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Steady-state global optimization of metabolic non-linear dynamic models through recasting into power-law canonical models

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      Abstract

      Background

      Design of newly engineered microbial strains for biotechnological purposes would greatly benefit from the development of realistic mathematical models for the processes to be optimized. Such models can then be analyzed and, with the development and application of appropriate optimization techniques, one could identify the modifications that need to be made to the organism in order to achieve the desired biotechnological goal. As appropriate models to perform such an analysis are necessarily non-linear and typically non-convex, finding their global optimum is a challenging task. Canonical modeling techniques, such as Generalized Mass Action (GMA) models based on the power-law formalism, offer a possible solution to this problem because they have a mathematical structure that enables the development of specific algorithms for global optimization.

      Results

      Based on the GMA canonical representation, we have developed in previous works a highly efficient optimization algorithm and a set of related strategies for understanding the evolution of adaptive responses in cellular metabolism. Here, we explore the possibility of recasting kinetic non-linear models into an equivalent GMA model, so that global optimization on the recast GMA model can be performed. With this technique, optimization is greatly facilitated and the results are transposable to the original non-linear problem. This procedure is straightforward for a particular class of non-linear models known as Saturable and Cooperative (SC) models that extend the power-law formalism to deal with saturation and cooperativity.

      Conclusions

      Our results show that recasting non-linear kinetic models into GMA models is indeed an appropriate strategy that helps overcoming some of the numerical difficulties that arise during the global optimization task.

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      Most cited references 42

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      Stochastic kinetic analysis of developmental pathway bifurcation in phage lambda-infected Escherichia coli cells.

      Fluctuations in rates of gene expression can produce highly erratic time patterns of protein production in individual cells and wide diversity in instantaneous protein concentrations across cell populations. When two independently produced regulatory proteins acting at low cellular concentrations competitively control a switch point in a pathway, stochastic variations in their concentrations can produce probabilistic pathway selection, so that an initially homogeneous cell population partitions into distinct phenotypic subpopulations. Many pathogenic organisms, for example, use this mechanism to randomly switch surface features to evade host responses. This coupling between molecular-level fluctuations and macroscopic phenotype selection is analyzed using the phage lambda lysis-lysogeny decision circuit as a model system. The fraction of infected cells selecting the lysogenic pathway at different phage:cell ratios, predicted using a molecular-level stochastic kinetic model of the genetic regulatory circuit, is consistent with experimental observations. The kinetic model of the decision circuit uses the stochastic formulation of chemical kinetics, stochastic mechanisms of gene expression, and a statistical-thermodynamic model of promoter regulation. Conventional deterministic kinetics cannot be used to predict statistics of regulatory systems that produce probabilistic outcomes. Rather, a stochastic kinetic analysis must be used to predict statistics of regulatory outcomes for such stochastically regulated systems.
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        BRENDA, the enzyme information system in 2011

        The BRENDA (BRaunschweig ENzyme Database, http://www.brenda-enzymes.org) enzyme information system is the main collection of enzyme functional and property data for the scientific community. The majority of the data are manually extracted from the primary literature. The content covers information on function, structure, occurrence, preparation and application of enzymes as well as properties of mutants and engineered variants. The number of manually annotated references increased by 30% to more than 100 000, the number of ligand structures by 45% to almost 100 000. New query, analysis and data management tools were implemented to improve data processing, data presentation, data input and data access. BRENDA now provides new viewing options such as the display of the statistics of functional parameters and the 3D view of protein sequence and structure features. Furthermore a ligand summary shows comprehensive information on the BRENDA ligands. The enzymes are linked to their respective pathways and can be viewed in pathway maps. The disease text mining part is strongly enhanced. It is possible to submit new, not yet classified enzymes to BRENDA, which then are reviewed and classified by the International Union of Biochemistry and Molecular Biology. A new SBML output format of BRENDA kinetic data allows the construction of organism-specific metabolic models.
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          Recent developments in parameter estimation and structure identification of biochemical and genomic systems.

          The organization, regulation and dynamical responses of biological systems are in many cases too complex to allow intuitive predictions and require the support of mathematical modeling for quantitative assessments and a reliable understanding of system functioning. All steps of constructing mathematical models for biological systems are challenging, but arguably the most difficult task among them is the estimation of model parameters and the identification of the structure and regulation of the underlying biological networks. Recent advancements in modern high-throughput techniques have been allowing the generation of time series data that characterize the dynamics of genomic, proteomic, metabolic, and physiological responses and enable us, at least in principle, to tackle estimation and identification tasks using 'top-down' or 'inverse' approaches. While the rewards of a successful inverse estimation or identification are great, the process of extracting structural and regulatory information is technically difficult. The challenges can generally be categorized into four areas, namely, issues related to the data, the model, the mathematical structure of the system, and the optimization and support algorithms. Many recent articles have addressed inverse problems within the modeling framework of Biochemical Systems Theory (BST). BST was chosen for these tasks because of its unique structural flexibility and the fact that the structure and regulation of a biological system are mapped essentially one-to-one onto the parameters of the describing model. The proposed methods mainly focused on various optimization algorithms, but also on support techniques, including methods for circumventing the time consuming numerical integration of systems of differential equations, smoothing overly noisy data, estimating slopes of time series, reducing the complexity of the inference task, and constraining the parameter search space. Other methods targeted issues of data preprocessing, detection and amelioration of model redundancy, and model-free or model-based structure identification. The total number of proposed methods and their applications has by now exceeded one hundred, which makes it difficult for the newcomer, as well as the expert, to gain a comprehensive overview of available algorithmic options and limitations. To facilitate the entry into the field of inverse modeling within BST and related modeling areas, the article presented here reviews the field and proposes an operational 'work-flow' that guides the user through the estimation process, identifies possibly problematic steps, and suggests corresponding solutions based on the specific characteristics of the various available algorithms. The article concludes with a discussion of the present state of the art and with a description of open questions.
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            Author and article information

            Affiliations
            [1]Departament d'Enginyeria Química, Universitat Rovira i Virgili, Avinguda Països Catalans 26, 43007-Tarragona, Spain
            [2]Technische Universität München. Fachgebiet für Systembiotechnologie, Boltzmannstr. 15 85748 Garching, Germany
            [3]Departament de Ciències Mèdiques Bàsiques, Institut de Recerca Biomèdica de Lleida (IRBLLEIDA), Universitat de Lleida, Montserrat Roig 2, 25008 Lleida, Spain
            Contributors
            Journal
            BMC Syst Biol
            BMC Systems Biology
            BioMed Central
            1752-0509
            2011
            25 August 2011
            : 5
            : 137
            3201032
            1752-0509-5-137
            21867520
            10.1186/1752-0509-5-137
            Copyright ©2011 Pozo et al; licensee BioMed Central Ltd.

            This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

            Categories
            Methodology Article

            Quantitative & Systems biology

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