Abstract

The kinetic model of cell growth is substantially capable to predict product formation. Mathematical models provide a strategy for solving problems encountered in fermentation process. A biochemical engineering approach to address this problem could be to develop a mathematical model which not only helps in the understanding of the system but also predicts various cultivation strategies to facilitate the optimization of a fermentation process, saving much of the time and cost for performing experiments. The presented overview indicates that many of the environmentally relevant aspects in growth kinetics are still waiting to be discovered, established, and exploited. A kinetic model that describes microbial growth, product formation and substrate consumption and the experimental data were fitted with modified logistic equation.

Keywords: cell growth, kinetics, fermentation, biomass, growth associated, product

#### 1. Introduction

Cell growth implies increase in its mass and physical size controlled by physical, biological and chemical environments. Microbial growth is quantified by increase in the macromolecular and chemical constituents of the cell and growth pattern of each microbe is unique. Cell growth and cell division are inseparable for microbes as bacteria divide by binary fission, yeast cells by budding and viruses divide intracellularly [1]. Microbial growth during log phase is very important for the analysis of cells due to division by binary fission [2]. A typical mammalian cell growth is influenced by nutrient availability and thus a threshold cell size is required for DNA synthesis and mitosis [3]. Thus, each class of organisms have a different growth pattern based on their cell cycle and cell division. Understanding the growth kinetics of different classes of organisms forms the basis for fermentation process to achieve optimum product concentration.

Growth kinetics is an autocatalytic reaction which implies that the rate of growth is directly proportional to the concentration of cell. The cell concentration is measured by direct and indirect methods. Direct methods include measuring the cell mass concentration and cell number density by its dry weight, turbidity (optical density), plate counts etc. Whereas, indirect methods of measuring cell density are done by measuring the concentration of proteins, ATP or DNA content [4].

Batch growth kinetics of a microbe follows a growth curve with lag phase as the initial phase during which cells adapt to a new environment. Multiple lag phases occur if the media is supplemented with more than one sugar and such type of

growth is referred to as diauxic growth. Following the lag phase is the log phase in which the cell mass and cell number increases exponentially and then the depletion of nutrients starts which indicates the deceleration phase. The accumulation of toxic products results in deceleration phase after which stationary phase commences in which growth rate equals the death rate. The continuous growth kinetics accessed by a perpetual feeding process in which the growth is controlled by the concentration of the rate limiting nutrient [5].

2. Growth kinetics

Kinetic Studies on Cell Growth

DOI: http://dx.doi.org/10.5772/intechopen.84353

generation in the cell:

• Growth associated

2.1 Growth associated

• Non-growth associated

• Mixed-growth associated

where P = concentration of product qp = specific rate of product formation

X = biomass concentration.

2.2 Non-growth associated

Figure 1. Growth associated.

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Classified based on the relationship between product synthesis and energy

Growth linked products are formed by growing cells and hence primary metabolites. Figure 1 clearly shows that product is formed simultaneously with growth of cells. That is product concentration increases with cell concentration. The formation of growth associated product may be described by Eq. (1);

They are formed by cells which are not metabolically active and hence are called secondary metabolites. Figure 2 clearly shows that product formation is unrelated

dt <sup>¼</sup> rp <sup>¼</sup> qpX (1)

dP

Microbial growth kinetics explains the relationship between the specific growth rate of a microbe and its substrate concentration. Microbial growth kinetics largely depends on the laboratory culture conditions. In batch culture, microbial cell composition and its state change as a function of time and thus the rate of increase in biomass concentration was monitored [6]. Alternatively, in continuous culture the concentration of substrate is at equilibrium and the culture grows at stable physiological state which provides more precise and reproducible data [7, 8]. However, the constant growth conditions represent an artificial growth environment which does not explain many microbial kinetic phenomena. Thus, growth of microbial cells was performed under mixed substrates rather than single substrate to understand the growth kinetics of microorganisms in their natural environment [9].

The substrate such as nutrients (carbon and nitrogen sources), hormones and growth factors influence the growth pattern of microbial and mammalian cells. Substrate limited and substrate-sufficient growth would be observed on the basis of the relative availability of the substrate and the organisms utilize more substrate and energy under substrate sufficient conditions which in turn produces different patterns of product formation. A term describing the residual substrate concentration in Leudeking-Piret model was thus extended in the product formation kinetics [10].

Product of interest is traditionally achieved in the fermentation industry by metabolic engineering of few microorganisms which involves many genetic engineering techniques. The complexity of such genetic modifications and microbial metabolism due to various interconnected pathways urges the need to focus on developing mathematical models for identifying targets of metabolic engineering [11, 12].

Mathematical models are kinetic models which explain the relationship between rates and the concentration of reactants/products and allows to predict the rate of conversion of reactions in to products. This simulated model thus paved way for the optimal design of the operating conditions and operating design of the process for optimal product formation. Qualitative models were mostly used by researchers rather than quantitative models for gene expression systems as quantitative prediction of process parameters are complicated. However, with the advancements in experimental techniques of life sciences and using powerful computer technology, complex mathematical models were developed which is used for the design of various bioprocesses [13]. Industrial Biotechnology largely makes use of such mathematical models and saves time and resources with a clear understanding of strategies to optimize the product yield. Other potential uses of mathematical models include increasing the range of substrates, reduction of undesirable product formation and on the whole optimization of fermentation processes [14, 15].

Studying growth of a microorganism is the basis of biotechnological exploitation of microflora for production of desired product. Optimization of growth of microorganism in a particular media is desirable due to economical and availability of particular growth constituent in a region. Despite this, some microorganisms have specific requirement and they grow in a particular growth media.

The presented overview thus provides a knowledge on the fundamental basics of microbial growth kinetics and energetics which forms the basis for bio-engineering in optimizing, producing and purification of commercially novel products.
