Abstract
A mathematical model based on Random Boolean Networks (RBNs) has been recently proposed to describe the main features of cell differentiation. The model captures in a unique framework all the main phenomena involved in cell differentiation and can be subject to experimental testing. A prominent role in the model is played by cellular noise, which somehow controls the cell ontogenetic process from the stem, totipotent state to the mature, completely differentiated one. Noise is high in stem cells and decreases while the cell undergoes the differentiation process. A limitation of the current mathematical model is that RBNs, as an ensemble, are not endowed with the property of showing a smooth relation between noise level and the differentiation stages of cells. In this work, we show that it is possible to generate an ensemble of Boolean networks (BNs) that can satisfy such a requirement, while keeping the other main relevant statistical features of classical RBNs. This ensemble is designed by means of an optimisation process, in which a stochastic local search (SLS) optimises an objective function which accounts for the requirements the network ensemble has to fulfil.
An erratum to this chapter can be found at http://dx.doi.org/10.1007/978-3-642-37577-4_18
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- 1.
Reachable by means of transition whose probability exceeds the threshold θ.
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There are some positive but not yet definitive experimental data.
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Of course, the property is typical of the ensemble and isolated exceptions could be found. The value θ 0 depends on the specific instance considered.
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We assume that constraints are either implicitly satisfied or that they are relaxed and included in the objective function.
- 5.
Ideally, the sum of transitions going out of a vertex, except for self-loops, should not be greater than 0. 2.
- 6.
Since the search process is stochastic, we can consider our design method as a biased sampling in the space of BNs.
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Benedettini, S., Roli, A., Serra, R., Villani, M. (2014). Automatic Design of Boolean Networks for Modelling Cell Differentiation. In: Cagnoni, S., Mirolli, M., Villani, M. (eds) Evolution, Complexity and Artificial Life. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37577-4_5
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