Advertisement

European Biophysics Journal

, Volume 48, Issue 3, pp 277–283 | Cite as

The optimal size of protocells from simple entropic considerations

  • Yoelsy LeyvaEmail author
  • Osmel Martin
  • Noel Perez
  • José Suarez-Lezcano
  • Manuel Fundora-Pozo
Original Article

Abstract

Potential constraints on protocell size are developed from simple entropic considerations. To do that, two new different indexes as measures of their structural and dynamic order were developed and applied to an elemental model of the heterotrophic protocell. According to our results, cell size should be a key factor determining the potential of these primitive systems to evolve and consequently to support life. Our analyses also suggest that the size of the optimal vesicles could be constrained to have radii in the interval \( (R_{\text{S}} \le R \le R_{\text{D}} ) \), where the two extreme limits \( R_{\text{S}} \) and \( R_{\text{D}} \) represent the states of maximum structural order (largest accumulation of substrate inside the vesicle) and the maximum flux of entropy production, respectively. According to the above criteria, the size of the optimum vesicles falls, approximately, in the same spatial range estimated for biological living cells assuming plausible values for the second-order rate constant involved in the catabolic process. Furthermore, the existence of very small vesicles could be seriously affected by the limited efficiency, far from the theoretical limits, with which these catabolic processes may proceed in a prebiotic system.

Keywords

Protocell Entropy Entropy production Proto-metabolism Primitive membranes 

Notes

Acknowledgements

Y. L. acknowledges the support of this research by the Dirección de Investigación y Extensión Académica de la Universidad de Tarapacá under project No. 4729-16.

