Rate-limiting nutrient

This is an old, familiar analysis that applies to any continuous culture with a single growth-limiting nutrient that meets the assumptions of perfect mixing and constant volume. The fundamental mass balance equations are used with the Monod equation, which has no time dependency and should be apphed with caution to transient states where there may be a time lag as [L responds to changing S. At steady state, the rates of change become zero, and [L = D. Substituting ... 

Aim3 aerobic bioprocess was operated in a continuous mode with nitrogen as the growth limiting nutrient. The steady state biomass concentration (x), the biomass yield coefficient (Yx/S) and the product yield coefficient (Yp/t) were determined at a low and at a high dilution rate (D). 

Nutrient availability also plays a major role in exudation, with deficiencies in N, P, or K often increasing the rate of exudation (218). It is believed that nutrient deficiency may trigger the release of substances such as organic acids or nonproteinogenic amino acids (phytosiderophores), which may enhance the acquisition of the limiting nutrient (219,220). An example here might be the release of phenolic acids such as caffeic acid in response to iron deficiency, which results in an increase in uptake of the cation (221). 

The permselectivity of the corneal and conjunctival paracellular routes was investigated by Huang et al. [159] in an attempt to show that nutrients can be extracted from the blood by the conjunctiva. Neither the blood vessels supplying the conjunctiva nor its basement membrane are rate-limiting to the transport of horseradish peroxidase. This 40 kDa tracer is restricted underneath the conjuncti-... 

S° the constant concentration input of the limiting nutrient (S° > 0) D the constant washout rate (D > 0) ... 

S° the constant concentration input of the limiting nutrient (S° > 0) D the constant washout rate (D>0) m1 the maximal specific growth rate of P. subcapitata (up > 0) m2 the maximal specific growth rate of C. vulgaris (m2> 0) ... 

The experiment contained sufficient nutrients and phenol was present at sufficiently low levels, about 40 mg kg-1 initially, that the substrate was the rate-limiting reactant. Methanogenic consortia are slow growing when observed on the time scale of the experiment, which lasted about 40 days. The biomass concentration, in fact, was not observed to change significantly. The reaction, furthermore, remained far from equilibrium, so the reverse reaction rate was negligible, compared to the forward reaction. 

For limiting nutrients, cellular concentrations are constant under conditions of steady-state growth. To ensure that the limiting nutrient is not diluted in the microbial population, kmt must be greater than the maximal growth rate, /imax. This limiting condition sets a minimum for the value of the Monod constant, Kmd = / max /[7]- Note that while Monod kinetics are more applicable than first-order kinetics for many ecological uptake processes, solutions of the above equations require considerably more a priori information [48]. 

Pasciak, W. J. and Gavis, J. (1975). Transport limited nutrient uptake rates in Ditylum brightwellii, Limnol. Oceanogr., 20, 604-617. 

If the interface reaction rate is extremely small so that mass/heat transfer is rapid enough to transport nutrients to the interface, then interface reaction rate (Equation 4-33) is the overall heterogeneous reaction rate (Figure 1-lla). If the interface reaction is relatively rapid and if the crystal composition is different from the melt composition, the heterogeneous reaction rate may be limited or slowed down by the mass transfer rate because nutrients must be transported to the interface and extra junk must be transported away from the interface (Figures 1-llb and 1-llc). If the crystal composition is the same as the melt composition, then mass transfer is not necessary. When interface reaction rate and mass transfer rate are comparable, both interface reaction and mass transfer would control the overall heterogeneous reaction (Figure 1-lld). 

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