Steady-state substrate-product balance

Substrate product balance in steady state For DH=DH (con-stanty eq. 7 leads to that (0s7p ) must be constant witS time. As OS/S is a function of DH and independent of S, cfr. eq, (5) we can see that S must be constant in steady state. Eq. (11) therefore leads to ... 

Material balances on the substrate and the product species can be used with a rate expression and yield coefficients to specify completely the compositions of the remaining streams in Figure 13.8. For a generic biomass specific rate law and steady-state operation, a balance on the growth-limiting substrate around the combination of the mixing point and the bioreactor indicates that... 

Figure 6.51. Diagrammatic representation of a steady-state bioprocess in balance area (reactor) following the macroscopic principle by analyzing elemental composition of significant process variables (substrate, nitrogen source, biomass, product, O2, CO2, H2O). (Adapted from Roels, 1980a.)...

For example, the kinetics may be different within cells, where molar concentrations of enzymes often exceed those of substrate, than in the laboratory. In most laboratory experiments the enzyme is present at an extremely low concentration (e.g., 10 8 M) while the substrate is present in large excess. Under these circumstances the steady-state approximation can be used. For this approximation the rate of formation ofES from free enzyme and substrate is assumed to be exactly balanced by the rate of conversion ofES on to P. That is, for a relatively short time during the duration of the experimental measurement of velocity, the concentration of ES remains essentially constant. To be more precise, the steady-state criterion is met if the absolute rate of change of a concentration of a transient intermediate is very small compared to that of the reactants and products.19... 

Using the mass balances, optimum operating conditions for continuous production in the EMR were calculated. Concentrations of 300 mmol L 1 ManNAc and 600 mmol L 1 pyruvate were found to be the most suitable to allow high conversion of ManNAc, high space-time yield, and easy product isolation. Figure 7-28 shows steady-state concentration and conversion as a function of substrate ratio in an EMR. 

Product concentration in the permeate can then be determined either with numerical procedures or with graphic techniques. True reactor operating point at steady state is given by the intersection point of the straight line representing mass balance and the curve of the reaction term.8 10 99 As can be seen from Figure 7.2, for a-ketoisocaproate conversion to L-leucine, the slope of the convective term is reciprocally proportional to the mean residence time. If multien-zymatic systems are used as the biocatalyst, it must be outlined that the reaction term is the course of the reaction rate relative to the substrate conversion of the key component.10... 

When the detailed balance kif 2b< s = ib 2fcp is not satisfied, the system will reach nonequilibrium steady state, in which 7rib. and the reaction will be forming a cycle from a substrate (S) to product (P), such as... 

In a review of their work, Caplan and Naparstek pointed out that a simpler system might have been an enzyme-free membrane separating the alkahne BAEE solution from a small chamber containing the papain [56]. The chamber could be treated as homogeneous, and quasi-steady-state ordinary differential equations could account for transport of substrate, acid, and base across the membrane as well as for the enzyme-catalyzed reaction. By fixing the external concentrations of BAEE and H+ (and hence OH since the dissociation product is constant), it was shown that conditions exist under which diffusional and reaction fluxes that balance each other are unstable, and the system is directed to a hmit cycle. This simplified membrane-chamber system was further investigated theoretically by Ohmori et al [59], who identified regions of parameter space that are predictive of pH oscillations for compartmentalized papain and other proteolytic... 

The rate equation for the formation of product, the equilibrium dissociation constant for the binaiy enzyme-substrate complexes EA and EB (K and Kf), the equilibrium dissociation (Ks) or steady-state Michaelis (Km) constants for the formation of the ternary enzyme-substrate complexes EAB and and the enzyme mass balance are, respectively. 

The measurement of internal metabolic fluxes is more difficult. The direct measurement of intracellular fluxes is possible with in vivo nuclear magnetic resonance (NMR) spectroscopy. However, the inherent insensitivity of NMR limits its applicability. An improvement over this approach can be found with isotopic tracer techniques [8]. In isotope tracer methods the cells to be studied are provided with a substrate specifically labeled with a detectable isotope (usually or C). The incorporation of label into cellular material and by-products is governed by the fluxes through the biochemical pathways. The quantity and distribution of label is measured and combined with knowledge of the metabolic network to estimate some of the intracellular fluxes. The choices of substrate labeling patterns, as well as which by-products to measure, are guided by careful analysis of the assumed biochemical network. These experiments are usually performed at isotopic steady state so that the flow of isotope into each atom of a metaboHte equals the flux out. For the nth atom of the fcth metabolite the flux balance is [9] ... 

The starting point in this analysis is the construction of a list of steady-state material balance equations to describe the conversion of substrates to metabolic products for the biochemical system of interest. For example, if one considers a simplified scheme of amino acid metabolism in liver, one can write a set of steady-state material balance equations that represent the flow of metabolites through the network (Fig. 9). The equations contain measurable quantities (these are marked with an asterisk) which are the rates of consumption/production of extracellular metabolites. The concentrations of strictly intracellular metabolites (e.g., argininosuccinate) are assumed to be constant. In this particular case, we have eight fluxes to be determined, five of which are measurable (F[, F, F, F, F ). The five equations listed here, which relate these fluxes to each other, can be reduced to four independent equations. Thus, the system can be solved to yield the three unknown intracellular fluxes (Fi, F2, F4). Because the system is overdetermined, it provides an internal check for consistency of the data with each other and the assumed biochemistry. 

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