Automated smoother for the numerical decoupling of dynamics models

Vilela, Marco; Borges, Carlos Cristiano Hasenclever; Vinga, Susana; Vasconcelos, Ana Tereza Ribeiro de; Santos, Helena; Voit, Eberhard O.; Almeida, Jonas S.

doi:10.1186/1471-2105-8-305

Cited by 62 publications

(53 citation statements)

References 19 publications

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“…the generalized profiling method (Ramsay et al 2007), as an auxiliary density, one would not be restricted to using only this kind of smoother. Other potential smoothing auxiliary models could be used, such as the perfect smoother of Eilers (2003) or the adaptation of Whitaker's smoother proposed by Vilela et al (2007). We have used the generalized profiling method because of our familiarity with the smoother and the ease with which one can interpret the single smoothing parameter as a temperature in the tempering process.…”

Section: Discussionmentioning

confidence: 99%

“…The wide extent of the sloppiness in biological systems problems is discussed in a paper by Gutenkunst et al (2007b), where they identify sloppiness issues with parameters in a large number of models extracted from the BioModels database (Le Novère et al 2006). There is a large amount of work that has been done to develop methods for identifying problems that are sloppy in nature and to choose parameterizations that remedy the problem (Gutenkunst et al 2007a;Vilela et al 2007;Raue et al 2009). The body of work on identifying and remedying sloppy parameterizations is interesting and could be potentially used in conjunction with our approach to improve inference, but it is beyond the scope of our work here.…”

Section: Introductionmentioning

confidence: 99%

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Smooth functional tempering for nonlinear differential equation models

Campbell

Steele

2011

Stat Comput

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Differential equations are used in modeling diverse system behaviors in a wide variety of sciences. Methods for estimating the differential equation parameters traditionally depend on the inclusion of initial system states and numerically solving the equations. This paper presents Smooth Functional Tempering, a new population Markov Chain Monte Carlo approach for posterior estimation of parameters. The proposed method borrows insights from parallel tempering and model based smoothing to define a sequence of approximations to the posterior. The tempered approximations depend on relaxations of the solution to the differential equation model, reducing the need for estimating the initial system states and obtaining a numerical differential equation solution. Rather than tempering via approximations to the posterior that are more heavily rooted in the prior, this new method tempers towards data features. Using our proposed approach, we observed faster convergence and robustness to both initial values and prior distributions that do not reflect the features of the data. Two variations of the method are proposed and their performance is examined through simulation studies and a real application to the chemical reaction dynamics of producing nylon.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Smooth functional tempering for nonlinear differential equation models

Campbell

Steele

2011

Stat Comput

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“…Seatzu proposed B-splines [335,336], and Vilela et al composed a smoother that accounted for the noise structure in the data [337,338]. Wang et al compared various alternatives, including B-splines [339].…”

Section: Parameter Estimation/inverse Problemsmentioning

confidence: 99%

Biochemical Systems Theory: A Review

Voit

2013

ISRN Biomathematics

146

154

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Biochemical systems theory (BST) is the foundation for a set of analytical andmodeling tools that facilitate the analysis of dynamic biological systems. is paper depicts major developments in BST up to the current state of the art in 2012. It discusses its rationale, describes the typical strategies and methods of designing, diagnosing, analyzing, and utilizing BST models, and reviews areas of application. e paper is intended as a guide for investigators entering the fascinating �eld of biological systems analysis and as a resource for practitioners and experts. PreambleBiochemical systems theory (BST) is a mathematical and computational framework for analyzing and simulating systems. It was originally developed for biochemical pathways but by now has become much more widely applied to systems throughout biology and beyond. BST is called "canonical, " which means that model construction, diagnosis, and analysis follow stringent rules, which will be discussed throughout this paper. e key ingredient of BST is the power-law representation of all processes in a system.BST has been the focus of a number of books [1-6], including some in Chinese and Japanese [7][8][9]. e most detailed modern text dedicated speci�cally to BST is [3]. Moreover, since its inception, numerous reviews have portrayed the evolving state of the art in BST. Most of these reviews summarized methodological advances for the analysis of biochemical pathway systems . Others compared BST models with alternative modeling frameworks [32,[51][52][53][54][55][56][57][58][59][60][61][62][63]; some of these comparisons will be discussed later. Yet other reviews focused on specialty areas, such as customized methods for optimizing BST models (e.g., [64][65][66][67]) or estimating their parameters (e.g., [68][69][70][71][72]), strategies for discovering design and operating principles in natural system (e.g., [73][74][75][76][77][78]), and even the use of BST models in statistics [79][80][81]. A historical account of the �rst twenty years of BST was presented in [82].Supporting the methodological developments in the �eld, several soware packages were developed for different aspects of BST analysis. e earliest was ESSYNS [83][84][85], which supported all standard steady-state analyses and also contained a numerical solver that, at the time, was many times faster than any off-the-shelf soware [86,87]; see also [88]. Utilizing advances in computing and an extension of the solver from ESSYNS, Ferreira created the very user-friendly package PLAS, which is openly available and still very widely used [89] (see also [3]). Yamada and colleagues developed soware to translate E-cell models into BST models in PLAS format [90]. Okamoto's group created the soware BestKit, which permits the graphical design and translation of models, along with their analysis [91][92][93]. Vera and colleagues developed the soware tool PLMaddon for analyzing BST models within SBML [94]; see also [95]. It expands the Matlab SBToolbox with speci�c functionalities for power-law repr...

