Turing Patterns from Dynamics of Early HIV Infection

Bulletin of Mathematical Biology

Volumn 75, Issue 5, 2013, Pages 774-795

  Stancevic, O ^a   Angstmann, C N ^a   Murray, J M ^a,b   Henry, B I ^a  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

^b UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

Chemotaxis; HIV; In host viral dynamics; Reaction diffusion; Turing patterns

Indexed keywords

HUMAN IMMUNODEFICIENCY VIRUS;

EID: 84877070324     PISSN: 00928240     EISSN: 15229602     Source Type: Journal    
DOI: 10.1007/s11538-013-9834-5     Document Type: Article

References (38)

1. Boukari, H., Brichacek, B., Stratton, P., Mahoney, S. F., Lifson, J. D., Margolis, L., & Nossal, R. (2009). Movements of HIV-virions in human cervical mucus. Biomacromolecules, 10(9), 2482-2488.
2. Chen, H. Y., Di Mascio, M., Perelson, A. S., Ho, D. D., & Zhang, L. (2007). Determination of virus burst size in vivo using a single-cycle SIV in rhesus macaques. Proc. Natl. Acad. Sci. USA, 104(48), 19079-19084.
3. Cooper, S. B., & Maini, P. K. (2012). The mathematics of nature at the Alan Turing centenary. Interface Focus, 2(4), 393-396.
4. De Boer, R. J. (2007). Understanding the failure of CD8+ T-cell vaccination against simian/human immunodeficiency virus. J. Virol., 81(6), 2838-2848.
5. Edelstein-Keshet, L. (2005). Classics in applied mathematics: Vol. 46. Mathematical models in biology. Philadelphia: SIAM.
6. Ewers, H., Jacobsen, V., Klotzsch, E., Smith, A. E., Helenius, A., & Sandoghdar, V. (2007). Label-free optical detection and tracking of single virions bound to their receptors in supported membrane bilayers. Nano Lett., 7(8), 2263-2266.
7. Haase, A. T. (2010). Targeting early infection to prevent HIV-1 mucosal transmission. Nature, 464, 217-223.
8. Haase, A. T., Henry, K., Zupancic, M., Sedgewick, G., Faust, R. A., Melroe, H., Cavert, W., Gebhard, K., Staskus, K., Zhang, Z. Q., Dailey, P. J., Balfour, H. H., Erice, A., & Perelson, A. S. (1996). Quantitative image analysis of HIV-1 infection in lymphoid tissue. Science, 274(5289), 985-989.
9. Harris, T. H., Banigan, E. J., Christian, D. A., Konradt, C., Tait Wojno, E. D., Norose, K., Wilson, E. H., John, B., Weninger, W., Luster, A. D., Liu, A. J., & Hunter, C. A. (2012). Generalized Levy walks and the role of chemokines in migration of effector CD8+ T cells. Nature, 486, 545-548.
10. Hillen, T., & Painter, K. J. (2009). A user's guide to PDE models for chemotaxis. J. Math. Biol., 58, 183-217.
11. Horstmann, D. (2003). From 1970 until present: the Keller-Segel model in chemotaxis and its consequences. I. Jahresber. Dtsch. Math.-Ver., 105(3), 103-165.
12. Hurwitz, A. (1964). On the conditions under which an equation has only roots with negative real parts. In Selected papers on mathematical trends in control theory (pp. 72-82). New York: Dover.
13. Jin, T., Xu, X., & Hereld, D. (2008). Chemotaxis, chemokine receptors and human disease. Cytokine, 44(1), 1-8.
14. Keele, B. F., Giorgi, E. E., Salazar-Gonzalez, J. F., Decker, J. M., Pham, K. T., Salazar, M. G., Sun, C., Grayson, T., Wang, S., Li, H., Wei, X., Jiang, C., Kirchherr, J. L., Gao, F., Anderson, J. A., Ping, L.-H., Swanstrom, R., Tomaras, G. D., Blattner, W. A., Goepfert, P. A., Kilby, J. M., Saag, M. S., Delwart, E. L., Busch, M. P., Cohen, M. S., Montefiori, D. C., Haynes, B. F., Gaschen, B., Athreya, G. S., Lee, H. Y., Wood, N., Seoighe, C., Perelson, A. S., Bhattacharya, T., Korber, B. T., Hahn, B. H., & Shaw, G. M. (2008). Identification and characterization of transmitted and early founder virus envelopes in primary HIV-1 infection. Proc. Natl. Acad. Sci. USA, 105(21), 7552-7557.
15. Klasse, P. J., Shattock, R. J., & Moore, J. P. (2006). Which topical microbicides for blocking HIV-1 transmission will work in the real world? PLoS Med., 3(9), e351.
16. Lin, F., & Butcher, E. C. (2006). T cell chemotaxis in a simple microfluidic device. Lab Chip, 6(11), 1462-1469.
17. Liu, Q. X., & Zhen, J. (2007). Formation of spatial patterns in an epidemic model with constant removal rate of the infectives. J. Stat. Mech. Theory Exp., 2007(05), P05002.
