PARTE II MERCADO INTERIOR
DISPOSICIONES GENERALES CAPÍTULO I
Microbial growth increases the number of cells and the mass of the bacteria as a consequence of cell division. Several factors can affect microbial growth, and these are classified as intracellular and extracellular factors. Intracellular factors include the internal structure, metabolic mechanisms, and genetic material of the cell. Extracellular factors are external environmental conditions that affect the cells, including pH, temperature, oxygen concentration, water, and food. The growth of biomass in a culture requires a suitable environment in which the microorganisms can live and grow. This environment must satisfy several conditions, including viable inoculums, an energy source, nutrients, absence of inhibitors which prevent growth, and suitable physicochemical conditions.
In the investigation of the kinetic behaviour of such a system, it is important to understand how the concentrations of representative components of the system, i.e., cells, substrate, products, and byproduct, change with time. The study of microbial growth in terms of various variables (various growth parameters) is useful for many
purposes and is required to predict and control the behavior of the system. These growth parameters are defined to describe the growth of both simple and complex cultures. These parameters include specific growth rate, growth yield, metabolic quotients for substrate utilization and product formation, and maximum biomass.
2.3.1 Specific growth rate
If all the requirements for growth are satisfied, then the biomass concentration increases exponentially with time, since the overall rate of change of biomass is proportional to the mass of biomass:
dX
dt = µX. (2.3.1)
The differential coefficient (dXdt ) is the population growth rate. X is the cell concen-tration (kg cell/m3) and the parameter µ, which represents the rate of growth per unit of biomass, is termed the specific growth rate.
2.3.2 Growth yield
Growth yield is a biological variable that allows us to assess the rates of production and consumption of energy and mass in a biological system. From the standpoint of modeling and describing such systems, the measured growth rate is quite beneficial.
The growth yield is defined by,
Yx/s = rx
rs, (2.3.2)
where rx is the amount of biomass produced and rs is the amount of substrate consumed. When the reaction rates are equal to accumulation rates, which occurs
in batch systems, the growth yield becomes,
Yx/s =−
dX dt dS dt
=−dX
dS, (2.3.3)
For a continuous system, the growth rate is given by,
Yx/s =−∆X
∆S =−X− X0
S− S0
, (2.3.4)
where X0 and S0 are the initial biomass and substrate concentrations, respectively, and X and S are the corresponding concentrations during the growth of the culture.
The growth rate of X and S have opposite signs, so the use of the negative sign is required to reflect that reality. For a growth-limiting substrate when the cul-ture reaches its maximum biomass (Xm) and is approximately 0, the growth yield becomes,
Yx/s = Xm− X0
S0 . (2.3.5)
Growth yield is an important variable because it is a quantitative expression of the nutrient requirements of an organisms. As early as 1869, Raulin expressed the nutrient requirements of fungus in term of growth yield. In some bacterial cultures, the growth yield is constant when the conditions are maintained constant [48]. In other studies, it is considered to be variable [49].
2.3.3 Metabolic quotient
The rate at which the substrate is utilized by organisms is called the rate of con-sumption of the substrate. This rate is given by
dS
dt = qX, (2.3.6)
where X is the biomass, and the coefficient q is known as the metabolic quotient or specific metabolic rate. If the biomass concentration is constant and the environ-mental factors are constant, then q must be constant. In terms of growth, the rate of consumption of a substrate is given by:
dS
dt = µX
Yx/s, (2.3.7)
2.3.4 Effect of substrate concentration on growth rate
The microorganism growth rate (and therefore the microorganism concentration) is related directly to the concentration of the substrate that is normally consumed by the microorganisms. In some bacterial cultures, however, the growth rate is virtually unaffected by substrate concentration, i.e., zero order kinetics exists. When the substrate consumption follows enzyme kinetics, the metabolic quotient is given by:
q = qmax
( S
Ks+ S )
, (2.3.8)
where Ks is the saturation constant, which is equivalent to the Michaelis-Menten constant [50], and qmax is the maximum value of q. If we make the substitutions, q = Yµ and qmax = µmaxY , then it follows that:
µ = µmax
( S
Ks+ S )
. (2.3.9)
This equation is known as the Monod equation.
2.3.5 Kinetic models of microbial growth
Two variables that may determine the rate at which microbial growth occurs are the microbial population’s specific growth rate (µ) and the concentration of the
sub-strate (S) such as in equation (2.3.9). This relationship is used to great benefit in many different specialties, including biotechnology, ecology, genetics, microbiology, and physiology. During the last two centuries, extensive studies of microbial cul-tivation were conducted, and, as early as the 1830s, Cagniard de Latour, Kutzing, and Schwann revealed that the growth of yeasts and other protists is responsible for fermentation. An overview of the historical development of knowledge concern-ing microbial growth is presented in [16]. The understandconcern-ing of microbial growth has been improved by the understanding of principle of metabolic fluxes and by a number of mathematical models that have been proposed [51,52]. In the 19th century, various classical models were used to characterize the growth of microbial populations, such as the Verhulst and Gompertz function [53–55].
In 1912, the first kinetic approach that was associated with the growth of microbes was posited by Penfold and Norris [56], who proposed a ”saturation” type of curve to express the relationship between µ and S. This curve indicated that the maximum rate of growth of the organisms (µmax ) is independent of high levels of substrate concentrations [56]. Monod’s model is consistent with the Penfold hypothesis, but some have been critical of it due to the fact that it includes the determination of µ at a wide range of substrate concentrations, ranging from high to low [57,58]. Later, Monod introduced a model that incorporated the concept that the substrate could limit the rate of growth of the microbes,
µ = µmax
( S
Ks+ S )
, (2.3.10)
where µ = specific growth rate, µmax = maximum specific growth rate, S = sub-strate concentration, and Ks = substrate saturation constant. Monod used several
parameters to define the relation between growth rate and the utilization of the substrate [48], i.e, Ks, µmax and the yield coefficient, Yx/s [58],
Yx/s = dX
dS (2.3.11)
µ = Yx/s
X .dS
dt ≈ Yx/sq.
Many researchers have attempted to improve Monod’s representation for the growth kinetics of cells by using three approaches. These are 1) investigating the effect of physicochemical factors on the Monod growth parameters [59–63] ; 2) adding a new parameter in Monod’s model to account for the inhibition of the substrate or product, the diffusion of the substrate, maintenance, or the effects of cell density on µmax [13,16,28,57,63–66] ; and 3) the development of innovative kinetic theories that support the mechanistic and empirical models [65,67–72]. Contois adapted the Monod model after discovering evidence that showed the specific microbial growth rate may also depend on the microorganism concentration. The Contois expression is given by
µ(S, X) = µmax
( S
KsX + S )
, (2.3.12)
where µ = specific growth rate, µmax= maximum specific growth rate, X= microor-ganism concentration, S = substrate concentration, and Ks = substrate saturation constant. In this thesis, we use the Contois model to describe the growth rate.
The choice of this model is motivated by the increasing number of the experimental studies showing the Contois model giving excellent fit with experimental data. For more detail see chapter 3.5.