Dynamics of stochastic mutation to immunodominance

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2012, 9(4): 937-952. doi: 10.3934/mbe.2012.9.937

Dynamics of stochastic mutation to immunodominance

Yu Wu ^1, , Xiaopeng Zhao ^2, and Mingjun Zhang ^1,

1.	Department of Mechanical, Aerospace and Biomedical Engineering, University of Tennessee, Knoxville, TN 37996, United States, United States
2.	Department of Mechanical, Aerospace, and Biomedical Engineering, University of Tennessee, Knoxville, TN 37996

Received September 2009 Revised September 2010 Published October 2012

Abstract
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Although a virus contains several epitopes that can be recognized by cytotoxic T lymphocytes (CTL), the immune responses against different epitopes are not uniform. Only a few CTLs (sometimes just one) will be immunodominant. Mutation of epitopes has been recognized as an important mechanism of immunodominance. Previous research has studied the influences of sporadic, discrete mutation events. In this work, we introduce a bounded noise term to account for the intrinsic stochastic nature of mutation. Monte Carlo simulations of the stochastic model show abounding complex phenomena, and patterns observed from the numerical simulations shed lights on long term trends of immunodominance.

Keywords: stochastic dynamics, mutation, Immunodominance, Monte Carlo simulation..

Mathematics Subject Classification: Primary: 92D25, 65C05; Secondary: 60H10, 62P1.

Citation: Yu Wu, Xiaopeng Zhao, Mingjun Zhang. Dynamics of stochastic mutation to immunodominance. Mathematical Biosciences & Engineering, 2012, 9 (4) : 937-952. doi: 10.3934/mbe.2012.9.937

References:

