Monod expression

The substrate concentration C is obtained from the Monod expression given by... 

The relationship between i. and S as depicted in Figure 2.7 is relevant because it quantifies the importance of a substrate in terms of its concentration on the growth rate. As seen from Equation (2.16), X= 1/2 imax for S=Ks. For this reason, Ks is also named the half saturation constant. Equation (2.16) and the corresponding curves shown in Figure 2.7 are called the Monod expression and Monod curve, respectively. 

Equation (5.15) may be extended to describe transformations under substrate-limited conditions by including a Monod expression (cf. Section 2.2.1). The information from Section 5.6.1 indicates that the saturation constant for nitrate, KS0, is about 2-3 gN03 nr. ... 

With both feed and cells entering the fermentor, the Monod expression (Eq. 1) in the performance expression for the MFR (Eq. 6) gives... 

Gates, W. E. and Marlar, J. T. J. Water Pollut. Cont. Fed. 40 (1968) R469. Graphical analysis of batch culture data using the Monod expressions. 

It has also been shown that aromatic hydrocarbon degradation maybe self-inhibited. That is, the rate of degradation of the hydrocarbon is slowed by high concentrations of the hydrocarbon itself [29,32]. Self-inhibition may be modeled by incorporating Haldane (or Andrews) kinetics into the Monod expression ... 

The parameters n, are the specific reaction rates for the uptake of sugar i. These reactions are first-order in the biomass concentration. The specific rates must refiect the catalyzed enzymatic reactions that occur within yeast cells that convert sugar into alcohol. These rates are given by the Monod expression for glucose,... 

The reaction rate is expressed by a Monod-type equation... 

Baughman and colleagues145 derive a second-order kinetic rate expression as a special case of the Monod kinetic equation. It appears to describe biodegradation of organics in natural surface waters reasonably well ... 

Conversion rate data obtained under a wide range of operating conditions may be worked out to provide a kinetic expression, most typically expressed according to well established models for bioprocess kinetics first and second order, Monod, Haldane, product-inhibited, etc. 

Equation (2.19), which concerns a situation without processes in the biofilm, can be extended to include transformation of a substrate, an electron donor (organic matter) or an electron acceptor, e.g., dissolved oxygen. If the reaction rate is limited by j ust one substrate and under steady state conditions, i.e., a fixed concentration profile, the differential equation for the combined transport and substrate utilization following Monod kinetics is shown in Equation (2.20) and is illustrated in Figure 2.8. Equation (2.20) expresses that under steady state conditions, the molecular diffusion determined by Fick s second law is equal to the bacterial uptake of the substrate. 

Equation (5.3) includes the influence of both the electron donor (organic substrate) and the electron acceptor (DO) on the growth of biofilm biomass. The expressions for these dependencies are of the Monod type and 1/2-order kinetics, respectively (cf. Section 2.2). 

The rate expressions can be simply given by the Monod Equation ... 

Inserting the Monod-type rate expressions gives For the cell balance... 

The Lac operon (Figure 3.8, described in Esherichia coli bacteria by Jacob and Monod), illustrates how gene expression can be switched on or off according to sudden changes in environmental conditions. Glucose (a monosaccharide) is the preferred... 

The classic expression for measurement of growth rate is the Monod Equation. 

Many other kinetic forms have been proposed and have been used in the past however, they have all been forgotten since Monod came out with his expression. Its simplicity won the day. So we will use this type of expression throughout to relate the rate of cell growth to substrate concentration. 

General Kinetic Expression. The simplest expression of the Monod type which can account for both factors in microbial fermentation is... 

For high C, thus put = 0 in the Monod equation. This gives Yq = A Cc, in which case the performance expression, Eq. 3, simplifies to... 

This intriguing expression was developed by Monod (1949), and independently, at about the same time, by Novick and Szilard (1950). 

The rate of cell growth is influenced by temperature, pH, composition of medium, rate of air supply, and other factors. In the case that all other conditions are kept constant, the specific growth rate may be affected by the concentration of a certain specific substrate (the limiting substrate). The simplest empirical expression for the effect ofthe substrate concentration on the specific growth rate is the following Monod equation, which is similar in form to the Michaelis-Menten equation for enzyme reactions ... 

Monod(40) proposed the use of a saturation-isotherm type of equation to relate the growth rate of a micro-organism culture to the prevailing feed concentration. This has become known as the Monod equation and is usually expressed as ... 

Monod-type equation. One expression used (Aiba et al. 2)) is ... 

KP being the constant of the inhibitory system. In both cases the expressions reduce to the Monod equation when the product concentration is zero. 

Gates and Marlar<<0) devised a graphical procedure to determine the kinetic constants which took into account the data in the Anal stages of the growth-phase of a batch fermentation. As a result, their procedure can be used to estimate values of fim, Ks and the yield coefficient Y. The method involves rewriting equation 5.125, which is the complementary expression to the integrated form of the Monod equation 5.124, but refers to the substrate ... 

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