Specific rate Substrate consumption

Table IV summarizes percent consumption of ethylene consequent upon reaction of the pure substrate and three of its mixtures with propane with six different ratios of N(4S). Table V summarizes analogous data for propane. The data for mixtures given in the two Tables are derived from the same sets of experiments. Table VI summarizes apparent relative specific rates of consumption, kr2H4/kc.,Hs These ratios were calculated by means of Equation 14, the expression which would be appropriate...

Specific growth rates (/Xx), specific substrate rates (/xs), and ethanol production rates (/Xp) were calculated, and results are shown in Fig. 2 for 5o= 103.1 g L. Similar profiles were obtained for the other initial substrate concentration studied (data not shown). As can be observed, specific growth rates, substrate consumption, and product formation followed a typical pattern for ethanol fermentation [16]. The specific rate of substrate consumption (ps) and ethanol production (/Xp) present sunilar profiles, thus correlating it very well. The specific growth rate (/Xx) presents, approximately, the same course of the others two curves. Then, ethanol formation is associated with growth, consumption of substrate, and catabolism reaction, typical of a primary metabolite (Fig. 2). 

From the entries for the rate of consumption of substrate in Table 113.1-2, one can estimate the biomass specific rate of consumption of substrate ( s) By dividing the entries for the former rate by the amount of biomass present at the corresponding time. Estimates for both and q are... 

In practice, carbon limited chemostat cultures are used to estimate the P/O quotient These conditions are used because they favour the most efficient conversion of the carbon substrate into cellular material, ie the highest efficiency of energy conservation. The steady state respiration rate (qo,) is measured as a function of dilution rate (specific growth rate) and Yq can be obtained from the reciprocal of the slope of the plot. qo, is also known as the metabolic quotient for oxygen or the specific rate of oxygen consumption. 

The effect of a particular cultivation environment on a system can be evaluated in terms of biomass (fresh/dry weight, cell number), secondary metabolite production [51,75,89,102,103,106,107] or substrate consumption (e.g. carbon source [57] or oxygen [53,108]). Using the Evan s Blue method to identify non-viable cells. Ho et al. [108] used viable cell density measurements to determine variations in specific growth rate attributable to hydrodynamic stress. 

Here, n, v, and p represent a specific growth rate, a specific substrate consumption rate, and a specific product formation rate, respectively. and are the mean values of data used for regression analysis and a, bp and C are the coefficients in the regression models that are determined based on selected operating data in a database. This model was linked with the dynamic programming method and successfully applied to the simulation and onhne optimization of glutamic acid production and Baker s yeast production. 

V specific substrate consumption rate (g-substrate g-cell h ) n osmotic pressure (atm or Pa) p density (kg m )... 

A limitation of the methods described so far is that they have assumed a constant overall yield coefficient and do not allow the endogenous respiration coefficient kd (or alternatively the maintenance coefficient, m) to be evaluated. Equation 5.54 shows that the overall yield, as measured when monitoring a batch reactor, is affected by the growth rate and has the greatest impact when the growth rate is low. Consequently, it is desirable to be able to estimate the values of kd or m, so that the yield coefficient reflects the true growth yield. An equivalent method would be one where the specific rates of formation of biomass and consumption of substrate were determined independently, again without the assumption of a constant overall yield-coefficient. 

Selection of mathematical equations able to represent the specific rates (for growth, product synthesis and substrate consumption) that can describe the phenomena identified in the previous steps. 

The identification of phenomena that explain the behavior of a studied system depends on the analysis of their kinetic data. Normally, this kinetic analysis is performed using characteristic variables calculated from the experimental data. The specific rates and the yield coefficients are the common values used in this task. When cell concentration data are available, cell growth and death rates, as well as cell viability, are the best kinetic variables to characterize the population physiological state. In the absence of this information - as can occur, for example, with immobilized cells - the treatment must be based on substrate consumption or on metabolites production (Miller and Reddy, 1998). 

It is possible define the specific substrate consumption rate (Equation 7) and specific product synthesis rates (Equation 8) in a similar way to the specific growth rate. 

Later, it was observed that substrate to cell yield factors (YX/s) could vary as a function of specific growth rate. Pirt (1966) described a linear relationship between growth and substrate consumption, as well as the statement of a term for cell maintenance (Equation 26). 

Frequently, the specific byproduct formation rate is presented as a function of specific substrate consumption rate and substrate-to-product yield (see Equation 12), but other structures can be assumed. The specific production rate can be limited by a precursor substrate and modeled by a Monod-type expression, as in Equation 73, or it may be inhibited by a substrate that is not, in principle, linked to its production, as in Equation... 

