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Voit, Eberhard O.

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Identification of neutral sets of biochemical systems models from time series data

2009-05 , Vilela, Marco , Vinga, Susana , Grivet, Marco A. , Maia, Mattoso , Voit, Eberhard O. , Almeida, Jonas S.

Background The major difficulty in modeling biological systems from multivariate time series is the identification of parameter sets that endow a model with dynamical behaviors sufficiently similar to the experimental data. Directly related to this parameter estimation issue is the task of identifying the structure and regulation of ill-characterized systems. Both tasks are simplified if the mathematical model is canonical, i.e., if it is constructed according to strict guidelines. Results In this report, we propose a method for the identification of admissible parameter sets of canonical S-systems from biological time series. The method is based on a Monte Carlo process that is combined with an improved version of our previous parameter optimization algorithm. The method maps the parameter space into the network space, which characterizes the connectivity among components, by creating an ensemble of decoupled S-system models that imitate the dynamical behavior of the time series with sufficient accuracy. The concept of sloppiness is revisited in the context of these S-system models with an exploration not only of different parameter sets that produce similar dynamical behaviors but also different network topologies that yield dynamical similarity. Conclusion The proposed parameter estimation methodology was applied to actual time series data from the glycolytic pathway of the bacterium Lactococcus lactis and led to ensembles of models with different network topologies. In parallel, the parameter optimization algorithm was applied to the same dynamical data upon imposing a pre-specified network topology derived from prior biological knowledge, and the results from both strategies were compared. The results suggest that the proposed method may serve as a powerful exploration tool for testing hypotheses and the design of new experiments

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Collective decision making in bacterial viruses

2008-09 , Weitz, Joshua S. , Mileyko, Yuriy , Joh, Richard I. , Voit, Eberhard O.

For many bacterial viruses, the choice of whether to kill host cells or enter a latent state depends on the multiplicity of coinfection. Here, we present a mathematical theory of how bacterial viruses can make collective decisions concerning the fate of infected cells. We base our theory on mechanistic models of gene regulatory dynamics. Unlike most previous work, we treat the copy number of viral genes as variable. Increasing the viral copy number increases the rate of transcription of viral mRNAs. When viral regulation of cell fate includes nonlinear feedback loops, very small changes in transcriptional rates can lead to dramatic changes in steady-state gene expression. Hence, we prove that deterministic decisions can be reached, e.g., lysis or latency, depending on the cellular multiplicity of infection within a broad class of gene regulatory models of viral decision-making. Comparisons of a parameterized version of the model with molecular studies of the decision structure in the temperate bacteriophage l are consistent with our conclusions. Because the model is general, it suggests that bacterial viruses can respond adaptively to changes in population dynamics, and that features of collective decision-making in viruses are evolvable life history traits.

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Systems Biology and its Role in Predictive Health and Personalized Medicine

2008-02-05 , Voit, Eberhard O.

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Optimization of biotechnological systems through geometric programming

2007-09 , Marin-Sanguino, Alaberto , Voit, Eberhard O. , Gonzalez-Alcon, Carlos , Torres, Nestor V.

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 Ssystems 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.

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Estimating parameters for generalized mass action models with connectivity information

2009-05 , Ko, Chih-Lung , Voit, Eberhard O. , Wang, Feng-Sheng

Background: Determining the parameters of a mathematical model from quantitative measurements is the main bottleneck of modelling biological systems. Parameter values can be estimated from steady-state data or from dynamic data. The nature of suitable data for these two types of estimation is rather different. For instance, estimations of parameter values in pathway models, such as kinetic orders, rate constants, flux control coefficients or elasticities, from steady-state data are generally based on experiments that measure how a biochemical system responds to small perturbations around the steady state. In contrast, parameter estimation from dynamic data requires time series measurements for all dependent variables. Almost no literature has so far discussed the combined use of both steady-state and transient data for estimating parameter values of biochemical systems. Results: In this study we introduce a constrained optimization method for estimating parameter values of biochemical pathway models using steady-state information and transient measurements. The constraints are derived from the flux connectivity relationships of the system at the steady state. Two case studies demonstrate the estimation results with and without flux connectivity constraints. The unconstrained optimal estimates from dynamic data may fit the experiments well, but they do not necessarily maintain the connectivity relationships. As a consequence, individual fluxes may be misrepresented, which may cause problems in later extrapolations. By contrast, the constrained estimation accounting for flux connectivity information reduces this misrepresentation and thereby yields improved model parameters. Conclusion: The method combines transient metabolic profiles and steady-state information and leads to the formulation of an inverse parameter estimation task as a constrained optimization problem. Parameter estimation and model selection are simultaneously carried out on the constrained optimization problem and yield realistic model parameters that are more likely to hold up in extrapolations with the model.

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Computational systems analysis of dopamine metabolism

2008-06 , Qi, Zhen , Miller, Gary W. , Voit, Eberhard O.

