Equation discovery for systems biology: finding the structure and dynamics of biological networks from time course data

Džeroski, Sašo; Todorovski, Ljupčo

doi:10.1016/j.copbio.2008.07.002

Cited by 58 publications

(26 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A class of general reconstruction methods exploit the time series obtained by quantifying the system behaviour. Some of them assume the knowledge of the internal interaction functions1617, while others do not18. Network couplings can be examined via an information-theoretic approach19.…”

mentioning

confidence: 99%

Untangling complex dynamical systems via derivative-variable correlations

Levnajić

Pikovsky

2014

Sci Rep

View full text Add to dashboard Cite

Inferring the internal interaction patterns of a complex dynamical system is a challenging problem. Traditional methods often rely on examining the correlations among the dynamical units. However, in systems such as transcription networks, one unit's variable is also correlated with the rate of change of another unit's variable. Inspired by this, we introduce the concept of derivative-variable correlation, and use it to design a new method of reconstructing complex systems (networks) from dynamical time series. Using a tunable observable as a parameter, the reconstruction of any system with known interaction functions is formulated via a simple matrix equation. We suggest a procedure aimed at optimizing the reconstruction from the time series of length comparable to the characteristic dynamical time scale. Our method also provides a reliable precision estimate. We illustrate the method's implementation via elementary dynamical models, and demonstrate its robustness to both model error and observation error.

show abstract

mentioning

confidence: 99%

Untangling complex dynamical systems via derivative-variable correlations

Levnajić

Pikovsky

2014

Sci Rep

View full text Add to dashboard Cite

show abstract

“…Equation discovery methods [18], on the other hand, allow the user to employ domain-specific knowledge and specify the appropriate space of candidate models. To this end, different formalisms for specifying equation fragments as components for building mathematical models have been proposed [9]. While these formalisms can, in principle, be used in the context of evolutionary methods [22], symbolic regression approaches rarely use them.…”

Section: Introductionmentioning

confidence: 99%

Equation Discovery for Nonlinear System Identification

et al. 2020

View full text Add to dashboard Cite

Equation discovery methods enable modelers to combine domain-specific knowledge and system identification to construct models most suitable for a selected modeling task. The method described and evaluated in this paper can be used as a nonlinear system identification method for gray-box modeling. It consists of two interlaced parts of modeling that are computer-aided. The first performs computeraided identification of a model structure composed of elements selected from user-specified domain-specific modeling knowledge, while the second part performs parameter estimation.In this paper, recent developments of the equation discovery method called process-based modeling, suited for nonlinear system identification, are elaborated and illustrated on two continuous-time case studies. The first case study illustrates the use of the process-based modeling on synthetic data while the second case-study evaluates on measured data for a standard system-identification benchmark. The experimental results clearly demonstrate the ability of process-based modeling to reconstruct both model structure and parameters from measured data. Index Terms-Software for system identification, Gray-box modeling, Nonlinear system identification, Equation discovery, Process-based modeling, Knowledge-based identification, Machine learningAll authors are affiliated with the Jožef Stefan Institute,

show abstract

“…Liu and colleagues devised a structure identi�cation method that combines parameter estimation with a pruning strategy that adds a regularization term to the objective function and prunes the solution according to a user-speci�ed threshold value [356]. Džeroski and Todorovski proposed machine-learning methods [212].…”

Section: �� T�or� ��Co�str�ctio� A�� St�� Ti�catio�mentioning

confidence: 99%

“…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

148

154

View full text Add to dashboard Cite

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...

show abstract

Equation discovery for systems biology: finding the structure and dynamics of biological networks from time course data

Cited by 58 publications

References 28 publications

Untangling complex dynamical systems via derivative-variable correlations

Untangling complex dynamical systems via derivative-variable correlations

Equation Discovery for Nonlinear System Identification

Biochemical Systems Theory: A Review

Contact Info

Product

Resources

About