Advantages and disadvantages of aggregating fluxes into synthetic and degradative fluxes when modelling metabolic pathways

A systemic approach to explore the flexibility of energy stores at the cellular scale: Examples from muscle cells

Variations in energy storage and expenditure are key elements for animals adaptation to rapidly changing environments. Because of the multiplicity of metabolic pathways, metabolic crossroads and interactions between anabolic and catabolic processes within and between different cells, the flexibility of energy stores in animal cells is difficult to describe by simple verbal, textual or graphic terms. We propose a mathematical model to study the influence of internal and external challenges on the dynamic behavior of energy stores and its consequence on cell energy status. The role of the flexibility of energy stores on the energy equilibrium at the cellular level is illustrated through three case studies: variation in eating frequency (i.e., glucose input), level of physical activity (i.e., ATP requirement), and changes in cell characteristics (i.e., maximum capacity of glycogen storage). Sensitivity analysis has been performed to highlight the most relevant parameters of the model; model simulations have then been performed to illustrate how variation in these key parameters affects cellular energy balance. According to this analysis, glycogen maximum accumulation capacity and homeostatic energy demand are among the most important parameters regulating muscle cell metabolism to ensure its energy equilibrium.

Biochemical Systems Theory: A Review

Biochemical systems theory (BST) is the foundation for a set of analytical andmodeling tools that facilitate the analysis of dynamic biological systems. This paper depicts major developments in BST up to the current state of the art in 2012. It discusses its rationale, describes the typical strategies and methods of designing, diagnosing, analyzing, and utilizing BST models, and reviews areas of application. The paper is intended as a guide for investigators entering the fascinating field of biological systems analysis and as a resource for practitioners and experts.

Modelling the effects of inhibitors of guanine nucleotide synthesis: implications for studies of cellular differentiation pathways

Mizoribine induces the differentiation of promyelocytes by an unknown mechanism that relies on compromised guanine nucleotide synthesis. I have found that mizoribine also perturbs adenosine nucleotide levels in HL-60 promyelocytes, particularly ATP. To reconcile these observations with the known actions of mizoribine I have adapted an existing model of human purine metabolism composed as an S-system familiar from Biochemical Systems Theory. Mizoribine's actions were then simulated and compared with experimental data.

Metabolic Engineering with power-law and linear-logarithmic systems

Metabolic Engineering aims to improve the performance of biotechnological processes through rational manipulation rather than random mutagenesis of the organisms involved. Such a strategy can only succeed when a mathematical model of the target process is available. Simplifying assumptions are often needed to cope with the complexity of such models in an efficient way, and the choice of such assumptions often leads to models that fall within a certain structural template or formalism. The most popular formalisms can be grouped in two categories: power-law and linear-logarithmic. As optimization and analysis of a model strongly depends on its structure, most methods in Metabolic Engineering have been defined within a given formalism and never used in any other. In this work, the four most commonly used formalisms (two power-law and two linear-logarithmic) are placed in a common framework defined within Biochemical Systems Theory. This framework defines every model as matrix equations in terms of the same parameters, enabling the formulation of a common steady state analysis and providing means for translating models and methods from one formalism to another. Several Metabolic Engineering methods are analysed here and shown to be variants of a single equation. Particularly, two problem solving philosophies are compared: the application of the design equation and the solution of constrained optimization problems. Generalizing the design equation to all the formalisms shows it to be interchangeable with the direct solution of the rate law in matrix form. Furthermore, optimization approaches are concluded to be preferable since they speed the exploration of the feasible space, implement a better specification of the problem and exclude unrealistic results. Beyond consolidating existing knowledge and enabling comparison, the systematic approach adopted here can fill the gaps between the different methods and combine their strengths.

Optimization of biotechnological systems through geometric programming

Background

In 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.

Results

A 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.

Conclusion

GMA 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.

Detection of potential enzyme targets by metabolic modelling and optimization: Application to a simple enzymopathy

MOTIVATION

A very promising approach in drug discovery involves the integration of available biomedical data through mathematical modelling and data mining. We have developed a method called optimization program for drug discovery (OPDD) that allows new enzyme targets to be identified in enzymopathies through the integration of metabolic models and biomedical data in a mathematical optimization program. The method involves four steps: (i) collection of the necessary information about the metabolic system and disease; (ii) translation of the information into mathematical terms; (iii) computation of the optimization programs prioritizing the solutions that propose the inhibition of a reduced number of enzymes and (iv) application of additional biomedical criteria to select and classify the solutions. Each solution consists of a set of predicted values for metabolites, initial substrates and enzyme activities, which describe a biologically acceptable steady state of the system that shifts the pathologic state towards a healthy state.

RESULTS

The OPDD was used to detect target enzymes in an enzymopathy, the human hyperuricemia. An existing S-system model and bibliographic information about the disease were used. The method detected six single-target enzyme solutions involving dietary modification, one of them coinciding with the conventional clinical treatment using allopurinol. The OPDD detected a large number of possible solutions involving two enzyme targets. All except one contained one of the previously detected six enzyme targets. The purpose of this work was not to obtain solutions for direct clinical implementation but to illustrate how increasing levels of biomedical information can be integrated together with mathematical models in drug discovery.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Optimization of biochemical systems by linear programming and general mass action model representations

A new method is proposed for the optimization of biochemical systems. The method, based on the separation of the stoichiometric and kinetic aspects of the system, follows the general approach used in the previously presented indirect optimization method (IOM) developed within biochemical systems theory. It is called GMA-IOM because it makes use of the generalized mass action (GMA) as the model system representation form. The GMA representation avoids flux aggregation and thus prevents possible stoichiometric errors. The optimization of a system is used to illustrate and compare the features, advantages and shortcomings of both versions of the IOM method as a general strategy for designing improved microbial strains of biotechnological interest. Special attention has been paid to practical problems for the actual implementation of the new proposed strategy, such as the total protein content of the engineered strain or the deviation from the original steady state and its influence on cell viability.

Metabolic control analysis aimed at the ribose synthesis pathways of tumor cells: a new strategy for antitumor drug development

Metabolic control analysis predicts that effects on tumor growth are likely to be obtained with lower concentrations of drug, if an enzyme with a high control coefficient on tumor growth is being inhibited. Here we measure glucose-6-phosphate dehydrogenase (G6PDH) control coefficient on in vivo tumor growth using mice bearing Ehrlich ascites tumor cells. We used dehydroepiandrosterone-sulphate (DHEA-S), an uncompetitive inhibitor of this enzyme and the in situ cytochemical method to measure the enzyme activity changes that accompany changes on tumor cell growth. This method ensures that the enzyme activity determined is the one existing in the in situ conditions and enables computing a control coefficient in in situ conditions. From the data obtained on tumor cell number and the in situ enzyme activities in absence and presence of DHEA-S, a control coefficient of 0.41 for G6PDH on tumor cell growth was computed. This value is approximately the half of the transketolase control coefficient value of 0.9 previously reported. Moreover, the use of in situ methods to assess enzyme activities, applied for first time for the calculation of control coefficients in this study, opens new avenues to the use of uncompetitive inhibitors for the measurement of in situ control coefficients.

Metabolic engineering as an integrating platform for strain development

Integration of the analytical framework and experimental tools of metabolic engineering with emerging technologies such as DNA microarrays and directed evolution stands to dramatically improve the approaches by which strain improvement and biocatalyst design are pursued in the future. Progress in genomics and applied molecular biology, together with increasing emphasis on renewable resource utilization for chemical production, has advanced metabolic engineering to the forefront of biotechnological interest.