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Nicolai B.M.,Catholic University of Leuven | Egea J.A.,Technical University of Cartagena | Scheerlinck N.,Catholic University of Leuven | Banga J.R.,Bio Process Engineering Group | Datta A.K.,Cornell University
Journal of Food Engineering | Year: 2011

In this article we have used four different global optimisation algorithms for interval finite element analysis of (non)linear heat conduction problems: (i) sequential quadratic programming (SQP), (ii) a scatter search method (SSm), (iii) the vertex algorithm, and (iv) the response surface method (RSM). Their performance was compared based on a thermal sterilisation problem and a food freezing problem. The vertex method proved to be by far the fastest method but is only effective if the solution is a monotonic function of the uncertain parameters. The RSM was also fast albeit much less than the vertex method. Both SQP and SSm were considerably slower than the former methods; SQP did not converge to the real solution in the food freezing test problem. The interval finite element method was used as a building block for a fuzzy finite element analysis based on the α-cuts method. The RSM fuzzy finite element method was identified as the fastest algorithm among all the tested methods. It was shown that uncertain parameters may cause large uncertainties in the process variables. The algorithms can be used to obtain more realistic modelling of food processes that often have significant uncertainty in the model parameters. © 2010 Elsevier Ltd. All rights reserved.

Johnston M.D.,University of Waterloo | Siegel D.,University of Waterloo | Szederkenyi G.,Bio Process Engineering Group | Szederkenyi G.,Hungarian Academy of Sciences
Journal of Mathematical Chemistry | Year: 2012

A numerically effective procedure for determining weakly reversible chemical reaction networks that are linearly conjugate to a known reaction network is proposed in this paper. The method is based on translating the structural and algebraic characteristics of weak reversibility to logical statements and solving the obtained set of linear (in)equalities in the framework of mixed integer linear programming. The unknowns in the problem are the reaction rate coefficients and the parameters of the linear conjugacy transformation. The efficacy of the approach is shown through numerical examples. © 2011 Springer Science+Business Media, LLC.

Szederkenyi G.,Bio Process Engineering Group | Szederkenyi G.,Hungarian Academy of Sciences | Banga J.R.,Bio Process Engineering Group | Alonso A.A.,Bio Process Engineering Group
Bioinformatics | Year: 2012

Chemical reaction network theory is widely used in modeling and analyzing complex biochemical systems such as metabolic networks and cell signalling pathways. Being able to produce all the biologically and chemically important qualitative dynamical features, chemical reaction networks (CRNs) have attracted significant attention in the systems biology community. It is well-known that the reliable inference of CRN models generally requires thorough identifiability and distinguishability analysis together with carefully selected prior modeling assumptions. Here, we present a software toolbox CRNreals that supports the distinguishability and identifiability analysis of CRN models using recently published optimization-based procedures. © The Author 2012. Published by Oxford University Press. All rights reserved.

Rodriguez-Fernandez M.,University of California at Santa Barbara | Banga J.R.,Bio Process Engineering Group | Doyle III F.J.,University of California at Santa Barbara
International Journal of Robust and Nonlinear Control | Year: 2012

The reliability of model predictions is affected by multiple sources of uncertainty; therefore, most of the efforts for modeling biological systems include a sensitivity analysis step aiming to identify the key contributors to uncertainty. This generates insight about the robustness of the model to variations in environmental conditions, kinetic parameters, initial concentration of the species, or any other source of uncertainty. Local sensitivities measure the robustness of the model to small perturbations on the inputs around their nominal value. There are several numerical methods for the calculation of local sensitivities, but the calculated values should be identical within the numerical accuracy of the method used. In contrast, as will be shown in this contribution, the results of different global sensitivity analysis methods can be very different and highly dependent on the distribution considered for the inputs under evaluation. In this work, derivative-based global sensitivities are extended to be able to consider an accurate probability density function for the parameters based on the likelihood function. This strategy enforces the areas of the parameter space most likely to reproduce the desired behavior, minimizing the importance of parameter sets with low probability of being optimal to dominate the sensitivity ranking. A model of a biochemical pathway with three enzymatic steps is used here to illustrate the performance of several relevant global sensitivity analysis methods considering different probability density functions for the parameters and revealing important hints about which method and distribution to choose for each type of model and purpose of the analysis. Copyright © 2012 John Wiley & Sons, Ltd.

Raimundez C.,University of Vigo | Barreiro A.,University of Vigo | Villaverde A.F.,Bio Process Engineering Group
Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME | Year: 2012

This paper presents a method for using reset control as an alternative way of obtaining dissipation for a class of port-Hamiltonian systems. One advantage of this approach is the simplicity of its implementation, which requires only a velocity observer. Another advantage is its robustness to modeling uncertainties, since it can be calculated independently of the plant structure. A gantry crane is selected as case study, yielding simulation and experimental results that show the good performance of this technique. © 2012 American Society of Mechanical Engineers.

Balsa-Canto E.,Bio Process Engineering Group | Banga J.R.,Bio Process Engineering Group | Egea J.A.,Technical University of Cartagena | Fernandez-Villaverde A.,Bio Process Engineering Group | De Hijas-Liste G.M.,Bio Process Engineering Group
Advances in Experimental Medicine and Biology | Year: 2012

Mathematical optimization is at the core of many problems in systems biology: (1) as the underlying hypothesis for model development, (2) in model identification, or (3) in the computation of optimal stimulation procedures to synthetically achieve a desired biological behavior. These problems are usually formulated as nonlinear programing problems (NLPs) with dynamic and algebraic constraints. However the nonlinear and highly constrained nature of systems biology models, together with the usually large number of decision variables, can make their solution a daunting task, therefore calling for efficient and robust optimization techniques. Here, we present novel global optimization methods and software tools such as cooperative enhanced scatter search (eSS), AMIGO, or DOTcvpSB, and illustrate their possibilities in the context of modeling including model identification and stimulation design in systems biology. © 2012 Springer Science+Business Media, LLC.

