Rate Expressions for Nutrient Uptake

The cell mass-specific uptake rate of nutrient Ni, cri, is usually related to activities accounting for consumption of that nutrient, namely cell growth (an aggregate of all reactions occurring in an individual cell), cell maintenance, and production (in significant amounts, amounts comparable to amount of cell mass) of certain metabolites of interest and is therefore expressed as n cr, = —--(- rrii + T,aij£j (2.19)

yx/N, with Yx/Ni being the biomass yield with respect to nutrient Ni; m* (referred to as the maintenance coefficient) accounting for consumption of TVj for maintenance activities of cells, and «¿j being the amount of N utilized for production of unit amount of metabolite Pj. (The reciprocal of a,ij is commonly referred to as the yield of Pj with respect to Ni.) Since production of metabolites Pj is a part of cellular metabolism, the biomass yield in Eq. 2.19 is the apparent biomass yield (and not the true biomass yield) when consumption of Ni for production of Pj is accounted for directly [as in the last term in Eq. 2.19] and also indirectly via uptake of Ni for biomass production. When the last term in Eq. 2.19 is trivial, the cell mass yield (Yx/jvJ in this relation represents the true cell mass yield. A direct accounting of utilization of a nutrient Ni for production of metabolite Pj, as represented by the last term in Eq. 2.19, is justified only when the amount of Pj is substantial, so that utilization of Ar, for synthesis of Pj is comparable to that for cell growth. The significance of utilization of Ar, for cell maintenance relative to utilization of the same nutrient for cell growth increases as the specific cell growth rate is reduced.

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