Abstract
Models are of great importance for protocell research, not only for the usual reasons why models matter, but also because real protocells are not yet available in the lab. There are indeed some cases where one or a few duplications have been achieved (Hanczyc and Szostak 2004; Luisi et al. 2004; Luisi 2006; Stano et al. 2006; Schrum et al. 2010; Stano and Luisi 2010a) but so far, to the best of our knowledge, a sustained growth of a population of protocells has never been observed.
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Notes
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Like the pioneering chemoton model, described in Gánti (1997).
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This is not the only proposed explanation, but a comprehensive discussion of the origin of allometric scaling laws lies beyond the aim of this book.
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Two major variants of this hypothesis have been suggested: (i) that real systems can indeed be in the ordered, more controllable region but close to the critical boundaries, so to be susceptible enough to external changes (Kauffman 1993) and (ii) that in biological systems the notion of criticality has to be taken in a wide sense (Bailly and Longo 2008): while in physical systems one finds critical points, in biological systems one can suppose that they have a finite size. An analogous remark applies as well to critical lines or (hyper)surfaces.
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This is of course the most appropriate choice to model a gene regulatory network, where the nodes are the genes and the links represent their mutual influences.
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The assumptions made here are equivalent to supposing that an avalanche never interferes with itself (see Di Stefano et al. 2016 for a precise definition). The non-interference assumption implies that the topology of a spreading avalanche is that of a tree, where each node has a single parent.
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Of course some hypotheses need to be made; in this case, the key hypothesis is that the level of cellular noise is high in stem cells and decreases during differentiation. There are some experimental indications in favor of this hypothesis, which can and should be subject to further testing.
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Serra, R., Villani, M. (2017). Generic Properties of Dynamical Models of Protocells. In: Modelling Protocells. Understanding Complex Systems. Springer, Dordrecht. https://doi.org/10.1007/978-94-024-1160-7_2
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DOI: https://doi.org/10.1007/978-94-024-1160-7_2
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