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.
Keywords
- Gene Regulatory Network
- Hybrid Automaton
- Transition Constant
- Strongly Connect Component
- Outgoing Transition
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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.
References
Ahmad, J., Bernot, J., Comet, J., Lime, D., Roux, O.: Hybrid modelling and dynamical analysis of gene regulatory networks with delays. Complexus 3, 231–251 (2007)
Alur, R., Belta, C., Ivančić, F., Kumar, V., Mintz, M., Pappas, G.J., Rubin, H., Schug, J.: Hybrid modeling and simulation of biomolecular networks. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A.L. (eds.) HSCC 2001. LNCS, vol. 2034, pp. 19–32. Springer, Heidelberg (2001)
Bartocci, E., Liò, P., Merelli, E., Paoletti, N.: Multiple verification in complex biological systems: the bone remodelling case study. In: Priami, C., Petre, I., de Vink, E. (eds.) Transactions on Computational Systems Biology XIV. LNCS, vol. 7625, pp. 53–76. Springer, Heidelberg (2012)
Batt, G., Ben Salah, R., Maler, O.: On timed models of gene networks. In: Raskin, J.-F., Thiagarajan, P.S. (eds.) FORMATS 2007. LNCS, vol. 4763, pp. 38–52. Springer, Heidelberg (2007)
Brazma, A., Schlitt, T.: Reverse engineering of gene regulatory networks: a finite state linear model. Genome Biol. 4(P5), 1–31 (2003)
Brazma, R., Cerans, K., Ruklisa, D., Schlitt, T., Viksna, J.: HSM - a hybrid system based approach for modelling intracellular networks. Gene 518, 70–77 (2013)
de Jong, H., Gouze, J., Hernandez, C., Page, M., Sari, T., Geiselmann, J.: Qualitative simulation of genetic regulatory networks using piecewise-linear models. Bull. Math. Biol. 66, 301–340 (2004)
Fromentin, J., Eveillard, D., Roux, O.: Hybrid modeling of biological networks: mixing temporal and qualitative biological properties. BMC Syst. Biol. 4(79), 11 (2010)
Ghosh, R., Tomlin, C.: Symbolic reachable set computation of piecewise affine hybrid automata and its application to biological modelling: Delta-notch protein signalling. Syst. Biol. 1, 170–183 (2004)
Grosu, R., Batt, G., Fenton, F.H., Glimm, J., Le Guernic, C., Smolka, S.A., Bartocci, E.: From cardiac cells to genetic regulatory networks. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 396–411. Springer, Heidelberg (2011)
McAdams, H., Shapiro, L.: Circuit simulation of genetic networks. Science 269, 650–656 (1995)
Ruklisa, D., Brazma, A., Viksna, J.: Reconstruction of gene regulatory networks under the finite state linear model. Genome Inform. 16, 225–236 (2005)
Schlitt, T., Brazma, A.: Modelling in molecular biology: describing transcription regulatory networks at different scales. Philos. Trans. R. Soc. Lond. B 361, 483–494 (2006)
Serra, R., Vilani, M., Barbieri, A., Kaufmfman, S., Colacci, A.: One the dynamics of random boolean networks subject to noise: attractors, ergodic sets and cell types. J. Theor. Biol. 265, 185–193 (2010)
Siebert, H., Bockmayr, A.: Temporal constraints in the logical analysis of regulatory networks. Theor. Comput. Sci. 391, 258–275 (2008)
Thomas, D., Thieffry, R., Kaufman, M.: Dynamic behaviour of biological regulatory networks. i. biological role of feedback loops and practical use of the concept of the loop-characteristic state. Bull. Math. Biol. 57, 247–276 (1995)
Thomas, D., Thieffry, R., Kaufman, M.: Dynamic behaviour of biological regulatory networks. ii. immunity control in bacteriophage lamda. Bull. Math. Biol. 57, 277–297 (1995)
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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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