Fig. 29. Origin of systematic errors in spite of potentially error-free analysis. On-line sampling setups (top) and time trajectories of limiting substrate concentration during sample preparation in the two paradigmatic setups depending on the actual culture density (bottom). Either a filter in bypass loop is used for the preparation of cell-free supernatant (upper part in top insert) or an aliquot of the entire culture is removed using an automatic sampler valve and a sample bus for further inactivation and transport of the samples taken (lower part). Both methods require some finite time for sample transportation from the reactor outlet (at z = 0) to the location where separation of cells from supernatant or inactivation by adding appropriate inactivators (at z = L) takes place. During transport from z = 0 to z = L, the cells do not stop consuming substrate. A low substrate concentration in the reactor (namely s KS) and a maximal specific substrate consumption rate of 3 g g h 1 were assumed in the simulation example to reflect the situation of either a fed-batch or a continuous culture of an industrially relevant organism such as yeast. The actual culture density (in g 1 1) marks some trajectories in the mesh plot. Note that the time scale is in seconds...

The maintenance energy model (Pirt, 1975) states that energy consumption can be divided into that needed for growth and that needed for maintenance. Through the use of yield ratios, an empirical expression can be written for a specific substrate consumption rate as a function of the maintenance energy requirement and the specific production rates of all products that require the consumption of that substrate. This type of model is useful in microbial systems, for which there... 

It is also relevant to consider the product yield on substrate in immobilized-cell reactors. The apparent yield of product from substrate, Fpg, can be monitored over time to detect changes in the yield. If other yields are relatively constant, then changes in Fps may indicate changes in the specific production rate (gp). However, if some or all of the other calculated metabolic yields change, then it would be very difficult to attribute changes in production rate directly to changes in 9p. Inhibition of substrate consumption or growth by waste products may contribute to a decrease in product yield. 

The experimental data of products, substrates, and cells concentrations in a given period of time were used to calculate the yields in product (Tp/s) and cells (Fx/s) related to substrate and the specific rates for growth (px), substrate consumption (/xg), and product formation (Pp)-... 

Fig. 2 Specific rates of growth (/ix). substrate consumption (/is), and ethanol production (/ip) for the fermentation of CAJ medium by S. cerevisiae at 30 C,...

Maximum ethanol concentration was obtained (=44 g L ) when 87.7 and 103.1 g of initial sugar concentration was used in the fermentation medium. Specific rates of growdi, substrate consumption, and product formation followed a typical pattern for ethanol fermentation. Maximum ethanol yield (0.488 g g ) and productivity (9.71 g L h ) were obtained when 87.7 g L of initial sugar concentration was used. Finally, initial sugar concentration had no important effect on selectivity. The results obtained indicate that CAJ is a suitable substrate for ethanol production. Moreover, the use of the CAJ as a medium will not only reduce the cost of the resulting ethanol production, but it will also make use of an agricultural waste that is otherwise discarded in the field. 

Consumption substrate is usually determined from the decline of chemical oxygen demand - COD. In a case of specific substrate, COD is assumed equal to its weight concentration multiplied by a coefficient equal to the product of the number of its carbon atoms by the ratio of molecular weight of and substrate. This coefficient describes the O mass (COD) expended for oxidizing on gram of substrate. For instance, for CH it is equal to 2.0, for CH3COO 1.08, for C H O N - 1.42, for C H - 2.46. Then the rate of substrate consumption may be expressed by equation... 

Equ. 2.38 has been proposed for the specific production of ATP (cf. Equ. 2.17, where q jp is a linear function of fi (Stouthamer, 1980 Stouthamer and Bettenhaussen, 1973). More detailed investigations show that, for example, the maximum specific growth rate is determined by the rate of energy production in the cells. As ATP production is correlated with substrate consumption, the growth behavior can be formally represented at the level of mass, that is, = f(s ... 

Figure 2.15. Schematic representation of the concept of interactions between physical transport phenomena (oxygen transfer rate, OTR heat transfer rate, H TR power consumption, P/V circulation time, and distribution, CTD residence time distribution, RTD) and biokinetics (specific rates of growth fi of consumption of substrates q, resp. consumption of oxygen, of production of heat,, of CO2 qc, of product qp and of all internal compartments (jinJ. The physical properties of the medium (temperature T, pH value, redox potential rH, density p, gas hold-up Eq, mean energy dissipation e, shear rate 7, resp. specific viscosity q — as a quantitative...

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