Modelling of Bioprocesses
Levins (1966) suggests that population biologists have arrived at three strategies (at least) for building models to cope with the biological complexities (Levins 1966):
Type I models: Generality is sacriﬁced for precision and realism Type II models: Realism is sacriﬁced for generality and precision Type III models: Precision is sacriﬁced for generality and realism
Thus, modelling is a trade-off between generality, realism and precision because a model addressing all three together requires a massive data and it is very difﬁcult to construct and almost impossible to interpret (Levin 1966). The usefulness of any particular model depends on the modeller's goals. For example, to describe general ecological principles, it is usually necessary to sacriﬁce realism and precision; to describe a particular population, it is usually necessary to sacriﬁce generality. Thus, the choice of type depends on the modeller. However, the modelling maxim should be “simplest theory” (Levins 1966).
Growth and Productivity Models
The performance of cells, in large, cell cultures can be controlled and enhanced, provided that the system properties can be maintained at the required state. Mathematical models are especially useful for simulation, optimisation and control purposes. A realistic cell model will not only aid in optimising productivity but once such a model is formulated, prediction results can be obtained for metabolite concentrations that may otherwise be difﬁcult to measure.
Principles Behind Model Formulation
In general, the quantitative description of a bioprocess in terms of a mathematical model involves formulation of three fundamental types of equations (Tziampazis and Sambanis 1994):
• Mass-Balance equations
• Yield equations
• Rate equations
The mass balance equations that are developed based on the reactor conﬁguration and are essentially same for all cell systems if intrinsic kinetics of the culture is not taken into account. The yield and rate equations that describe cellular metabolism are independent of the reactor conﬁguration. The yield equations are based on material and energy balances and relate the amounts/rates of the metabolite consumption and production. Although they may involve several underlying assumptions about metabolism, they have a theoretical basis and hence are reliable. The rate equations describe the kinetics of various processes, generally as functions of intracellular parameters and the composition of the extracellular medium. Being empirical in nature, rate equations are the most unreliable segment constituting a model (Tziampazis and Sambanis 1994). The process mass balances and the yield equations are not sufﬁcient to fully describe the system. To remove the remaining degrees of freedom, formulation of rate equations or measurements of the rates on-line is required (Andrews 1993; Hu and Himes 1989). However, it is not always feasible to make on-line rate measurements but for a few compounds. Consequently, certain rate equations need to be speciﬁed. In the absence of sufﬁcient knowledge, experimental results are utilized to obtain information about cellular processes and hypothesize kinetic expressions (Glacken et al. 1988).