Biomass specific rate

A more useful approach to quantifying the relative amounts of substrate that are allocated to different metabolic pathways by individual cells is to employ the concept of biomass specific rates, sometimes referred to as q-rates. In a sense, these rates are analogous to the expression of rates per unit surface area that is often employed in heterogeneous catalysis (see Chapters 6 and 12). The various -rates are defined by normalizing the... 

Values of biomass specific rates are influenced by both genetic and environmental factors. The genes of a particular microorganism and the composition of the growth medium (including the presence of coenzymes, vitamins, hormones, mineral salts, and a variety of other soluble substrates) can affect the numerical values of the various -rates. Other environmental variables that may influence q -rates are temperature, pH, intensity and wavelength of incident radiation, and ionic strength. 

ILLUSTRATION 13.1 Determination of Biomass Specific Rates (pmax 4 and qs) and Yield Coefficients from Data Obtained Using a Batch Reactor... 

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... 

Substitution of the average values of the biomass specific -rates into equations (D) and (I) yields relations that may be employed in a spreadsheet format to generate plots of the total masses of substrate and cells present in the bioreactor as functions of time. These plots are shown in Figure 113.2 together with points representing the data employed in Illustration 13.1 to determine the q-rate values used here in Illustration 13.2. 

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... 

The corresponding concentration of the substrate in the effluent from the CSTBR can be determined by recognizing that (1) at steady state, equation (13.2.59) is again applicable, and (2) in the absence of cell death and cell maintenance effects, the biochemical reaction obeys a biomass-specific rate law of the Monod form ... 

In these equations, [L = specific growth rate coefficient, v = specific rate of substrate uptake, t = time, x = biomass concentration, Sj = intracellular substrate, and Cj = concentration of intracellular substrate. Several examples where these equations can be applied include nitrogen hmitations in M. citrifolia cultures and phosphate hmited growth in C. roseus, N. tahacum, a.nd Papaver. somniferum. 

Similarly we can estimate the specific secretion rate. It is obvious from the previous analysis that an accurate estimation of the average specific rates can only be done if the integral Jxvdt is estimated accurately. If measurements of biomass or cell concentrations have been taken very frequently, simple use of the trapezoid rule for the computation of Jxvdt may suffice. If however the measurements are very noisy or they have been infrequently collected, the data must be first smoothed through polynomial fitting and then the integrals can be obtained analytically using the fitted polynomial. 

In this example, it is easy to see that, the dynamics of C is quite independent of the kinetics p, which gives a specific solution to the well known problem of the biomass growth rate ignorance in the bioprocess [66]. It is also verified that the convergence rate cannot be tuned because it depends exclusively on the value of the dilution rate. Indeed, Bastin and Dochain [6] have shown that a condition to guarantee the convergence of the observer is that the dilution rate D must be a persisting input, i.e., that there are two positive constants Cl and C2 such as, at every time t ... 

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. 

Volume of first and second vessels Liquid volume Enzyme velocity constant Maximum enzyme velocity constant in unprotonated form Initial enzyme velocity constant Enzyme velocity constant based on unit volume of immobilised biocatalyst Maximum rate of reaction involving substance S Maximum rate of reaction involving substance P Specific rate of generation of biomass fraction Biomass concentration Initial or feed biomass concentration Average biomass concentration Concentration of prey Concentration of predator Biomass concentration at optimum dilution rate... 

Several of the terms above have been discussed in Sec. 7 rg and r are the specific rates (per broth volume) for cell growth and death, respectively rsm is the specific rate of substrate consumed for cell maintenance, and are the stoichiometric yield coefficient of species i relative to biomass x. The maintenance term in Eq. (19-81) can result... 

Although the yields and total growth rate are useful parameters, it is the state variables like the concentrations of biomass, substrate and product, and the culture parameters like the specific rates of growth, substrate uptake, etc., that provide a complete description of the bioreactor. One attempt in estimating these variables from R and the yields consisted of integrating the governing differential equation with known initial conditions and the measured values for R and the yields (9). For a batch reactor, for example, b was estimated by integrating... 

The measure of mass is important with respect to calculating mass balance. However, the elemental composition of biomass is normally ill defined. Another reason for determining biomass is the need for a reference when calculating specific rates (q ) q = r /x. An ideal measure for the biocatalysts in a bioreaction system of interest would be their activity, physiological state, morphology or other classification rather than just their mass. Unfortunately, these are even more difficult to quantify objectively and this is obviously why the biomass concentration is still of the greatest interest. 

Absolute rates were obtained by multiplying specific rates by total nitrogen biomass. Total nitrogen biomass was calculated from C biomass using a C N of 6.6. 

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