Many interesting problems that include convective transport arise in chemical reactor engineering (for example, tubular reactors). To solve these boundary-value problems, finite-difference schemes with a type of discretization of the convection term have been traditionally used. Some controversy about the discretization form of the convection term has arisen because of the different possibilities, including backward, forward and central discretizations. To overcome this problem, the usage of Green's function formulations for the numerical solution of typical chemical engineering problems with both linear and nonlinear kinetics, diffusion and convection phenomena, is presented. A distinctive feature of the proposed scheme is that boundary conditions are exactly incorporated. The results show that the integral formulation is, in general, superior in accuracy to the different finite-differences schemes. That is, more accurate calculations of the performance factor are obtained in terms of less mesh points and computer time.
The industrial production of plants promoter like auxins is gaining interest, in consequence it is important to un- derstand the metabolism of the microorganisms involved and the optimal conditions for their industrial production. In this study the metabolic model of Bacillus subtilis was used to estimate intracellular fluxes and the robustness of the principal branching points of aerobic propionate metabolism for the 3-indoleacetic acid (IAA) production. The robustness analyzes of the metabolic network showed the enzymes that participate in the synthesis of erythrose 4-phosphate and glyceraldehyde 3-phosphate as possible limiting metabolites in the synthesis of IAA and might be a target for metabolic engineering strategies. The phenotype phase plane analysis allowed the identification of the opti- mal rate growth conditions to produce the auxin (less than 0.1 h).
The genera Bacillus belongs to the group of microorganisms that are known as plant growth-promoting bacteria, their metabolism has evolved to produce molecules that benefit the growth of the plant, and the production of 3-indole acetic acid (IAA) is part of its secondary metabolism. In this work, Bacillus subtilis was cultivated in a bioreactor to produce IAA using propionate and glucose as carbon sources in an M9-modified media; in both cases, tryptophan was added as a co-substrate. The yield of IAA using propionate is 17% higher compared to glucose. After 48 h of cultivation, the final concentration was 310 mg IAA/L using propionate and 230 mg IAA/L using glucose, with a concentration of 500 mg Trp/L. To gain more insight into propionate metabolism and its advantages, the genome-scale metabolic model of B. subtilis (iBSU 1147) and computational analysis were used to calculate flux distribution and evaluate the metabolic capabilities to produce IAA using propionate. The metabolic fluxes demonstrate that propionate uptake favors the production of precursors needed for the synthesis of the hormone, and the sensitivity analysis shows that the control of a specific growth rate has a positive impact on the production of IAA.
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