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Defining Kinetic Properties of HIV-Specific CD8^{+} T-Cell Responses in Acute Infection

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## Abstract

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## 1. Introduction

## 2. Material and Methods

#### 2.1. Experimental Data

#### 2.2. Mathematical Model of CD8${}^{+}$ T-Cell Response to a Viral Infection

#### 2.3. Statistics

#### 2.4. Ethics Statement

#### 2.5. Competing Interests Statement

## 3. Results

#### 3.1. Moderate Changes in the Breadth of HIV-Specific CD8${}^{+}$ T-Cell Response over the Course of Infection

#### 3.2. Variable Correlations between Immune Response Breadth and Viral Load

#### 3.3. Most HIV-Specific CD8${}^{+}$ T-Cell Responses Expand Slowly and Peak Early

#### 3.4. Evidence of Intraclonal Competition of CD8${}^{+}$ T Cells

#### 3.5. Evidence of Interclonal Competition of CD8${}^{+}$ T Cells

## 4. Discussion

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

CTL | cytotoxic T lymphocyte |

HIV | human immunodeficiency virus |

SE | Shannon entropy |

EI | Evenness index |

PBMC | peripheral blood mononuclear cells |

SFC | spot-forming cells |

IFN | interferon |

## References

- Demberg, T.; Robert-Guroff, M. Controlling the HIV/AIDS epidemic: Current status and global challenges. Front. Immunol.
**2012**, 3, 250. [Google Scholar] [CrossRef] [PubMed] - Maartens, G.; Celum, C.; Lewin, S.R. HIV infection: Epidemiology, pathogenesis, treatment, and prevention. Lancet
**2014**, 384, 258–271. [Google Scholar] [CrossRef] - Uberla, K. HIV vaccine development in the aftermath of the STEP study: Re-focus on occult HIV infection? PLoS Pathog.
**2008**, 4, e1000114. [Google Scholar] [CrossRef] [PubMed] - Cohen, J. HIV/AIDS research. Beyond Thailand: Making sense of a qualified AIDS vaccine “success”. Science
**2009**, 326, 652–653. [Google Scholar] [CrossRef] [PubMed] - Fuchs, J.D.; Sobieszczyk, M.E.; Hammer, S.M.; Buchbinder, S.P. Lessons drawn from recent HIV vaccine efficacy trials. J. Acquir. Immune Defic. Syndr.
**2010**, 55 (Suppl. 2), S128–S131. [Google Scholar] [CrossRef] [PubMed] - Barouch, D.; Santra, S.; Schmitz, J.; Kuroda, M.; Fu, T.; Wagner, W.; Bilska, M.; Craiu, A.; Zheng, X.; Krivulka, G.; et al. Control of viremia and prevention of clinical AIDS in rhesus monkeys by cytokine-augmented DNA vaccination. Science
**2000**, 290, 486–492. [Google Scholar] [CrossRef] [PubMed] - Shiver, J.W.; Fu, T.M.; Chen, L.; Casimiro, D.R.; Davies, M.E.; Evans, R.K.; Zhang, Z.Q.; Simon, A.J.; Trigona, W.L.; Dubey, S.A.; et al. Replication-incompetent adenoviral vaccine vector elicits effective anti-immunodeficiency-virus immunity. Nature
**2002**, 415, 331–335. [Google Scholar] [CrossRef] [PubMed] - Watkins, D.I.; Burton, D.R.; Kallas, E.G.; Moore, J.P.; Koff, W.C. Nonhuman primate models and the failure of the Merck HIV-1 vaccine in humans. Nat. Med.
**2008**, 14, 617–621. