In the case of protein synthesis, the knowledge of pertinent mechanisms at the molecular level allows formulation of genetically structured models. Protein synthesis assumes particular importance in manufacture of enzymes of industrial importance, hormones, and other commercial polypeptides. These models are robust, that is, these can be used for reliable prediction at conditions different from those used for estimation of model parameters and model evaluation and as such are very useful for optimization with respect to environmental and genetic parameters. A simple illustration is considered here that focuses on transcription and translation processes involved in synthesis of a target protein. One must consider conservation equations for the messenger RNA (mRNA) obtained by transcription of a particular gene G and the product of translation of the message carried by the mRNA, viz., the target protein (P). Let [G], [mRNA], and [P] denote the molar intracellular concentrations (moles per unit cell mass) of G, mRNA, and P, respectively. The conservation equations for rnRNA and P then are provided by Eq. 2.14b [329, 330] with c* = [i], i = mRNA, P and r\
kprj[G} - [mRNA], rfa = fc,£[mRNA] - ke[P], trans _ n 'mRNA — u-
In Eqs. (2.44), kp and kq are the kinetic coefficients for transcription of the gene and translation of mRNA, rj the efficiency of promoter utilization, £ the efficiency of utilization of the mRNA at the ribosomes, and kd and ke the kinetic coefficients for deactivation of the mRNA and the active protein, respectively. For intracellular proteins, r~pans is trivial, while for proteins partially excreted from living cells, rpans is non-trivial and positive. In balanced growth, pseudo-steady state hypothesis (PSSH) is often invoked for the specific mRNA and the target protein, i.e., the rate of intracellular accumulation of each species (left side of Eq. 2.14b) is considered to be insignificant compared to rates of other processes (the non-trivial terms on the right side of Eq. 2.14b). Application of PSSH for an intracellular protein results in the following algebraic relations.
[mRNA] = kpr)[G]/(kd + fi), [P} = fc,£[mRNA]/(*e + n). (2.45)
The cell mass-specific rate of synthesis of the target protein, r®en, therefore can be deduced to be
From this the cell mass-specific production rate of the target protein (sp, total rate of protein production in the culture = EpXV) can be obtained as follows. If the cells are subject to death, then £p = ip" — rrj, while if the cells are subject to lysis, then assuming total release of protein from the cells undergoing lysis into the abiotic phase, fip"Va — r(i[P]XV and in that case ep — rp". If the target protein is partially excreted, then one must consider mass balances for it in both biotic and abiotic phases with j,trans providing the linkage between the two balances.
The rate of expression of an operator-regulated gene depends on the efficiency of transcription of that gene (tj), which in turn is determined by interactions of modulating species at operator sites and RNA polymerase binding. This efficiency is thus proportional to the probability that the operator site O is not bound to repressor protein R. The genetically structured model involves a large number of model parameters representing various molecular interactions. A specific genetic change would affect only certain interactions and therefore specific model parameters. Further details on this model [329, 330] are spared here and interested readers are referred r'
to the source references ([33, 329, 330]). For Escherichia coli, the kinetic parameters for the transcription and translation processes, viz., kp and kq, have been correlated to the specific cell growth rate (/i), with both parameters increasing with increasing fj, [329, 330]. Such kinetic models will allow mapping of nucleotide sequence into cell population productivity and therefore afford the user capability for systematic optimization of cloned DNA inserts and in the long run the genetic makeup of the organism.
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