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Computational and Mathematical Methods in Medicine
Volume 2012 (2012), Article ID 784512, 17 pages
http://dx.doi.org/10.1155/2012/784512
Research Article

Immune Response to a Variable Pathogen: A Stochastic Model with Two Interlocked Darwinian Entities

Biomedical Optics Research Laboratory, Clinic of Neonatology, University Hospital Zürich, Frauenklinikstrasse 10, CH-8091 Zürich, Switzerland

Received 4 January 2012; Revised 13 April 2012; Accepted 28 June 2012

Academic Editor: Zvia Agur

Copyright © 2012 Christoph Kuhn. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. C. Janeway, M. J. Shlomchik, M. Walport, and P. Travers, Immunobiology, Garland, 2004.
  2. D. Wodarz, “Evolution of immunological memory and the regulation of competition between pathogens,” Current Biology, vol. 13, no. 18, pp. 1648–1652, 2003. View at Publisher · View at Google Scholar · View at Scopus
  3. M. A. Nowak and C. R. M. Bangham, “Population dynamics of immune responses to persistent viruses,” Science, vol. 272, no. 5258, pp. 74–79, 1996. View at Scopus
  4. D. Wodarz, P. Klenerman, and M. A. Nowak, “Dynamics of cytotoxic T-lymphocyte exhaustion,” Proceedings of the Royal Society B, vol. 265, no. 1392, pp. 191–203, 1998. View at Publisher · View at Google Scholar · View at Scopus
  5. M. A. Nowak, “Immune responses against multiple epitopes: a theory for immunodominance and antigenic variation,” Seminars in Virology, vol. 7, no. 1, pp. 83–92, 1996. View at Publisher · View at Google Scholar · View at Scopus
  6. R. N. Germain, M. Meier-Schellersheim, A. Nita-Lazar, and I. D. C. Fraser, “Systems biology in immunology: a computational modeling perspective,” Annual Review of Immunology, vol. 29, pp. 527–585, 2011. View at Publisher · View at Google Scholar · View at Scopus
  7. C. A. Arias and B. E. Murray, “Antibiotic-resistant bugs in the 21st century—a clinical super-challenge,” The New England Journal of Medicine, vol. 360, no. 5, pp. 439–443, 2009. View at Publisher · View at Google Scholar · View at Scopus
  8. N. K. Jerne, “The natural-selection theory of antibody formation,” PNAS USA, vol. 41, no. 11, pp. 849–857, 1955.
  9. F. M. Burnet, “A modification of Jerne's theory of antibody production using the concept of clonal selection,” Ca-A Cancer Journal for Clinicians, vol. 26, no. 2, pp. 119–121, 1976. View at Publisher · View at Google Scholar · View at Scopus
  10. R. M. Zinkernagel, “Immunology taught by viruses,” Science, vol. 271, no. 5246, pp. 173–178, 1996. View at Scopus
  11. T. S. Gourley, E. J. Wherry, D. Masopust, and R. Ahmed, “Generation and maintenance of immunological memory,” Seminars in Immunology, vol. 16, no. 5, pp. 323–333, 2004. View at Publisher · View at Google Scholar · View at Scopus
  12. M. K. Slifka and R. Ahmed, “Long-term humoral immunity against viruses: revisiting the issue of plasma cell longevity,” Trends in Microbiology, vol. 4, no. 10, pp. 394–400, 1996. View at Publisher · View at Google Scholar · View at Scopus
  13. S. G. Tangye and P. D. Hodgkin, “Divide and conquer: the importance of cell division in regulating B-cell responses,” Immunology, vol. 112, no. 4, pp. 509–520, 2004. View at Publisher · View at Google Scholar · View at Scopus
  14. E. Traggiai, R. Puzone, and A. Lanzavecchia, “Antigen dependent and independent mechanisms that sustain serum antibody levels,” Vaccine, vol. 21, no. 2, pp. S35–S37, 2003. View at Publisher · View at Google Scholar · View at Scopus
