Cell kinetics structured models

In this chapter, cell kinetic equations are derived from the unstructured, distributed model, and those equations are applied for the analysis and design of ideal fermenters. More realistic models which consider the multiplicity of cell components, structured model, are introduced at the end of the chapter. 

Few models include the effects of in situ gas formation on the fluidization properties of the reactors this improvement, along with improvements in other areas, such as inclusion of improved structured models of microbial kinetics or inclusion of maintenance energy requirements or the effects of suspended cells on the reaction rate, might produce more accurate models, though it is unclear at this point whether the increased complexity would be justified. 

Figure 4.15a shows the structure of a modified Randles cell. This circuit models a cell in which polarization is due to a combination of kinetic and diffusion processes with infinite thickness. 

One can distinguish between structured and unstructured models, the latter neglecting intracellular phenomena. On the contrary, structured models account for intracellular processes and states in different compartments of the cell or include explicit kinetics for various intracellular steps of virus replication. 

Capeillere-Blandin, C. and Albani, J. 1987, Cytochrome b2, an electi on carrier between flavocytochrome b, and cytochrome c Rapid kinetic characterisation of the electron transfer parameters with ionic strength dependence. Biochemical Journal 245, 159-165. Carpita, N. C. and Gibeaut, D. M. 1993, Structural models of primary cell walls in flowering plants consistency of molecular structure with the physical properties of the walls during growth. Plant Journal 3, 1 -30. 

Thus, the kinetics of conversions In metabolic cellular sequences, and even in whole cell kinetics, at or near steady state may be expected to resemble the kinetic rate form appropriate to one or a very small number of sequential enzyme catalyzed steps. The implications of this point in kinetic models of structured cell systems are reflected in later contributions in this conference. 

To a large extent, the formal kinetic analysis techniques presented in this chapter relate to discontinuous batch operations. Even if the goal is a continuous operation, the batch process kinetic model serves as a start-up. The most significant element of a kinetic analysis is the time dependence of the macroscopic process variables mentioned in Chap. 2. Bacteria, molds, viruses, and yeasts all have different reproduction mechanisms, and formulating a structured kinetic model more closely related to the actual mechanism is a desirable goal. More structured models are desirable not only to deal with active cells but also to extend kinetic analysis to more complex situations involving inactive cells, mixed populations of cells, multiple substrates, and... 

Basic requirements on feasible systems and approaches for computational modeling of fuel cell materials are (i) the computational approach must be consistent with fundamental physical principles, that is, it must obey the laws of thermodynamics, statistical mechanics, electrodynamics, classical mechanics, and quantum mechanics (ii) the structural model must provide a sufficiently detailed representation of the real system it must include the appropriate set of species and represent the composition of interest, specified in terms of mass or volume fractions of components (iii) asymptotic limits, corresponding to uniform and pure phases of system components, as well as basic thermodynamic and kinetic properties must be reproduced, for example, density, viscosity, dielectric properties, self-diffusion coefficients, and correlation functions (iv) the simulation must be able to treat systems of sufficient size and simulation time in order to provide meaningful results for properties of interest and (v) the main results of a simulation must be consistent with experimental findings on structure and transport properties. 

Summing up this section, we would like to note that understanding size effects in electrocatalysis requires the application of appropriate model systems that on the one hand represent the intrinsic properties of supported metal nanoparticles, such as small size and interaction with their support, and on the other allow straightforward separation between kinetic, ohmic, and mass transport (internal and external) losses and control of readsorption effects. This requirement is met, for example, by metal particles and nanoparticle arrays on flat nonporous supports. Their investigation allows unambiguous access to reaction kinetics and control of catalyst structure. However, in order to understand how catalysts will behave in the fuel cell environment, these studies must be complemented with GDE and MEA tests to account for the presence of aqueous electrolyte in model experiments. 

The O Flaherty Model simulates the age-dependence of lead kinetics on such factors as absorption efficiency, excretion efficiency, uptake into bone and loss from bone, and partitioning between plasma and red blood cells. The model does not incorporate age, dose rate, or time dependence of lead accumulation in every organ (e g., kidney) because the complex patterns of lead accumulation in certain tissues are not known (O Flaherty 1991a) (see Section 2.4.1). However, the basic model structure allows for additional modules to be incorporated, depending on its intended use in risk assessment. For example, additional modules that are currently being developed are a pregnancy model and a model of net bone loss in older women and men. 

The Leggett Model simulates the age-dependence of lead kinetics on such factors as bone turnover rates, partitioning between soft tissues and excreta, removal half-times in liver, kidneys, and red blood cells, and the deposition fraction in brain. The model structure represents a compromise between biological realism and practical considerations regarding the quantity and quality of information available to determine parameter values (Leggett 1993). 

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