- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Computational and Mathematical Methods in Medicine
Volume 2012 (2012), Article ID 784512, 17 pages
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.
- C. Janeway, M. J. Shlomchik, M. Walport, and P. Travers, Immunobiology, Garland, 2004.
- D. Wodarz, “Evolution of immunological memory and the regulation of competition between pathogens,” Current Biology, vol. 13, no. 18, pp. 1648–1652, 2003.
- 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.
- 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.
- 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.
- 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.
- 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.
- N. K. Jerne, “The natural-selection theory of antibody formation,” PNAS USA, vol. 41, no. 11, pp. 849–857, 1955.
- 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.
- R. M. Zinkernagel, “Immunology taught by viruses,” Science, vol. 271, no. 5246, pp. 173–178, 1996.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- A. S. Perelson and G. Weisbuch, “Immunology for physicists,” Reviews of Modern Physics, vol. 69, no. 4, pp. 1219–1267, 1997.
- A. S. Perelson, “Modelling viral and immune system dynamics,” Nature Reviews Immunology, vol. 2, no. 1, pp. 28–36, 2002.
- G. I. Marchuk, Mathematical Modelling of Immune Response in Infectious Diseases. Mathematics and Its Applications, Springer, Amsterdam, The Netherlands, 1997.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- P. Haccou, P. Jagers, and V. A. Vatutin, Branching Processes: Variation, Growth and Extinction of Populations, Cambridge University Press, Cambridge, UK, 2005.
- M. Kimmel and D. E. Axelrod, Branching Processes in Biology, Springer, New York, NY, USA, 2002.
- 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.
- 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.
- T. E. Harris, The Theory of Branching Processes, Springer, Berlin, Germany, 1963.
- K. B. Athreya and P. E. Ney, Branching Processes, Dover, Mineola, NY, USA, 2004.
- S. Resnick, Adventures in Stochastic Processes, Birkhäuser, 1992.
- 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.
- 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.
- C. Kuhn, “Survival chances of mutants starting with one individual,” Journal of Biological Physics, vol. 31, no. 3-4, pp. 587–597, 2005.
- 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.
- H. Kuhn and C. Kuhn, “Diversified world: drive to life's origin?!,” Angewandte Chemie, vol. 42, no. 3, pp. 262–266, 2003.
- C. Kuhn, “A computer-glimpse of the origin of life,” Journal of Biological Physics, vol. 31, no. 3-4, pp. 571–585, 2005.
- 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.
- J. D. Murray, Mathematical Biology I, Springer, 2002.
- M. Eigen, “Selforganization of matter and the evolution of biological macromolecules,” Die Naturwissenschaften, vol. 58, no. 10, pp. 465–523, 1971.