  15. G. A. Bocharov, “Modelling the dynamics of LCMV infection in mice: conventional and exhaustive CTL responses,” Journal of Theoretical Biology, vol. 192, no. 3, pp. 283–308, 1998. View at Publisher · View at Google Scholar · View at Scopus
  16. S. Bonhoeffer, H. Mohri, D. Ho, and A. S. Perelson, “Quantification of cell turnover kinetics using 5-bromo-2'-deoxyuridine,” Journal of Immunology, vol. 164, no. 10, pp. 5049–5054, 2000. View at Scopus
  17. F. Celada and P. E. Seiden, “A computer model of cellular interactions in the immune system,” Immunology Today, vol. 13, no. 2, pp. 56–62, 1992. View at Scopus
  18. B. R. Levin, M. Lipsitch, and S. Bonhoeffer, “Population biology, evolution, and infectious disease: convergence and synthesis,” Science, vol. 283, no. 5403, pp. 806–809, 1999. View at Publisher · View at Google Scholar · View at Scopus
  19. A. S. Perelson and G. Weisbuch, “Immunology for physicists,” Reviews of Modern Physics, vol. 69, no. 4, pp. 1219–1267, 1997. View at Scopus
  20. A. S. Perelson, “Modelling viral and immune system dynamics,” Nature Reviews Immunology, vol. 2, no. 1, pp. 28–36, 2002. View at Scopus
  21. G. I. Marchuk, Mathematical Modelling of Immune Response in Infectious Diseases. Mathematics and Its Applications, Springer, Amsterdam, The Netherlands, 1997.
  22. G. A. Bocharov and G. I. Marchuk, “Applied problems of mathematical modeling in immunology,” Computational Mathematics and Mathematical Physics, vol. 40, no. 12, pp. 1830–1844, 2000. View at Scopus
  23. G. I. Marchuk, V. Shutyaev, and G. Bocharov, “Adjoint equations and analysis of complex systems: application to virus infection modelling,” Journal of Computational and Applied Mathematics, vol. 184, no. 1, pp. 177–204, 2005. View at Publisher · View at Google Scholar · View at Scopus
  24. J. R. Gog and B. T. Grenfell, “Dynamics and selection of many-strain pathogens,” Proceedings of the National Academy of Sciences of the United States of America, vol. 99, no. 26, pp. 17209–17214, 2002. View at Publisher · View at Google Scholar · View at Scopus
  25. S. Gupta, M. C. J. Maiden, I. M. Feavers, S. Nee, R. M. May, and R. M. Anderson, “The maintenance of strain structure in populations of recombining infectious agents,” Nature Medicine, vol. 2, no. 4, pp. 437–442, 1996. View at Publisher · View at Google Scholar · View at Scopus
  26. S. Gupta, N. Ferguson, and R. Anderson, “Chaos, persistence, and evolution of strain structure in antigenically diverse infectious agents,” Science, vol. 280, no. 5365, pp. 912–915, 1998. View at Publisher · View at Google Scholar · View at Scopus
  27. S. Gupta and R. M. Anderson, “Population structure of pathogens: the role of immune selection,” Parasitology Today, vol. 15, no. 12, pp. 497–501, 1999. View at Publisher · View at Google Scholar · View at Scopus
  28. N. M. Shnerb, Y. Louzoun, E. Bettelheim, and S. Solomon, “The importance of being discrete: life always wins on the surface,” Proceedings of the National Academy of Sciences of the United States of America, vol. 97, no. 19, pp. 10322–10324, 2000. View at Scopus
  29. Y. Louzoun, S. Solomon, H. Atlan, and I. R. Cohen, “Modeling complexity in biology,” Physica A, vol. 297, no. 1-2, pp. 242–252, 2001. View at Publisher · View at Google Scholar · View at Scopus
