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Open AccessArticle

Sustainable Growth and Synchronization in Protocell Models

by Roberto Serra 1,2,3 and Marco Villani 1,2,*
Department of Physics, Informatics and Mathematics, Modena and Reggio Emilia University, Via Campi 213/A, 41125 Modena, Italy
European Centre for Living Technology, Ca’ Bottacin, Dorsoduro 3911, Calle Crosera, 30123 Venice, Italy
Institute for Advanced Study, University of Amsterdam, Oude Turfmarkt 147, 1012 GC Amsterdam, The Netherlands
Author to whom correspondence should be addressed.
Received: 19 July 2019 / Revised: 6 August 2019 / Accepted: 14 August 2019 / Published: 21 August 2019
The growth of a population of protocells requires that the two key processes of replication of the protogenetic material and reproduction of the whole protocell take place at the same rate. While in many ODE-based models such synchronization spontaneously develops, this does not happen in the important case of quadratic growth terms. Here we show that spontaneous synchronization can be recovered (i) by requiring that the transmembrane diffusion of precursors takes place at a finite rate, or (ii) by introducing a finite lifetime of the molecular complexes. We then consider reaction networks that grow by the addition of newly synthesized chemicals in a binary polymer model, and analyze their behaviors in growing and dividing protocells, thereby confirming the importance of (i) and (ii) for synchronization. We describe some interesting phenomena (like long-term oscillations of duplication times) and show that the presence of food-generated autocatalytic cycles is not sufficient to guarantee synchronization: in the case of cycles with a complex structure, it is often observed that only some subcycles survive and synchronize, while others die out. This shows the importance of truly dynamic models that can uncover effects that cannot be detected by static graph theoretical analyses. View Full-Text
Keywords: protocell; synchronization; replication; reproduction; Gillespie algorithm; autocatalytic set; RAF set protocell; synchronization; replication; reproduction; Gillespie algorithm; autocatalytic set; RAF set
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Serra, R.; Villani, M. Sustainable Growth and Synchronization in Protocell Models. Life 2019, 9, 68.

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