Mathematical modelling of molecule evolution in protocells

Dariusz Myszor; Krzysztof A. Cyran

International Journal of Applied Mathematics and Computer Science (2013)

  • Volume: 23, Issue: 1, page 213-229
  • ISSN: 1641-876X

Abstract

top
In this article, we analyse the process of the emergence of RNA polynucleotides located in an enclosed environment, at an early stage of the RNA world. Therefore we prepared a mathematical model, composed of a set of differential equations, which simulates the behaviour of an early biological system bounded by a protocell membrane. There is evidence that enclosed environments were available on the primordial Earth. There are also experimental proofs that RNA strands can develop in these formations. The proposed model allows analysis of the influence of membrane permeability on the composition of internal material. It takes into account phenomena that lead to the elongation of an RNA strand (ligation), fission of molecules (phosphodiester bond breakage) and replication of polynucleotides. Results obtained from the model point out that the existence of protocells might support concentration of material and creation of longer molecules.

How to cite

top

Dariusz Myszor, and Krzysztof A. Cyran. "Mathematical modelling of molecule evolution in protocells." International Journal of Applied Mathematics and Computer Science 23.1 (2013): 213-229. <http://eudml.org/doc/251296>.

@article{DariuszMyszor2013,
abstract = {In this article, we analyse the process of the emergence of RNA polynucleotides located in an enclosed environment, at an early stage of the RNA world. Therefore we prepared a mathematical model, composed of a set of differential equations, which simulates the behaviour of an early biological system bounded by a protocell membrane. There is evidence that enclosed environments were available on the primordial Earth. There are also experimental proofs that RNA strands can develop in these formations. The proposed model allows analysis of the influence of membrane permeability on the composition of internal material. It takes into account phenomena that lead to the elongation of an RNA strand (ligation), fission of molecules (phosphodiester bond breakage) and replication of polynucleotides. Results obtained from the model point out that the existence of protocells might support concentration of material and creation of longer molecules.},
author = {Dariusz Myszor, Krzysztof A. Cyran},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {RNA world; proto-cell; mathematical model; protocell; mathematical modeling},
language = {eng},
number = {1},
pages = {213-229},
title = {Mathematical modelling of molecule evolution in protocells},
url = {http://eudml.org/doc/251296},
volume = {23},
year = {2013},
}

TY - JOUR
AU - Dariusz Myszor
AU - Krzysztof A. Cyran
TI - Mathematical modelling of molecule evolution in protocells
JO - International Journal of Applied Mathematics and Computer Science
PY - 2013
VL - 23
IS - 1
SP - 213
EP - 229
AB - In this article, we analyse the process of the emergence of RNA polynucleotides located in an enclosed environment, at an early stage of the RNA world. Therefore we prepared a mathematical model, composed of a set of differential equations, which simulates the behaviour of an early biological system bounded by a protocell membrane. There is evidence that enclosed environments were available on the primordial Earth. There are also experimental proofs that RNA strands can develop in these formations. The proposed model allows analysis of the influence of membrane permeability on the composition of internal material. It takes into account phenomena that lead to the elongation of an RNA strand (ligation), fission of molecules (phosphodiester bond breakage) and replication of polynucleotides. Results obtained from the model point out that the existence of protocells might support concentration of material and creation of longer molecules.
LA - eng
KW - RNA world; proto-cell; mathematical model; protocell; mathematical modeling
UR - http://eudml.org/doc/251296
ER -