18. Maini, P. K., Woolley, T. E., Baker, R. E., Gaffney, E. A., & Lee, S. S. (2012). Turing's model for biological pattern formation and the robustness problem. Interface Focus, 2(4), 487-496.
19. Mandl, J. N., Regoes, R. R., Garber, D. A., & Feinberg, M. B. (2007). Estimating the effectiveness of simian immunodeficiency virus-specific CD8+ T cells from the dynamics of viral immune escape. J. Virol., 81(21), 11982-11991.
20. Meinhardt, H. (2012). Turing's theory of morphogenesis of 1952 and the subsequent discovery of the crucial role of local self-enhancement and long-range inhibition. Interface Focus, 2(4), 407-416.
21. Miller, M. J., Wei, S. H., Parker, I., & Cahalan, M. D. (2002). Two-photon imaging of lymphocyte motility and antigen response in intact lymph node. Science, 296(5574), 1869-1873.
22. Miller, M. J., Wei, S. H., Cahalan, M. D., & Parker, I. (2003). Autonomous T cell trafficking examined in vivo with intravital two-photon microscopy. Proc. Natl. Acad. Sci. USA, 100(5), 2604-2609.
23. Murray, J. D. (2002). Biomathematics: Vol. 19. Mathematical biology: an introduction. Berlin: Springer.
24. Murray, J. M., Kaufmann, G., Kelleher, A. D., & Cooper, D. A. (1998). A model of primary HIV-1 infection. Math. Biosci., 154(2), 57-85.
25. Murray, J. M., Emery, S., Kelleher, A. D., Law, M., Chen, J., Hazuda, D. J., Nguyen, B.-Y. T., Teppler, H., & Cooper, D. A. (2007). Antiretroviral therapy with the integrase inhibitor Raltegravir alters decay kinetics of HIV, significantly reducing the second phase. AIDS, 21, 2315-2321.
26. Murray, J. M., Kelleher, A. D., & Cooper, D. A. (2011). Timing of the components of the HIV life cycle in productively infected CD4+ T cells in a population of HIV-infected individuals. J. Virol., 85(20), 10798-10805.
27. Nelson, P. W., Murray, J. D., & Perelson, A. S. (2000). A model of HIV-1 pathogenesis that includes an intracellular delay. Math. Biosci., 163(2), 201-215.
28. Nowak, M. A., & May, R. (2000). Virus dynamics: mathematical principles of immunology and virology. London: Oxford University Press.
29. Nowak, M. A., Bonhoeffer, S., & Hill, A. M. (1996). Viral dynamics in Hepatitis B virus infection. Proc. Natl. Acad. Sci. USA, 93(9), 4398-4402.
30. Ouyang, Q., & Swinney, H. L. (1991). Transition from a uniform state to hexagonal and striped Turing patterns. Nature, 352, 610-612.
31. Perelson, A. S., Neumann, A. U., Markowitz, M., Leonard, J. M., & Ho, D. D. (1996). HIV-1 dynamics in vivo: virion clearance rate, infected cell life-span, and viral generation time. Science, 271, 1582-1586.
32. Perelson, A. S., Essunger, P., Cao, M., Vesanen, Y., Hurley, K., Saksela, A., Markowitz, M., & Ho, D. D. (1997). Decay characteristics of HIV-1-infected compartments during combination therapy. Nature, 387, 188-191.
33. Ramratnam, B., Bonhoeffer, S., Binley, J., Hurley, A., Zhang, L., Mittler, J. E., Markowitz, M., Moore, J. P., Perelson, A. S., & Ho, D. D. (1999). Rapid production and clearance of HIV-1 and Hepatitis C virus assessed by large volume plasma apheresis. Lancet, 354(9192), 1782-1785.
34. Reilly, C., Wietgrefe, S., Sedgewick, G., & Haase, A. (2007). Determination of simian immunodeficiency virus production by infected activated and resting cells. AIDS, 21(2), 163.
35. Ribeiro, R. M., Qin, L., Chavez, L. L., Li, D., Self, S. G., & Perelson, A. S. (2010). Estimation of the initial viral growth rate and basic reproductive number during acute HIV-1 infection. J. Virol., 84(12), 6096-6102.
36. Turing, A. M. (1952). The chemical basis of morphogenesis. Philos. Trans. R. Soc. Lond. B, Biol. Sci., 237(641), 37-72.
37. Velasquez, T. J. L. (2004). Point dynamics for a singular limit of the Keller-Segel model. SIAM J. Appl. Math., 64(4), 1198-1223.
38. Wei, X., Ghosn, S. K., Taylor, M. E., Johnson, V. A., Emini, E. A., Deutsch, P., Lifson, J. D., Bonhoeffer, S., Nowak, M. A., Hahn, B. H., Saag, M. S., & Shaw, G. M. (1995). Viral dynamics in human immunodeficiency virus type 1 infection. Nature, 373, 117-122.