Johnston M.D.,University of Waterloo | Siegel D.,University of Waterloo | Szederkenyi G.,Bio Process Engineering Group | Szederkenyi G.,Hungarian Academy of Sciences
Match | Year: 2012

In the first part of this paper, we propose new optimization-based methods for the computation of preferred (dense, sparse, reversible, detailed and complex balanced) linearly conjugate reaction network structures with mass action dynamics. The developed methods are extensions of previously published results on dynamically equivalent reaction networks and are based on mixed-integer linear programming. As related theoretical contributions we show that (i) dense linearly conjugate networks define a unique super-structure for any positive diagonal state transformation if the set of chemical complexes is given, and (ii) the existence of linearly conjugate detailed balanced and complex balanced networks do not depend on the selection of equilibrium points. In the second part of the paper it is shown that determining dynamically equivalent realizations to a network that is structurally fixed but parametrically not can also be written and solved as a mixed-integer linear programming problem. Several examples illustrate the presented computation methods.

Szederkenyi G.,Bio Process Engineering Group | Szederkenyi G.,Process Control Research Group | Banga J.R.,Bio Process Engineering Group | Alonso A.A.,Bio Process Engineering Group
BMC Systems Biology | Year: 2011

Background: The inference of biological networks from high-throughput data has received huge attention during the last decade and can be considered an important problem class in systems biology. However, it has been recognized that reliable network inference remains an unsolved problem. Most authors have identified lack of data and deficiencies in the inference algorithms as the main reasons for this situation.Results: We claim that another major difficulty for solving these inference problems is the frequent lack of uniqueness of many of these networks, especially when prior assumptions have not been taken properly into account. Our contributions aid the distinguishability analysis of chemical reaction network (CRN) models with mass action dynamics. The novel methods are based on linear programming (LP), therefore they allow the efficient analysis of CRNs containing several hundred complexes and reactions. Using these new tools and also previously published ones to obtain the network structure of biological systems from the literature, we find that, often, a unique topology cannot be determined, even if the structure of the corresponding mathematical model is assumed to be known and all dynamical variables are measurable. In other words, certain mechanisms may remain undetected (or they are falsely detected) while the inferred model is fully consistent with the measured data. It is also shown that sparsity enforcing approaches for determining 'true' reaction structures are generally not enough without additional prior information.Conclusions: The inference of biological networks can be an extremely challenging problem even in the utopian case of perfect experimental information. Unfortunately, the practical situation is often more complex than that, since the measurements are typically incomplete, noisy and sometimes dynamically not rich enough, introducing further obstacles to the structure/parameter estimation process. In this paper, we show how the structural uniqueness and identifiability of the models can be guaranteed by carefully adding extra constraints, and that these important properties can be checked through appropriate computation methods. © 2011 Szederkényi et al; licensee BioMed Central Ltd.

Chis O.,Bio Process Engineering Group | Banga J.R.,Bio Process Engineering Group | Balsa-Canto E.,Bio Process Engineering Group
Bioinformatics | Year: 2011

Summary: Mathematical modeling has a key role in systems biology. Model building is often regarded as an iterative loop involving several tasks, among which the estimation of unknown parameters of the model from a certain set of experimental data is of central importance. This problem of parameter estimation has many possible pitfalls, and modelers should be very careful to avoid them. Many of such difficulties arise from a fundamental (yet often overlooked) property: the so-called structural (or a priori) identifiability, which considers the uniqueness of the estimated parameters. Obviously, the structural identifiability of any tentative model should be checked at the beginning of the model building loop. However, checking this property for arbitrary non-linear dynamic models is not an easy task. Here we present a software toolbox, GenSSI (Generating Series for testing Structural Identifiability), which enables non-expert users to carry out such analysis. The toolbox runs under the popular MATLAB environment and is accompanied by detailed documentation and relevant examples. © The Author(s) 2011. Published by Oxford University Press.

Rodriguez-Fernandez M.,Bio Process Engineering Group | Banga J.R.,Bio Process Engineering Group
Bioinformatics | Year: 2010

Summary: SensSB (Sensitivity Analysis for Systems Biology) is an easy to use, MATLAB-based software toolbox, which integrates several local and global sensitivity methods that can be applied to a wide variety of biological models. In addition to addressing the sensitivity analysis problem, SensSB aims to cover all the steps involved during the modeling process. The main features of SensSB are: (i) derivative and variance-based global sensitivity analysis, (ii) pseudo-global identifiability analysis, (iii) optimal experimental design (OED) based on global sensitivities, (iv) robust parameter estimation, (v) local sensitivity and identifiability analysis, (vi) confidence intervals of the estimated parameters and (vii) OED based on the Fisher Information Matrix (FIM). SensSB is also able to import models in the Systems Biology Mark-up Language (SBML) format. Several examples from simple analytical functions to more complex biological pathways have been implemented and can be downloaded together with the toolbox. The importance of using sensitivity analysis techniques for identifying unessential parameters and designing new experiments is quantified by increased identifiability metrics of the models and decreased confidence intervals of the estimated parameters. Availability: SensSB is a software toolbox freely downloadable from http://www.iim.csic.es/~gingproc/SensSB.html. The web site also contains several examples and an extensive documentation. Contact: mrodriguez@iim.csic.es. Supplementary information: Supplementary data are available at Bioinformatics online. © The Author 2010. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org.

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