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Modeling Phage–Bacteria Dynamics

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Immunoinformatics

Part of the book series: Methods in Molecular Biology ((MIMB,volume 2131))

Abstract

Phage–bacteria interaction is a classic example of competitive coevolution in nature. Mathematical modeling of such interactions furnishes new insight into the dynamics of phage and bacteria. Besides its intrinsic value, a somewhat underutilized aspect of such insight is that it can provide beneficial inputs toward better experimental design. In this chapter, we discuss several modeling techniques that can be used to study the dynamics between phages and their host bacteria. Monte Carlo simulations and differential equations (both ordinary and delay differential equations) can be used to successfully model phage–bacteria dynamics in well-mixed populations. The presence of spatial restrictions in the interaction media significantly affects the dynamics of phage–bacteria interactions. For such cases, techniques like cellular automata and reaction–diffusion equations can be used to capture these effects adequately. We discuss details of the modeling techniques with specific examples.

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References

  1. Calendar R (ed) (2012) The bacteriophages, vol 1. Springer, Berlin

    Google Scholar 

  2. Maurice CF, Bouvier CD, De Wit R et al (2013) Linking the lytic and lysogenic bacteriophage cycles to environmental conditions, host physiology and their variability in coastal lagoons. Environ Microbiol 15:2463–2475

    Article  CAS  Google Scholar 

  3. Hendrix RW (2002) Bacteriophages: evolution of the majority. Theor Pop Biol 61:471–480

    Article  Google Scholar 

  4. Gomez P, Buckling A (2011) Phage-bacteria antagonistic coevolution in soil. Science 332:106–109

    Article  CAS  Google Scholar 

  5. Weitz JS, Hartman H, Levin SA (2005) Coevolutionary arms races between bacteria and bacteriophage. Proc Natl Acad Sci U S A 102:9535–9540

    Article  CAS  Google Scholar 

  6. Sinha S, Grewal RK, Roy S (2018) Modelling Bacteria–Phage Interactions and Its Implications for Phage Therapy. Adv Appl Microbiol 103:103–141

    Article  Google Scholar 

  7. Lenski RE (1988) Dynamics of interactions between bacteria and virulent bacteriophage. In: Advances in microbial ecology. Springer, Boston, MA, pp 1–44

    Google Scholar 

  8. Manly BF (2018) Randomization, bootstrap and Monte Carlo methods in biology. Chapman and Hall/CRC, London

    Google Scholar 

  9. Rothfield L, Justice S, Garcia-Lara J (1999) Bacterial cell division. Ann Rev Genet 33:423–448

    Article  CAS  Google Scholar 

  10. Moldovan R, Chapman-McQuiston E, Wu XL (2007) On kinetics of phage adsorption. Biophys J 93:303–315

    Article  CAS  Google Scholar 

  11. Flunkert V, Schoell E (2009) Pydelay-a python tool for solving delay differential equations arXiv preprint arXiv:0911.1633

    Google Scholar 

  12. Thompson S, Shampine LF (2006) A friendly Fortran DDE solver. Appl Numer Math 56:503–516

    Article  Google Scholar 

  13. Campbell A (1961) Conditions for the existence of bacteriophage. Evolution 15:153–165

    Article  Google Scholar 

  14. Abedon ST, Culler RR (2007) Optimizing bacteriophage plaque fecundity. J Theor Biol 249:582–592

    Article  CAS  Google Scholar 

  15. Koch AL (1964) The growth of viral plaques during the enlargement phase. J Theor Biol 6:413–431

    Article  CAS  Google Scholar 

  16. Yin J, McCaskill JS (1992) Replication of viruses in a growing plaque: a reaction-diffusion model. Biophys J 61:1540–1549

    Article  CAS  Google Scholar 

  17. Fort J, Mendez V (2002) Time-delayed spread of viruses in growing plaques. Phys Rev Lett 89:178101

    Article  Google Scholar 

  18. Ermentrout GB, Edelstein-Keshet L (1993) Cellular automata approaches to biological modelling. J Theor Biol 160:97–133

    Article  CAS  Google Scholar 

  19. Samaddar S et al (2016) Dynamics of mycobacteriophage-mycobacterial host interaction: evidence for secondary mechanisms for host lethality. Appl Environ Microbiol 82:124–133

