American Institute of Mathematical Sciences

Advanced
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

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.  Google Scholar

[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.  Google Scholar

[3]

D. Wodarz, "Killer Cell Dynamics: Mathematical and Computational Approaches to Immunology," Springer, New York, USA, 2007.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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-A*0201 are influenced by epitope mutation, J. Exp. Med., 185 (1997), 1423-1433. doi: 10.1084/jem.185.8.1423.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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. Google Scholar

[14]

U. Karrer, et al., Memory inflation: continuous accumulation of antiviral CD8+ T cells over time, J. Immunol., 170 (2003), 2022-2029. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[19]

M. A. Nowak, et al., Antigenic oscillations and shifting immunodominance in HIV-1 infections, Nature, 375 (1995), 606-611. doi: 10.1038/375606a0.  Google Scholar

[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.  Google Scholar

[21]

M. A. Nowak and R. M. May, "Virus Dynamics: Mathematical Principles of Immunology and Virology,'' Oxford University Press, New York, USA, 2000.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[27]

R. M. Anderson, Mathematical studies of parasitic infection and immunity, Science, 264 (1994), 1884-1886. doi: 10.1126/science.8009218.  Google Scholar

[28]

Y. K. Lin and G. Q. Cai, "Probabilistic Structural Dynamics: Advanced Theory and Applications,'' McGraw-Hill, New York, 1995. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

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.  Google Scholar

[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.  Google Scholar

[3]

D. Wodarz, "Killer Cell Dynamics: Mathematical and Computational Approaches to Immunology," Springer, New York, USA, 2007.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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-A*0201 are influenced by epitope mutation, J. Exp. Med., 185 (1997), 1423-1433. doi: 10.1084/jem.185.8.1423.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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. Google Scholar

[14]

U. Karrer, et al., Memory inflation: continuous accumulation of antiviral CD8+ T cells over time, J. Immunol., 170 (2003), 2022-2029. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[19]

M. A. Nowak, et al., Antigenic oscillations and shifting immunodominance in HIV-1 infections, Nature, 375 (1995), 606-611. doi: 10.1038/375606a0.  Google Scholar

[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.  Google Scholar

[21]

M. A. Nowak and R. M. May, "Virus Dynamics: Mathematical Principles of Immunology and Virology,'' Oxford University Press, New York, USA, 2000.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[27]

R. M. Anderson, Mathematical studies of parasitic infection and immunity, Science, 264 (1994), 1884-1886. doi: 10.1126/science.8009218.  Google Scholar

[28]

Y. K. Lin and G. Q. Cai, "Probabilistic Structural Dynamics: Advanced Theory and Applications,'' McGraw-Hill, New York, 1995. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

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