Single-cell kinetics, steady-state models

The value of combinations of steady-state and transient experiments In formulating and testing models of single cell kinetics and controls will be apparent In the examples which follow. 

Omran et al. have proposed a 3D, single phase steady-state model of a liquid feed DMFC [181]. Their model is implemented into the commercial computational fluid dynamics (CFD) software package FLUENT . The continuity, momentum, and species conservation equations are coupled with mathematical descriptions of the electrochemical kinetics in the anode and cathode channel and MEA. For electrochemical kinetics, the Tafel equation is used at both the anode and cathode sides. Results are validated against DMFC experimental data with reasonable agreement and used to explore the effects of cell temperature, channel depth, and channel width on polarization curve, power density and crossover rate. The results show that the power density peak and crossover increase as the operational temperature increases. It is also shown that the increasing of the channel width improves the cell performance at a methanol concentration below 1 M. 

Almost all works on optimization of a multi-product microbial cell factory focussed on a single objective (e.g., Schmid et al., 2004 Visser et al, 2004 Vital-Lopez et al, 2006). A common feature in these works is the pseudo-stationary assumption. Enzymatic reaction kinetics in a microbial cell factory are reversible and interdependent. In reality, the fluxes due to enzymatic reactions are never stationary. Given the limitations of a model, it is necessary to assume a pseudo-stationary state where some variables fluctuate about an averaged steady state within certain bounds. 

Other related models have been proposed for Ca oscillations, one of which invokes the inhibition by intravesicular Ca of its transport into the cytosol (Swillens Mercan, 1990) since total cell Ca is assumed to be constant, however, such regulation is tantamount to CICR. In that model, oscillations of IP3 occur due to the assumed activation by Ca of the metabolic transformation of IP3. Another model, directly based on CICR, has been proposed (Somogyi Stucki, 1991) for Ca oscillations in hepatocytes. Fundamentally, that model does not differ significantly from the one described above (fig. 9.4c) what differentiates it is the recourse to polynomial kinetics, similar to that considered in the Brusselator model (Lefever Nicolis, 1971), to describe the underlying biochemical processes, and the consideration of a single pool of Ca sensitive to IP3 as well as Ca ". In contrast to experimental observations, the steady-state level of cytosolic Ca " in that model remains independent of external stimulation. 

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