References

top
  1. Breaker, R.R. (2010). Riboswitches and the RNA world, Cold Spring Harbor Perspectives in Biology 4(2): 1-15. 
  2. Cary, S.C., Shank, T. and Stein, J. (1998). Worms bask in extreme temperatures, Nature 391(6667): 545-546. 
  3. Cech, T. and Golden, B. (1999). Building a catalytic active site using only RNA, in R.F. Gesteland, T.R. Cech and J.F. Atkins (Eds.), The RNA World, 2nd Edn., Cold Spring Harbor Laboratory Press, New York, NY, Vol. 37, pp. 321-349. 
  4. Chen, I.A., Roberts, R.W. and Szostak, J.W. (2004). The emergence of competition between model protocells, Science 305(5689): 1474-1476. 
  5. Chen, I.A. and Walde, P. (2010). From self-assembled vesicles to protocells, Cold Spring Harbor Perspectives in Biology 2(7): 1-13. 
  6. Chen, I., Hanczyc, M., Sazani, P. and Szostak, J. (2006). Protocells: Genetic polymers inside membrane vesicles, in I.A. Chen, M.M. Hanczyc, P.L. Sazani and J.W. Szostak (Eds.), The RNA World, 3rd Edn., Cold Spring Harbor Laboratory Press, New York, NY, Vol. 43, pp. 57-88. 
  7. Cyran, K.A. (2009). Information amount threshold in self-replicating RNA-protospecies: Branching processes approach, International Journal of Mathematics and Computers in Sumulation 3(1): 20-29. 
  8. De Lucrezia, D., Anella, F. and Chiarabelli, C. (2007). Question 5: On the chemical reality of the RNA world, Origins of Life and Evolution of Biospheres 37(4): 379-385. 
  9. Deamer, D. (2008). Experimental approaches to fabricating artificial cellular life, in S. Rasmussen (Ed.), Protocells: From Bridging Nonliving and Living Matter, MIT Press, Cambridge, MA, pp. 19-38. 
  10. Deamer, D.W. (1985). Boundary structures are formed by organic components of the Murchison carbonaceous chondrite, Nature 317(6040): 792-794. 
  11. Deamer, D.W. and Pashley, R.M. (1989). Amphiphilic components of the murchison carbonaceous chondrite: Surface properties and membrane formation, Origins of Life and Evolution of Biospheres 19(1): 21-38. 
  12. Dobson, C.M., Ellison, G.B., Tuck, A.F. and Vaida, V. (2000). Atmospheric aerosols as prebiotic chemical reactors, Proceedings of the National Academy of Sciences 97(22): 11864-11868. 
  13. Ertem, G. (2004). Montmorillonite, oligonucleotides, RNA and origin of life, Origins of Life and Evolution of the Biosphere 34(6): 549-570. 
  14. Feig, A. and Uhlenbeck, O. (1999). The role of metal ions in RNA biochemistry, in R.F. Gesteland, T.R. Cech and J.F. Atkins (Eds.), The RNA World, 2 nd Edn., Cold Spring Harbor Laboratory Press, New York, NY, pp. 287-319. 
  15. Ferris, J.P. (2005). Mineral catalysis and prebiotic synthesis: Montmorillonite-catalyzed formation of RNA, Elements 1(3): 145-149. 
  16. Ferris, J.P. (2006). Montmorillonite-catalysed formation of RNA oligomers: The possible role of catalysis in the origins of life, Philosophical Transactions of the Royal Society, B: Biological Sciences 361(1474): 1777-1786. 
  17. Ferris, J.P., Hill, A.R., Liu, R. and Orgel, L.E. (1996). Synthesis of long prebiotic oligomers on mineral surfaces, Nature 381(6577): 59-61. 
  18. Fishkis, M. (2007). Steps towards the formation of a protocell: The possible role of short peptides, Origins of Life and Evolution of Biospheres 37(6): 537-553. 
  19. Fishkis, M. (2010). Emergence of self-reproduction in cooperative chemical evolution of prebiological molecules, Origins of Life and Evolution of the Biosphere 41(3): 261-275. 
  20. Gaucher, E.A., Kratzer, J.T. and Randall, R.N. (2010). Deep phylogeny: How a tree can help characterize early life on earth, Cold Spring Harbor Perspectives in Biology 2(1): 1-16. 
  21. Gilbert, W. (1986). The RNA world, Nature 319(6055): 618. 
  22. Hanczyc, M.M., Fujikawa, S.M. and Szostak, J.W. (2003). Experimental models of primitive cellular compartments: Encapsulation, growth, and division, Science 302(5645): 618-622. 
  23. Joyce, G.F. (2002). The antiquity of RNA-based evolution, Nature 418(6894): 214-221. 
  24. Joyce, G. and Orgel, L. (1999). Prospects for understanding the origin of the rna world, in R.F. Gesteland, T.R. Cech and J.F. Atkins (Eds.), The RNA World, 2nd Edn., Cold Spring Harbor Laboratory Press, New York, NY, Vol. 37, pp. 49-77. 
  25. Kimmel, M. and Axelrod, D. (2002). Branching Processes in Biology, Springer-Verlag, New York, NY. Zbl0994.92001
  26. Koshland, D.E. (2002). The seven pillars of life, Science 295(5563): 2215-2216. 
  27. Lazcano, A. (2010). Historical development of origins research, Cold Spring Harbor Perspectives in Biology 2(11): 1-16. 
  28. Luisi, P. (2010). The Emergence of Life: From Chemical Origins to Synthetic Biology, Cambridge University Press, New York, NY. 
