Abstract
Pattern formation is an important spatio-temporal emergent behaviour in biology. Mathematical models of pattern formation in the stochastic setting are extremely challenging to execute and analyse. Here we propose a formal analysis of the emergent behaviour of stochastic reaction diffusion systems in terms of Signal Spatio-Temporal Logic, a recently proposed logic for reasoning on spatio-temporal systems. We present a formal analysis of the spatio-temporal dynamics of the Bicoid morphogen in Drosophila melanogaster, one of the most important proteins in the formation of the horizontal segmentation in the development of the fly embryo. We use a recently proposed framework for statistical model checking of stochastic systems with uncertainty on parameters to characterise the parametric dependence and robustness of the French Flag pattern, highlighting non-trivial correlations between the parameter values and the emergence of the patterning.
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Acknowledgements
L.B. acknowledges partial support from the EU-FET project QUANTICOL (nr. 600708) and by FRA-UniTS. G.S. and D.M. acknowledge the support from the ERC under grant MLCS306999. E.B. acknowledges the partial support of the Austrian National Research Network S 11405-N23 (RiSE/SHiNE) of the Austrian Science Fund (FWF), the ICT COST Action IC1402 Runtime Verification beyond Monitoring (ARVI) and the IKT der Zukunft of Austrian FFG project HARMONIA (nr. 845631).
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Bartocci, E., Bortolussi, L., Milios, D., Nenzi, L., Sanguinetti, G. (2015). Studying Emergent Behaviours in Morphogenesis Using Signal Spatio-Temporal Logic. In: Abate, A., Šafránek, D. (eds) Hybrid Systems Biology. HSB 2015. Lecture Notes in Computer Science(), vol 9271. Springer, Cham. https://doi.org/10.1007/978-3-319-26916-0_9
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