A reliable Taylor series-based computational method for the calculation of dynamic sensitivities in large-scale metabolic reaction systems: Algorithm and software evaluation

Shiraishi, Fumihidé; Tomita, Tomofumi; Iwata, Michio; Berrada, Aziz A.; Hirayama, Hiroshi

doi:10.1016/j.mbs.2009.09.001

Cited by 16 publications

(15 citation statements)

References 27 publications

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“…As an example, a numerical solver for systems of power-law differential equations does not have to anticipate the occurrence of poles or other ill-de�ned situations and can therefore be optimized in unique ways [85][86][87]. Similarly, different efficient solvers for sensitivity computations and boundary value problems made use of the homogeneous structure of BST models [88,[120][121][122][123][124][125][126][127].…”

Section: Bst and Other Canonicalmentioning

confidence: 99%

“…Shi and colleagues studied the balance between robustness and fragility in biochemical networks [406]. Several articles expanded the concepts of gains and sensitivities to questions of dynamics [124][125][126][127][407][408][409][410][411][412]. ese analyses assess how changes in initial values affect the transient responses of a system.…”

Section: Sensitivity and Robustnessmentioning

confidence: 99%

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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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Section: Bst and Other Canonicalmentioning

confidence: 99%

Section: Sensitivity and Robustnessmentioning

confidence: 99%

Biochemical Systems Theory: A Review

Voit

2013

ISRN Biomathematics

146

154

View full text Add to dashboard Cite

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“…[18] Numerical differentiation method SOFTCADS includes a simple but highly-accurate numerical differentiation method. [18] Numerical differentiation method SOFTCADS includes a simple but highly-accurate numerical differentiation method.…”

Section: Sensitivity Equationsmentioning

confidence: 99%

“…[18] However, the present software cannot calculate the sensitivity values at a level of super high accuracy despite the fact that the differential equations are solved by the Taylorseries method. [18] However, the present software cannot calculate the sensitivity values at a level of super high accuracy despite the fact that the differential equations are solved by the Taylorseries method.…”

Section: Introductionmentioning

confidence: 97%

Highly reliable computation of dynamic sensitivities in metabolic reaction systems by a variable‐step Taylor series method

Shiraishi

Egashira

Iwata

et al. 2011

Asia-Pacific J Chem Eng

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Dynamic sensitivities are useful to characterize time-varying systems efficiently. In metabolic reaction systems, however, analysis using these values is not so popular. This is mainly due to the following two reasons. One is that the calculation of dynamic sensitivities requires us to derive differential equations for sensitivities from those for metabolite concentrations by partial differentiation, and it is not easy for experimentalists to perform this mathematical operation. The other is that the metabolic reaction systems are mostly described by stiff differential equations, from which it may not be easy to obtain reliable numerical solutions. We have previously developed software for calculation of dynamic sensitivities (SOFTCADS), in which one can calculate dynamic sensitivities with high accuracy by setting only differential equations for metabolite concentrations. This paper further improves the algorithm of SOFTCADS to enhance its performance. The results clearly show that regardless of the degree of stiffness, the improved SOFTCADS provides dynamic sensitivities with the super high accuracy that is comparable to the machine accuracy and also completes the calculation in a shorter time.

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“…The influence of each designed parameter on the structural reliability of the system is thoroughly revealed by the reliability sensitivity analysis, which provides a necessary theoretic basis for structural reliability-based robust and optimization design [1][2][3] . In recent years, both domestic and overseas researchers have made a distinct progress in reliability computation methods, including the finite difference method [4][5][6] , the first-order second-moment method or other higher order methods [7][8][9] , the method based on the perturbation theory [10][11][12][13][14] , the important sampling Monte-Carlo simulation method [15][16][17] , and the response surface approach [18][19][20] . Being one of moment methods, the perturbation theory method requires neither iteration nor the computation of derivatives and can easily solve the system reliability with multimode and multiple design points.…”

Section: Introductionmentioning

confidence: 99%

Advanced method to estimate reliability-based sensitivity of mechanical components with strongly nonlinear performance function

Zhang

Zhu

Wang

2010

Appl. Math. Mech.-Engl. Ed.

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Based on the random perturbation technique for reliability sensitivity design, some realistic reliability-based sensitivity issues are discussed, some of which have a structure of high nonlinear performance functions. Combining the related theories of the moment method of the reliability analysis, the matrix differential, and the Kronecker algebra, the reliability-based sensitivity method based on the perturbation method is modified if the first four moments of random variables are given. Meanwhile, a reliability-based sensitivity computation method is proposed. Some examples are used to show that using this method can effectively improve the accuracy of the reliability-based sensitivity computation and offer a reliable theoretic basis in engineering.

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A reliable Taylor series-based computational method for the calculation of dynamic sensitivities in large-scale metabolic reaction systems: Algorithm and software evaluation

Cited by 16 publications

References 27 publications

Biochemical Systems Theory: A Review

Biochemical Systems Theory: A Review

Highly reliable computation of dynamic sensitivities in metabolic reaction systems by a variable‐step Taylor series method

Advanced method to estimate reliability-based sensitivity of mechanical components with strongly nonlinear performance function

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