A prominent feature of Parkinson’s disease (PD) is the loss of dopamine in the striatum, and many therapeutic interventions for the disease are aimed at restoring dopamine signaling. Dopamine signaling includes the synthesis, storage, release, and recycling of dopamine in the presynaptic terminal and activation of pre- and post-synaptic receptors and various downstream signaling cascades. As an aid that might facilitate our understanding of dopamine dynamics in the pathogenesis and treatment in PD, we have begun to merge currently available information and expert knowledge regarding presynaptic dopamine homeostasis into a computational model, following the guidelines of biochemical systems theory. After subjecting our model to mathematical diagnosis and analysis, we made direct comparisons between model predictions and experimental observations and found that the model exhibited a high degree of predictive capacity with respect to genetic and pharmacological changes in gene expression or function. Our results suggest potential approaches to restoring the dopamine imbalance and the associated generation of oxidative stress. While the proposed model of dopamine metabolism is preliminary, future extensions and refinements may eventually serve as an in silico platform for prescreening potential therapeutics, identifying immediate side effects, screening for biomarkers, and assessing the impact of risk factors of the disease.

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Systems Biology—What’s All the Buzz About?

2008 , Voit, Eberhard O.

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Canonical Modeling as a Tool in Metabolic Engineering

2008-11-12 , Voit, Eberhard O.

A growing branch of metabolic engineering uses mathematical pathway models for the development of strategies for optimizing yield in microbes. The use of such models is necessary because the production pathways are often complex, both in structure and in regulation. For reasons of simplicity, many metabolic engineers use stoichiometric and flux balance models. However, these models ignore cellular regulation. As an alternative, I will discuss canonical models within the modeling framework of Biochemical Systems Theory (BST) as good default representations of fully regulated pathway systems. The presentation will begin with a general introduction to BST, provide some representative examples, and then focus on two questions of optimization. The first concerns the actual optimization of BST models toward yield improvements, which can be formulated as a single linear program or as a series of linear programs. The second type of optimization addresses the de novo design and estimation of BST models from biological data. Of special interest here is the use of in vivo NMR data that characterize time trends in microbial metabolic profiles in a non-invasive fashion. As a specific example I will discuss the production of lactate and other compounds in the bacterium Lactococcus lactis, which is widely used in the food and dairy industry.

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Parameter optimization in S-system models

2008-04 , Vilela, Marco , Chou, I-Chun , Vinga, Susana , Vasconcelos, Ana Tereza R. , Voit, Eberhard O. , Almeida, Jonas S.

Background: The inverse problem of identifying the topology of biological networks from their time series responses is a cornerstone challenge in systems biology. We tackle this challenge here through the parameterization of S-system models. It was previously shown that parameter identification can be performed as an optimization based on the decoupling of the differential Ssystem equations, which results in a set of algebraic equations. Results: A novel parameterization solution is proposed for the identification of S-system models from time series when no information about the network topology is known. The method is based on eigenvector optimization of a matrix formed from multiple regression equations of the linearized decoupled S-system. Furthermore, the algorithm is extended to the optimization of network topologies with constraints on metabolites and fluxes. These constraints rejoin the system in cases where it had been fragmented by decoupling. We demonstrate with synthetic time series why the algorithm can be expected to converge in most cases. Conclusion: A procedure was developed that facilitates automated reverse engineering tasks for biological networks using S-systems. The proposed method of eigenvector optimization constitutes an advancement over S-system parameter identification from time series using a recent method called Alternating Regression. The proposed method overcomes convergence issues encountered in alternate regression by identifying nonlinear constraints that restrict the search space to computationally feasible solutions. Because the parameter identification is still performed for each metabolite separately, the modularity and linear time characteristics of the alternating regression method are preserved. Simulation studies illustrate how the proposed algorithm identifies the correct network topology out of a collection of models which all fit the dynamical time series essentially equally well.

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Coordination of the dynamics of yeast sphingolipid metabolism during the diauxic shift

2007-10 , Alvarez-Vasquez, Fernando , Sims, Kellie J. , Voit, Eberhard O. , Hannun, Yusuf A.

Background: The diauxic shift in yeast requires cells to coordinate a complicated response that involves numerous genes and metabolic processes. It is unknown whether responses of this type are mediated in vivo through changes in a few "key" genes and enzymes, which are mathematically characterized by high sensitivities, or whether they are based on many small changes in genes and enzymes that are not particularly sensitive. In contrast to global assessments of changes in gene or protein interaction networks, we study here control aspects of the diauxic shift by performing a detailed analysis of one specific pathway–sphingolipid metabolism–which is known to have signaling functions and is associated with a wide variety of stress responses. Results: The approach uses two components: publicly available sets of expression data of sphingolipid genes and a recently developed Generalized Mass Action (GMA) mathematical model of the sphingolipid pathway. In one line of exploration, we analyze the sensitivity of the model with respect to enzyme activities, and thus gene expression. Complementary to this approach, we convert the gene expression data into changes in enzyme activities and then predict metabolic consequences by means of the mathematical model. It was found that most of the sensitivities in the model are low in magnitude, but that some stand out as relatively high. This information was then deployed to test whether the cell uses a few of the very sensitive pathway steps to mount a response or whether the control is distributed throughout the pathway. Pilot experiments confirm qualitatively and in part quantitatively the predictions of a group of metabolite simulations. Conclusion: The results indicate that yeast coordinates sphingolipid mediated changes during the diauxic shift through an array of small changes in many genes and enzymes, rather than relying on a strategy involving a few select genes with high sensitivity. This study also highlights a novel approach in coupling data mining with mathematical modeling in order to evaluate specific metabolic pathways.

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