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Watkins, D.I. The hope for an HIV vaccine based on induction of CD8+ T lymphocytes—A review. Memórias Inst. Oswaldo Cruz
**2008**, 103, 119–129. [Google Scholar] [CrossRef] - Haynes, B.F.; Shaw, G.M.; Korber, B.; Kelsoe, G.; Sodroski, J.; Hahn, B.H.; Borrow, P.; McMichael, A.J. HIV-Host Interactions: Implications for Vaccine Design. Cell Host Microbe
**2016**, 19, 292–303. [Google Scholar] [CrossRef] [PubMed] - Mascola, J.R.; Haynes, B.F. HIV-1 neutralizing antibodies: Understanding nature’s pathways. Immunol. Rev.
**2013**, 254, 225–244. [Google Scholar] [CrossRef] [PubMed] - Barouch, D.H.; Picker, L.J. Novel vaccine vectors for HIV-1. Nat. Rev. Microbiol.
**2014**, 12, 765–771. [Google Scholar] [CrossRef] [PubMed] - Haynes, B.F. New approaches to HIV vaccine development. Curr. Opin. Immunol.
**2015**, 35, 39–47. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Sadanand, S.; Suscovich, T.J.; Alter, G. Broadly Neutralizing Antibodies Against HIV: New Insights to Inform Vaccine Design. Annu. Rev. Med.
**2016**, 67, 185–200. [Google Scholar] [CrossRef] [PubMed] - Makedonas, G.; Betts, M.R. Living in a house of cards: Re-evaluating CD8+ T-cell immune correlates against HIV. Immunol. Rev.
**2011**, 239, 109–124. [Google Scholar] [CrossRef] [PubMed] - McMichael, A.J.; Borrow, P.; Tomaras, G.D.; Goonetilleke, N.; Haynes, B.F. The immune response during acute HIV-1 infection: Clues for vaccine development. Nat. Rev. Immunol.
**2010**, 10, 11–23. [Google Scholar] [CrossRef] [PubMed] - Hersperger, A.R.; Migueles, S.A.; Betts, M.R.; Connors, M. Qualitative features of the HIV-specific CD8+ T-cell response associated with immunologic control. Curr. Opin. HIV AIDS
**2011**, 6, 169–173. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Demers, K.R.; Reuter, M.A.; Betts, M.R. CD8(+) T-cell effector function and transcriptional regulation during HIV pathogenesis. Immunol. Rev.
**2013**, 254, 190–206. [Google Scholar] [CrossRef] [PubMed] - Borrow, P.; Lewicki, H.; Hahn, B.H.; Shaw, G.M.; Oldstone, M.B. Virus-specific CD8+ cytotoxic T-lymphocyte activity associated with control of viremia in primary human immunodeficiency virus type 1 infection. J. Virol.
**1994**, 68, 6103–6110. [Google Scholar] [PubMed] - Koup, R.A.; Safrit, J.T.; Cao, Y.; Andrews, C.A.; McLeod, G.; Borkowsky, W.; Farthing, C.; Ho, D.D. Temporal association of cellular immune responses with the initial control of viremia in primary human immunodeficiency virus type 1 syndrome. J. Virol.
**1994**, 68, 4650–4655. [Google Scholar] [PubMed] - Abdel-Motal, U.M.; Gillis, J.; Manson, K.; Wyand, M.; Montefiori, D.; Stefano-Cole, K.; Montelaro, R.C.; Altman, J.D.; Johnson, R.P. Kinetics of expansion of SIV Gag-specific CD8+ T lymphocytes following challenge of vaccinated macaques. Virology
**2005**, 333, 226–238. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Newberg, M.H.; McEvers, K.J.; Gorgone, D.A.; Lifton, M.A.; Baumeister, S.H.; Veazey, R.S.; Schmitz, J.E.; Letvin, N.L. Immunodomination in the evolution of dominant epitope-specific CD8+ T lymphocyte responses in simian immunodeficiency virus-infected rhesus monkeys. J. Immunol.
