Kinetics and Process Models

2.1 Introduction and Background

Growth of living (viable) cells requires intimate contact of a small quantity of living cells with a liquid solution (medium) containing appropriate levels of nutrients at a suitable pH and temperature. Depending on the morphology of cells under consideration, one needs to consider two different manifestations of cell growth. For unicellular organisms which divide as they grow, an increase in biomass (mass of viable cells) is accompanied by an increase in the number of cells present in the culture (cell-medium suspension). The situation is very different in the case of growth of molds, which are popular organisms for industrial production of a variety of antibiotics. In the case of molds, the length and number of mycelia increase as the growth proceeds. The growing mold therefore increases in size and density (concentration) but not necessarily in numbers. (There isn't a one-to-one relation between the number of distinct multicellular units and amount of biomass.)

The extent of complexity of the kinetic description to be considered depends on the complexity of the physical situation under consideration and the intended application of the kinetics (fundamental understanding of cellular processes, design and simulation of bioprocesses, optimization and control of bioprocesses). However simple or however complex the kinetic description be, it must incorporate certain key cellular processes, such as cell replication (cell growth), consumption of essential nutrients, synthesis of end products (followed by intracellular accumulation or excretion of these), and cell death/lysis.

Biological reactors employed for production of commercially significant metabolites using living cells involve two or more phases (a single gas phase, at least one liquid phase, and at least one solid phase). The cells are usually in contact with a liquid phase. Whether the cells are suspended in the liquid phase (suspension culture) or attached to a suitable solid support (immobilized) and in contact with the liquid phase, the interactions between the two phases [biotic phase (cell population) and abiotic phase (liquid)] must be considered and fully accounted for. Both phases are multicomponent systems. The abiotic phase usually contains all of the nutrients essential for cell growth and various end products of cellular metabolism that are excreted. Some of the end products may undergo further reactions in this phase. A classic example is the hydrolysis of antibiotics such as penicillin in the liquid medium. Transport of nutrients from abiotic phase to biotic phase is essential for utilization of these for cell growth and maintenance and for formation of a host of metabolic intermediates and end products. Some of the end products are retained within the cells (intracellular metabolites), while others are excreted by the cells (transport from biotic phase to abiotic phase). The large number of chemical reactions occurring within a cell result in accumulation or depletion of energy. Exchange of energy between abiotic and biotic phases must be accounted for to determine the culture temperature. The temperature of the abiotic phase usually determines the temperature of the biotic phase. Some of the cellular reactions impact the acid-base equilibria in the biotic phase and in turn the pH of the abiotic phase, which in turn influences cellular activities and transport processes across the abiotic - biotic two-phase interface. In addition to transport of essential nutrients and end products of cellular metabolism between the two phases, one must also consider transport of ionic species (such as protons and cations). As a result of cellular reactions, the properties of the abiotic phase, such as viscosity, may change during the course of cell cultivation.

An individual cell is a complex multicomponent system in which a large number of independent enzyme-catalyzed chemical reactions occur simultaneously, subject to a variety of constraints. In a growing cell population, there is cell-to-cell variation as concerns cell age and cell function (cell activity). Thus, at a given time and in a sufficiently small region of physical space in a culture, some cells may be newly born, others may be of intermediate age and dividing, while still others may be much older and subject to death or lysis. In the case of molds, in an individual multicellular unit, there may be significant variation as concerns cell age. There is also differentiation among different cells as concerns replication, utilization of essential nutrients and formation of the target end product (for example, antibiotics such as cephalosporin and penicillin). Some of the cells thus may be actively dividing but incapable of or less efficient in synthesizing the target metabolite, while some others may be fully capable of synthesis of the target end product.

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