{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,2]],"date-time":"2026-08-02T22:06:36Z","timestamp":1785708396813,"version":"3.56.0"},"reference-count":31,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,2,2]],"date-time":"2025-02-02T00:00:00Z","timestamp":1738454400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Universit\u00e0 degli Studi di Modena e Reggio Emilia"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Two different processes take place in self-reproducing protocells, i.e., (i) cell reproduction by fission and (ii) duplication of the genetic material. One major problem is indeed that of assuring that the two processes take place at the same pace, i.e., that they synchronize, which is a necessary condition for sustainable growth. In previous theoretical works, using dynamical models, we had shown that such synchronization can spontaneously emerge, generation after generation, under a broad set of hypotheses about the architecture of the protocell, the nature of the self-replicating molecules, and the types of kinetic equations. However, an important class of cases (quadratic or higher-order self-replication) did not synchronize in the models we had used, but could actually lead to divergence of the concentration of replicators. We show here that this behavior is due to a simplification of the previous models, i.e., the \u201cbuffering\u201d hypothesis, which assumes instantaneous equilibrium of the internal and external concentrations of those compounds which can cross the cell membrane. That divergence disappears if we make use of more realistic dynamical models, with finite transmembrane diffusion rates of the precursors of replicators.<\/jats:p>","DOI":"10.3390\/e27020154","type":"journal-article","created":{"date-parts":[[2025,2,3]],"date-time":"2025-02-03T05:36:32Z","timestamp":1738560992000},"page":"154","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Protocells Either Synchronize or Starve"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5991-5470","authenticated-orcid":false,"given":"Marco","family":"Villani","sequence":"first","affiliation":[{"name":"Department of Physics, Informatics and Mathematics, Modena and Reggio Emilia University, 41121 Modena, Italy"},{"name":"European Centre for Living Technology, 30123 Venice, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1417-5106","authenticated-orcid":false,"given":"Roberto","family":"Serra","sequence":"additional","affiliation":[{"name":"Department of Physics, Informatics and Mathematics, Modena and Reggio Emilia University, 41121 Modena, Italy"},{"name":"European Centre for Living Technology, 30123 Venice, Italy"},{"name":"Institute of Advanced Studies, University of Amsterdam, 1012 WX Amsterdam, The Netherlands"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,2]]},"reference":[{"key":"ref_1","unstructured":"Alberts, B., Johnson, A., Lewis, J., Morgan, D., Raff, M., Roberts, K., and Walter, P. 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