**2006**, 176, 319–328. [Google Scholar] [CrossRef] [PubMed] - Carrington, M.; Nelson, G.W.; Martin, M.P.; Kissner, T.; Vlahov, D.; Goedert, J.J.; Kaslow, R.; Buchbinder, S.; Hoots, K.; O’Brien, S.J. HLA and HIV-1: Heterozygote advantage and B*35-Cw*04 disadvantage. Science
**1999**, 283, 1748–1752. [Google Scholar] [CrossRef] [PubMed] - Carrington, M.; O’Brien, S. The influence of HLA genotype on AIDS. Annu. Rev. Med.
**2003**, 54, 535–551. [Google Scholar] [CrossRef] [PubMed] - McLaren, P.J.; Carrington, M. The impact of host genetic variation on infection with HIV-1. Nat. Immunol.
**2015**, 16, 577–583. [Google Scholar] [CrossRef] [PubMed] - Goulder, P.; Watkins, D. HIV and SIV CTL escape: Implications for vaccine design. Nat. Rev. Immunol.
**2004**, 4, 630–640. [Google Scholar] [CrossRef] [PubMed] - Ogg, G.S.; Jin, X.; Bonhoeffer, S.; Dunbar, P.R.; Nowak, M.A.; Monard, S.; Segal, J.P.; Cao, Y.; Rowland-Jones, S.L.; Cerundolo, V.; et al. Quantitation of HIV-1-specific cytotoxic T lymphocytes and plasma load of viral RNA. Science
**1998**, 279, 2103–2106. [Google Scholar] [CrossRef] [PubMed] - Kalams, S.A.; Buchbinder, S.P.; Rosenberg, E.S.; Billingsley, J.M.; Colbert, D.S.; Jones, N.G.; Shea, A.K.; Trocha, A.K.; Walker, B.D. Association between virus-specific cytotoxic T-lymphocyte and helper responses in human immunodeficiency virus type 1 infection. J. Virol.
**1999**, 73, 6715–6720. [Google Scholar] [PubMed] - Betts, M.; Ambrozak, D.; Douek, D.; Bonhoeffer, S.; Brenchley, J.; Casazza, J.; Koup, R.; Picker, L. Analysis of total human immunodeficiency virus (HIV)-specific CD4(+) and CD8(+) T-cell responses: Relationship to viral load in untreated HIV infection. J. Virol.
**2001**, 75, 11983–11991. [Google Scholar] [CrossRef] [PubMed] - Novitsky, V.; Gilbert, P.; Peter, T.; McLane, M.F.; Gaolekwe, S.; Rybak, N.; Thior, I.; Ndungu, T.; Marlink, R.; Lee, T.H.; et al. Association between Virus-Specific T-Cell Responses and Plasma Viral Load in Human Immunodeficiency Virus Type 1 Subtype C Infection. J. Virol.
**2003**, 77, 882–890. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Day, C.L.; Kiepiela, P.; Leslie, A.J.; van der Stok, M.; Nair, K.; Ismail, N.; Honeyborne, I.; Crawford, H.; Coovadia, H.M.; Goulder, P.J.; et al. Proliferative capacity of epitope-specific CD8 T-cell responses is inversely related to viral load in chronic human immunodeficiency virus type 1 infection. J. Virol.
**2007**, 81, 434–438. [Google Scholar] [CrossRef] [PubMed] - Gray, C.M.; Mlotshwa, M.; Riou, C.; Mathebula, T.; de Assis Rosa, D.; Mashishi, T.; Seoighe, C.; Ngandu, N.; van Loggerenberg, F.; Morris, L.; et al. Human immunodeficiency virus-specific gamma interferon enzyme-linked immunospot assay responses targeting specific regions of the proteome during primary subtype C infection are poor predictors of the course of viremia and set point. J. Virol.
**2009**, 83, 470–478. [Google Scholar] [CrossRef] [PubMed] - Kiepiela, P.; Ngumbela, K.; Thobakgale, C.; Ramduth, D.; Honeyborne, I.; Moodley, E.; Reddy, S.; de Pierres, C.; Mncube, Z.; Mkhwanazi, N.; et al. CD8+ T-cell responses to different HIV proteins have discordant associations with viral load. Nat. Med.
