Application of cybernetic models to metabolic engineering: investigation of storage pathways

Modeling with a view to target identification in metabolic engineering: a critical evaluation of the available tools

The state of the art tools for modeling metabolism, typically used in the domain of metabolic engineering, were reviewed. The tools considered are stoichiometric network analysis (elementary modes and extreme pathways), stoichiometric modeling (metabolic flux analysis, flux balance analysis, and carbon modeling), mechanistic and approximative modeling, cybernetic modeling, and multivariate statistics. In the context of metabolic engineering, one should be aware that the usefulness of these tools to optimize microbial metabolism for overproducing a target compound depends predominantly on the characteristic properties of that compound. Because of their shortcomings not all tools are suitable for every kind of optimization; issues like the dependence of the target compound's synthesis on severe (redox) constraints, the characteristics of its formation pathway, and the achievable/desired flux towards the target compound should play a role when choosing the optimization strategy.

Systems interface biology

The field of systems biology has attracted the attention of biologists, engineers, mathematicians, physicists, chemists and others in an endeavour to create systems-level understanding of complex biological networks. In particular, systems engineering methods are finding unique opportunities in characterizing the rich behaviour exhibited by biological systems. In the same manner, these new classes of biological problems are motivating novel developments in theoretical systems approaches. Hence, the interface between systems and biology is of mutual benefit to both disciplines.

Minimization of glycerol production during the high-performance fed-batch ethanolic fermentation process in Saccharomyces cerevisiae, using a metabolic model as a prediction tool

On the basis of knowledge of the biological role of glycerol in the redox balance of Saccharomyces cerevisiae, a fermentation strategy was defined to reduce the surplus formation of NADH, responsible for glycerol synthesis. A metabolic model was used to predict the operating conditions that would reduce glycerol production during ethanol fermentation. Experimental validation of the simulation results was done by monitoring the inlet substrate feeding during fed-batch S. cerevisiae cultivation in order to maintain the respiratory quotient (RQ) (defined as the CO2 production to O2 consumption ratio) value between 4 and 5. Compared to previous fermentations without glucose monitoring, the final glycerol concentration was successfully decreased. Although RQ-controlled fermentation led to a lower maximum specific ethanol production rate, it was possible to reach a high level of ethanol production: 85 g.liter-1 with 1.7 g.liter-1 glycerol in 30 h. We showed here that by using a metabolic model as a tool in prediction, it was possible to reduce glycerol production in a very high-performance ethanolic fermentation process.

Genetic network driven control of PHBV copolymer composition

We developed a detailed mathematical model describing the coupling between the molecular weight distribution dynamics of poly(3-hydroxybutyrate-co-3hydroxyvalerate) (PHBV) copolymer chains with those of hydroxybutyrate (HB) and hydroxyvalerate (HV) monomer formation. Sensitivity analysis of the model revealed that both the monomer composition and the molecular weight distribution of the copolymer chains are strongly affected by the ratio between the rates at which the two-monomer units are incorporated into the chains. This ratio depends on the relative HB and HV availability, which in turn is a function of the expression levels of genes encoding enzymes that catalyze monomer formation. Regulation of gene expression was accomplished through the aid of an artificial genetic network, the patterns of expression of which can be controlled by appropriately tuning the concentration of an extracellular inducer. Extensive simulations were used to study the effects of operating conditions and parameter uncertainties on the range of achievable copolymer compositions. Since the predicted conditions fell in the range of feasible bioprocessing manipulations, it is expected that such strategy could be successfully employed. Thus, the presented model constitutes a powerful tool for designing genetic networks that can drive the formation of PHBV copolymer structures with desirable characteristics.

The principle of flux minimization and its application to estimate stationary fluxes in metabolic networks

Cellular functions are ultimately linked to metabolic fluxes brought about by thousands of chemical reactions and transport processes. The synthesis of the underlying enzymes and membrane transporters causes the cell a certain 'effort' of energy and external resources. Considering that those cells should have had a selection advantage during natural evolution that enabled them to fulfil vital functions (such as growth, defence against toxic compounds, repair of DNA alterations, etc.) with minimal effort, one may postulate the principle of flux minimization, as follows: given the available external substrates and given a set of functionally important 'target' fluxes required to accomplish a specific pattern of cellular functions, the stationary metabolic fluxes have to become a minimum. To convert this principle into a mathematical method enabling the prediction of stationary metabolic fluxes, the total flux in the network is measured by a weighted linear combination of all individual fluxes whereby the thermodynamic equilibrium constants are used as weighting factors, i.e. the more the thermodynamic equilibrium lies on the right-hand side of the reaction, the larger the weighting factor for the backward reaction. A linear programming technique is applied to minimize the total flux at fixed values of the target fluxes and under the constraint of flux balance (= steady-state conditions) with respect to all metabolites. The theoretical concept is applied to two metabolic schemes: the energy and redox metabolism of erythrocytes, and the central metabolism of Methylobacterium extorquens AM1. The flux rates predicted by the flux-minimization method exhibit significant correlations with flux rates obtained by either kinetic modelling or direct experimental determination. Larger deviations occur for segments of the network composed of redundant branches where the flux-minimization method always attributes the total flux to the thermodynamically most favourable branch. Nevertheless, compared with existing methods of structural modelling, the principle of flux minimization appears to be a promising theoretical approach to assess stationary flux rates in metabolic systems in cases where a detailed kinetic model is not yet available.

