Scalability Properties of the S-Distribution

Voit, Eberhard O.; Schwacke, Lorelei H.

doi:10.1002/(sici)1521-4036(199810)40:6<665::aid-bimj665>3.0.co;2-g

Cited by 7 publications

(4 citation statements)

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“…1a or 1b), the numerical value of X 0 shifts the distribution along the X-axis. It does not affect the shape or variance of the distribution, since the random variable does not appear on the right-hand side of the differential equation (see also Voit and Schwacke, 1998). Thus, optimization of the location of the S-distribution consists of computing a ªtrialº S-distribution with parametersâ;ĝ;k and some arbitrary X 0 , and optimizing a simple horizontal shift t, as indicated in Fig.…”

Section: Methods and Resultsmentioning

confidence: 99%

A Maximum Likelihood Estimator for Shape Parameters of S-Distributions

Voit

2000

Biom. J.

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Section: Methods and Resultsmentioning

confidence: 99%

A Maximum Likelihood Estimator for Shape Parameters of S-Distributions

Voit

2000

Biom. J.

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“…The models are also very flexible from a statistical point of view, because they can represent the probabilities of events such as molecular collisions or the spread of diseases. In fact, if probability distributions are formulated as power-law models, they exhibit features of limiting distributions similar to the normal distribution [64] .…”

Section: Discussionmentioning

confidence: 99%

150 Years of the Mass Action Law

2015

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This year we celebrate the 150th anniversary of the law of mass action. This law is often assumed to have been “there” forever, but it has its own history, background, and a definite starting point. The law has had an impact on chemistry, biochemistry, biomathematics, and systems biology that is difficult to overestimate. It is easily recognized that it is the direct basis for computational enzyme kinetics, ecological systems models, and models for the spread of diseases. The article reviews the explicit and implicit role of the law of mass action in systems biology and reveals how the original, more general formulation of the law emerged one hundred years later ab initio as a very general, canonical representation of biological processes.

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“…Further analysis showed that the S-distribution has interesting scalability features that permit analyses analogous to z-score computations with normal distributions [81,745].…”

Section: Recastingmentioning

confidence: 99%

Biochemical Systems Theory: A Review

Voit

2013

ISRN Biomathematics

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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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Scalability Properties of the S-Distribution

Cited by 7 publications

References 11 publications

A Maximum Likelihood Estimator for Shape Parameters of S-Distributions

A Maximum Likelihood Estimator for Shape Parameters of S-Distributions

150 Years of the Mass Action Law

Biochemical Systems Theory: A Review

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