Abstract
Autocatalytic cycles are rather widespread in nature and in several theoretical models of catalytic reaction networks their emergence is hypothesized to be inevitable when the network is or becomes sufficiently complex. Nevertheless, the emergence of autocatalytic cycles has been never observed in wet laboratory experiments. Here, we present a novel model of catalytic reaction networks with the explicit goal of filling the gap between theoretical predictions and experimental findings. The model is based on previous study of Kauffman, with new features in the introduction of a stochastic algorithm to describe the dynamics and in the possibility to increase the number of elements and reactions according to the dynamical evolution of the system. Furthermore, the introduction of a temporal threshold allows the detection of cycles even in our context of a stochastic model with asynchronous update. In this study, we describe the model and present results concerning the effect on the overall dynamics of varying (a) the average residence time of the elements in the reactor, (b) both the composition of the firing disk and the concentration of the molecules belonging to it, (c) the composition of the incoming flux.
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Notes
We also mention the lipid-world hypothesis (Segre et al. 1998).
The reaction volume was taken to be similar to that of a small bacterium, i.e. 1 μm3.
In this case one single reaction is enough to produce two different polymers of equal length, so the total amount of reactions have to be reduced by 2 × 22L−L = 2L+1 reactions.
Notice also that in all the simulations that we describe in this article we use firing disks and incoming fluxes without any ACS and that in all the simulations the alphabet is composed of two letters, A and B.
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Acknowledgments
This study has been partially supported by the Fondazione di Venezia, http://www.fondazionedivenezia.it (DICE project). Interesting discussions with Davide De Lucrezia and Timoteo Carletti are gratefully acknowledged.
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Filisetti, A., Graudenzi, A., Serra, R. et al. A stochastic model of autocatalytic reaction networks. Theory Biosci. 131, 85–93 (2012). https://doi.org/10.1007/s12064-011-0136-x
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DOI: https://doi.org/10.1007/s12064-011-0136-x