Emergence of Protocellular Growth Laws

Template directed replication is known to obey a parabolic growth law due to product inhibition [18, 6, 9, 25]. We investigate a template directed replication with a coupled template catalysed lipid aggregate production as a model of a minimal protocell and show analytically that the autocatalytic template-container feedback ensures balanced exponential replication kinetics; both the genes and the container grow exponentially with the same exponent. The parabolic gene replication does not limit the protocellular growth and a detailed stoichiometric control of the individual protocell components is not necessary to ensure a balanced gene-container growth as conjectured by various authors [5]. Our analysis also suggests that the exponential growth of most modern biological systems emerge from the inherent spatial quality of the container replication process as we show analytically how the internal gene and metabolic kinetics determine the cell population's generation time and not the growth law [2, 11, 24]. Previous extensive replication reaction kinetic studies have mainly focused on template replication and have not included a coupling to metabolic container dynamics [20, 21] . The reported results extend these investigations. Finally, the coordinated exponential gene-container growth law stemming from catalysis is an encouraging circumstance for the many experimental groups currently engaged in assembling self-replicating minimal artificial cells [16, 3].