3,223 research outputs found

    Evaluation of rate law approximations in bottom-up kinetic models of metabolism.

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    BackgroundThe mechanistic description of enzyme kinetics in a dynamic model of metabolism requires specifying the numerical values of a large number of kinetic parameters. The parameterization challenge is often addressed through the use of simplifying approximations to form reaction rate laws with reduced numbers of parameters. Whether such simplified models can reproduce dynamic characteristics of the full system is an important question.ResultsIn this work, we compared the local transient response properties of dynamic models constructed using rate laws with varying levels of approximation. These approximate rate laws were: 1) a Michaelis-Menten rate law with measured enzyme parameters, 2) a Michaelis-Menten rate law with approximated parameters, using the convenience kinetics convention, 3) a thermodynamic rate law resulting from a metabolite saturation assumption, and 4) a pure chemical reaction mass action rate law that removes the role of the enzyme from the reaction kinetics. We utilized in vivo data for the human red blood cell to compare the effect of rate law choices against the backdrop of physiological flux and concentration differences. We found that the Michaelis-Menten rate law with measured enzyme parameters yields an excellent approximation of the full system dynamics, while other assumptions cause greater discrepancies in system dynamic behavior. However, iteratively replacing mechanistic rate laws with approximations resulted in a model that retains a high correlation with the true model behavior. Investigating this consistency, we determined that the order of magnitude differences among fluxes and concentrations in the network were greatly influential on the network dynamics. We further identified reaction features such as thermodynamic reversibility, high substrate concentration, and lack of allosteric regulation, which make certain reactions more suitable for rate law approximations.ConclusionsOverall, our work generally supports the use of approximate rate laws when building large scale kinetic models, due to the key role that physiologically meaningful flux and concentration ranges play in determining network dynamics. However, we also showed that detailed mechanistic models show a clear benefit in prediction accuracy when data is available. The work here should help to provide guidance to future kinetic modeling efforts on the choice of rate law and parameterization approaches

    Evaluation of rate law approximations in bottom-up kinetic models of metabolism

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    BACKGROUND: The mechanistic description of enzyme kinetics in a dynamic model of metabolism requires specifying the numerical values of a large number of kinetic parameters. The parameterization challenge is often addressed through the use of simplifying approximations to form reaction rate laws with reduced numbers of parameters. Whether such simplified models can reproduce dynamic characteristics of the full system is an important question. RESULTS: In this work, we compared the local transient response properties of dynamic models constructed using rate laws with varying levels of approximation. These approximate rate laws were: 1) a Michaelis-Menten rate law with measured enzyme parameters, 2) a Michaelis-Menten rate law with approximated parameters, using the convenience kinetics convention, 3) a thermodynamic rate law resulting from a metabolite saturation assumption, and 4) a pure chemical reaction mass action rate law that removes the role of the enzyme from the reaction kinetics. We utilized in vivo data for the human red blood cell to compare the effect of rate law choices against the backdrop of physiological flux and concentration differences. We found that the Michaelis-Menten rate law with measured enzyme parameters yields an excellent approximation of the full system dynamics, while other assumptions cause greater discrepancies in system dynamic behavior. However, iteratively replacing mechanistic rate laws with approximations resulted in a model that retains a high correlation with the true model behavior. Investigating this consistency, we determined that the order of magnitude differences among fluxes and concentrations in the network were greatly influential on the network dynamics. We further identified reaction features such as thermodynamic reversibility, high substrate concentration, and lack of allosteric regulation, which make certain reactions more suitable for rate law approximations. CONCLUSIONS: Overall, our work generally supports the use of approximate rate laws when building large scale kinetic models, due to the key role that physiologically meaningful flux and concentration ranges play in determining network dynamics. However, we also showed that detailed mechanistic models show a clear benefit in prediction accuracy when data is available. The work here should help to provide guidance to future kinetic modeling efforts on the choice of rate law and parameterization approaches. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s12918-016-0283-2) contains supplementary material, which is available to authorized users

