The sustained growth of a population of protocells which undergo symmetrical division (where each individual splits into two equal daughter protocells) requires synchronization between the two processes of (i) duplication of the genetic material and (ii) fission of the lipid container. It has however been observed that one often encounters uneven division, where daughters of different sizes may be generated. Here we analyze the case of asymmetrical division, where each protocell has exactly two daughters of different sizes. In this case no true synchronization is possible, and we introduce the notion of homogeneous growth which guarantees that sustained population growth is possible. We consider different abstract models of protocells growth and reproduction and we show by simulation that homogeneous growth is encountered, both in Surface Reaction Models, where the replicators are located in the membrane, and in Internal Reaction Models where they are found in the internal water phase, under a broad set of different kinetic equations. We argue that, when there are different kinds of replicators, it is legitimate to identify the “chemical signature” of the protocell with the set of the ratios between the quantities of these replicators at fission time: it is shown that, in the case of linear kinetic equations, the ratios and therefore the chemical identity are conserved through generations.

In this extended abstract two novel concepts are defined in the study of Random Boolean Networks, i.e. those of “pseudoattractors” and “common sea”, and it is shown how their analogues can be measured in experimental data on gene expression in single cells.

Cellular types of multicellular organisms are the stable results of complex intertwined processes that occur in biological cells. Among the many others, chromatin dynamics significantly contributes—by modulating access to genes—to differential gene expression, and ultimately to determine cell types. Here, we propose a dynamical model of differentiation based on a simplified bio-inspired methylation mechanism in Boolean models of GRNs. Preliminary results show that, as the number of methylated nodes increases, there is a decrease in attractor number and networks tend to assume dynamical behaviours typical of ordered ensembles. At the same time, results show that this mechanism does not affect the possibility of generating path dependent differentiation: cell types determined by the specific sequence of methylated genes.

The detection of critical states is a task of utmost importance in complex systems; to this aim, measures to identify such conditions are required. In general, the term criticality concerns the existence of two qualitatively different behaviours that a system can exhibit, which depends on some parameter values. In this short communication, we summarise our recent findings on the use of the Relevance Index to identify critical states in complex systems. Although the Relevance Index method was originally developed to identify relevant sets of variables in dynamical systems, we show that it is also able to detect features of criticality. The index is applied to two notable examples showing slightly different meanings of criticality, namely, the Ising model and Random Boolean Networks. Results show that this index is maximised at critical states and is robust with respect to system size and sampling effort.