Emergence of protocellular growth laws

Abstract

Template-directed replication is known to obey a parabolic growth law due to product inhibition (Sievers & Von Kiedrowski 1994 Nature 369, 221; Lee et al. 1996 Nature 382, 525; Varga & Szathmáry 1997 Bull. Math. Biol. 59, 1145). 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 (Gánti 2004 Chemoton theory). Our analysis also suggests that the exponential growth of most modern biological systems emerges 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 (Burdett & Kirkwood 1983 J. Theor. Biol. 103, 11-20; Novak et al. 1998 Biophys. Chem. 72, 185-200; Tyson et al. 2003 Curr. Opin. Cell Biol. 15, 221-231). Previous extensive replication reaction kinetic studies have mainly focused on template replication and have not included a coupling to metabolic container dynamics (Stadler et al. 2000 Bull. Math. Biol. 62, 1061-1086; Stadler & Stadler 2003 Adv. Comp. Syst. 6, 47). 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 (Szostak 2001 et al. Nature 409, 387-390; Pohorille & Deamer 2002 Trends Biotech. 20 123-128; Rasmussen et al. 2004 Science 303, 963-965; Szathma ry 2005 Nature 433, 469-470; Luisi et al. 2006 Naturwissenschaften 93, 1-13).

On the Growth Rate of Non-Enzymatic Molecular Replicators

“…Consequently, several strategies have been designed to overcome product inhibition in order to reestablish Darwinian evolution and survival of only the fittest [20,22,26,27]. Most of these approaches hinge on a mechanism to lower the hybridization tendency of the product to the template.…”

“…Following and extending the derivation of [21,22], we assume that ligation is the rate limiting step. This translates into the following conditions for the rate constants:…”

Generating minimal living systems from non-living materials and increasing their evolutionary abilities

“…Variation of the metabolic reaction rates across a protocellular population would mean different growth and division rates and thus different overall replication rates for different protocells. Thus, different protocellular replication rates open up for protocellular selection, and if the process is iterated, it results in Darwinian evolution, recall the theoretical documentation for exponential growth in §2 [23,24]. Such a process is expected to result in protocellular populations with increasing replication rates.…”

“…Our simulation studies have focused on both detailed processes [16] and full protocell life-cycle simulations, where one study demonstrates how a catalytic coupling between the container and information growth results in an orchestrated overall exponential protocellular growth rate [23,24]; and another demonstrates the intricate interdependencies and challenges of integrating the timescales between the different components and processes [25].…”

Life Cycle of a Minimal Protocell—A Dissipative Particle Dynamics Study

“…What is the effect on the overall protocell replication if both the gene precursors (oligomers) and the lipid precursors are supplied to the solution and have to diffuse to the protocell? In such a case, will we see the coordinated gene and container growth based on reaction kinetics predicted by Rocheleau et al [29]? As gene replication is necessary before container division for two viable daughters, can that be ensured in other ways than through a sequential resource supply?…”