Modeling of yeast metabolism and process dynamics in batch fermentation

Much is known about yeast metabolism and the kinetics of industrial batch fermentation processes. In this study, however, we provide the first tool to evaluate the dynamic interaction that exists between them. A stoichiometric model, using wine fermentation as a case study, was constructed to simulate batch cultures of Saccharomyces cerevisiae. Five differential equations describe the evolution of the main metabolites and biomass in the fermentation tank, while a set of underdetermined linear algebraic equations models the pseudo-steady-state microbial metabolism. Specific links between process variables and the reaction rates of metabolic pathways represent microorganism adaptation to environmental changes in the culture. Adaptation requirements to changes in the environment, optimal growth, and homeostasis were set as the physiological objectives. A linear programming routine was used to define optimal metabolic mass flux distribution at each instant throughout the process. The kinetics of the process arise from the dynamic interaction between the environment and metabolic flux distribution. The model assessed the effect of nitrogen starvation and ethanol toxicity in wine fermentation and it was able to simulate fermentation profiles qualitatively, while experimental fermentation yields were reproduced successfully as well.

Prediction of temporal gene expression. Metabolic opimization by re-distribution of enzyme activities

A computational approach is used to analyse temporal gene expression in the context of metabolic regulation. It is based on the assumption that cells developed optimal adaptation strategies to changing environmental conditions. Time-dependent enzyme profiles are calculated which optimize the function of a metabolic pathway under the constraint of limited total enzyme amount. For linear model pathways it is shown that wave-like enzyme profiles are optimal for a rapid substrate turnover. For the central metabolism of yeast cells enzyme profiles are calculated which ensure long-term homeostasis of key metabolites under conditions of a diauxic shift. These enzyme profiles are in close correlation with observed gene expression data. Our results demonstrate that optimality principles help to rationalize observed gene expression profiles.

Microbial metabolism as an evolutionary response: the cybernetic approach to modeling

The growth and metabolic capabilities of microorganisms depend on their interactions with the culture medium. Many media contain two or more key substrates, and an organism may have different preferences for the components. Microorganisms adjust their preferences according to the prevailing conditions so as to favor their own survival. Cybernetic modeling describes this evolutionary strategy by defining a goal that an organism tries to attain optimally at all times. The goal is often, but not always, maximization of growth, and it may require the cells to manipulate their metabolic processes in response to changing environmental conditions. The cybernetic approach overcomes some of the limitations of metabolic control analysis (MCA), but it does not substitute MCA. Here we review the development of the cybernetic modeling of microbial metabolism, how it may be combined with MCA, and what improvements are needed to make it a viable technique for industrial fermentation processes.

Characterizing the metabolic phenotype: a phenotype phase plane analysis

Genome-scale metabolic maps can be reconstructed from annotated genome sequence data, biochemical literature, bioinformatic analysis, and strain-specific information. Flux-balance analysis has been useful for qualitative and quantitative analysis of metabolic reconstructions. In the past, FBA has typically been performed in one growth condition at a time, thus giving a limited view of the metabolic capabilities of a metabolic network. We have broadened the use of FBA to map the optimal metabolic flux distribution onto a single plane, which is defined by the availability of two key substrates. A finite number of qualitatively distinct patterns of metabolic pathway utilization were identified in this plane, dividing it into discrete phases. The characteristics of these distinct phases are interpreted using ratios of shadow prices in the form of isoclines. The isoclines can be used to classify the state of the metabolic network. This methodology gives rise to a "phase plane" analysis of the metabolic genotype-phenotype relation relevant for a range of growth conditions. Phenotype phase planes (PhPPs) were generated for Escherichia coli growth on two carbon sources (acetate and glucose) at all levels of oxygenation, and the resulting optimal metabolic phenotypes were studied. Supplementary information can be downloaded from our website (http://epicurus.che.udel.edu).

Computer applications in bioprocessing

Biotechnologists have stayed at the forefront for practical applications for computing. As hardware and software for computing have evolved, the latest advances have found eager users in the area of bioprocessing. Accomplishments and their significance can be appreciated by tracing the history and the interplay between the computing tools and the problems that have been solved in bioprocessing.

Dynamic optimal control of homeostasis: an integrative system approach for modeling of the central nitrogen metabolism in Saccharomyces cerevisiae

The theory of dynamic optimal metabolic control (DOMC), as developed by Giuseppin and Van Riel (Metab. Eng., 2000), is applied to model the central nitrogen metabolism (CNM) in Saccharomyces cerevisiae. The CNM represents a typical system encountered in advanced metabolic engineering. The CNM is the source of the cellular amino acids and proteins, including flavors and potentially valuable biomolecules; therefore, it is also of industrial interest. In the DOMC approach the cell is regarded as an optimally controlled system. Given the metabolic genotype, the cell faces a control problem to maintain an optimal flux distribution in a changing environment. The regulation is based on strategies and balances feedback control of homeostasis and feedforward regulation for adaptation. The DOMC approach is an integrative, holistic approach, not based on mechanistic descriptions and (therefore) not biased by the variation present in biochemical and molecular biological data. It is an effective tool to structure the rapidly increasing amount of data on the function of genes and pathways. The DOMC model is used successfully to predict the responses of pulses of ammonia and glutamine to nitrogen-limited continuous cultures of a wild-type strain and a glutamine synthetase-negative mutant. The simulation results are validated with experimental data.