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“…This strategy emphasizes the utility of using smoothing techniques for representing the time course of some variables while fitting parameter values. The smoothing techniques reduces the fitting problem to an iterative procedure that fits the values for a few parameters at each step of the iteration (Vilela et al, 2007).…”

Section: Parameter Estimation Through Fitting Of Models To Dynamic Datamentioning

confidence: 99%

Mathematical formalisms based on approximated kinetic representations for modeling genetic and metabolic pathways

Alves

Vilaprinyó

Hernández‐Bermejo

et al. 2008

Biotechnology and Genetic Engineering Reviews

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Citing articles: 16 View citing articles Biotechnology and Genetic Engineering Reviews -Vol. 25, 1-40 (2008) AbstractThere is a renewed interest in obtaining a systemic understanding of metabolism, gene expression and signal transduction processes, driven by the recent research focus on Systems Biology. From a biotechnological point of view, such a systemic understanding of how a biological system is designed to work can facilitate the rational manipulation of specific pathways in different cell types to achieve specific goals. Due to the intrinsic complexity of biological systems, mathematical models are a central tool for understanding and predicting the integrative behavior of those systems. Particularly, models are essential for a rational development of biotechnological applications and in understanding system's design from an evolutionary point of view. Mathematical models can be obtained using many different strategies. In each case, their utility will depend upon the properties of the mathematical representation and on the possibility of obtaining meaningful parameters from available data. In practice, there are several issues at stake when one has to decide which mathematical model is more appropriate for the study of a given problem. First, one needs a model that can represent the aspects of the system one wishes to study. Second, one must choose a mathematical representation that allows an accurate analysis of the system with respect to different aspects of interest (for example, robustness of the system, dynamical behavior, optimization of the system with respect to some production goal, parameter value determination, etc). Third, before choosing between alternative and equally appropriate mathematical representations for the system, one should compare representations with respect to easiness of automation for model set-up, simulation, and analysis of results. Fourth, one should also consider how to facilitate model transference and re-usability by other researchers and for distinct purposes. Finally, one factor that is important for all four aspects is the regularity in the mathematical structure of the equations because it facilitates computational manipulation. This regularity is a mark of kinetic representations based on approximation theory. The use of approximation theory to derive mathematical representations with regular structure for modeling purposes has a long tradition in science. In most applied fields, such as engineering and physics, those approximations are often required to obtain practical solutions to complex problems. In this paper we review some of the more popular mathematical representations that have been derived using approximation theory and are used for modeling in molecular systems biology. We will focus on formalisms that are theoretically supported by the Taylor Theorem. These include the Power-law formalism, the recently proposed (log)linear and Lin-log formalisms as well as some closely related alternatives. We will analyze the similarities and differences between...

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Automated smoother for the numerical decoupling of dynamics models

Cited by 62 publications

References 19 publications

Smooth functional tempering for nonlinear differential equation models

Smooth functional tempering for nonlinear differential equation models

Biochemical Systems Theory: A Review

Mathematical formalisms based on approximated kinetic representations for modeling genetic and metabolic pathways

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