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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.

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.

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
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.,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.

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