Néstor V. Torres

Metabolism of citric acid production by Aspergillus niger: Model definition, steady-state analysis and constrained optimization of citric acid production rate

In an attempt to provide a rational basis for the optimization of citric acid production by A. niger, we developed a mathematical model of the metabolism of this filamentous fungus when in conditions of citric acid accumulation. The present model is based in a previous one, but extended with the inclusion of new metabolic processes and updated with currently available kinetic data. Among the different alternatives to represent the system behavior we have chosen the S-system representation within power-law formalism. This type of representation allows us to verify not only the ability of the model to exhibit a stable steady state of the integrated system but also the robustness and quality of the representation. The model analysis is shown to be self-consistent, with a stable steady state, and in good agreement with experimental evidence. Moreover, the model representation is sufficiently robust, as indicated by sensitivity and steady-state and dynamic analyses. From the steady-state results we concluded that the range of accuracy of the S-system representation is wide enough to model realistic deviations from the nominal steady state. The dynamic analysis indicated a reasonable response time, which provided further indication that the model is adequate. The extensive assessment of the reliability and quality of the model put us in a position to address questions of optimization of the system with respect to increased citrate production. We carried out the constrained optimization of A. niger metabolism with the goal of predicting an enzyme activity profile yielding the maximum rate of citrate production, while, at the same time, keeping all enzyme activities within predetermined, physiologically acceptable ranges. The optimization is based on a method described and tested elsewhere that utilizes the fact that the S-system representation of a metabolic system becomes linear at steady state, which allows application of linear programming techniques. Our results show that: (i) while the present profile of enzyme activities in A. niger at idiophase steady state yields high rates of citric acid production, it still leaves room for changes and suggests possible optimization of the activity profile to over five times the basal rate synthesis; (ii) when the total enzyme concentration is allowed to double its basal value, the citric acid production rate can be increased by more than 12-fold, and even larger values can be attained if the total enzyme concentration is allowed to increase even more (up to 50-fold when the total enzyme concentration may rise up to 10-fold the basal value); and (iii) the systematic search of the best combination of subsets of enzymes shows that, under all conditions assayed, a minimum of 13 enzymes need be modified if significant increases in citric acid are to be obtained. This implies that improvements by single enzyme modulation are unlikely, which is in agreement with the findings of some investigators in this and other fields.

Optimization of nonlinear biotechnological processes with linear programming: Application to citric acid production by Aspergillus niger

The metabolic pathway and the properties of many of the enzymes involved in the citric acid biosynthesis in the mold Aspergillus niger are well known. This fact, together with the availability of new theoretical frameworks aimed at quantitative analyses of control and dynamics in metabolic systems, has allowed us to construct a mathematical model of the carbohydrate metabolism in Aspergillus niger under conditions of citric acid accumulation. The model makes use of the S‐system representation of biochemical systems, which renders it possible to use linear programming to optimize the process. It was found that maintaining the metabolite pools within narrow physiological limits (20% around the basal steady‐state level) and allowing the enzyme concentrations to vary within a range of 0.1 to 50 times their basal values it is possible to triple the glycolytic flux while maintaining 100% yield of substrate transformation. To achieve these improvements it is necessary to modulate seven or more enzymes simultaneously. Although this seems difficult to implement at present, the results are useful because they indicate what the theoretical limits are and because they suggest several alternative strategies.

Uptake and export of citric acid by Aspergillus niger is reciprocally regulated by manganese ions

The uptake as well as the export of citric acid by Aspergillus niger occur by active, deltapH-driven, H(+)-symport dependent systems. They are inhibited by nonmetabolizable tricarboxylic acid analogues and phthalic acid, and by several other mono-, di- and tribasic organic acids. However, citrate export could only be demonstrated in a mycelium cultivated under manganese-deficient growth conditions, whereas the uptake of citrate from the medium was only detectable upon precultivation of A. niger in a medium supplemented with Mn2+ ions. In addition, the uptake of citrate was dependent on the presence of Mn2+ ions in the assay, and inhibited by EDTA. This requirement for Mn2+ could also be partially fulfilled by Mg2+, Fe2+ or Zn2+, whereas Cu2+ ions inhibited citrate transport. The observed divergent effects of manganese ions on citrate uptake and citrate export may be a major reason for the well documented requirement for manganese deficiency of citric acid accumulation.

