Abstract
We describe a hybrid system based framework for modeling gene regulation and other biomolecular networks and a method for analysis of the dynamic behavior of such models. A particular feature of the proposed framework is the focus on qualitative experimentally testable properties of the system. With this goal in mind we introduce the notion of the frame of a hybrid system, which allows for the discretisation of the state space of the network. We propose two different methods for the analysis of this state space. The result of the analysis is a set of attractors that characterize the underlying biological system.
Whilst in the general case the problem of finding attractors in the state space is algorithmically undecidable, we demonstrate that our methods work for comparatively complex gene regulatory network model of \(\lambda \)-phage. For this model we are able to identify attractors corresponding to two known biological behaviors of \(\lambda \)-phage: lysis and lysogeny and also to show that there are no other stable behavior regions for this model.
The authors are listed in alphabetical order and have equally contributed to the paper. The work was supported by Latvian Council of Science grant 258/2012 and Latvian State Research programme project NexIT (2014-2017).
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Notes
- 1.
For biomolecular networks the value \(''\rightarrow ''\) describing the situation where concentration of some substance does not change is generally reserved for the cases in which concentration is either 0 or the maximal biologically feasible saturation value.
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Brazma, A., Cerans, K., Ruklisa, D., Schlitt, T., Viksna, J. (2015). Modeling and Analysis of Qualitative Behavior of Gene Regulatory Networks. In: Maler, O., Halász, Á., Dang, T., Piazza, C. (eds) Hybrid Systems Biology. HSB 2014. Lecture Notes in Computer Science(), vol 7699. Springer, Cham. https://doi.org/10.1007/978-3-319-27656-4_3
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