Effects of small particle numbers on long-term behaviour in discrete biochemical systems

Kreyssig, Peter; Wozar, Christian; Peter, Stephan; Veloz, Tomás; Ibrahim, Bashar; Dittrich, Peter

doi:10.1093/bioinformatics/btu453

Cited by 31 publications

(24 citation statements)

References 43 publications

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“…From a technical perspective, it has been proven that the vast majority of stable regimes of a continuous dynamical system described by reaction networks, including fixed points [11], and higher dimensional attractors such as periodic orbits and limit cycles [43], correspond to organizations. Similar results can be obtained for the case of a discrete dynamical system [35], and methods to rule out organizations that are dynamically unfeasible have also been developed [44].…”

Section: Chemical Organization Theorysupporting

confidence: 55%

The Complexity–Stability Debate, Chemical Organization Theory, and the Identification of Non-classical Structures in Ecology

Veloz

2019

Found Sci

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We present a novel approach to represent ecological systems using reaction networks, and show how a particular framework called Chemical Organization Theory (COT) sheds new light on the longstanding complexity-stability debate. Namely, COT provides a novel conceptual landscape plenty of analytic tools to explore the interplay between structure and stability of ecological systems. Given a large set of species and their interactions, COT identifies, in a computationally feasible way, each and every sub-collection of species that is closed and self-maintaining. These sub-collections, called organizations, correspond to the groups of species that can survive together (co-exist) in the long-term. Thus, the set of organizations contains all the stable regimes that can possibly happen in the dynamics of the ecological system. From here, we propose to conceive the notion of stability from the properties of the organizations, and thus apply the vast knowledge on the stability of reaction networks to the Complexity-Stability debate. As an example of the potential of COT to introduce new mathematical tools, we show that the set of organizations can be equipped with suitable joint and meet operators, and that for certain ecological systems the organizational structure is a non-boolean lattice, providing in this way an unexpected connection between logico-algebraic structures, popular in the foundations of quantum theory, and ecology. networks [46]. From here, a myriad of studies have supported the two opposite views. This controversy became known as the Complexity-Stability problem, or the Complexity-Stability debate [47].Recently, some of the most prominent figures around the Complexity-Stability debate have concluded that radically novel approaches are required to understand how different types of ecological interactions develop multi-dimensional architectures that lead to stable ecosystems. For example,in [14] they claim:We assess the scientific and policy literature and show that this disconnect is one consequence of an inconsistent and one-dimensional approach that ecologists have taken to both disturbances and stability.This has led to confused communication of the nature of stability and the level of our insight into it. Disturbances and stability are multidimensional. Our understanding of them is not.

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Section: Chemical Organization Theorysupporting

confidence: 55%

The Complexity–Stability Debate, Chemical Organization Theory, and the Identification of Non-classical Structures in Ecology

Veloz

2019

Found Sci

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“…Kreyssig et. al [14] studied the effects of small particle numbers on long-term behaviours in discrete biochemical systems. We build on their notion of discrete organisation but focus on quantitative analysis of the transitive dynamics among the organisations, which was not considered in [14].…”

Section: Related Workmentioning

confidence: 99%

“…al [14] studied the effects of small particle numbers on long-term behaviours in discrete biochemical systems. We build on their notion of discrete organisation but focus on quantitative analysis of the transitive dynamics among the organisations, which was not considered in [14]. Other approaches for approximate analysis of discrete models of reaction networks include the use of Linear Noise Approximation [4], the Central Limit Approximation [3] and "sliding window" abstractions [17].…”

Section: Related Workmentioning

confidence: 99%

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Formal Quantitative Analysis of Reaction Networks Using Chemical Organisation Theory

Dittrich

Parker

et al. 2016

Computational Methods in Systems Biology

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Abstract. Chemical organisation theory is a framework developed to simplify the analysis of long-term behaviour of chemical systems. An organisation is a set of objects which are closed and self-maintaining. In this paper, we build on these ideas to develop novel techniques for formal quantitative analysis of chemical reaction networks, using discrete stochastic models represented as continuous-time Markov chains. We propose methods to identify organisations, to study quantitative properties regarding movement between these organisations and to construct an organisation-based coarse graining of the model that can be used to approximate and predict the behaviour of the original reaction network.

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“…Kreyssig et. al [15] studied the effects of small particle numbers on long-term behaviours in discrete biochemical systems. We build on their notion of discrete organisation but focus on quantitative analysis of the transitive dynamics among the organisations, which was not considered in [15].…”

Section: Introductionmentioning

confidence: 99%

Organisation-Oriented Coarse Graining and Refinement of Stochastic Reaction Networks

Dittrich

Parker

et al. 2018

IEEE/ACM Trans. Comput. Biol. and Bioinf.

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Chemical organisation theory is a framework developed to simplify the analysis of long-term behaviour of chemical systems. In this work, we build on these ideas to develop novel techniques for formal quantitative analysis of chemical reaction networks, using discrete stochastic models represented as continuous-time Markov chains. We propose methods to identify organisations, and to study quantitative properties regarding movements between these organisations. We then construct and formalise a coarse-grained Markov chain model of hierarchic organisations for a given reaction network, which can be used to approximate the behaviour of the original reaction network. As an application of the coarse-grained model, we predict the behaviour of the reaction network systems over time via the master equation. Experiments show that our predictions can mimic the main pattern of the concrete behaviour in the long run, but the precision varies for different models and reaction rule rates. Finally, we propose an algorithm to selectively refine the coarse-grained models and show experiments demonstrating that the precision of the prediction has been improved.

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Effects of small particle numbers on long-term behaviour in discrete biochemical systems

Cited by 31 publications

References 43 publications

The Complexity–Stability Debate, Chemical Organization Theory, and the Identification of Non-classical Structures in Ecology

The Complexity–Stability Debate, Chemical Organization Theory, and the Identification of Non-classical Structures in Ecology

Formal Quantitative Analysis of Reaction Networks Using Chemical Organisation Theory

Organisation-Oriented Coarse Graining and Refinement of Stochastic Reaction Networks

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