Monod-kinetics

Product formation kinetics in mammalian cells has been studied extensively for hybridomas. Most monoclonal antibodies are produced at an enhanced rate during the Gq phase of the cell cycle (8—10). A model for antibody production based on this cell cycle dependence and traditional Monod kinetics for cell growth has been proposed (11). However, it is not clear if this cell cycle dependence carries over to recombinant CHO cells. In fact it has been reported that dihydrofolate reductase, the gene for which is co-amplified with the gene for the recombinant protein in CHO cells, synthesis is associated with the S phase of the cell cycle (12). Hence it is possible that the product formation kinetics in recombinant CHO cells is different from that of hybridomas. 

Monod kinetics Kinetics of microbial cell growth as a function of substrate concentration proposed by Jacques Monod and widely used to understand growth-substrate relationships. 

Monod kinetics are considered in a CSTR with an organism growing with an initial substrate concentration of 50g-l 1 and kinetic parameters of Ks = 2g-l 1 and /Amax = 0.5lr. (a) What would be the maximum dilution rate for 100% yield of biomass with maximum rate (b) If the same dilution is used, what would be number of CSTRs in series ... 

A Langmuir-Hanes plot based on the Monod rate equation is presented in Figure 8.7. The Monod kinetic model can be used for microbial cell biocatalyst and is described as follows ... 

A limiting case of Monod kinetics has Ks = 0 so that cell growth is zero order with respect to substrate concentration. Rework Example 12.7 for this situation, but do remember to stop cell growth when S = 0. Compare your results for X and p with those of Example 12.7. Make the comparison at the end of the exponential phase. 

The Monod kinetic parametos were evaluated by least squares fitting procedures, for tiie single and multiple substrate systems with/without mutual inhibition, and were indicated in Table 1 [6]. The value of indicates the linear decomposition rate. It is dear that the decomposition rate for prc iionic acid is significantly lower than those for acetic add and butyric acid. 

In the following, tiie performance of a UASB reactor with the same size of a pilot plant [7] is evaluated according to the reactor simulation model incorporated with the Monod kinetic paramet for fire hypothetical influait coirqxwiticHi for the three VFA componaits as indicated in Table 2. 

A pilot scale UASB reactor was simulated by the dispersed plug flow model with Monod kinetic parameters for the hypothetical influent composition for the three VPA ccmiponents. As a result, the COD removal efflciency for the propionic acid is smallest because its decomposition rate is cptite slow compared with other substrate components their COD removal eflSciencies are in order as, acetic acid 0.765 > butyric acid 0.705 > propionic acid 0.138. And the estimated value of the total COD removal efficiency is 0.561. This means that flie inclusion of large amount of propionic acid will lead to a significant reduction in the total VFA removal efficiency. 

Model 1 (Monod kinetics with constant specific death rate)... 

At each temperature the simple Monod kinetic model can be used that can be combined with material balances to arrive at the following unstructured model... 

When microorganisms use an organic compound as a sole carbon source, their specific growth rate is a function of chemical concentration and can be described by the Monod kinetic equation. This equation includes a number of empirical constants that depend on the characteristics of the microbes, pH, temperature, and nutrients.54 Depending on the relationship between substrate concentration and rate of bacterial growth, the Monod equation can be reduced to forms in which the rate of degradation is zero order with substrate concentration and first order with cell concentration, or second order with concentration and cell concentration.144... 

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 ... 

When a pilot-scale fermenter is run in continuous mode with a fresh feed flowrate of 65 1/h, the effluent from the fermenter contains 12 mg/1 of the original substrate. The same fermenter is then connected to a settler-thickener which has the ability to concentrate the biomass in the effluent from the tank by a factor of 3.2, and from this a recycle stream of concentrated biomass is set up. The flowrate of this stream is 40 1/h and the fresh feed flowrate is at the same time increased to 100 1/h. Assuming that the microbial system follows Monod kinetics, calculate the concentration of the final clarified liquid effluent from the system. /x, = 0.15 h-1 and Ks = 95 mg/1. 