Glucose transport byAspergillus niger: the low-affinity carrier is only formed during growth on high glucose concentrations

The filamentous fungusAspergillus niger accumulates large levels of citric acid in the medium when grown under conditions favouring a high rate of sugar catabolism. With the aim of understanding the mechanisms involved in this process we investigated glucose transport in this fungus. To this end a medium was designed that enables growth of the fungus into a fine, hairy filamentous mycelium, suitable for transport studies. It was found thatA. niger contains a single, high-affinity glucose transporter when grown on a low (1% w/v) glucose concentration, but forms an additional low-affinity transporter when grown on a high (15% w/v) glucose concentration. Both glucose transporters exhibit decreased activities at low pH and are inhibited by citric acid. However, the activity of the low-affinity transporter is much less affected by these conditions. Two 2-deoxyglucose-resistant (dgr) mutants ofA. niger, which produce citric acid at a much lower rate than the parent strain, are impaired in the formation of the low-affinity transporter, but form the high-affinity transporter with higher activities. We conclude that the low-affinity glucose transporter takes part in the mechanism by whichA. niger responds to high extracellular glucose concentrations leading to citric acid accumulation.

Optimization of Tryptophan Production in Bacteria. Design of a Strategy for Genetic Manipulation of the Tryptophan Operon for Tryptophan Flux Maximization

In the present work we have applied the indirect optimization method (Torres, N. V. et al.Biotechnol. Bioeng.1996, 49, 247–258) to the maximization of tryptophan biosynthesis in Escherichia coli. The optimization procedure is applied to an updated model of this biochemical system (Xiu, Z‐L et al., J. Biotechnol.1997, 58,125–140) and thus extended to a problem that includes the processes of transcription and translation. The model representation used by these authors is first translated into the corresponding S‐system version. Then, to guarantee cell viability, we impose a set of constraints on some variable and parameter values, all of which are able to be modulated by available techniques. Our results show that it is possible to attain a stable and robust steady state with a rate of tryptophan production increased more than 4 times. This is achieved by changing four key parameters related to the efflux of tryptophan, the growth rate, the inhibition constant, and the tryptophan repressor level. Moreover, it is demonstrated that we can reach this optimum state in a sequential manner, each step leading us to a better situation in relation to the previous one. Thus, only by doubling the tryptophan excretion we can triplicate the rate of tryptophan production. A further, although lesser, improvement can be attained by increasing 4‐fold the rate of growth and subsequently by weakening the inhibitory feedback interaction of tryptophan on the enzymes leading to its synthesis. Finally, a significant jump in the rate of production can be obtained if the level of the trp operon could be decreased. When a second approach was considered, in which the growth rate is kept constant in the optimized profile, we found out that by modulation of the parameters it is possible to increase more than 2‐fold the rate of tryptophan production.

13C-NMR analysis of glucose metabolism during citric acid production by Aspergillus niger.

Abstract. The effect of glucose concentration on glycolytic metabolism under conditions of citric acid accumulation by Aspergillus niger was studied with 13C-labelled glucose. The results show that during cultivation at high glucose (14%, w/v), most of the label in citric acid is in C-2/C-4, and is thus due to the pyruvate carboxylase reaction. However, a significant portion is also present in C-1/C-5, whose origin is less clear but most likely due to reconsumption of glycerol and erythritol. Formation of trehalose and mannitol is high during the early phase of fermentation and declines thereafter. The early fermentation phase is further characterized by a high rate of anaplerosis from oxaloacetate to pyruvate, which also decreases with time. At low glucose concentrations (2%, w/v), which lead to a significantly reduced citric acid yield and formation rate, labelling of citrate in C-2/C-4 is decreased and C-1/C-5 labelling increased. Growth on 2% glucose is also characterized by an appreciable scrambling of mannitol and considerable backflux from mannitol to trehalose (indicating tight glycolytic control at the fructose-6-phosphate step) and an increased anaplerotic formation of pyruvate from oxaloacetate. These data indicate that cultivation on high sugar concentrations shifts control of glycolysis from fructose-6-phosphate to the glyceraldehyde-3-phosphate dehydrogenase step.

