Automated piecewise power-law modeling of biological systems

Machina, Anna; Ponosov, A.K.; Voit, Eberhard O.

doi:10.1016/j.jbiotec.2009.12.016

Cited by 14 publications

(19 citation statements)

References 36 publications

(32 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The use of time-series concentrations (data analysis) allows first extracting a dynamic flux profile using model-free smoothing functions and linear algebra operations, then to estimate enzyme kinetic parameters in the flux versus concentration domain (model characterization). In a later work [38], hybrid models have been employed for the reconstruction of enzyme kinetic functions -however, unlike the present work, [38] uses power laws and allows the identification of discontinuous models. Both [37,38] work exclusively with unlabeled data.…”

mentioning

confidence: 99%

“…In a later work [38], hybrid models have been employed for the reconstruction of enzyme kinetic functions -however, unlike the present work, [38] uses power laws and allows the identification of discontinuous models. Both [37,38] work exclusively with unlabeled data. Methodologically, whereas our approach is similar to that in [37] in breaking the problem into two sequential parts, we use for both parts a model-based approach (indeed, based on PWA models), whereas [37] exploits a model-free approach as a first step, followed by a second step that leverages A. ABATE, R. C. HILLEN AND S. A. WAHL…”

mentioning

confidence: 99%

See 1 more Smart Citation

Piecewise affine approximations of fluxes and enzyme kinetics from in vivo¹³C labeling experiments

Abate

Hillen

Wahl

2012

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

Owing to the ever increasing amount of available information on metabolic networks and, in particular, to the increase in information content from in vivo 13 C dynamic labeling experiments, this work investigates the problem of reconstructing dynamic fluxes and enzyme kinetics. The model structure is based on the use of piecewise affine approximations. The optimization procedure at the basis of the model identification is improved by separating the parameter estimation procedure into two different phases. As a first step, a dynamic flux profile in time is reconstructed using functions that are piecewise affine (in time). To achieve scalability for this step, several approaches have been developed and compared. Afterwards, the time-dependent profiles are embedded in the concentration space and the enzyme kinetic functions for single reactions are identified independently. This is an advantage compared with standard complete kinetic network approaches, which are typically characterized by hundreds of parameters, because now only a few need to be optimized simultaneously. Additionally, different kinetic formats can be rapidly compared. The overall approach is demonstrated using an informative in silico experiment. availability is not sufficient for a statistically reliable parameter estimation [14], and thus further motivated the development of models from data.To enhance the modeling of metabolic networks, four main challenges have to be tackled:(i) In vivo kinetic mechanisms. Many enzymes have been studied in much detail in vitro; however, it has been shown that their in vivo conditions can differ drastically [15]. In fact, physiological parameters and enzyme kinetic mechanisms are peculiar to the living cell. A variety of models with large parameter space have to be employed and tested [14,16] in order to select proper ones fitting in vivo data. (ii) Data availability. Data sets, even coming from rapid sampling [11] techniques, usually contain only few observations, typically compounded with noise. The gathering of data is impaired by technological limitations or sheer experimental costs. (iii) Limited excitation. In vivo experiments have typically limited dynamical ranges and, besides the substrate, only a few metabolites in the network can be fully excited. Additionally, the limited information content associated to time-series of metabolite concentrations leads to multiple possible outcomes for model identification problems. (iv) Computational overhead. Optimization procedures applied to large-scale kinetic modelsespecially when isotopomer states are included -are demanding because of size, existence of nonlinearities in the flux versus concentration dependence, and again presence of noise.With regards to the challenges in (ii) and (iii) (scarceness of data with limited information content), this study leverages dynamic datasets that are enriched by 13 C labeling measurements. Previous studies [17][18][19] have shown that adding 13 C labeled tracers increases the information content on pool turnover and with t...

show abstract

mentioning

confidence: 99%

mentioning

confidence: 99%

Piecewise affine approximations of fluxes and enzyme kinetics from in vivo¹³C labeling experiments

Abate

Hillen

Wahl

2012

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

show abstract

“…As a compromise, piecewise S-system formulations have been proposed, which improve accuracy, but require more parameters. [174][175][176] Furthermore, Löwe et al 177 proposed a BST model reduction based on hierarchies of time-scales, which indeed can span several orders of magnitude in actual applications. 178 An entirely different type of metabolic model makes use of typical control strategies in cybernetics.…”

Section: Selecting Metabolic Rate Functions From a Smorgasbord Of Optmentioning

confidence: 99%

The best models of metabolism

Voit

2017

WIREs Mechanisms of Disease

Self Cite

View full text Add to dashboard Cite

Biochemical systems are among of the oldest application areas of mathematical modeling. Spanning a time period of over one hundred years, the repertoire of options for structuring a model and for formulating reactions has been constantly growing, and yet, it is still unclear whether or to what degree some models are better than others and how the modeler is to choose among them. In fact, the variety of options has become overwhelming and difficult to maneuver for novices and experts alike. This review outlines the metabolic model design process and discusses the numerous choices for modeling frameworks and mathematical representations. It tries to be inclusive, even though it cannot be complete, and introduces the various modeling options in a manner that is as unbiased as that is feasible. However, the review does end with personal recommendations for the choices of default models.

show abstract

“…One option is the use of piecewise approximations, which were already mentioned in the original BST papers [101] and which are directly related to breakpoint analysis [112], which is one root of BST models. e pieces may be concatenated in an ad hoc fashion, in response to some input, or in an automated fashion that optimizes the overall data �t [36,385,386,688]. A second option is the inclusion of higher-order derivatives in the Taylor approximation.…”

Section: Mathematical Features Of Bst Modelsmentioning

confidence: 99%

Biochemical Systems Theory: A Review

Voit

2013

ISRN Biomathematics

Self Cite

147

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

Automated piecewise power-law modeling of biological systems

Cited by 14 publications

References 36 publications

Piecewise affine approximations of fluxes and enzyme kinetics from in vivo¹³C labeling experiments

Piecewise affine approximations of fluxes and enzyme kinetics from in vivo¹³C labeling experiments

The best models of metabolism

Biochemical Systems Theory: A Review

Contact Info

Product

Resources

About

Automated piecewise power-law modeling of biological systems

Cited by 14 publications

References 36 publications

Piecewise affine approximations of fluxes and enzyme kinetics from in vivo13C labeling experiments

Piecewise affine approximations of fluxes and enzyme kinetics from in vivo13C labeling experiments

The best models of metabolism

Biochemical Systems Theory: A Review

Contact Info

Product

Resources

About

Piecewise affine approximations of fluxes and enzyme kinetics from in vivo¹³C labeling experiments

Piecewise affine approximations of fluxes and enzyme kinetics from in vivo¹³C labeling experiments