Skip to main content
SpringerLink
Log in

Computer Simulation of the Evolution of Microbial Population: Overcoming Local Minima When Reaching a Peak on the Fitness Landscape

  • MATHEMATICAL MODELS AND METHODS
  • Published:
Russian Journal of Genetics Aims and scope Submit manuscript

Abstract

The study focuses on the mechanisms of crossing the valleys of fitness by a population of haploid microorganisms, whose fitness depends on allelic values at two different loci and is determined by a complex landscape, the shape of which corresponds to the pattern “a mountain in the field surrounded by a trench”; these mechanisms are analyzed using computer modeling. We have studied the influence of various biological factors on the evolutionary perspective of microbial colonies, the reproduction rate of which is controlled by a protein consisting of two subunits encoded at different loci. Molecular genetic (mutation rate, affinity of subunits), population (fitness function landscape and population density), and ecological (concentration of available substrate in the habitat, flow intensity) factors have been considered. Our results demonstrate that the difference in fitness for various allelic combinations, while determining the shape of the fitness landscape, sets the optimal mutation rates to overcome its valleys and opens a window of opportunity for the evolution of the population toward the state of the highest average fitness. Moreover, depending on the fitness landscape type, either gradual or saltational evolutionary regimes are optimal for reaching the peak.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.

Similar content being viewed by others

REFERENCES

  1. Epistasis, Moore, J.H. and Williams, S.M., Eds., New York: Springer-Verlag, 2015, vol. 1253. https://doi.org/10.1007/978-1-4939-2155-3

    Google Scholar 

  2. Kimura, M., The role of compensatory neutral mutations in molecular evolution, J. Genet., 1985, vol. 64, no. 1, pp. 7—19. https://doi.org/10.1007/BF02923549

    Article  CAS  Google Scholar 

  3. Wright, S., Evolution and the Genetics of Population, vol. 3: Experimental Results and Evolutionary Deductions, Chicago: University of Chicago Press, 1984.

    Google Scholar 

  4. Whitlock, M.C., Phillips, P.C., Moore, F.B.-G., and Tonsor, S.J., Multiple fitness peaks and epistasis, Annu. Rev. Ecol. Syst., 1995, vol. 26, pp. 601—629.

    Article  Google Scholar 

  5. Altukhov, Yu.P., Geneticheskie protsessy v populyatsiyakh (Genetic Processes in Populations), Moscow: Akademkniga, 2003, 3rd ed.

  6. Kuchner, O. and Arnold, F.H., Directed evolution of enzyme catalysts, Trends Biotechnol., 1997, vol. 15, no. 12, pp. 523—530. https://doi.org/10.1016/S0167-7799(97)01138-4

    Article  CAS  PubMed  Google Scholar 

  7. Gatenby, R.A. and Vincent, T.L., Application of quantitative models from population biology and evolutionary game theory to tumor therapeutic strategies, Mol. Cancer Ther., 2003, vol. 2, no. 9, pp. 919—927.

    CAS  PubMed  Google Scholar 

  8. Turelli, M., Barton, N.H., and Coyne, J.A., Theory and speciation, Trends Ecol. Evol., 2001, vol. 16, no. 7, pp. 330—343. https://doi.org/10.1016/S0169-5347(01)02177-2

    Article  CAS  PubMed  Google Scholar 

  9. Domingo, E. and Holland, J.J., RNA virus mutations and fitness for survival, Annu. Rev. Microbiol., 1997, vol. 51, no. 1, pp. 151—178. https://doi.org/10.1146/annurev.micro.51.1.151

    Article  CAS  PubMed  Google Scholar 

  10. Szendro, I.G., Schenk, M.F., Franke, J. et al., Quantitative analyses of empirical fitness landscapes, J. Stat. Mech. Theory Exp., 2013, vol. 2013, no. 1, p. P01005. https://doi.org/10.1088/1742-5468/2013/01/P01005

    Article  Google Scholar 

  11. Meer, M.V., Kondrashov, A.S., Artzy-Randrup, Y., and Kondrashov, F.A., Compensatory evolution in mitochondrial tRNAs navigates valleys of low fitness, Nature, 2010, vol. 464, no. 7286, pp. 279—282. https://doi.org/10.1038/nature08691

    Article  CAS  PubMed  Google Scholar 

  12. Mackay, T.F.C., Epistasis and quantitative traits: using model organisms to study gene—gene interactions, Nat. Rev. Genet., 2013, vol. 15, no. 1, pp. 22—33. https://doi.org/10.1038/nrg3627

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  13. Handel, A. and Rozen, D.E., The impact of population size on the evolution of asexual microbes on smooth versus rugged fitness landscapes, BMC Evol. Biol., 2009, vol. 9, no. 1, p. 236. https://doi.org/10.1186/1471-2148-9-236

    Article  PubMed  PubMed Central  Google Scholar 

  14. Whitlock, M.C., Griswold, C.K., and Peters, A.D., Compensating for the meltdown: the critical effective size of a population with deleterious and compensatory mutations, Ann. Zool. Fennici, 2003, vol. 40, no. 2, pp. 169—183.