References

  1. Bar-Even A, Noor E, Savir Y, Liebermeister W, Davidi D, Tawfik DS, Milo R (2011) The moderately efficient enzyme: evolutionary and physicochemical trends shaping enzyme parameters. Biochemistry 50:4402–4410CrossRefGoogle Scholar
  2. Bell EA, Boehnke P, Harrison TM, Mao WL (2015) Potentially biogenic carbon preserved in a 4.1 billion-year-old zircon. Proc Natl Acad Sci 112:14518–14521CrossRefGoogle Scholar
  3. Benner SA (2010) Defining Life. Astrobiology 10:1021–1030CrossRefGoogle Scholar
  4. Bormashenko E, Voronel A (2018) Spatial scales of living cells and their energetic and informational capacity. Eur Biophys J 47:515CrossRefGoogle Scholar
  5. Brack A (2007) From interstellar amino acids to prebiotic catalytic peptides: a review. Chem Biodivers 4:665–679CrossRefGoogle Scholar
  6. Chodasewicz K (2014) Evolution, reproduction and definition of life. Theory Biosci 133:39–45CrossRefGoogle Scholar
  7. Cleland CE, Chyba CF (2002) Defining life. Orig Life Evol Biosph 32:387CrossRefGoogle Scholar
  8. Collier J (1988) The dynamics of biological order. In: Weber BH, Depew DJ, Smiths JD (eds) Entropy, information, and evolution. MIT Press, Cambridge MAGoogle Scholar
  9. Davies PCW, Rieper E, Tuszynski JA (2013) Self-organization and entropy reduction in a living cell. Bio Systems 111:1–10CrossRefGoogle Scholar
  10. Dewar RC (2010) Maximum entropy production and plant optimization theories. Philos Trans R Soc Lond B Biol Sci 365:1429–1435CrossRefGoogle Scholar
  11. Juretić D, Županović P (2003) Photosynthetic models with maximum entropy production in irreversible charge transfer steps. Comput Biol Chem 27:541–553CrossRefGoogle Scholar
  12. Laiterä T, Lehto K (2009) Protein-mediated selective enclosure of early replicators inside of membranous vesicles: first step towards cell membranes. Origins Life Evol Biospheres 39:545–558CrossRefGoogle Scholar
  13. Lazcano A (2008) What is life? A brief historical overview. Chem Biodivers 5:1–15CrossRefGoogle Scholar
  14. Leyva Y, Martín O, García-Jacas CR (2018) Constraining the prebiotic cell size limits in extremely hostile environments: a dynamical perspective. Astrobiology 18:403–411CrossRefGoogle Scholar
  15. Luisi PL, Ruiz-Mirazo K (2010) Open questions on the origins of life: introduction to the special issue. Orig Life Evol Biosph 40(4–5):353–355Google Scholar
  16. Ma W, Feng Y (2015) Protocells: at the interface of life and non-life. Life 5:447–458CrossRefGoogle Scholar
  17. Marchetti MC, Joanny JF, Ramaswamy S, Liverpool TB, Prost J, Rao M, Simha RA (2013) Hydrodynamics of soft active matter. Rev Mod Phys 85:1143–1189CrossRefGoogle Scholar
  18. Marshall WF, Young KD, Swaffer M, Wood E, Nurse P, Kimura A, Frankel J, Wallingford J, Walbot V, Qu X et al (2012) What determines cell size? BMC Biol 10:101CrossRefGoogle Scholar
  19. Martín O, Peñate L, Alvaré A, Cárdenas R, Horvath JE (2009) some possible dynamical constraints for life’s origin. Origins Life Evol Biospheres 39:533–544CrossRefGoogle Scholar
  20. Martyushev LM, Seleznev VD (2006) Maximum entropy production principle in physics, chemistry and biology. Phys Rep 426:1–45CrossRefGoogle Scholar
  21. Murtola T, Bunker A, Vattulainen I, Deserno M, Karttunen M (2009) Multiscale modeling of emergent materials: biological and soft matter. Phys Chem Chem Phys 11:1869–1892CrossRefGoogle Scholar
  22. Piedrafita G, Montero F, Morán F, Cárdenas ML, Cornish-Bowden A (2010) A simple self-maintaining metabolic system: robustness, autocatalysis, bistability. PLOS Comput Biol 6:e1000872CrossRefGoogle Scholar
  23. Piedrafita G, Ruiz-Mirazo K, Monnard P-A, Cornish-Bowden A, Montero F (2012) Viability conditions for a compartmentalized protometabolic system: a semi-empirical approach. PLoS One 7:e39480CrossRefGoogle Scholar
  24. Piedrafita G, Monnard P-A, Mavelli F, Ruiz-Mirazo K (2017) Permeability-driven selection in a semi-empirical protocell model: the roots of prebiotic systems evolution. Scientific Reports 7:3141CrossRefGoogle Scholar
  25. Prigogine I (1977) Time, structure and fluctuations. Université Libre de Bruxelles, Brussels, Belgium and the University of Texas at Austin, Austin, Texas, USAGoogle Scholar
  26. Pross A (2005) Stability in chemistry and biology: life as a kinetic state of matter. Pure Appl Chem 77:1905–1921CrossRefGoogle Scholar
  27. Ruiz-Mirazo K, Briones C, de la Escosura A (2014) Prebiotic systems chemistry: new perspectives for the origins of life. Chem Rev 114:285–366CrossRefGoogle Scholar
  28. Sakuma Y, Imai M (2015) From vesicles to protocells: the roles of amphiphilic molecules. Life 5:651CrossRefGoogle Scholar
  29. Stenholm S (2008) On entropy production. Ann Phys 323:2892–2904CrossRefGoogle Scholar
  30. Young KD (2006) The selective value of bacterial shape. Microbiol Mol Biol Rev 70:660–703CrossRefGoogle Scholar

Copyright information

© European Biophysical Societies' Association 2019

Authors and Affiliations

  1. 1.Departamento de Física, Facultad de CienciasUniversidad de TarapacáAricaChile
  2. 2.Laboratorio de Ciencia PlanetariaUniversidad Central “Marta Abreu” de las VillasSanta ClaraCuba
  3. 3.Escuela de Enfermería, Pontificia Universidad Católica del Ecuador Sede Esmeraldas (PUCESE)EsmeraldasEcuador

Personalised recommendations