Abstract
BackgroundThe mechanisms underlying complex biological systems are routinely represented as networks. Network kinetics is widely studied, and so is the connection between network structure and behavior. However, similarity of mechanism is better revealed by relationships between network structures.ResultsWe define morphisms (mappings) between reaction networks that establish structural connections between them. Some morphisms imply kinetic similarity, and yet their properties can be checked statically on the structure of the networks. In particular we can determine statically that a complex network will emulate a simpler network: it will reproduce its kinetics for all corresponding choices of reaction rates and initial conditions. We use this property to relate the kinetics of many common biological networks of different sizes, also relating them to a fundamental population algorithm.ConclusionsStructural similarity between reaction networks can be revealed by network morphisms, elucidating mechanistic and functional aspects of complex networks in terms of simpler networks.
Highlights
The mechanisms underlying complex biological systems are routinely represented as networks
We show that these morphism can characterize functional properties and provide an explanation of kinetic similarity based on structural similarity
Mass action interpretation of influence networks A chemical reaction network is given by a set of irreversible reactions R over a set of species S
Summary
The mechanisms underlying complex biological systems are routinely represented as networks. Chemical reaction networks Chemical reaction networks provide a compact language for describing complex dynamical systems of the kind found in inorganic chemistry, biochemistry, and systems biology They can be presented as certain graphs or as lists of reactions over a set of species. The aforementioned literature is focused on properties of individual reaction networks or their subnetworks Another way to try to understand the properties of a network is to relate it to another network, perhaps a better known one, either by comparing graph structures [12,13,14,15], or more deeply by preserving kinetic features [3,10]. As an application we obtain analytical justification of empirical relationships that have been observed in conjunction with cell cycle switch models [16]
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