Mathematical models cultures

The main choice of these functions should be based on data from suitable laboratory experiments. This approach has been recently applied to the mathematical study of the allelopathic competition between Pseudokirchneriella subcapitata and Chlorella vulgaris in an open culture (a chemostat-like device), where the nutrient is a mixture of inorganic phosphates Pi. Here we will illustrate step by step the four mentioned features, observing that each equation of the mathematical model can be actually constructed as a balance equation. 

J. Andrews. A mathematical model for the continous culture of microorganisms utilizing inhibitory substrates. Biotechnol. Bioeng., 10 707-723, 1968. 

In this part the application of mathematical models to CLP and VLP production with baculovirus infected insect cell cultures is discussed. Special emphasis on model evaluation is made along with the definition of directions in future process development research with this system. 

Andrews, J. F., "A Mathematical Model for the Continuous Culture of Microorganisms Utilizing Inhibitory Substrates," Biotechnol. Bioeng. 10(1968) 707-723. 

Mathematical models for growth and product synthesis in animal cell culture... 

The systematization of biological data through mathematical modeling is not a trivial task and requires the intensive use of material and human resources. Moreover, the models often incorporate experimental uncertainties that do not always allow the identification of the trends of the culture, with the desired precision. Figure 8.1 summarizes the main types of models applied to the description of cellular metabolism, according to the classification proposed by Tsuchiya et al., (1966). 

The identification of such phenomena, as the basis for any mathematical model building, assumes certain knowledge about cell metabolism, under different culture conditions. Chapter 4 discusses the metabolism of animal cells, and should be consulted for a full understanding of the kinetic models presented below. 

Zeng AP, Deckwer WD (1995b), Mathematical modeling and analysis of glucose and glutamine utilization and regulation in cultures of continuous mammalian cells, Biotechnol. Bioeng. 47 334-346. 

Alternative methods include (1) computer-based methods (mathematical models and expert systems) (2) physicochemical methods, in which physical or chemical effects are assessed in systems lacking cells and, most typically, (3) in vitro methods, in which biological effects are observed in cell cultures, tissues, or organs. 

Several interesting parameter-control models or systems have been reported in recent years. These are a five-state mathematical model for temperature control by Bailey and Nicholson [106], a mathematical-model description of the phenomenon of light absorption of Coffea arabica suspension cell cultures in a photo-culture vessel by Kurata and Furusaki [107], and a bioreactor control system for controlling dissolved concentrations of both 02 and C02 simultaneously by Smith et al. [108]. 

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