Two continuous stirred-tank fermenters are arranged in series such that the effluent of one forms the feed stream of the other. The first fermenter has a working volume of 100 1 and the other has a working volume of 50 1. The volumetric flowrate through the fermenters is 18 h-1 and the substrate concentration in the fresh feed is 5 g/1. If the microbial growth follows Monod kinetics with //, = 0.25 h-1, Ks = 0.12 g/1, and the yield coefficient is 0.42, calculate the substrate and biomass concentrations in the effluent from the second vessel. What would happen if the flow were from the 50 1 fermenter to the 100 1 fermenter ... 

The simple kinetics for uptake of soluble substrate of the bacteria in a biofilm is traditionally described by a combination of mass transport across the water/biofilm interface, transport in the biofilm itself and the corresponding relevant biotransformations. Transport through the stagnant water layer at the biofilm surface is described by Fick s first law of diffusion. Fick s second law of diffusion and Michaelis-Menten (Monod) kinetics are used for describing the combined transport and transformations in the biofilm itself (Williamson... 

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. 

For limiting nutrients, cellular concentrations are constant under conditions of steady-state growth. To ensure that the limiting nutrient is not diluted in the microbial population, kmt must be greater than the maximal growth rate, /imax. This limiting condition sets a minimum for the value of the Monod constant, Kmd = / max /[7]- Note that while Monod kinetics are more applicable than first-order kinetics for many ecological uptake processes, solutions of the above equations require considerably more a priori information [48]. 

Monod kinetic relationship, 25 898 Monoethanolamine (MEA) physical properties of, 2 123t specifications, 2 132t Monoethanolamine carbonate, 4 812 Monoethanolamine lauryl sulfate, effect of coconut diethanolamide on foaming, 2 453t... 

Below the results of Sensitivity Runs with MADONNA are given from the BIOREACT example that is run as a batch fermenter system. This example involves Monod growth kinetics, as explained in Section 1.4. In this example, the sensitivity of biomass concentration X, substrate concentration S and product concentration to changes in the Monod kinetic parameter, Ks, was investigated. Qualitatively, it can be deduced that the sensitivity of the concentrations to Ks should increase as the concentration of S becomes low at the end of the batch. This is verified by the results in Fig. 2.30. The results in Fig. 2.31 give the sensitivity of biomass concentration X and substrate concentration S to another biological kinetic parameter, the yield coefficient Y, as defined in Section 1.4. 

The rate of substrate utilisation is assumed to follow Monod kinetics as... 

The growth of biomass in the reactor is assumed to follow Monod kinetics with a first-order death rate. A mass balance on the biomass in the reactor yields the following differential equation (assuming that no biomass enters the reactor in the feed) ... 

The oxygen demand of the heterotrophic microbes can be measured as the loss of COD. In the absence of oxygen limitation this was also described by equations (6, 7 8) developed from Monod kinetics (15). 

The equations, developed from the model based on Monod kinetics and the additional equations, developed empirically to describe the effects of oxygen limitation on aerobic treatment of piggery slurry, will provide this information as the most suitable mean treatment time, reaction temperature, and DO level. 

Respiration inhibition kinetics analysis (RIKA) involves the measurement of the effect of toxicants on the kinetics of biogenic substrate (e.g., butyric acid) removal by activated sludge microorganisms. The kinetic parameters studied are max> the maximum specific substrate removal rate (determined indirectly by measuring the maximum respiration rate), and Ks, the half-saturation coefficient [19]. The procedure consists of measuring with a respirometer the Monod kinetic parameters, Vinax and Ks, in the absence and in the presence of various concentrations of the inhibitory compound. 

Assume Monod kinetics (no product poisoning), constant fractional yields 9, and no cells entering in the feed stream. Then the mixed flow performance equation becomes... 

Figure 29.5 Summary of the mixed flow behavior of reactions which follow Monod kinetics.

With poison-free Monod kinetics and a given feed, we have a U-shaped 1/r versus C curve, as shown in Fig. 29.6. 

Figure 29.6 Rate-concentration behavior of Monod kinetics.

---