Monod results

The system of induced synthesis of/ -galactosidase has served as basic model for years of research in several laboratories studying the mechanisms of this synthesis. The most widely known studies are those of Jacob and Monod, resulting in the creation of an experimentally based concept of regulation of genetic activity, which we shall describe briefly on the basis of the publications summarizing their conclusions (Jacob and Monod, 1963, 1964). 

The basic kinetic properties of this allosteric enzyme are clearly explained by combining Monod s theory and these structural results. The tetrameric enzyme exists in equilibrium between a catalytically active R state and an inactive T state. There is a difference in the tertiary structure of the subunits in these two states, which is closely linked to a difference in the quaternary structure of the molecule. The substrate F6P binds preferentially to the R state, thereby shifting the equilibrium to that state. Since the mechanism is concerted, binding of one F6P to the first subunit provides an additional three subunits in the R state, hence the cooperativity of F6P binding and catalysis. ATP binds to both states, so there is no shift in the equilibrium and hence there is no cooperativity of ATP binding. The inhibitor PEP preferentially binds to the effector binding site of molecules in the T state and as a result the equilibrium is shifted to the inactive state. By contrast the activator ADP preferentially binds to the effector site of molecules in the R state and as a result shifts the equilibrium to the R state with its four available, catalytically competent, active sites per molecule. 

The results obtained by measuring the affinity to oxygen in the presence of various monohydric alcohols (methanol, ethanol, 2-propanol, 1-propanol) 140-144> were interpreted in terms of the Monod-Wyman-Changeux model145), by which the change of the standard free-energy difference between R and T state in the absence of oxygen, due to the addition of alcohol, can be determined, i.e. 

Substituting specific growth rate based on the Monod rate equation into (6.8.2), the rearranging results in ... 

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. 

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. 

I am surely not going to describe all of these complicated discussions which took place after the famous Monod-Wyman-Changeux paper, with the result that an increasing number of molecular states were introduced and that both kinds of processes, the induced-fit one, the concerted or... 

Fig. 18.2. Results of modeling at 25 °C bacterial sulfate reduction using acetate as the electron donor, according to a thermodynamically consistent form of the Monod equation. Labels identify values and line slopes after seven days of reaction.

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. 

Under steady state conditions, the specific growth rate becomes equal to the dilution rate, ju=D. Using the Monod equation, calculate a set of steady state S versus D values. Verify this result by simulation. 

Odour will return in treated slurry as a result of post treatment fermentation. The concentration of readily fermentable substrates, measured as BOD5, provide an indicator of this problem. In continuous culture without oxygen limitation the BOD5 can be described by a model derived from the Monod (13) model of microbial growth (14). The supernatant BOD5 (g/1) from treatment at 15 to 45°C, was described by equation 3 and the whole BOD5 by equations 4 and 5(15). 

Note that negative cooperativity cannot occur in the Monod-Wyman-Changeux allosteric transition model, because the dissociation constant is equivalent for all sites. Thus, positive cooperativity can only result in this binding mechanism as a consequence of the recruitment of binding sites from the T-state in an all-or-none transition to the R-state. Any occurrence of negative cooperativity can be regarded as prima facie evidence... 

In his thesis, which was published as a book in 1948, Monod first proposed the celebrated equation that bears his name. As experimental support for this equation he presented results from four batch reactor runs on the... 

Non-competitive inhibitors. These inhibitors bind to the enzyme or the enzyme-substrate complex at a site other than the active site. This results in a decrease in the maximum rate of reaction, but the substrate can still bind to the enzyme. An analogous concept is that of allosteric inhibition. The site of binding of an allosteric inhibitor is distinct from the substrate binding site. In this case, the inhibitor is not a steric analog of the substrate and instead binds to the allosteric site (the phenomenon was termed thus by Monod and Jacob). 

Finally, if the metabolism of the chemical results in substantial energy yield and/or cell-building materials, then the microorganism may increase in cell numbers in response. Then, the overall rate of biodegradation will be dictated by the rate of microbial population increase. In these cases, microbial population dynamics, an approach developed by Monod (1949), must be included in our analysis of the chemical of interest. This too will be expanded upon in Section 17.5. 

Now you can solve for the resultant steady-state glycerol concentration using the Monod growth relation, Eq. 17-61, and values of = 28.8 d1 and KiM = 120 /iM from Table 17.6 ... 

It should be noted that this result is independent of the type of growth kinetics which the micro-organisms follow. If the dependence of specific growth rate on substrate concentration is described by the Monod equation, then substitution from equation 5.62 will give for the steady-state condition ... 

At the exit point of the reactor X = Xe. The incorporation of Monod kinetics for the growth rate results in ... 

The result for Monod growth kinetics, and assuming a constant yield coefficient is ... 

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 ... 

In merodiploids of the type o+z+/ocz+. -galactosidase is constitutively expressed, showing that the oc allele is dominant to o+ in this situation. In merodiploids of the type ocz+/o+z the oc-allele is dominant also but in ocz /o+z+, it is recessive. Thus, the oc-allele is dominant only when it is located cis to the structural genes it influences. From this result, Fran ois Jacob and Jacques Monod inferred that o+ — oc mutations correspond to a modification of the DNA structure that affects the ability of the repressor to bind. 

The existence of a repressor in lac operon regulation was first suggested by the results of studies of merodiploids. In merodiploids of the type i1 z I FCz+, Jacob and Monod were able to demonstrate that the i (inducible) allele is dominant to the i (constitutive) allele when on the same chromosome (cis) or on a different chromosome (trans) with respect to the z.+ allele. 

Table 6.1 shows the ACSL program and Figure 6.6 shows the results. Comparison of Figure 6.6 with Figure 6.1 shows that Monod kinetics can predict the cell growth from the start of the exponential growth phase to the stationary phase. 

As a result, this model can also predict the change of the average cell size with respect to time, which is not possible with the Monod model. Eqs. (6.73), (6.78), (6.79), and (6.80) can be expressed with the concentrations in terms of mass per unit culture volume as... 

Compare your simulation result with Figure 14 of the paper by Ramkrishna et al. (1967). If you showed the change of the cell concentrations in g dry weight/liter, the shape of the curves are quite different from those in the paper. What are the differences Explain. Do the parameter values predict realistic growth curves What new features can this model predict which the Monod model cannot ... 

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