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Italian Workshop on Artificial Life and Evolutionary Computation

WIVACE 2015: Advances in Artificial Life, Evolutionary Computation and Systems Chemistry pp 92–105Cite as

On the Dynamics of Autocatalytic Cycles in Protocell Models

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Part of the book series: Communications in Computer and Information Science ((CCIS,volume 587))

Abstract

The emergence of autocatalytic sets of molecules seems to have played an important role in the origin of life, allowing a sustainable systems’ growth and reproduction. Several frameworks have been proposed, one of the most recent and promising being that of RAF (Reflexively Autocatalytic – Food generated) sets. As it often happens when topological properties only are taken into account, RAFs are however only potentially able of supporting continuous growth. Dynamics can also play a significant role: it is shown here how dynamical interactions may sometimes lead to unexpected behaviors.

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Notes

  1. 1.

    The usual basic choice for network-based approaches – see also [2, 9].

  2. 2.

    Note that the aim of the model is not to provide a detailed description of a specific set of reactions; rather, it wants to focus the attention on the general characteristics emerging from the interaction of a large number of interacting molecules.

  3. 3.

    It is generally believed that \( L_{mincat} \) should not be very small (chemical species should reach an enough high complexity to carry catalytic activities) [24]. However, there could be significant exceptions [25].

  4. 4.

    The probability p is fixed, and the basic model does not hypothesize particular functional relationship between sequences of the catalysts and the reactions they catalyze, as for example chemical affinities among molecules because of their internal composition. These limits do not affect the description capabilities of the model, as discussed in [7].

  5. 5.

    Note that \( L_{mincat} \) and \( L_{max} \) help in defining some characteristics of the simulated artificial word, without changing in significant way its dynamics. A different role is played by p, as we discuss in the following.

  6. 6.

    We deal with the backward reactions theme in [26], and with the energy theme in [27].

  7. 7.

    Moreover, RAFs can be composed also by linear chains of reactions, provided that the presence of the first element of the chain is guaranteed by the environment (a case not present in this work, because of the chemical species that can pass through the membrane have not catalytic activities).

  8. 8.

    Given our assumptions the difference in chemical potential is due only to differences in concentrations.

  9. 9.

    Note that the other possible outcomes are dilution (at division the internal materials have always smaller concentrations, leading to huge division times and starvation) and excessive concentration (at division at least a part of the internal materials have always higher concentrations, leading to the protocell breakage). This last event is out of the model’s range of validity, but can be simply detected by observing the internal material concentrations and stopping the simulation in case of too high concentration values. In the following we refer to both these events as “not synchronizing situations”.

  10. 10.

    The great part of the simulations presented in this work was performed by using a home-made tool implementing stochastic dynamics (an extension of the Gillespie algorithm [29] to the case of variable volumes, already presented in [30]), because in some cases the effects of randomness may be very relevant [10]. When concentrations were sufficiently high the simulations was double-checked by means another tool implementing a deterministic Euler schema using a with step size control (already used in [31]).

  11. 11.

    In order to find 20 different chemistries satisfying this last vinculum we created 600 different chemistries having <c> = 1.0 (580 chemistries discarded) and 50 different chemistries having <c> = 1.0 (30 chemistries discarded).

  12. 12.

    In particular, the kinetic Gillespie constant for the first step of the condensations (the union of the first substrate with the catalyst to build a short-life complex) is cs = 8.3e−3, the constant for the first-order complex dissociations is c s  = 250, the constant for the final step of the condensations (the union of the second substrate with the complex releasing the catalyzer and the final product)) is c s  = 8.3e−4, and finally the constant for the cleavages is c s  = 8.3e−5.

  13. 13.

    Note that the particular subdivision chosen for the condensation process involves steps having different kinetics: in particular, steps (1) and (3) described in Sect. 2.1 involve collisions between two objects, whereas step (2) follows a simple first order kinetic. So, if the volume of the reaction container changes in time (as in our case) the relative reaction rates can correspondingly change: the effect of this phenomenon on the competition among sRAF will be explored in next works.

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Acknowledgments

Useful discussions with Stuart Kauffman, Timoteo Carletti, Chiara Damiani, Alex Graudenzi, Wim Hordijk and Irene Poli are gratefully acknowledged.

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Author notes

  1. Alessandro Filisetti

    Present address: Explora s.r.l, Rome, Italy

Authors and Affiliations

  1. Department of Physics, Informatics and Mathematics, University of Modena and Reggio Emilia, v. Campi 213a, 41125, Modena, Italy

    Marco Villani, Alessandro Filisetti, Matthieu Nadini & Roberto Serra

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  1. Marco Villani
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  2. Alessandro Filisetti
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Correspondence to Marco Villani .

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Editors and Affiliations

  1. Department of Chemistry and Biology, University of Salerno, Fisciano, Italy

    Federico Rossi

  2. Department of Chemistry, University of Bari, Bari, Italy

    Fabio Mavelli

  3. Science Department, Roma Tre University, Roma, Italy

    Pasquale Stano

  4. Department of Informatics, University of Bari, Bari, Italy

    Danilo Caivano

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Villani, M., Filisetti, A., Nadini, M., Serra, R. (2016). On the Dynamics of Autocatalytic Cycles in Protocell Models. In: Rossi, F., Mavelli, F., Stano, P., Caivano, D. (eds) Advances in Artificial Life, Evolutionary Computation and Systems Chemistry. WIVACE 2015. Communications in Computer and Information Science, vol 587. Springer, Cham. https://doi.org/10.1007/978-3-319-32695-5_9

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  • DOI: https://doi.org/10.1007/978-3-319-32695-5_9

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