axially uniform radial convective flow of nutrients across the fiber bed. Cells attach and proliferate on the outer surface of the fibers. The fibers are pretreated with polylysine to facilitate cell attachment and long-term maintenance of tissuelike densities of cell mass. A mixture of air and CO(2) is fed through the tube side of the hollow fibers, ensuring direct oxygenation of the cells and maintenance of pH. Spent medium diffuses across the cell layer into the tube side of the fibers and is convected away along with the spent gas stream. The bioreactor was run as a recycle reactor to permit maximum utilization of nutrient medium. A bioreactor with a membrane surface area of 1150 cm(2) was developed and H1 cells were grown to a density of 7.3 x 10(6) cells/cm(2).
102 citations