  29. Lunine, J.I. (2006). Physical conditions on the early Earth, Philosophical Transactions of the Royal Society, B: Biological Sciences 361(1474): 1721-1731. 
  30. Ma, W., Yu, C. and Zhang, W. (2007). Monte Carlo simulation of early molecular evolution in the RNA World, Biosystems 90(1): 28-39. 
  31. Manapat, M., Ohtsuki, H., Bürger, R. and Nowak, M.A.A. (2009). Originator dynamics, Journal of Theoretical Biology 256(4): 586-595. 
  32. Matsuura, T., Yamaguchi, M., Ko-Mitamura, E.P., Shima, Y., Urabe, I. and Yomo, T. (2002). Importance of compartment formation for a self-encoding system, Proceedings of the National Academy of Sciences 99(11): 7514-7517. 
  33. Mojzsis, S., Krishnamurthy, R. and Arrhenius, G. (1999). Before RNA and after: Geophysical and geochemical constraints on molecular evolution, in R.F. Gesteland, T.R. Cech and J.F. Atkins (Eds.), The RNA World, 2nd Edn., Cold Spring Harbor Laboratory Press, New York, NY, pp. 1-47. 
  34. Myszor, D. and Cyran, K.A. (2009). Estimation of the number of primordial genes in a compartment model of RNA world, in K.A. Cyran, S. Kozielski, J.F. Peters, U. Stańczyk and A. Wakulicz-Deja (Eds.), Man-Machine Interactions, Advances in Intelligent and Soft Computing, Vol. 59, Springer, Berlin/Heidelberg, Chapter 15, pp. 151-161. Zbl1182.92008
  35. Myszor, D. and Cyran, K.A. (2010). Influence of non-enzymatic template-directed RNA recombination processes on polynucleotides lengths in Monte Carlo simulation model of the RNA world, International Journal of Applied Mathematics and Informatics 4(1): 1-8. 
  36. Niesert, U. (1987). How many genes to start with? A computer simulation about the origin of life, Origins of Life and Evolution of the Biosphere 17(2): 155-169. 
  37. Noller, H.F. (2006). Evolution of ribosomes and translation from an RNA world, in I.A. Chen, M.M. Hanczyc, P.L. Sazani and J.W. Szostak (Eds.), The RNA World, 3rd Edn., Cold Spring Harbor Laboratory Press, New York, NY, Vol. 43, pp. 287-307. 
  38. Nowak, M. A. and Ohtsuki, H. (2008). Prevolutionary dynamics and the origin of evolution, Proceedings of the National Academy of Sciences 105(39): 14924-14927. 
  39. Ohtsuki, H. and Nowak, M. A. (2009). Prelife catalysts and replicators, Proceedings of the Royal Society, B: Biological Sciences 276(1674): 3783-3790. 
  40. Pohorille, A. and Deamer, D. (2002). Artificial cells: Prospects for biotechnology, Trends in Biotechnology 20(3): 123-128. 
  41. Pohorille, A. and Deamer, D. (2009). Self-assembly and function of primitive cell membranes, Research in Microbiology 160(7): 449-456. 
  42. Rasmussen, S., Bedau, M.A., Chen, L., Deamer, D., Krakauer, D.C., Packard, N.H. and Stadler, P.F. (2008). Protocells: Bridging Nonliving and Living Matter, Vol. 8, MIT Press, Cambridge, MA. 
  43. Schleper, C., Piihler, G., Kuhlmorgen, B. and Zillig, W. (1995). Life at extremely low pH, Nature 375(6534): 741-742. 
  44. Schrum, J.P., Zhu, T.F. and Szostak, J.W. (2010). The origins of cellular life, Cold Spring Harbor Perspectives in Biology 2(9): a002212. 
  45. Sleep, N.H. (2010). The Hadean-Archaean environment, Cold Spring Harbor Perspectives in Biology 2(6): 1-14. 
  46. Stetter, K.O. (2007). Hyperthermophilic life on Earth-and on Mars?, in R. Pudritz, P. Higgs and J. Stone (Eds.), Planetary Systems and the Origins of Life, Cambridge University Press, New York, NY, pp. 135-147. 
  47. Sutherland, J.D. (2010). Ribonucleotides, Cold Spring Harbor Perspectives in Biology 2(4):1-13. 
  48. Szabó, P., Scheuring, I., Czárán, T. and Szathmáry, E. (2002). In silico simulations reveal that replicators with limited dispersal evolve towards higher efficiency and fidelity, Nature 420(6913): 340-343. 
  49. Szostak, J.W., Bartel, D.P. and Luisi, P.L. (2001). Synthesizing life, Nature 409(6818): 387-390. 
  50. Wieczorek, R. (2010). Markov chain model of phytoplankton dynamics, International Journal of Applied Mathematics and Computer Science 20(4): 763-771, DOI: 10.2478/v10006-010-0058-7. Zbl05869750
  51. Woese, C.R. (1968). Genetic Code, Harper & Row, New York, NY. 
  52. Xu, C., Liao, M. and He, X. (2011). Stability and Hopf bifurcation analysis for a Lotka-Volterra predator-prey model with two delays, International Journal of Applied Mathematics and Computer Science 21(1): 97-107, DOI: 10.2478/v10006-011-0007-0. Zbl1231.34151
  53. Zahnle, K., Schaefer, L. and Fegley, B. (2010). Earth's earliest atmospheres, Cold Spring Harbor Perspectives in Biology 2(10): 1-17. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.