Alternative designs for a genetic switch: Analysis of switching times using the piecewise power-law representation

Savageau, Michael A.

doi:10.1016/s0025-5564(02)00113-x

Cited by 42 publications

(61 citation statements)

References 14 publications

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“…It is useful to think of this model as being analogous to a Mϕ cell culture system, with the results averaged over a large population of Mϕs. The model is built with a nondimensionalized form of the local and piecewise S-system representations of the power law formalism (Savageau, 1996;Savageau, 2002). Each of n molecular components of the system is described by a differential equation (1) v i + and v i − are aggregate power law fluxes describing the production and consumption of molecule x i that may be affected by any of m independent variables.…”

Section: A Macrophage Network Model With Mycobacterial Infectionmentioning

confidence: 99%

The timing of TNF and IFN-γ signaling affects macrophage activation strategies during Mycobacterium tuberculosis infection

Ray

Wang

Chan

et al. 2008

Journal of Theoretical Biology

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During most infections, the population of immune cells known as macrophages are key to taking up and killing bacteria as an integral part of the immune response. However, during infection with Mycobacterium tuberculosis (Mtb), host macrophages serve as the preferred environment for mycobacterial growth. Further, killing of Mtb by macrophages is impaired unless they become activated. Activation is induced by stimulation from bacterial antigens and inflammatory cytokines derived from helper T cells. The key macrophage-activating cytokines in Mtb infection are tumor necrosis factor-α (TNF) and interferon (IFN)-γ. Due to differences in cellular sources and secretion pathways for TNF and IFN-γ, the possibility of heterogeneous cytokine distributions exists, suggesting that the timing of macrophage activation from these signals may affect activation kinetics and thus impact the outcome of Mtb infection. Here we use a mathematical model to show that negative feedback from production of nitric oxide (the key mediator of mycobacterial killing) that typically optimizes macrophage responses to activating stimuli may reduce effective killing of Mtb. Statistical sensitivity analysis predicts that if TNF and IFN-γ signals precede infection, the level of negative feedback may have a strong effect on how effectively macrophages kill Mtb. However, this effect is relaxed when IFN-γ or TNF + IFN-γ signals are received coincident with infection. Under these conditions, the model suggests that negative feedback induces fast responses and an initial overshoot of nitric oxide production for given doses of TNF and IFN-γ, favoring killing of Mtb. Together, our results suggest that direct entry of macrophages into a granuloma site (and not distal to it) from lung vascular sources represents a preferred host strategy for mycobacterial control. We examine implications of these results in establishment of latent Mtb infection.

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Section: A Macrophage Network Model With Mycobacterial Infectionmentioning

confidence: 99%

The timing of TNF and IFN-γ signaling affects macrophage activation strategies during Mycobacterium tuberculosis infection

Ray

Wang

Chan

et al. 2008

Journal of Theoretical Biology

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“…[13], [5], [6], [7], [8], and [9], and are more detailed than those used in Refs. [3], [4], [15], and [2], and they therefore constitute intermediate complexity equations describing lac induction. Compared to the simpler models, the intermediate level of detail provides increased contact between model parameters and biophysical measurements, and compared to more detailed models, it facilitates analysis of the equations and interpretation of the results.…”

Section: Modelmentioning

confidence: 99%

“…Both Savageau [4] and van Hoek & Hogeweg [8] found that bistability increases the time required to respond to sudden increases in environmental lactose, which can be a disadvantage in competition for nutrients. These results argue against the natural relevance of bistability in lac expression.…”

Section: Introductionmentioning

confidence: 99%

Determinants of bistability in induction of the Escherichia coli lac operon

Dreisigmeyer

Stajic

Nemenman

et al. 2008

IET Systems Biology

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We have developed a mathematical model of regulation of expression of the Escherichia coli lac operon, and have investigated bistability in its steady-state induction behavior in the absence of external glucose.Numerical analysis of equations describing regulation by artificial inducers revealed two natural bistability parameters that can be used to control the range of inducer concentrations over which the model exhibits bistability. By tuning these bistability parameters, we found a family of biophysically reasonable systems that are consistent with an experimentally determined bistable region for induction by thio-methylgalactoside (Ozbudak et al. Nature 427:737, 2004). The model predicts that bistability can be abolished when passive transport or permease export becomes sufficiently large; the former case is especially relevant to induction by isopropyl-β, D-thiogalactopyranoside. To model regulation by lactose, we developed similar equations in which allolactose, a metabolic intermediate in lactose metabolism and a natural inducer of lac, is the inducer. For biophysically reasonable parameter values, these equations yield no bistability in response to induction by lactose; however, systems with an unphysically small permease-dependent export effect can exhibit small amounts of bistability for limited ranges of parameter values. These results cast doubt on the relevance of bistability in the lac operon within the natural context of E. coli, and help shed light on the controversy among existing theoretical studies that address this issue. The results also suggest an experimental approach to address the relevance of bistability in the lac operon within the natural context of E. coli.

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“…In relatively rarer cases, biological systems may also have two (or more) stable steady states, and it is possible that external or internal controls cause these systems to "toggle" between the two states (e.g., see [36,385,386]). In such a case, the system may also exhibit hysteresis, which means that its approach toward either one of the states depends on its recent "history. "…”

Section: Localmentioning

confidence: 99%

Biochemical Systems Theory: A Review

Voit

2013

ISRN Biomathematics

147

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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Alternative designs for a genetic switch: Analysis of switching times using the piecewise power-law representation

Cited by 42 publications

References 14 publications

The timing of TNF and IFN-γ signaling affects macrophage activation strategies during Mycobacterium tuberculosis infection

The timing of TNF and IFN-γ signaling affects macrophage activation strategies during Mycobacterium tuberculosis infection

Determinants of bistability in induction of the Escherichia coli lac operon

Biochemical Systems Theory: A Review

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