Optimal Performance of the Tryptophan Operon of E. coli: A stochastic, Dynamical, Mathematical-Modeling Approach

Abstract

In this work, we develop a detailed, stochastic, dynamical model for the tryptophan operon of E. coli, and estimate all of the model parameters from reported experimental data. We further employ the model to study the system performance, considering the amount of biochemical noise in the trp level, the system rise time after a nutritional shift, and the amount of repressor molecules necessary to maintain an adequate level of repression, as indicators of the system performance regime. We demonstrate that the level of cooperativity between repressor molecules bound to the first two operators in the trp promoter affects all of the above enlisted performance characteristics. Moreover, the cooperativity level found in the wild-type bacterial strain optimizes a cost-benefit function involving low biochemical noise in the tryptophan level, short rise time after a nutritional shift, and low number of regulatory molecules.

Fed‐batch production of l‐tryptophan from glycerol using recombinant Escherichia coli

“…l ‐tryptophan is an aromatic amino acid with a high molar weight of 204 g mol −1 and has the highest demand for metabolic energy equivalents during its biosynthesis compared with all other proteinogenic amino acids (Salazar‐Cavazos & Santillan, ). It is an essential aromatic amino acid that is used industrially as an additive for food and feed industry.…”

“…l ‐tryptophan molecules inside the cells control the biosynthesis on three regulation levels: they serve as corepressors for the transcription of the genes in the tryptophan operon ( trpLEDCBA ) and as effectors for the feedback‐inhibition of allosteric enzymes (AroH and TrpE) and furthermore they influence the secondary structure of trpL messenger RNA which can attenuate transcription and translation depending on the loading of tRNA Trp (Yanofsky, ). In combination, these mechanisms allow an accurate adjustment of the intracellular l ‐tryptophan level (Ikeda, ; Salazar‐Cavazos & Santillan, ; Sprenger, ; Yanofsky, ).…”

The utility of simple mathematical models in understanding gene regulatory dynamics

“…This means that, either explicitly or implicitly, they assume that promoter gating between the various repressed and the non-repressed states is much faster than the transcription and translation processes. Nevertheless, recent detailed measurements of the repressor-promoter kinetics revealed that this assumption is not valid—see [ 55 ] and references therein. This further implies that the assumed separation of time scales employed to obtain the simplified model in Equations (3.42) – (3.44) does not exist, and one is obliged to work with the full model: Equations (3.27) – (3.37) .…”

“…This further implies that the assumed separation of time scales employed to obtain the simplified model in Equations (3.42) – (3.44) does not exist, and one is obliged to work with the full model: Equations (3.27) – (3.37) . In a recent paper [ 55 ] we studied the stochastic behaviour of such a model, but analytical and numerical studies of the deterministic counterpart are still missing.…”

Probability of <i>Escherichia coli</i> contamination spread in ground beef production

“…Most of the existing deterministic mathematical models about E. coli, published in recent years, are devoted to the study of the bacterium itself, rather than the study of the illness caused by it or the estimation of the risk of contamination [5,10,11].…”