**2007**, 13, 46–53. [Google Scholar] [CrossRef] [PubMed] - Geldmacher, C.; Currier, J.R.; Herrmann, E.; Haule, A.; Kuta, E.; McCutchan, F.; Njovu, L.; Geis, S.; Hoffmann, O.; Maboko, L.; et al. CD8 T-cell recognition of multiple epitopes within specific Gag regions is associated with maintenance of a low steady-state viremia in human immunodeficiency virus type 1-seropositive patients. J. Virol.
**2007**, 81, 2440–2448. [Google Scholar] [CrossRef] [PubMed] - Rolland, M.; Heckerman, D.; Deng, W.; Rousseau, C.M.; Coovadia, H.; Bishop, K.; Goulder, P.J.R.; Walker, B.D.; Brander, C.; Mullins, J.I. Broad and Gag-biased HIV-1 epitope repertoires are associated with lower viral loads. PLoS ONE
**2008**, 3, e1424. [Google Scholar] [CrossRef] [PubMed] - Brennan, C.A.; Ibarrondo, F.J.; Sugar, C.A.; Hausner, M.A.; Shih, R.; Ng, H.L.; Detels, R.; Margolick, J.B.; Rinaldo, C.R.; Phair, J.; et al. Early HLA-B*57-restricted CD8+ T lymphocyte responses predict HIV-1 disease progression. J. Virol.
**2012**, 86, 10505–10516. [Google Scholar] [CrossRef] [PubMed] - Jin, X.; Bauer, D.E.; Tuttleton, S.E.; Lewin, S.; Gettie, A.; Blanchard, J.; Irwin, C.E.; Safrit, J.T.; Mittler, J.; Weinberger, L.; et al. Dramatic rise in plasma viremia after CD8(+) T cell depletion in simian immunodeficiency virus-infected macaques. J. Exp. Med.
**1999**, 189, 991–998. [Google Scholar] [CrossRef] [PubMed] - Schmitz, J.E.; Kuroda, M.J.; Santra, S.; Sasseville, V.G.; Simon, M.A.; Lifton, M.A.; Racz, P.; Tenner-Racz, K.; Dalesandro, M.; Scallon, B.J.; et al. Control of viremia in simian immunodeficiency virus infection by CD8+ lymphocytes. Science
**1999**, 283, 857–860. [Google Scholar] [CrossRef] [PubMed] - Klatt, N.R.; Shudo, E.; Ortiz, A.M.; Engram, J.C.; Paiardini, M.; Lawson, B.; Miller, M.D.; Else, J.; Pandrea, I.; Estes, J.D.; et al. CD8+ lymphocytes control viral replication in SIVmac239-infected rhesus macaques without decreasing the lifespan of productively infected cells. PLoS Pathog.
**2010**, 6, e1000747. [Google Scholar] [CrossRef] [PubMed] - Wong, J.K.; Strain, M.C.; Porrata, R.; Reay, E.; Sankaran-Walters, S.; Ignacio, C.C.; Russell, T.; Pillai, S.K.; Looney, D.J.; Dandekar, S. In vivo CD8+ T-cell suppression of SIV viremia is not mediated by CTL clearance of productively infected cells. PLoS Pathog.
**2010**, 6, e1000748. [Google Scholar] [CrossRef] [PubMed] - Hansen, S.G.; Ford, J.C.; Lewis, M.S.; Ventura, A.B.; Hughes, C.M.; Coyne-Johnson, L.; Whizin, N.; Oswald, K.; Shoemaker, R.; Swanson, T.; et al. Profound early control of highly pathogenic SIV by an effector memory T-cell vaccine. Nature
**2011**, 473, 523–527. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Stephenson, K.E.; Li, H.; Walker, B.D.; Michael, N.L.; Barouch, D.H. Gag-specific cellular immunity determines in vitro viral inhibition and in vivo virologic control following simian immunodeficiency virus challenges of vaccinated rhesus monkeys. J. Virol.
**2012**, 86, 9583–9589. [Google Scholar] [CrossRef] [PubMed] - Hansen, S.G.; Piatak, M.; Ventura, A.B.; Hughes, C.M.; Gilbride, R.M.; Ford, J.C.; Oswald, K.; Shoemaker, R.; Li, Y.; Lewis, M.S.; et al. Immune clearance of highly pathogenic SIV infection. Nature
**2013**, 502, 100–104. