Abstract
Metabolic networks, formed by a series of metabolic pathways, are made of intracellular and extracellular reactions that determine the biochemical properties of a cell, and by a set of interactions that guide and regulate the activity of these reactions. Cancer, for example, can sometimes appear in a cell as a result of some pathology in a metabolic pathway. Most of these pathways are formed by an intricate and complex network of chain reactions, and can be represented in a human readable form using graphs which describe the cell signaling pathways. In this paper, we define a logic, called Molecular Interaction Logic (MIL), able to represent these graphs and we present a method to automatically translate graphs into MIL formulas. Then we show how MIL formulas can be translated into linear time temporal logic, and then grounded into propositional classical logic. This enables us to solve complex queries on graphs using only propositional classical reasoning tools such as SAT solvers.
Dedicated to Jair Minoro Abe for his 60th birthday
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Notes
- 1.
The Nobel prize was awarded to Monod, Jacob and Lwoff in 1965 partly for the discovery of the lac operon by Monod and Jacob [16], which was the first genetic regulatory mechanism to be understood clearly, and is now a “standard” introductory example in molecular biology classes.
- 2.
It is important here to notice that lactose can be either considered as a weak endogenous variable, or as an exogenous variable if we consider that the environment is always providing “enough” lactose. It is a simple example which shows that variables in a graph can be interpreted differently according to what is going to be observed.
- 3.
For a more detailed survey of temporal extension of Answer Set Programming see [1].
- 4.
The dual problem, which could be easily adapted to suit our needs.
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Acknowledgments
This work is partially supported by ANR-11-LABX-0040-CIMI within the program ANR-11-IDEX-0002-02, by IREP Associated European Laboratory and by project CLE from Région Midi-Pyrénées.
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Alliot, JM. et al. (2016). Temporal Logic Modeling of Biological Systems. In: Akama, S. (eds) Towards Paraconsistent Engineering. Intelligent Systems Reference Library, vol 110. Springer, Cham. https://doi.org/10.1007/978-3-319-40418-9_11
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