The analysis of dynamical systems that attempts to model chemical reaction , gene-regulatory, population, and ecosystem networks all rely on models having interacting components. When the details of these interactions are unknown for biological systems of interest, one effective approach is to study the dynamical properties of an ensemble of models determined by evolutionary constraints that may apply to all such systems. One such constraint is that of dynamical robustness. Despite previous investigations, the relationship between dynamical robustness-an important functional characteristic of many biological systems-and network structure is poorly understood . Here we analyze the stability and robustness of a large class of dynamical systems and demonstrate that the most hierarchical network structures, those equivalent to the total ordering, are the most robust. In particular, we determine the probability distribution of robustness over system connectivity and show that robustness is maximized by maximizing the number of links between strongly connected components of the graph representing the underlying system connectivity. We demonstrate that this can be understood in terms of the fact that permutation of strongly connected components is a fundamental symmetry of dynamical robustness , which applies to networks of any number of components and is independent of the distribution from which the strengths of interconnection among components are sampled. The classification of dynamical robustness based upon a purely topological property provides a URLanizing principle that can be used in the context of experimental validation to select among models that break or preserve network hierarchy. This result contributes to an explanation for the observation of hierarchical modularity in biological networks at all scales .
The relationship between network topology and system dynamics has significant implications for unifying our understanding of the interplay among metabolic , gene-regulatory, and ecosystem network architecures . Here we analyze the stability and robustness of a large class of dynamics on such networks. We determine the probability distribution of robustness as a function of network topology and show that robustness is classified by the number of links between modules of the network. We also demonstrate that permutation of these modules is a fundamental symmetry of dynamical robustness . Analysis of these findings leads to the conclusion that the most robust systems have the most hierarchical structure. This relationship provides a means by which evolutionary selection for a purely dynamical phenomenon may shape network architectures across scales of the biological hierarchy .
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analysis of dynamical systems that attempts to model chemical reaction
relationship between network topology and system dynamics has significant implications for unifying our understanding of the interplay among metabolic
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population, and ecosystem networks all rely on models having interacting components. When the details of these interactions are unknown for biological systems of interest, one effective approach is to study the dynamical properties of an ensemble of models determined by evolutionary constraints that may apply to all such systems. One such constraint is that of dynamical robustness. Despite previous investigations, the relationship between dynamical robustness-an important functional characteristic of many biological systems-and network structure is poorly understood
and ecosystem network architecures
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dynamical systems and demonstrate that the most hierarchical network structures, those equivalent to the total ordering, are the most robust. In particular, we
dynamics on such networks. We
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over system connectivity
as a function of network topology
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maximized by maximizing
classified by
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strongly connected components of the graph representing the underlying system connectivity. We demonstrate that this can be understood in terms of the fact that permutation of strongly connected components
modules of the network. We also demonstrate that permutation of these modules
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, which applies to networks of any number of components and is independent of the distribution from which the strengths of interconnection among components are sampled. The classification of dynamical robustness based upon a purely topological property provides a URLanizing principle that can be used in the context of experimental validation to select among models that break or preserve network hierarchy. This result contributes to an explanation for the observation of hierarchical modularity in biological networks at all scales
. Analysis of these findings leads to the conclusion that the most robust systems have the most hierarchical structure. This relationship provides a means by which evolutionary selection for a purely dynamical phenomenon may shape network architectures across scales of the biological hierarchy