Abstract
Metabolic Networks, formed by 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. Cancers, 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 they can be represented in a human readable form using graphs which describe the cell signaling pathways.
In this paper we present a logic, called Molecular Equilibrium Logic, a nonmonotonic logic which allows representing metabolic pathways. We also show how this logic can be presented in terms of a syntactical subset of Temporal Equilibrium Logic, the temporal extension of Equilibrium Logic, called Splittable Temporal Logic Programs.
This research was partially supported by the French Spanish Laboratory for Advanced Studies in Information, Representation and Processing (LEA-IREP). Martín Diéguez was supported by the Centre international de mathématiques et d’informatique (contract ANR-11-LABX-0040-CIMI).
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Notes
- 1.
Regarding non-monotonic approaches to model biological systems, there are several contributions in the area of Answer Set Programming [9, 28], action languages [29] or Inductive Logic Programming [12]. In these contributions the temporal behaviour is considered in [29] but both representation and query languages are different.
- 2.
The Nobel prize was awarded to Monod, Jacob and Lwoff in 1965 partly for the discovery of the lac operon by Monod and Jacob [18], which was the first genetic regulatory mechanism to be understood clearly, and is now a “standard” introductory example in molecular biology classes.
- 3.
A less formal explanation can be found in https://en.wikipedia.org/wiki/Lac_operon.
- 4.
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.
- 5.
Notice that only the pathway formula associated with the production of Galactosidase has an associated context, defined in (1), while the rest of pathway formulas have an empty context.
- 6.
- 7.
- 8.
We refer the reader to [4] for details about the computation of such loop formulas.
- 9.
We omitted the completion at time step 0 since the formula at the initial state depends on the extensional database, which is not considered here.
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Alliot, JM., Diéguez, M., Fariñas del Cerro, L. (2016). Metabolic Pathways as Temporal Logic Programs. In: Michael, L., Kakas, A. (eds) Logics in Artificial Intelligence. JELIA 2016. Lecture Notes in Computer Science(), vol 10021. Springer, Cham. https://doi.org/10.1007/978-3-319-48758-8_1
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