A Mass Action Model of a Fibroblast Growth Factor Signaling Pathway and Its Simplification

Gaffney, Eamonn A.; Heath, John K.; Kwiatkowska, MZ

doi:10.1007/s11538-008-9342-1

Cited by 9 publications

(9 citation statements)

References 45 publications

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“…The system of equations was assembled using mostly the law of mass action [74] and linear degradation kinetics. A Michaelis-Menten degradation kinetics could be used as done in other models allowing smaller Hill coefficients [36], [75].…”

Section: Resultsmentioning

confidence: 99%

Tuning the Mammalian Circadian Clock: Robust Synergy of Two Loops

et al. 2011

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The circadian clock is accountable for the regulation of internal rhythms in most living organisms. It allows the anticipation of environmental changes during the day and a better adaptation of physiological processes. In mammals the main clock is located in the suprachiasmatic nucleus (SCN) and synchronizes secondary clocks throughout the body. Its molecular constituents form an intracellular network which dictates circadian time and regulates clock-controlled genes. These clock-controlled genes are involved in crucial biological processes including metabolism and cell cycle regulation. Its malfunction can lead to disruption of biological rhythms and cause severe damage to the organism. The detailed mechanisms that govern the circadian system are not yet completely understood. Mathematical models can be of great help to exploit the mechanism of the circadian circuitry. We built a mathematical model for the core clock system using available data on phases and amplitudes of clock components obtained from an extensive literature search. This model was used to answer complex questions for example: how does the degradation rate of Per affect the period of the system and what is the role of the ROR/Bmal/REV-ERB (RBR) loop? Our findings indicate that an increase in the RNA degradation rate of the clock gene Period (Per) can contribute to increase or decrease of the period - a consequence of a non-monotonic effect of Per transcript stability on the circadian period identified by our model. Furthermore, we provide theoretical evidence for a potential role of the RBR loop as an independent oscillator. We carried out overexpression experiments on members of the RBR loop which lead to loss of oscillations consistent with our predictions. These findings challenge the role of the RBR loop as a merely auxiliary loop and might change our view of the clock molecular circuitry and of the function of the nuclear receptors (REV-ERB and ROR) as a putative driving force of molecular oscillations.

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Section: Resultsmentioning

confidence: 99%

Tuning the Mammalian Circadian Clock: Robust Synergy of Two Loops

et al. 2011

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“…In this section, based on the analysis of the FGF pathway given in [46], we present three approaches for reducing the complexity of the complete model of the FGF pathway as given in Section 5.…”

Section: Approximate Reduction Techniquesmentioning

confidence: 99%

Probabilistic model checking of complex biological pathways

Heath

Kwiatkowska

Norman

et al. 2008

Theoretical Computer Science

133

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Probabilistic model checking is a formal verification technique that has been successfully applied to the analysis of systems from a broad range of domains, including security and communication protocols, distributed algorithms and power management. In this paper we illustrate its applicability to a complex biological system: the FGF (Fibroblast Growth Factor) signalling pathway. We give a detailed description of how this case study can be modelled in the probabilistic model checker PRISM, discussing some of the issues that arise in doing so, and show how we can thus examine a rich selection of quantitative properties of this model. We present experimental results for the case study under several different scenarios and provide a detailed analysis, illustrating how this approach can be used to yield a better understanding of the dynamics of the pathway. Finally, we outline a number of exact and approximate techniques to enable the verification of larger and more complex pathways and apply several of them to the FGF case study.

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“…The latter task, which will be enormously demanding computationally, emphasizes the vital exercise of devising accurate asymptotics for larger scale networks, even if the goal is to speed up numerical calculations rather than to write down analytical solutions. This is certainly possible with biological systems as large as those envisaged even in the current context [106][107][108].…”

Section: Network Systems and Synthetic Biology Parameter Estimationmentioning

confidence: 99%

Partial differential equations for self-organization in cellular and developmental biology

2008

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Understanding the mechanisms governing and regulating the emergence of structure and heterogeneity within cellular systems, such as the developing embryo, represents a multiscale challenge typifying current integrative biology research, namely, explaining the macroscale behaviour of a system from microscale dynamics. This review will focus upon modelling how cell-based dynamics orchestrate the emergence of higher level structure. After surveying representative biological examples and the models used to describe them, we will assess how developments at the scale of molecular biology have impacted on current theoretical frameworks, and the new modelling opportunities that are emerging as a result. We shall restrict our survey of mathematical approaches to partial differential equations and the tools required for their analysis. We will discuss the gap between the modelling abstraction and biological reality, the challenges this presents and highlight some open problems in the field.Mathematics Subject Classification: 35−02; 35−R99; 92−02; 92B05; 92C15; 92C17; 92C37

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A Mass Action Model of a Fibroblast Growth Factor Signaling Pathway and Its Simplification

Cited by 9 publications

References 45 publications

Tuning the Mammalian Circadian Clock: Robust Synergy of Two Loops

Tuning the Mammalian Circadian Clock: Robust Synergy of Two Loops

Probabilistic model checking of complex biological pathways

Partial differential equations for self-organization in cellular and developmental biology

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