[1]	M. A. Nowak, R. M. May and K. Sigmund, Immune responses against multiple epitopes, J. Theor. Biol., 175 (1995), 325-353. doi: 10.1006/jtbi.1995.0146.
[2]	M. A. Nowak, Immune responses against multiple epitopes: a theory for immunodominance and antigenic variation, Semin. Virol., 7 (1996), 83-92. doi: 10.1006/smvy.1996.0010.
[3]	D. Wodarz, "Killer Cell Dynamics: Mathematical and Computational Approaches to Immunology," Springer, New York, USA, 2007.
[4]	L. Adorini, E. Appella, G. Doria and Z. A. Nagy, Mechanisms influencing the immunodominance of T cell determinants, J. Exp. Med., 168 (1988), 2091-2104. doi: 10.1084/jem.168.6.2091.
[5]	A. J. McMichael and R. E. Phillips, Escape of human immunodeficiency virus from immune control, Annu. Rev. Immunol., 15 (1997), 271-296. doi: 10.1146/annurev.immunol.15.1.271.
[6]	P. J. R. Goulder, et al., Late escape from an immunodominant cytotoxic T-lymphocyte response associated with progression to AIDS, Nature Med., 3 (1997), 212-217. doi: 10.1038/nm0297-212.
[7]	P. J. R. Goulder, et al., Patterns of immunodominance in HIV-1-specific cytotoxic T lymphocyte responses in two human histocompatibility leukocyte antigens (HLA)-identical siblings with HLA-A0201 are influenced by epitope mutation, J. Exp. Med., 185* (1997), 1423-1433. doi: 10.1084/jem.185.8.1423.
[8]	J. W. Yewdell and J. R. Bennink, Immunodominance in major histocompatibility complex class I-restricted T lymphocyte responses, Annu. Rev. Immunol., 17 (1999), 51-88. doi: 10.1146/annurev.immunol.17.1.51.
[9]	S. Gupta and R. M. Anderson, Population structure of pathogens: the role of immune selection, Parasitology Today, 15 (1999), 497-501. doi: 10.1016/S0169-4758(99)01559-8.
[10]	C. C. Bergmann, J. D. Altman, D. Hinton and S. A. Stohlman, Inverted immunodominance and impaired cytolytic function of CD8+ T cells during viral persistence in the central nervous system, J. Immunol. 163 (1999), 3379-3387.
[11]	W. S. Chen, L. C. Antón, J. R. Bennink and J. W. Yewdell, Dissecting the multifactorial causes of immunodominance in class I-restricted T cell responses to viruses, Immunity, 12 (2000), 83-93. doi: 10.1016/S1074-7613(00)80161-2.
[12]	X. G. Yu, et al., Consistent patterns in the development and immunodominance of human immunodificiency virus type 1 (HIV-1)-specific CD8+ T-cell responses following acute HIV-1 infection, J. Virol., 76 (2002), 8690-8701. doi: 10.1128/JVI.76.17.8690-8701.2002.
[13]	M. A. Brehm, A. K. Pinto, K. A. Daniels, J. P. Schneck, R. M. Welsh and L. K. Selin, T cell immunodominance and maintenance of memory regulated by unexpectedly cross-reactive pathogens, Nature Immunol., 3 (2002), 627-634.
[14]	U. Karrer, et al., Memory inflation: continuous accumulation of antiviral CD8+ T cells over time, J. Immunol., 170 (2003), 2022-2029.
[15]	E. J. Wherry, J. N. Blattman, K. Murali-Krishna, R. van der Most and R. Ahmed, Viral persistence alters CD8 T-cell immunodominance and tissue distribution and results in distinct stages of functional impairment, J. Virol., 77 (2003), 4911-4927. doi: 10.1128/JVI.77.8.4911-4927.2003.
[16]	P. K. C. Goon, et al., Human T cell lymphotropic virus (HTLV) type-1-specific CD8+ T cells: frequency and immunodominance hierarchy, J. Infect. Dis., 189 (2004), 2294-2298. doi: 10.1086/420832.
[17]	R. Draenert, et al., Constraints on HIV-1 evolution and immunodominance revealed in monozygotic adult twins infected with the same virus, J. Exp. Med., 203 (2006), 529-539. doi: 10.1084/jem.20052116.
[18]	M. A. Nowak, R. M. Anderson, A. R. McLean, T. F. W. Wolfs, J. Goudsmit and R. M. May, Antigenic diversity thresholds and the development of AIDS, Science, 254 (1991), 963-969. doi: 10.1126/science.1683006.
[19]	M. A. Nowak, et al., Antigenic oscillations and shifting immunodominance in HIV-1 infections, Nature, 375 (1995), 606-611. doi: 10.1038/375606a0.
[20]	D. Wodarz and M. A. Nowak, CD8 memory, immunodominance, and antigenic escape, Eur. J. Immunol., 30 (2000), 2704-2712. doi: 10.1002/1521-4141(200009)30:9<2704::AID-IMMU2704>3.0.CO;2-0.
[21]	M. A. Nowak and R. M. May, "Virus Dynamics: Mathematical Principles of Immunology and Virology,'' Oxford University Press, New York, USA, 2000.
[22]	C. L. Althaus and R. J. De Boer, Dynamics of immune escape during HIV/SIV infection, PLOS Comput. Biol., 4 (2008), e1000103. doi: 10.1371/journal.pcbi.1000103.
[23]	A. Handel and R. Antia, A simple methematical model helps to explain the immunodominance of CD8 T cells in influenza a virus infections, J. Virol., 82 (2008), 7768-7772. doi: 10.1128/JVI.00653-08.
[24]	M. A. Nowak, R. M. May and R. M. Anderson, The evolutionary dynamics of HIV-1 quasispecies and the development of immunodeficiency disease, AIDS, 4 (1990), 1095-1103. doi: 10.1097/00002030-199011000-00007.
[25]	M. A. Nowak and R. M. May, Coexistence and competition in HIV infections, J. Theor. Biol., 159 (1992), 329-342. doi: 10.1016/S0022-5193(05)80728-3.
[26]	M. A. Nowak and R. M. May, AIDS pathogenesis: mathematical models of HIV and SIV infections, AIDS 7, Suppl., 1 (1993), S3-S18. doi: 10.1097/00002030-199301001-00002.
[27]	R. M. Anderson, Mathematical studies of parasitic infection and immunity, Science, 264 (1994), 1884-1886. doi: 10.1126/science.8009218.
[28]	Y. K. Lin and G. Q. Cai, "Probabilistic Structural Dynamics: Advanced Theory and Applications,'' McGraw-Hill, New York, 1995.
[29]	W. Q. Zhu, Z. L. Huang, J. M. Ko and Y. Q. Ni, Optimal feedback control of strongly non-linear systems excited by bounded noise, J. Sound Vib., 274 (2004), 701-724. doi: 10.1016/S0022-460X(03)00746-6.
[30]	Z. L. Huang, W. Q. Zhu, Y. Q. Ni and J. M. Ko, Stochastic averaging of strongly non-linear oscillators under bounded noise excitation, J. Sound Vib., 254 (2002), 245-267. doi: 10.1006/jsvi.2001.4093.

