Stoichiometric Model

When a stoichiometric model is used, local changes in weak-acid concentrations as a result of microbial growth can be predicted. Information on the stoichiometry of the conversion of carbon source to metabolic products is essential in order to relate the increase in cell biomass to the changes in the local chemical environment. This information is then used to predict changes in pH. However, this is not in any way straightforward, because of unknown properties of the buffering capacity of the microbial growth medium (Wilson et al., 2002). 

Stoichiometric models forged the flrstrationalization of the retention patterns of IPC. AU stoichiometric models are pictorial and do not need sophisticated mathematical descriptions of analyte retention. What is the link between ion-pairing and chromatography  

However, it was qnickly realized during the introduction of this technique that an IPR having a hydrophobic region to interact with the stationary phase was prone to adsorb onto the reversed phase chromatographic bed because (1) the fuU impact of the reagent was felt after many void volumes of the column were displaced, (2) if the analyte and the IPR carried the same charge status, analyte retention decreased upon introduction of the IPR in the eluent, and (3) when the presence of IPRs in the eluent was discontinued, the previous eolumn retentive behavior was not restored promptly. The IPR adsorption could be measured and modeled via the adsorption isotherm [6]. 

Model makers named the technique solvent generated ion exchange [7] and hydrophobic chromatography with dynamically coated stationary phase [8], thereby emphasizing a dynamic ion exchange model. 

Lipophilic ions first adsorb at the surface of the stationary phase, and the dynamically generated charge sites provide an ion exchange character that explains the retention of oppositely charged analytes [7-11]. This retention mechanism does not explain the contribution of solute hydrophobicity to retention because it should not be relevant if retention is only charge driven. It can be speculated that both mechanisms act and the extent to which one is more significant than the other depends on the experimental set-up and the nature of the IPR [12]. 

Many subsequent stoichiometric mixed mode models are based on various combinations of these ion-pair and dynamic ion exchange extreme mechanisms. The effect of the IPR counter ion [13] and the reduction of available hydrophobic surfaces 

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For nonlinear systems, however, the evaluation of the flow rates is not straightforward. Morbidelli and co-workers developed a complete design of the binary separation by SMB chromatography in the frame of Equilibrium Theory for various adsorption equilibrium isotherms the constant selectivity stoichiometric model [21, 22], the constant selectivity Langmuir adsorption isotherm [23], the variable selectivity modified Langmuir isotherm [24], and the bi-Langmuir isotherm [25]. The region for complete separation was defined in terms of the flow rate ratios in the four sections of the equivalent TMB unit ... 

The very basis of the kinetic model is the reaction network, i.e. the stoichiometry of the system. Identification of the reaction network for complex systems may require extensive laboratory investigation. Although complex stoichiometric models, describing elementary steps in detail, are the most appropriate for kinetic modelling, the development of such models is time-consuming and may prove uneconomical. Moreover, in fine chemicals manufacture, very often some components cannot be analysed or not with sufficient accuracy. In most cases, only data for key reactants, major products and some by-products are available. Some components of the reaction mixture must be lumped into pseudocomponents, sometimes with an ill-defined chemical formula. Obviously, methods are needed that allow the development of simple... 

The stoichiometric model developed using the method described in Appendix A is as follows ... 

In this stoichiometric model it was assumed that the first reaction is of second order while the second reaction is of first order. Using these assumptions and the data given in Table 5.4-17 kinetic parameters were estimated for both reactions, see Table 5.4-18. 

The stoichiometric model precision was not attained yet. For the next iteration A2, A, and Af, were masked because 2(2), 2(3), and 2(6) were less than 4. In the third iteration the following stoichiometric coefficients were estimated ... 

The final step in our quasi-chemical development is merely to recognize that a stoichiometric model for chemical association provides a correct description of %o. We imagine following a specific solute molecule of interest through chemical conversions defined by changes in the inner shell populations,... 

Stoichiometric model reactions in alkene hydroformylation by platinum-tin systems have been studied for the independent steps involved in the hydroformylation process, insertion of the alkene, insertion of CO, and hydrogenolysis, with use of Pt-Sn catalysts and 1-pentene as alkene at low pressure and temperature.92... 