    Drug absorption through a cell monolayer: a theoretical work on a non-linear three-compartment model

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    The subject of analysis is a non-linear three-compartment model, widely used in pharmacological absorption studies. It has been transformed into a general form, thus leading automatically to an appropriate approximation. This made the absorption profile accessible and expressions for absorption times, apparent permeabilities and equilibrium values were given. These findings allowed a profound analysis of results from non-linear curve fits and delivered the dependencies on the systems' parameters over a wide range of values. The results were applied to an absorption experiment with multidrug transporter-affected antibiotic CNV97100 on Caco-2 cell monolayers.Comment: 21 pages, 8 figures (v4: detailed definition of the treated model - additional information about limitations

    The protein cost of metabolic fluxes: prediction from enzymatic rate laws and cost minimization

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    Bacterial growth depends crucially on metabolic fluxes, which are limited by the cell's capacity to maintain metabolic enzymes. The necessary enzyme amount per unit flux is a major determinant of metabolic strategies both in evolution and bioengineering. It depends on enzyme parameters (such as kcat and KM constants), but also on metabolite concentrations. Moreover, similar amounts of different enzymes might incur different costs for the cell, depending on enzyme-specific properties such as protein size and half-life. Here, we developed enzyme cost minimization (ECM), a scalable method for computing enzyme amounts that support a given metabolic flux at a minimal protein cost. The complex interplay of enzyme and metabolite concentrations, e.g. through thermodynamic driving forces and enzyme saturation, would make it hard to solve this optimization problem directly. By treating enzyme cost as a function of metabolite levels, we formulated ECM as a numerically tractable, convex optimization problem. Its tiered approach allows for building models at different levels of detail, depending on the amount of available data. Validating our method with measured metabolite and protein levels in E. coli central metabolism, we found typical prediction fold errors of 3.8 and 2.7, respectively, for the two kinds of data. ECM can be used to predict enzyme levels and protein cost in natural and engineered pathways, establishes a direct connection between protein cost and thermodynamics, and provides a physically plausible and computationally tractable way to include enzyme kinetics into constraint-based metabolic models, where kinetics have usually been ignored or oversimplified

    Stochastic modelling and analysis of metabolic heterogeneity in single cells

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    A wide range of cellular processes are inherently stochastic. While stochasticity of gene transcription and translation or cellular growth profiles is well-understood, little is known about the stochastic properties of metabolism. Recent experimental findings strongly suggest that metabolism may indeed be subject to stochastic phenomena, which has questioned the traditional deterministic view of metabolism and casts crucial doubt on the general validity of this modelling paradigm. In this thesis, we examine stochastic aspects of metabolic reactions in detail. We focus on stochastic versions of classic deterministic models for metabolic reactions coupled with well-established stochastic models for gene expression. We incorporate experimental measurements of kinetic parameters in the study, which results in a specific multiscale structure of the presented class of models. In the course of this thesis, we present numerous models with increasing complexity, focussing on three key contributions. Firstly, we present the derivation of an analytical tool to approximate stationary metabolite distributions in closed-form by exploiting the multiple scales. As a result, we propose a strikingly-accurate analytical tool for exploring the parameter space. Secondly, we reveal which parameters have strong impacts on the stationary metabolite distributions and identify conditions for increased coefficients of variation and highly-complex bimodal and multimodal patterns. Finally, we propose a general strategy to obtain closed-form approximations in more complex models, such as multi-step pathways and regulatory processes commonly found in metabolism, such as allostery or end-product inhibition. The results in this thesis lay the groundwork for future studies of metabolic heterogeneity and offer numerous biological hypotheses that could soon be tested in light of recent progress in single-cell measurements of cellular metabolites.Open Acces

