Growth limiting substrate

The multi-stream multi-stage system is a valuable means for obtaining steady-state growth when, in a simple chemostat, the steady-state is unstable eg when the growth-limiting substrate is also a growth inhibitor. This system can also be used to achieve stable conditions with maximum growth rate, an achievement that is impossible in a simple chemostat (substrate-limited continuous culture). 

Biomass feedback refers to increasing the concentration of biomass in the culture vessel. This is achieved by fitting some device, either internally or externally, to the continuous culture which retains or returns biomass to the vessel. The main advantage of biomass feedback is that the maximum output rate of biomass (and products) in the vessel with a given medium can be increased. This is particularly useful when the growth-limiting substrate is unavoidably dilute, for example if substrate has low solubility or has to be limited because of the formation of an inhibitory product. 

Where p = specific growth rate, p max = maximum specific growth rate, X = microorganism concentration, S= growth limiting substrate concentration, and Ks= half saturation coefficient for hydrolysis. 

Now, we can see how to estimate the biodegradation of chemicals that prove to be growth-limiting substrates of particular microbial species. 

First, solve for rsu using the information given in the table and the following equation, in which X is biomass concentration, S is growth-limiting substrate concentration, and Ks is the substrate concentration at one-half the maximum specific substrate-utilization rate ... 

The value for Kk, the saturation coefiicient or growth-limiting substrate concentration at which organism growth rate is one-half its maximum value, varies considerably with the reaction, the species mediating the reaction, and environmental conditions. In anaerobic methane fermentations, Kk tends to be much larger, at least with acetate and propionate, than for aerobic oxidations. Values of 10" moles/liter seem appropriate for the former and 10" for the latter. Kk also tends to increase with decrease in temperature. 

Basic Equations. The relationship between microbial growth and substrate utilization can be formulated in two basic equations (2, 7). Equation 1 describes the relationship between net rate of growth of microorganisms and the rate of utilization of the growth limiting substrate ... 

Erickson et al. (E3) developed a model for batch growth in fermentations with two liquid phases present in which the growth-limiting substrate is dissolved in the dispersed phase. The model accounts for drop size distribution and considers the effect of droplet coalescence and redispersion by an interaction model similar to that of Eq. (110). Droplet interactions were shown to be important if drop size distributions have large variance. 

The term represents the maximum specific growth rate that occurs when the growth-limiting substrate is in excess, i.e. when s is very large and x = The saturation constant (K ) is equal to the substrate concentration at Both... 

Whereas the specific growth rate is determined by the rate of addition of the growth-limiting substrate, the cell concentration in the fermenter is determined by the concentration of the limiting substrate in the feed medium. At steady state the cell yield (Y) on the growth-limiting substrate can be represented by ... 

The concentration of the growth-limiting substrate in the feed medium should be set to that it becomes limiting while other nutrients are still present in relative excess. Small-scale batch culture experiments in which the cell yield is determined at different initial substrate concentrations will give some indication of a suitable substrate feed concentration (5 r). Once at steady state, it can be confirmed that the cells are limited by the chosen substrate because a change in the substrate feed concentration should give a proportionate change in the cell concentration. 

Figure 1 shows a generalized picture of the relationship between the growth limiting substrate and the specific growth rate of a specialist and a generalist. 

Figure 4. Competition in continuous culture between T. neapolitanus (the specialist) and T. A2 (the generalist) for thiosulfate as the only growth-limiting substrate. Key , relative cell number of T. A2 O, T. neapolitanus. Reproduced, with permission, from Ref. 4. Copyright 1979, Springer-Verlag.

T. neapolitanus and Spirillum G7 for thiosulfate and acetate as growth-limiting substrates in the chemostat at a dilution rate of 0.07 h . Concentrations in the inflowing medium ranged from 0-20 mM for acetate and from 0-40 mM for thiosulfate. After a steady state had been established relative cell numbers were determined. Solid line, experimental data dashed line, outcome of the competition as predicted from mathematical modeling. 

Although several types of models have been explored in the description of biological systems, the unstructured black box continuum models based on a linear equation for substrate consumption are still most frequently used for the description of fermentation processes. In these models the growth rate of the cells generally is assumed to be a function of the external concentration of the growth-limiting substrate Cs according to Monod kinetics ... 

The conversion rate of the growth-limiting substrate is divided into a growth rate-dependent term and a growth rate-independent term according to the following linear equation ... 

We can also write an equation akin to equation (13.2.22) for the growth-limiting substrate that takes into account the manner in which the substrate is used by the microorganism for growth, maintenance, product formation, and so on. A balance on this substrate for a time increment Af can be expressed as... 

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... 

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