show all references

References:

[1]	M. A. Nowak, R. M. May and K. Sigmund, Immune responses against multiple epitopes, J. Theor. Biol., 175 (1995), 325-353. doi: 10.1006/jtbi.1995.0146.
[2]	M. A. Nowak, Immune responses against multiple epitopes: a theory for immunodominance and antigenic variation, Semin. Virol., 7 (1996), 83-92. doi: 10.1006/smvy.1996.0010.
[3]	D. Wodarz, "Killer Cell Dynamics: Mathematical and Computational Approaches to Immunology," Springer, New York, USA, 2007.
[4]	L. Adorini, E. Appella, G. Doria and Z. A. Nagy, Mechanisms influencing the immunodominance of T cell determinants, J. Exp. Med., 168 (1988), 2091-2104. doi: 10.1084/jem.168.6.2091.
[5]	A. J. McMichael and R. E. Phillips, Escape of human immunodeficiency virus from immune control, Annu. Rev. Immunol., 15 (1997), 271-296. doi: 10.1146/annurev.immunol.15.1.271.
[6]	P. J. R. Goulder, et al., Late escape from an immunodominant cytotoxic T-lymphocyte response associated with progression to AIDS, Nature Med., 3 (1997), 212-217. doi: 10.1038/nm0297-212.
[7]	P. J. R. Goulder, et al., Patterns of immunodominance in HIV-1-specific cytotoxic T lymphocyte responses in two human histocompatibility leukocyte antigens (HLA)-identical siblings with HLA-A0201 are influenced by epitope mutation, J. Exp. Med., 185* (1997), 1423-1433. doi: 10.1084/jem.185.8.1423.
[8]	J. W. Yewdell and J. R. Bennink, Immunodominance in major histocompatibility complex class I-restricted T lymphocyte responses, Annu. Rev. Immunol., 17 (1999), 51-88. doi: 10.1146/annurev.immunol.17.1.51.
[9]	S. Gupta and R. M. Anderson, Population structure of pathogens: the role of immune selection, Parasitology Today, 15 (1999), 497-501. doi: 10.1016/S0169-4758(99)01559-8.
[10]	C. C. Bergmann, J. D. Altman, D. Hinton and S. A. Stohlman, Inverted immunodominance and impaired cytolytic function of CD8+ T cells during viral persistence in the central nervous system, J. Immunol. 163 (1999), 3379-3387.
[11]	W. S. Chen, L. C. Antón, J. R. Bennink and J. W. Yewdell, Dissecting the multifactorial causes of immunodominance in class I-restricted T cell responses to viruses, Immunity, 12 (2000), 83-93. doi: 10.1016/S1074-7613(00)80161-2.
[12]	X. G. Yu, et al., Consistent patterns in the development and immunodominance of human immunodificiency virus type 1 (HIV-1)-specific CD8+ T-cell responses following acute HIV-1 infection, J. Virol., 76 (2002), 8690-8701. doi: 10.1128/JVI.76.17.8690-8701.2002.
[13]	M. A. Brehm, A. K. Pinto, K. A. Daniels, J. P. Schneck, R. M. Welsh and L. K. Selin, T cell immunodominance and maintenance of memory regulated by unexpectedly cross-reactive pathogens, Nature Immunol., 3 (2002), 627-634.
[14]	U. Karrer, et al., Memory inflation: continuous accumulation of antiviral CD8+ T cells over time, J. Immunol., 170 (2003), 2022-2029.
