Modeling of the biotransformation of crotonobetaine into L‐(−)‐carnitine by Escherichia coli strains

Abstract

A simple unstructured model, which includes carbon source as the limiting and essential substrate and oxygen as an enhancing substrate for cell growth, has been implemented to depict cell population evolution of two Escherichia coli strains and the expression of their trimethylammonium metabolism in batch and continuous reactors. Although the model is applied to represent the trans-crotonobetaine to L-(-)-carnitine biotransformation, it is also useful for understanding the complete metabolic flow of trimethylammonium compounds in E. coli. Cell growth and biotransformation were studied in both anaerobic and aerobic conditions. For this reason we derived equations to modify the specific growth rate, mu, and the cell yield on the carbon source (glycerol), Y(xg), as oxygen increased the rate of growth. Inhibition functions representing an excess of the glycerol and oxygen were included to depict cell evolution during extreme conditions. As a result, the model fitted experimental data for various growth conditions, including different carbon source concentrations, initial oxygen levels, and the existence of a certain degree of cell death. Moreover, the production of enzymes involved within the E. coli trimethylammonium metabolism and related to trans-crotonobetaine biotransformation was also modeled as a function of both the cell and oxygen concentrations within the system. The model describes all the activities of the different enzymes within the transformed and wild strains, able to produce L-(-)-carnitine from trans-crotonobetaine under both anaerobic and aerobic conditions. Crotonobetaine reductase inhibition by either oxygen or the addition of fumarate as well as its non-reversible catalytic action was taken into consideration. The proposed model was useful for describing the whole set of variables under both growing and resting conditions. Both E. coli strains within membrane high-density reactors were well represented by the model as results matched the experimental data.

Modeling, optimization and experimental assessment of continuous L‐(−)‐carnitine production by Escherichia coli cultures

“…In the present case, the S-system was derived as an approximation of a previous process model (Cánovas et al, 2002; see Appendix). The parameter profile of the optimum Ssolution should be used as input to the original model.…”

“…Once this information is available, it will be possible to derive an optimal process design and to attain its optimal operation. This line of reasoning was re-cently followed by Cánovas et al (2002), who presented a model of such a process, which included carbon source and oxygen as the limiting substrates for cell growth. From this model, the dynamics of the microbial-based process appears as the result of the interactions between the microbial cells and their environment, both affecting the biochemistry and the physiology of the cell culture.…”

“…The mathematical model of the above system was recently presented by Cánovas et al (2002) and is reproduced here with some minor modifications (see Appendix). In their original presentation, the authors included the metabolic transformation of crotonobetaine into ␥-butyrobetaine, through the activity of a previously described crotonobetaine reductase (Preusser et al, 1999;Roth et al, 1994).…”

“…Accordingly, the rate equations describing the synthesis of ␥-butyrobetaine from crotonobetaine through crotonobetaine reductase, which was contained in the original model formulation, were eliminated from the current version (see Appendix). The values of parameters and variables, rate equations, fluxes, and any other experimental condition are taken from Cánovas et al (2002) and Obón et al (1999). These values permitted us to translate the original model describing the steady state operation of the system to its corresponding S-system version.…”

“…The kinetic orders in this representation were calculated from experimental data (Cánovas et al, 2002;Obón et al, 1999), and the values of ␣ i and ␤ i were determined from the kinetic order values and steady-state variable values, as is commonly done in power-law approximations (e.g., Voit, 2000). The corresponding numerical version of the model thus obtained is as follows:…”