  30. Y. Louzoun, S. Solomon, H. Atlan, and I. R. Cohen, “Proliferation and competition in discrete biological systems,” Bulletin of Mathematical Biology, vol. 65, no. 3, pp. 375–396, 2003. View at Publisher · View at Google Scholar · View at Scopus
  31. U. Hershberg, Y. Louzoun, H. Atlan, and S. Solomon, “HIV time hierarchy: winning the war while, loosing all the battles,” Physica A, vol. 289, no. 1-2, pp. 178–190, 2001. View at Publisher · View at Google Scholar · View at Scopus
  32. C. W. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences. Springer Series in Synergetics, Edited by H. Haken, Springer, Berlin, Germany, 2004.
  33. P. Haccou, P. Jagers, and V. A. Vatutin, Branching Processes: Variation, Growth and Extinction of Populations, Cambridge University Press, Cambridge, UK, 2005.
  34. M. Kimmel and D. E. Axelrod, Branching Processes in Biology, Springer, New York, NY, USA, 2002.
  35. L. E. Harnevo and Z. Agur, “The dynamics of gene amplification described as a multitype compartmental model and as a branching process,” Mathematical Biosciences, vol. 103, no. 1, pp. 115–138, 1991. View at Publisher · View at Google Scholar · View at Scopus
  36. A. Swierniak, A. Polanski, J. Śmieja, M. Kimmel, and J. Rzeszowska-Wolny, “Asymptotic analysis of three random branching walk models arising in molecular biology,” Control and Cybernetics, vol. 32, no. 1, pp. 147–161, 2003. View at Scopus
  37. T. E. Harris, The Theory of Branching Processes, Springer, Berlin, Germany, 1963.
  38. K. B. Athreya and P. E. Ney, Branching Processes, Dover, Mineola, NY, USA, 2004.
  39. S. Resnick, Adventures in Stochastic Processes, Birkhäuser, 1992.
  40. M. J. Mackinnon, “Survival probability of drug resistant mutants in malaria parasites,” Proceedings of the Royal Society B, vol. 264, no. 1378, pp. 53–59, 1997. View at Scopus
  41. D. E. Taneyhill, A. M. Dunn, and M. J. Hatcher, “The Galton-Watson branching process as a quantitative tool in parasitology,” Parasitology Today, vol. 15, no. 4, pp. 159–165, 1999. View at Publisher · View at Google Scholar · View at Scopus
  42. C. Kuhn, “Survival chances of mutants starting with one individual,” Journal of Biological Physics, vol. 31, no. 3-4, pp. 587–597, 2005. View at Publisher · View at Google Scholar · View at Scopus
  43. C. Kuhn, “Computer-modeling origin of a simple genetic apparatus,” Proceedings of the National Academy of Sciences of the United States of America, vol. 98, no. 15, pp. 8620–8625, 2001. View at Publisher · View at Google Scholar · View at Scopus
  44. H. Kuhn and C. Kuhn, “Diversified world: drive to life's origin?!,” Angewandte Chemie, vol. 42, no. 3, pp. 262–266, 2003. View at Publisher · View at Google Scholar · View at Scopus
  45. C. Kuhn, “A computer-glimpse of the origin of life,” Journal of Biological Physics, vol. 31, no. 3-4, pp. 571–585, 2005. View at Publisher · View at Google Scholar · View at Scopus
  46. C. Kuhn, “An information-carrying and knowledge-producing molecular machine. A Monte-Carlo Simulation,” Journal of Molecular Modeling, vol. 18, no. 2, pp. 607–609, 2012. View at Publisher · View at Google Scholar
  47. J. D. Murray, Mathematical Biology I, Springer, 2002.
  48. M. Eigen, “Selforganization of matter and the evolution of biological macromolecules,” Die Naturwissenschaften, vol. 58, no. 10, pp. 465–523, 1971. View at Publisher · View at Google Scholar · View at Scopus