    Google Scholar 

  15. Szendro, I.G., Franke, J., de Visser, J.A.G.M., and Krug, J., Predictability of evolution depends nonmonotonically on population size, Proc. Natl. Acad. Sci. U.S.A., 2013, vol. 110, no. 2, pp. 571—576. https://doi.org/10.1073/pnas.1213613110

    Article  PubMed  Google Scholar 

  16. Gokhale, C.S., Iwasa, Y., Nowak, M.A., and Traulsen, A., The pace of evolution across fitness valleys, J. Theor. Biol., 2009, vol. 259, no. 3, pp. 613—620. https://doi.org/10.1016/j.jtbi.2009.04.011

    Article  PubMed  PubMed Central  Google Scholar 

  17. Weissman, D.B., Feldman, M.W., and Fisher, D.S., The rate of fitness-valley crossing in sexual populations, Genetics, 2010, vol. 186, no. 4, pp. 1389—1410. https://doi.org/10.1534/genetics.110.123240

    Article  PubMed  PubMed Central  Google Scholar 

  18. Weissman, D.B., Desai, M.M., Fisher, D., and Feldman, M.W., The rate at which asexual populations cross fitness valleys, Theor. Popul. Biol., 2009, vol. 75, no. 4, pp. 286—300. https://doi.org/10.1016/j.tpb.2009.02.006

    Article  PubMed  PubMed Central  Google Scholar 

  19. Haarsma, L.L., Nelesen, S., VanAndel, E., et al., Simulating evolution of protein complexes through gene duplication and co-option, J. Theor. Biol., 2016, vol. 399, pp. 22—32. https://doi.org/10.1016/j.jtbi.2016.03.028

    Article  CAS  PubMed  Google Scholar 

  20. Aita, T. and Husimi, Y., Fitness spectrum among random mutants on Mt. Fuji-type fitness landscape, J. Theor. Biol., 1996, vol. 182, no. 4, pp. 469—485. https://doi.org/10.1006/jtbi.1996.0189

    Article  CAS  PubMed  Google Scholar 

  21. Iordanskii, N.N., Evolyutsiya zhizni (The Evolution of Life), Moscow: Akademia, 2001.

  22. Lashin, S.A., Suslov, V.V., and Matushkin, Y.G., Theories of biological evolution from the viewpoint of the modern systemic biology, Russ. J. Genet., 2012, vol. 48, no. 5, pp. 481— 496. https://doi.org/10.1134/S1022795412030064

    Article  CAS  Google Scholar 

  23. Afonnikov, D.A., Oshchepkov, D.Y., and Kolchanov, N.A., Detection of conserved physico-chemical characteristics of proteins by analyzing clusters of positions with co-ordinated substitutions, Bioinformatics, 2001, vol. 17, no. 11, pp. 1035—1046. https://doi.org/10.1093/bioinformatics/17.11.1035

    Article  CAS  PubMed  Google Scholar 

  24. Dayhoff, M.O., Schwartz, R.M., and Orcutt, B.C., A model of evolutionary change in proteins, Atlas of Protein Sequence and Structure, vol. 5, suppl. 3, Dayhoff, M.O., Ed., Washington, DC: Natl. Biomed. Res. Found., 1978, pp. 345—352.

  25. Ewens, W., Mathematical Population Genetics: 1. Theoretical Introduction, New York: Springer-Verlag, 2004. https://doi.org/10.1007/978-0-387-21822-9

    Book  Google Scholar 

  26. Drake, J.W., Charlesworth, B., Charlesworth, D., and Crow, J.F., Rates of spontaneous mutation, Genetics, 1998, vol. 148, no. 4, pp. 1667—1686.

    CAS  PubMed  PubMed Central  Google Scholar 

  27. Lynch, M., Evolution of the mutation rate, Trends Genet., 2010, vol. 26, no. 8, pp. 345—352. https://doi.org/10.1016/j.tig.2010.05.003

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  28. Markel’, A.L., Stress and evolution, Russ. J. Genet. Appl. Res., 2008, vol. 12, nos. 1—2, pp. 206—215.