    Article  CAS  Google Scholar 

  20. Bremermann HJ (1983) Parasites at the origin of life. J Math Biol 16:165–180

    Article  CAS  Google Scholar 

  21. Payne RJH, Jansen VAA (2001) Understanding bacteriophage therapy as a density-dependent kinetic process. J Theor Biol 208:37–48

    Article  CAS  Google Scholar 

  22. Smith HL, Trevino RT (2009) Bacteriophage infection dynamics: multiple host binding sites. Math Model Nat Phenom 4:111–136

    Article  Google Scholar 

  23. Wang X, Wang J (2017) Modelling the within-host dynamics of cholera: bacterial–viral interaction. J Biol Dyn 11:484–501

    Article  Google Scholar 

  24. Holguin AV et al (2019) Host resistance, genomics and population dynamics in a salmonella enteritidis and phage system. Viruses 11:188

    Article  CAS  Google Scholar 

  25. Levin BR, Stewart FM, Chao L (1977) Resource-limited growth, competition and predation: a model and experimental studies with bacteria and bacteriophage. Am Nat 111:3–24

    Article  Google Scholar 

  26. Lenski RE, Levin BR (1985) Constraints on the coevolution of bacteria and virulent phage: a model, some experiments, and predictions for natural communities. Am Nat 125:585–602

    Article  Google Scholar 

  27. Chapman-McQuiston E, Wu XL (2008) Stochastic receptor expression allows sensitive bacteria to evade phage attack. Part II: theoretical analyses. Biophys J 94:4537–4548

    Article  CAS  Google Scholar 

  28. Cairns BJ et al (2009) Quantitative models of in vitro bacteriophage-host dynamics and their application to phage therapy. PLoS Pathog 5(1):e1000253

    Article  Google Scholar 

  29. Han Z, Smith HL (2012) Bacteriophage-resistant and Bacteriophage-sensitive bacteria in a chemostat. Math Biosci Eng 9:737–765

    Article  Google Scholar 

  30. Da K et al (1981) Appendix: a model of plaque formation. Gene 13:221–225

    Article  Google Scholar 

  31. Lee Y, Eisner SD, Yin J (1997) Antiserum inhibition of propagating viruses. Biotechnol Bioeng 55:542–546

    Article  CAS  Google Scholar 

  32. You L, Yin J (1999) Amplification and spread of viruses in a growing plaque. J Theor Biol 200:365–373

    Article  CAS  Google Scholar 

  33. Ortega-Cejas V et al (2004) Approximate solution to the speed of spreading viruses. Phys Rev E 031909:69

    Google Scholar 

  34. Gourley SA, Kuang Y (2005) A delay reaction-diffusion model of the spread of bacteriophage infection. SIAM J Appl Math 65:550–566

    Article  Google Scholar 

  35. Jones DA, Smith HL (2011) Bacteriophage and Bacteria in a flow reactor. Bull Math Biol 73:2357–2383

    Article  Google Scholar 

  36. Mitarai N, Brown S, Sneppen K (2016) Population dynamics of phage and bacteria in spatially structured habitats using phage and Escherichia coli. J Bacteriol 198:1783–1793

    Article  CAS  Google Scholar 

  37. Simmons M et al (2018) Phage mobility is a core determinant of phage–bacteria coexistence in biofilms. ISME J 12:531

    Article  Google Scholar 

  38. Kerr B et al (2006) Local migration promotes competitive restraint in a host–pathogen ‘tragedy of the commons’. Nature 442:75

    Article  CAS  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, Bose Institute, Kolkata, India

    Saptarshi Sinha, Rajdeep Kaur Grewal & Soumen Roy

Authors
  1. Saptarshi Sinha
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  2. Rajdeep Kaur Grewal
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  3. Soumen Roy
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Corresponding author

Correspondence to Soumen Roy .

Editor information

Editors and Affiliations

  1. Department of BioMedical Engineering, Medical College of Wisconsin, Milwaukee, WI, USA

    Namrata Tomar

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Sinha, S., Grewal, R.K., Roy, S. (2020). Modeling Phage–Bacteria Dynamics. In: Tomar, N. (eds) Immunoinformatics. Methods in Molecular Biology, vol 2131. Humana, New York, NY. https://doi.org/10.1007/978-1-0716-0389-5_18

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  • DOI: https://doi.org/10.1007/978-1-0716-0389-5_18

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  • Publisher Name: Humana, New York, NY

  • Print ISBN: 978-1-0716-0388-8

  • Online ISBN: 978-1-0716-0389-5

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