Abstract
For many aspects of health and disease, it is important to understand different phenomena in biology and medicine. To gain the required insight, experiments are performed and the resulting experimental data have to be interpreted. This leads to the Network Reconstruction Problem, the challenging task to generate all models that explain the observed phenomena. As in systems biology, the framework of Petri nets is often used to describe models for the regulatory mechanisms of biological systems, our aim is to predict all the possible network structures being conformal with the given experimental data. We discuss a combinatorial approach proposed by Marwan et al. (Math. Methods Oper. Res. 67:117–132, 2008) and refined by Durzinsky et al. (Proc. of CMSB 2008, LNBI, vol. 5307, pp. 328–346, Springer, Berlin, 2008) to solve this problem. In addition, we also present an algorithm by Durzinsky et al. (J. Theor. Comput. Sci., 2009) that, based on these results, generates a complete list of all potential networks reflecting the experimentally observed behavior.
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Notes
- 1.
We use super-indices to reflect the order of the states x j and to allow sub-indices for the entries \(x^{j}_{p}\) in a particular component p.
- 2.
In usual mathematical terms, the column of a matrix C indexed by t is denoted by C ⋅t . As this notion interferes with the notion •t of preplaces of a transition t, we here use C ∗t instead of C ⋅t .
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Wagler, A. (2011). Prediction of Network Structure. In: Koch, I., Reisig, W., Schreiber, F. (eds) Modeling in Systems Biology. Computational Biology, vol 16. Springer, London. https://doi.org/10.1007/978-1-84996-474-6_14
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DOI: https://doi.org/10.1007/978-1-84996-474-6_14
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