    Lung Circulation Modeling: Status and Prospect

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    Mathematical modeling has been used to interpret anatomical and physiological data obtained from metabolic and hemodynamic studies aimed at investigating structure-function relationships in the vasculature of the lung, and how these relationships are affected by lung injury and disease. The indicator dilution method was used to study the activity of redox processes within the lung. A steady-state model of the data was constructed and used to show that pulmonary endothelial cells may play an important role in reducing redox active compounds and that those reduction rates can be altered with oxidative stress induced by exposure to high oxygen environments. In addition, a morphometric model of the pulmonary vasculature was described and used to detect, describe,and predict changes in vascular morphology that occur in response to chronic exposure to low-oxygen environments, a common model of pulmonary hypertension. Finally, the model was used to construct simulated circulatory networks designed to aid in evaluation of competing hypotheses regarding the relative contribution of various morphological and biomechanical changes observed with hypoxia. These examples illustrate the role of mathematical modeling in the integration of the emerging metabolic, hemodynamic, and morphometric databases

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

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    <p>Abstract</p> <p>Background</p> <p>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.</p> <p>Results</p> <p>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.</p> <p>Conclusions</p> <p>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.</p

    Prediction from Enzymatic Rate Laws and Cost Minimization

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    Bacterial growth depends crucially on metabolic fluxes, which are limited by the cell’s capacity to maintain metabolic enzymes. The necessary enzyme amount per unit flux is a major determinant of metabolic strategies both in evolution and bioengineering. It depends on enzyme parameters (such as kcat and KM constants), but also on metabolite concentrations. Moreover, similar amounts of different enzymes might incur different costs for the cell, depending on enzyme-specific properties such as protein size and half-life. Here, we developed enzyme cost minimization (ECM), a scalable method for computing enzyme amounts that support a given metabolic flux at a minimal protein cost. The complex interplay of enzyme and metabolite concentrations, e.g. through thermodynamic driving forces and enzyme saturation, would make it hard to solve this optimization problem directly. By treating enzyme cost as a function of metabolite levels, we formulated ECM as a numerically tractable, convex optimization problem. Its tiered approach allows for building models at different levels of detail, depending on the amount of available data. Validating our method with measured metabolite and protein levels in E. coli central metabolism, we found typical prediction fold errors of 4.1 and 2.6, respectively, for the two kinds of data. This result from the cost-optimized metabolic state is significantly better than randomly sampled metabolite profiles, supporting the hypothesis that enzyme cost is important for the fitness of E. coli. ECM can be used to predict enzyme levels and protein cost in natural and engineered pathways, and could be a valuable computational tool to assist metabolic engineering projects. Furthermore, it establishes a direct connection between protein cost and thermodynamics, and provides a physically plausible and computationally tractable way to include enzyme kinetics into constraint-based metabolic models, where kinetics have usually been ignored or oversimplified

    Elasticity sampling links thermodynamics to metabolic control

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    Metabolic networks can be turned into kinetic models in a predefined steady state by sampling the reaction elasticities in this state. Elasticities for many reversible rate laws can be computed from the reaction Gibbs free energies, which are determined by the state, and from physically unconstrained saturation values. Starting from a network structure with allosteric regulation and consistent metabolic fluxes and concentrations, one can sample the elasticities, compute the control coefficients, and reconstruct a kinetic model with consistent reversible rate laws. Some of the model variables are manually chosen, fitted to data, or optimised, while the others are computed from them. The resulting model ensemble allows for probabilistic predictions, for instance, about possible dynamic behaviour. By adding more data or tighter constraints, the predictions can be made more precise. Model variants differing in network structure, flux distributions, thermodynamic forces, regulation, or rate laws can be realised by different model ensembles and compared by significance tests. The thermodynamic forces have specific effects on flux control, on the synergisms between enzymes, and on the emergence and propagation of metabolite fluctuations. Large kinetic models could help to simulate global metabolic dynamics and to predict the effects of enzyme inhibition, differential expression, genetic modifications, and their combinations on metabolic fluxes. MATLAB code for elasticity sampling is freely available
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