[15]	E. J. Wherry, J. N. Blattman, K. Murali-Krishna, R. van der Most and R. Ahmed, Viral persistence alters CD8 T-cell immunodominance and tissue distribution and results in distinct stages of functional impairment, J. Virol., 77 (2003), 4911-4927. doi: 10.1128/JVI.77.8.4911-4927.2003.
[16]	P. K. C. Goon, et al., Human T cell lymphotropic virus (HTLV) type-1-specific CD8+ T cells: frequency and immunodominance hierarchy, J. Infect. Dis., 189 (2004), 2294-2298. doi: 10.1086/420832.
[17]	R. Draenert, et al., Constraints on HIV-1 evolution and immunodominance revealed in monozygotic adult twins infected with the same virus, J. Exp. Med., 203 (2006), 529-539. doi: 10.1084/jem.20052116.
[18]	M. A. Nowak, R. M. Anderson, A. R. McLean, T. F. W. Wolfs, J. Goudsmit and R. M. May, Antigenic diversity thresholds and the development of AIDS, Science, 254 (1991), 963-969. doi: 10.1126/science.1683006.
[19]	M. A. Nowak, et al., Antigenic oscillations and shifting immunodominance in HIV-1 infections, Nature, 375 (1995), 606-611. doi: 10.1038/375606a0.
[20]	D. Wodarz and M. A. Nowak, CD8 memory, immunodominance, and antigenic escape, Eur. J. Immunol., 30 (2000), 2704-2712. doi: 10.1002/1521-4141(200009)30:9<2704::AID-IMMU2704>3.0.CO;2-0.
[21]	M. A. Nowak and R. M. May, "Virus Dynamics: Mathematical Principles of Immunology and Virology,'' Oxford University Press, New York, USA, 2000.
[22]	C. L. Althaus and R. J. De Boer, Dynamics of immune escape during HIV/SIV infection, PLOS Comput. Biol., 4 (2008), e1000103. doi: 10.1371/journal.pcbi.1000103.
[23]	A. Handel and R. Antia, A simple methematical model helps to explain the immunodominance of CD8 T cells in influenza a virus infections, J. Virol., 82 (2008), 7768-7772. doi: 10.1128/JVI.00653-08.
[24]	M. A. Nowak, R. M. May and R. M. Anderson, The evolutionary dynamics of HIV-1 quasispecies and the development of immunodeficiency disease, AIDS, 4 (1990), 1095-1103. doi: 10.1097/00002030-199011000-00007.
[25]	M. A. Nowak and R. M. May, Coexistence and competition in HIV infections, J. Theor. Biol., 159 (1992), 329-342. doi: 10.1016/S0022-5193(05)80728-3.
[26]	M. A. Nowak and R. M. May, AIDS pathogenesis: mathematical models of HIV and SIV infections, AIDS 7, Suppl., 1 (1993), S3-S18. doi: 10.1097/00002030-199301001-00002.
[27]	R. M. Anderson, Mathematical studies of parasitic infection and immunity, Science, 264 (1994), 1884-1886. doi: 10.1126/science.8009218.
[28]	Y. K. Lin and G. Q. Cai, "Probabilistic Structural Dynamics: Advanced Theory and Applications,'' McGraw-Hill, New York, 1995.
[29]	W. Q. Zhu, Z. L. Huang, J. M. Ko and Y. Q. Ni, Optimal feedback control of strongly non-linear systems excited by bounded noise, J. Sound Vib., 274 (2004), 701-724. doi: 10.1016/S0022-460X(03)00746-6.
[30]	Z. L. Huang, W. Q. Zhu, Y. Q. Ni and J. M. Ko, Stochastic averaging of strongly non-linear oscillators under bounded noise excitation, J. Sound Vib., 254 (2002), 245-267. doi: 10.1006/jsvi.2001.4093.

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