Optimization of biotechnological systems through geometric programming

BackgroundIn the past, tasks of model based yield optimization in metabolic engineering were either approached with stoichiometric models or with structured nonlinear models such as S-systems or linear-logarithmic representations. These models stand out among most others, because they allow the optimization task to be converted into a linear program, for which efficient solution methods are widely available. For pathway models not in one of these formats, an Indirect Optimization Method (IOM) was developed where the original model is sequentially represented as an S-system model, optimized in this format with linear programming methods, reinterpreted in the initial model form, and further optimized as necessary.ResultsA new method is proposed for this task. We show here that the model format of a Generalized Mass Action (GMA) system may be optimized very efficiently with techniques of geometric programming. We briefly review the basics of GMA systems and of geometric programming, demonstrate how the latter may be applied to the former, and illustrate the combined method with a didactic problem and two examples based on models of real systems. The first is a relatively small yet representative model of the anaerobic fermentation pathway in S. cerevisiae, while the second describes the dynamics of the tryptophan operon in E. coli. Both models have previously been used for benchmarking purposes, thus facilitating comparisons with the proposed new method. In these comparisons, the geometric programming method was found to be equal or better than the earlier methods in terms of successful identification of optima and efficiency.ConclusionGMA systems are of importance, because they contain stoichiometric, mass action and S-systems as special cases, along with many other models. Furthermore, it was previously shown that algebraic equivalence transformations of variables are sufficient to convert virtually any types of dynamical models into the GMA form. Thus, efficient methods for optimizing GMA systems have multifold appeal.

Model based optimization of biochemical systems using multiple objectives: a comparison of several solution strategies

In this work we consider multi-objective optimization problems arising from the domain of biochemical systems, namely metabolic pathways, with the ethanol production by Saccharomyces cerevisiae as a case study. The goals are to maximize the rate of production of ethanol and simultaneously minimize several internal metabolite concentrations, imposing additional constraints in order to ensure cell viability. As a result, the Pareto-optimal set is obtained for different formulations of the optimization problem. Starting from a detailed, nonlinear, kinetic model of the pathway, several recent solution strategies and other well-known techniques are compared, highlighting the advantages and drawbacks of each one.

Optimization of biochemical systems through mathematical programming: Methods and applications

In this work we present a general (mono and multiobjective) optimization framework for the technological improvement of biochemical systems. The starting point of the method is a mathematical model in ordinary differential equations (ODEs) of the investigated system, based on qualitative biological knowledge and quantitative experimental data. In the method we take advantage of the special structural features of a family of ODEs called power-law models to reduce the computational complexity of the optimization program. In this way, the genetic manipulation of a biochemical system to meet a certain biotechnological goal can be expressed as an optimization program with some desired properties such as linearity or convexity. The general method of optimization is presented and discussed in its linear and geometric programming versions. We furthermore illustrate the use of the method by several real case studies. We conclude that the technological improvement of microorganisms can be afforded using the combination of mathematical modelling and optimization. The systematic nature of this approach facilitates the redesign of biochemical systems and makes this a predictive exercise rather than a trial-and-error procedure.

Non-linear optimization of biotechnological processes by stochastic algorithms: Application to the maximization of the production rate of ethanol, glycerol and carbohydrates by Saccharomyces cerevisiae

A non-linear optimization, based on an stochastic multi-start search algorithm, has been applied to the maximization of the production rates of ethanol, glycerol and carbohydrates by Saccharomyces cerevisiae. This optimization is applied to two alternative (non-linear) model representations of the same system, namely the Michaelis-Menten and the generalized mass action forms. We find a complete agreement between the results obtained using both representations. This is, maximization of the ethanol production rate requires modulation of up to six enzymes, while modification of only one enzyme is sufficient to obtain a significant improvement in the production rate of glycerol and carbohydrates. When the results are compared with those previously obtained using an indirect linear optimization method (Torres, N.V., Voit, E.O., González-Alcón, C., Rodríguez, F. 1997. An integrated optimization method for biochemical systems. Description of method and application to ethanol, glycerol and carbohydrate production in S. cerevisiae. Biotechnol. Bioeng. 55(5), 758-772.), we find close agreement between both optimization techniques. Qualitatively, both optimization approaches render the same profile of enzymes to be modulated, while quantitatively, discrepancies arise when the objective function is the maximization of the ethanol production rate. Reasons for such discrepancies and an evaluation of the advantages of each method (linear vs non-linear) are given.