$\sqrt n$-consistent parameter estimation for systems of ordinary differential equations: bypassing numerical integration via smoothing

Gugushvili, Shota; Klaassen, Chris A. J.

doi:10.3150/11-bej362

Cited by 61 publications

(90 citation statements)

References 53 publications

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“…Nonetheless, the slope estimation strategy is statistically valid [204] and can, at the very least, be used to develop coarse solutions from which to start regular parameter optimization approaches. Reviews of this sub�eld include [68,69,[205][206][207][208][209][210][211][212][213][214].…”

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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Section: Parameter Estimation/inverse Problemsmentioning

confidence: 99%

Biochemical Systems Theory: A Review

Voit

2013

ISRN Biomathematics

146

154

View full text Add to dashboard Cite

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“…Recent years have witnessed enormous efforts in the area of parameter estimation, indicating that parameter estimation is an unavoidable and very difficult task that is not yet completely solved ( e.g. , [1; 2; 3; 4; 5]). Some of its difficulties are of computational nature, while others are due to the noisiness of biological data and the fact that several computed solutions often lead to similarly good data fits [6; 7; 8; 9; 10; 11].…”

Section: Introductionmentioning

confidence: 99%

Characterizability of metabolic pathway systems from time series data

Voit

2013

Mathematical Biosciences

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Over the past decade, the biomathematical community has devoted substantial effort to the complicated challenge of estimating parameter values for biological systems models. An even more difficult issue is the characterization of functional forms for the processes that govern these systems. Most parameter estimation approaches tacitly assume that these forms are known or can be assumed with some validity. However, this assumption is not always true. The recently proposed method of Dynamic Flux Estimation (DFE) addresses this problem in a genuinely novel fashion for metabolic pathway systems. Specifically, DFE allows the characterization of fluxes within such systems through an analysis of metabolic time series data. Its main drawback is the fact that DFE can only directly be applied if the pathway system contains as many metabolites as unknown fluxes. This situation is unfortunately rare. To overcome this roadblock, earlier work in this field had proposed strategies for augmenting the set of unknown fluxes with independent kinetic information, which however is not always available. Employing Moore-Penrose pseudo-inverse methods of linear algebra, the present article discusses an approach for characterizing fluxes from metabolic time series data that is applicable even if the pathway system is underdetermined and contains more fluxes than metabolites. Intriguingly, this approach is independent of a specific modeling framework and unaffected by noise in the experimental time series data. The results reveal whether any fluxes may be characterized and, if so, which subset is characterizable. They also help with the identification of fluxes that, if they could be determined independently, would allow the application of DFE.

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“…This approach, or variants on it, has been studied by numerous authors (Brunel 2008;Ellner, Seifu, and Smith 2002;Gugushvili and Klaassen 2012;Wu, Xue, and Kumar 2012) in recent statistical literature, but the idea goes back to Varah (1982) and Bellman and Roth (1971) as well as several other early re-inventions, and we would be frankly unsurprised to discover that Newton also thought of it.…”

Section: Gradient Matching With Estimated Derivativesmentioning

confidence: 99%

CollocInfer: Collocation Inference in Differential Equation Models

Hooker¹,

Ramsay²,

Xiao³

2016

J. Stat. Soft.

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This monograph details the implementation and use of the CollocInfer package in R for smoothing-based estimation of continuous-time nonlinear dynamic systems. These routines represent an extension of the generalized profiling methods in Ramsay, Hooker, Campbell, and Cao (2007) for estimating parameters in nonlinear ordinary differential equations. An interface to the fda package is included. The package also supports discretetime systems. We describe the methodological and computational framework and the necessary steps to use the software. Equivalent functionality is available in MATLAB.

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$\sqrt n$-consistent parameter estimation for systems of ordinary differential equations: bypassing numerical integration via smoothing

Abstract: where θ is the unknown parameter of interest and ξ is the initial condition. With x θ (t) the solution vector corresponding to the parameter value θ, we observe

Cited by 61 publications

References 53 publications

Biochemical Systems Theory: A Review

Biochemical Systems Theory: A Review

Characterizability of metabolic pathway systems from time series data

CollocInfer: Collocation Inference in Differential Equation Models

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