Unstructured kinetic models

Cell growth involves numerous complicated networks of biochemical and chemical reactions. A simple unstructured kinetic model was formulated based on the assumptions that... 

To some extent, the simple unstructured kinetic models can be used for... 

Basic Unstructured Kinetic Models for Growth and Substrate Utilization (Homogeneous Rate Equations)... 

At each temperature the simple Monod kinetic model can be used that can be combined with material balances to arrive at the following unstructured model... 

Esener, A. A., Roels, J. A. and Kossen, N. W. F. Biotechnoi. Bioeng. 25 (1983) 2803. Theory and applications of unstructured growth models Kinetic and energetic aspects. 

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. 

Assuming that oxygen supply is sufficient to avoid local oxygen limitations, the kinetic model required for the simulation includes only the material balance equation for the substrate. As suggested in earfier simulations based on recirculation models (micro-macromixer) by Bajpai and Reuss [60], the uptake kinetics are only considered in the vicinity of the so-called critical sugar concentration. Thus, a rather simple unstructured empirical model is chosen for the purpose of this study. It involves a Monod type of kinetics for substrate uptake... 

In the literature there are several ways of classifying different types of models (cf. Roels and Kossen, 1978, and Sect. 2.4.3). From the viewpoint of process engineering, in this book distinctions will be made among macrokinetic, microkinetic, formal kinetic, and process kinetic models (see Fig. 2.14). The formal models that will be discussed individually in Chap. 5 are sometimes referred to in the literature as unsegregated or unstructured models that have a descriptive or predictive nature. 

Figure 2.19. Flowchart of the construction of unstructured biokinetic models as a consequence of joint activity between kinetic work and stoichiometry. (Adapted from Reels, 1980a. With permission of John Wiley Sons, Inc.).

Aerobic The growth kinetics was described by an interacting, balanced and unstructured model characterized by phenol inhibition and oxygen limitation according to a double limiting kinetics [60, 62],... 

A substantial number of models have been proposed for the insect cells/BEVS system ranging from empirical approaches [103], through unstructured [102, 104],structuxed and mechanistic [60,61] to a recent kinetic and statistical-thermodynamic model [105]. 

Even though Williams s model provides many features that unstructured models are unable to predict, it requires only two parameters, which is the same number of parameters required for Monod kinetics. 

From kinetics studies of unicellular organisms, a set of mathematical expressions have been established to represent the most frequent phenomena in bioprocesses. These phenomena involve a limitation or inhibition of growth and product formation, caused by the presence of substrates, products, or byproducts in culture media. Many of these expressions do not derive from known kinetic mechanisms. In fact, they are simply mathematical expressions with fitted parameters that are able to reproduce experimentally observed kinetic profiles. These equations have been derived and used in many unstructured microbial or cell models. 

Many of the equations employed in unstructured and non-segregated models derive from those of enzymatic kinetics (Sinclair and Kristiansen, 1987 Nielsen and Nikolajsen, 1988). Cells are considered as chemical reactors that support thousands of complex reactions catalyzed by enzymes that allow the conversion of substrates into secreted products. The equation formulated by Michaelis and Menten represents the enzymatic conversion rate of a unique substrate into one product (Equation 14). 

Unstructured models, as detailed in Sections 8.3.1 and 8.3.2, are formulated by a series of kinetic and differential non-linear equations that represent the dynamics of all the state variables during the process. Thus, to simulate a model that consists of parameters and state variables, it is necessary to attribute values to the parameters. 

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. 

Where S, G, X, E and Enz are respectively the starch, glucose, cells, ethanol and enzyme concentrations inside the reactor, Si is the starch concentration on the feed, F is the feed flow rate, V is the volume of hquid in the fermentor and (pi, (p2, (ps represent the reaction rates for starch degradation, cells growth and ethanol production, respectively. The unstructured model presented in (Ochoa et al., 2007) is used here as the real plant. The ki (for i=l to 4) kinetic parameters of the model for control were identified by an optimization procedure given in Mazouni et al. (2004), using as error index the mean square error between the state variables of the unstructured model and the model for control. 

Various models ranging from unstructured, nonse-gregated to structured, segregated are used to describe cell growth. The most common kinetic expression is the Monod equation ... 

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