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On the Growth Rate of Non-Enzymatic Molecular Replicators
Center for Fundamental Living Technology, University of Southern Denmark, Campusvej 55, 5230 Odense M, Denmark
ICREA-Complex Systems Lab, Universitat Pompeu Fabra (GRIB), Dr Aiguader 80, 08003 Barcelona, Spain
Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA
* Author to whom correspondence should be addressed.
Received: 27 September 2011; Accepted: 13 October 2011 / Published: 21 October 2011
Abstract: It is well known that non-enzymatic template directed molecular replicators X + nO -> 2X exhibit parabolic growth d[X]/dt -> k[X]1/2. Here, we analyze the dependence of the effective replication rate constant k on hybridization energies, temperature, strand length, and sequence composition. First we derive analytical criteria for the replication rate k based on simple thermodynamic arguments. Second we present a Brownian dynamics model for oligonucleotides that allows us to simulate their diffusion and hybridization behavior. The simulation is used to generate and analyze the effect of strand length, temperature, and to some extent sequence composition, on the hybridization rates and the resulting optimal overall rate constant k. Combining the two approaches allows us to semi-analytically depict a replication rate landscape for template directed replicators. The results indicate a clear replication advantage for longer strands at lower temperatures in the regime where the ligation rate is rate limiting. Further the results indicate the existence of an optimal replication rate at the boundary between the two regimes where the ligation rate and the dehybridization rates are rate limiting.
Keywords: non-enzymatic molecular replication; minimal replicators; protocell; growthrates; product inhibition; reaction kinetics; Brownian dynamics
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MDPI and ACS Style
Fellermann, H.; Rasmussen, S. On the Growth Rate of Non-Enzymatic Molecular Replicators. Entropy 2011, 13, 1882-1903.
Fellermann H, Rasmussen S. On the Growth Rate of Non-Enzymatic Molecular Replicators. Entropy. 2011; 13(10):1882-1903.
Fellermann, Harold; Rasmussen, Steen. 2011. "On the Growth Rate of Non-Enzymatic Molecular Replicators." Entropy 13, no. 10: 1882-1903.