For a complex system, determination of the stoichiometry of a reacting system in the form of the maximum number (R) of linearly independent chemical equations is described in Examples 1-3 and 14. This can be a useful preliminary step in a kinetics study once all the reactants and products are known. It tells us the minimum number (usually) of species to be analyzed for, and enables us to obtain corresponding information about the remaining species. We can thus use it to construct a stoichiometric table corresponding to that for a simple system in Example 2-4. Since the set of equations is not unique, the individual chemical equations do not necessarily represent reactions, and the stoichiometric model does not provide a reaction network without further information obtained from kinetics. 

The yield of a product is a measure of the reaction extent at some point (time or position) in terms of a specified product and reactant. The most direct way of calculating the yield of a product in a complex system from experimental data is by means of a stoichiometric model in canonical form, with the product as a noncomponent. This is because that product appears only once in the set of equations, as illustrated for each of CO, CO and HCHO in Example 5-1. 

The general solution of this equation was obtained and applied for a special case where/(c) is defined according to the stoichiometric model of protein retention as ... 

A stoichiometric model can conveniently be invoked to explain the ion-exchange retention process [43 6]. As discussed in detail in these cited papers on ion-exchange theory, useful information about the involved ion-exchange process can be deduced from plots of log k vs. the log of the counterion concentration [X], which commonly show linear dependencies according to the stoichiometric displacement model (Equation 1.1)... 

Busch et al. studied the applicability of CZE to the examination of hapten-antibody complex formation (11). The catalytic antibodies examined have been used to accelerate a Diels-Alder reaction. Association constants of two hapten-antibody complexes were investigated and compared to the ELISA method. The samples contained buffer, hapten, and antibody. The constants obtained with CZE are a factor of 3-5 larger than those found with the ELISA method. The free-hapten concentration is measured directly this allows confirmation of the stoichiometric model. Because of the poor concentration sensitivity of UV detection, the application of an extended optical path length such as a bubble cell is necessary to obtain reliable binding parameters. 

Using stoichiometric model systems, it can be shown that some naturally occurring redox processes have a pronounced pH-controlling action, even in the presence of substances that act as buffers. High pH values can be reached particularly in systems where higher metal oxides act as oxidizers whereas an acid condition often develops when free oxygen is the oxidizer. However, in most natural systems carbonates and silicates have a more pronounced pH controlling effect than redox processes. 

Tribble G.W., Sansone F.J. and Smith, S.V. (1990) Stoichiometric modeling of carbon diagenesis within a coral reef framework. Geochim. Cosmochim. Acta, (submitted). 

The catabolism of 2 includes 118 reactions many of which are reversible (Fig. 3.5). Since kinetic data on micro-metabolites are difficult to determine experimentally, and in order to obtain an overall view of the xenobiotic metabolism, a stoichiometric model of the full network of degradation pathways of 2 was set up in addition to the network shown in Fig. 3.5. This network was then analyzed by means of elementary flux mode analysis [78]. 

This influence of the valence and activity coefficients of the displacer salt on the retention behavior of polypeptides and proteins can be anticipated from theoretical treatments of the ion-exchange chromatographic separation of proteins. According to the nonmechanistic stoichiometric model of protein retention behavior in HP-IEX80,82-85 the influence of a divalent cation salt such as CaCl2 on the retention behavior of a protein in HP-IEC can be evaluated in terms of the following relationships ... 

Table 1 Statistical data on the genome-scale stoichiometric model of Corynebacterium glutamicum ATCC 13032 constructed on basis of the genome with 3002 open reading frames [55]...

C-mol Summarizing, stoichiometric modeling studies for C. glutamicum provide a sound basis for strain or process optimization. By calculating the theoretical capacity of an organism for a novel product they also allow useful estimates on the general economical feasibility [56],... 

Mathematical models are widely applied in biosciences and different modeling routes can be taken to describe biological systems. The type of model to use depends completely on the objective of the study. Models can be dynamic or static, deterministic or stochastic. Kinetic models are commonly used to study transient states of the cell such as the cell cycle [101] or signal transduction pathways [102], whereas stoichiometric models are generally used when kinetics parameters are unknown and steady state systems is assumed [48, 103]. 

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