  29. Foster, P.L., Stress responses and genetic variation in bacteria, Mutat. Res. Mol. Mech. Mutagen., 2005, vol. 569, nos. 1—2, pp. 3—11. https://doi.org/10.1016/j.mrfmmm.2004.07.017

    Article  CAS  Google Scholar 

  30. Hoffmann, A.A. and Hercus, M.J., Environmental stress as an evolutionary force, Bioscience, 2000, vol. 50, no. 3, p. 217. https://doi.org/10.1641/0006-3568(2000)050[0217:ESAAEF]2.3.CO;2

    Article  Google Scholar 

  31. Korogodin, V.I., Korogodina, V.L., Fajszi, C., et al., On the dependence of spontaneous mutation rates on the functional state of genes, Yeast, 1991, vol. 7, no. 2, pp. 105—117. https://doi.org/10.1002/yea.320070204

    Article  CAS  PubMed  Google Scholar 

  32. Il’ina, V.L., Korogodin, V.I., and Fajszi, C., Dependence of spontaneous reversion frequencies in adenin auxotrophic yeasts on the concentration of adenine in the medium, Genetika (Moscow), 1987, vol. 23, no. 4, pp. 637—642.

    PubMed  Google Scholar 

  33. Lashin, S.A., and Matushkin, Y.G., Haploid evolutionary constructor: new features and further challenges, In Silico Biol., 2012, vol. 11, nos. 3—4, pp. 125—135. https://doi.org/10.3233/ISB-2012-0447

    Article  Google Scholar 

  34. Lashin, S.A., Klimenko, A. I., Mustafin, Z.S., et al., HEC 2.0: improved simulation of the evolution of prokaryotic communities, Math. Biol. Bioinf., 2014, vol. 9, no. 2, pp. 585—596. https://doi.org/10.17537/2014.9.585

    Article  Google Scholar 

  35. Lashin, S.A., Suslov, V.V., and Matushkin, Y.G., Comparative modeling of coevolution in communities of unicellular organisms: adaptability and biodiversity, J. Bioinf. Comput. Biol., 2010, vol. 08, no. 03, pp. 627—643. https://doi.org/10.1142/S0219720010004653

    Article  CAS  Google Scholar 

  36. Lashin, S.A., Matushkin, Yu.G., Suslov, V.V., and Kolchanov, N.A., Evolutionary trends in the prokaryotic community and prokaryotic community-phage systems, Russ. J. Genet., 2011, vol. 47, no. 12, pp. 1487—1495. https://doi.org/10.1134/S1022795411110123

    Article  CAS  Google Scholar 

  37. Klimenko, A.I., Matushkin, Yu.G., Kolchanov, N.A., and Lashin, S.A., Bacteriophages affect evolution of bacterial communities in spatially distributed habitats: a simulation study, BMC Microbiol., 2016, vol. 16, no. S1, p. S10. https://doi.org/10.1186/s12866-015-0620-4

    Article  CAS  Google Scholar 

  38. Lashin, S.A., Matushkin, Yu.G., Suslov, V.V., and Kolchanov, N.A., Computer modeling of genome complexity variation trends in prokaryotic communities under varying habitat conditions, Ecol. Modell., 2012, vol. 224, no. 1, pp. 124—129. https://doi.org/10.1016/j.ecolmodel.2011.11.004

    Article  Google Scholar 

  39. Klimenko, A.I., Matushkin, Yu.G., Kolchanov, N.A., and Lashin, S.A., Modeling evolution of spatially distributed bacterial communities : a simulation with the haploid evolutionary constructor, BMC Evol. Biol., 2015, vol. 15, p. S3. https://doi.org/10.1186/1471-2148-15-S1-S3

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  40. Wilke, C., Dynamic fitness landscapes in molecular evolution, Phys. Rep., 2001, vol. 349, no. 5, pp. 395—446. https://doi.org/10.1016/S0370-1573(00)00118-6

    Article  CAS  Google Scholar 

  41. Kawashima, S., Pokarowski, P., Pokarowska, M., et al., AAindex: amino acid index database, progress report 2008, Nucleic Acids Res., 2007, vol. 36, database issue, pp. D202—D205. https://doi.org/10.1093/nar/gkm998

    Article  Google Scholar 

Download references

Funding

This study was supported by budget project no. 0324-2019-0040.

Author information

Authors and Affiliations

  1. Institute of Cytology and Genetics, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    S. A. Lashin, Z. S. Mustafin, A. I. Klimenko, D. A. Afonnikov & Yu. G. Matushkin

  2. Department of Information Biology, Novosibirsk State University, 630090, Novosibirsk, Russia

    S. A. Lashin, D. A. Afonnikov & Yu. G. Matushkin

Authors
  1. S. A. Lashin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Z. S. Mustafin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. I. Klimenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. D. A. Afonnikov
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yu. G. Matushkin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. A. Lashin.

Ethics declarations

The authors declare that they have no conflict of interest. This article does not contain any studies involving animals or human participants performed by any of the authors.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lashin, S.A., Mustafin, Z.S., Klimenko, A.I. et al. Computer Simulation of the Evolution of Microbial Population: Overcoming Local Minima When Reaching a Peak on the Fitness Landscape. Russ J Genet 56, 242–252 (2020). https://doi.org/10.1134/S1022795420020076

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1022795420020076

Keywords:

Search

Navigation