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Iwamoto, N.; Takahashi, N.; Seki, S.; Nomura, T.; Yamamoto, H.; Inoue, M.; Shu, T.; Naruse, T.K.; Kimura, A.; Matano, T. Control of simian immunodeficiency virus replication by vaccine-induced Gag- and Vif-specific CD8+ T cells. J. Virol.
**2014**, 88, 425–433. [Google Scholar] [CrossRef] [PubMed] - Cohen, M.S.; Shaw, G.M.; McMichael, A.J.; Haynes, B.F. Acute HIV-1 Infection. N. Engl. J. Med.
**2011**, 364, 1943–1954. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Migueles, S.A.; Connors, M. Success and failure of the cellular immune response against HIV-1. Nat. Immunol.
**2015**, 16, 563–570. [Google Scholar] [CrossRef] [PubMed] - Migueles, S.; Laborico, A.; Shupert, W.; Sabbaghian, M.; Rabin, R.; Hallahan, C.; Van Baarle, D.; Kostense, S.; Miedema, F.; McLaughlin, M.; et al. HIV-specific CD8+ T cell proliferation is coupled to perforin expression and is maintained in nonprogressors. Nat. Immunol.
**2002**, 3, 1061–1068. [Google Scholar] [CrossRef] [PubMed] - Walker, B.D. Elite control of HIV Infection: Implications for vaccines and treatment. Top. HIV Med.
**2007**, 15, 134–136. [Google Scholar] [PubMed] - Lobritz, M.A.; Lassen, K.G.; Arts, E.J. HIV-1 replicative fitness in elite controllers. Curr. Opin. HIV AIDS
**2011**, 6, 214–220. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Zaunders, J.; Dyer, W.B.; Churchill, M. The Sydney Blood Bank Cohort: Implications for viral fitness as a cause of elite control. Curr. Opin. HIV AIDS
**2011**, 6, 151–156. [Google Scholar] [CrossRef] [PubMed] - Poropatich, K.; Sullivan, D.J. Human immunodeficiency virus type 1 long-term non-progressors: The viral, genetic and immunological basis for disease non-progression. J. Gen. Virol.
**2011**, 92, 247–268. [Google Scholar] [CrossRef] [PubMed] - Goulder, P.J.; Walker, B.D. HIV and HLA class I: An evolving relationship. Immunity
**2012**, 37, 426–440. [Google Scholar] [CrossRef] [PubMed] - Kløverpris, H.N.; Leslie, A.; Goulder, P. Role of HLA adaptation in HIV evolution. Front. Immunol.
**2015**, 6, 665. [Google Scholar] [CrossRef] [PubMed] - Goonetilleke, N.; Liu, M.K.; Salazar-Gonzalez, J.F.; Ferrari, G.; Giorgi, E.; Ganusov, V.V.; Keele, B.F.; Learn, G.H.; Turnbull, E.L.; Salazar, M.G.; et al. The first T cell response to transmitted/founder virus contributes to the control of acute viremia in HIV-1 infection. J. Exp. Med.
**2009**, 206, 1253–1272. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Turnbull, E.L.; Wong, M.; Wang, S.; Wei, X.; Jones, N.A.; Conrod, K.E.; Aldam, D.; Turner, J.; Pellegrino, P.; Keele, B.F.; et al. Kinetics of expansion of epitope-specific T cell responses during primary HIV-1 infection. J. Immunol.
**2009**, 182, 7131–7145. [Google Scholar] [CrossRef] [PubMed] - Liu, M.K.P.; Hawkins, N.; Ritchie, A.J.; Ganusov, V.V.; Whale, V.; Brackenridge, S.; Li, H.; Pavlicek, J.W.; Cai, F.; Rose-Abrahams, M.; et al. Vertical T cell immunodominance and epitope entropy determine HIV-1 escape. J. Clin. Investig.
**2013**, 123, 380–393. [Google Scholar] [CrossRef] [PubMed] - Riou, C.; Ganusov, V.V.; Campion, S.; Mlotshwa, M.; Liu, M.K.P.; Whale, V.E.; Goonetilleke, N.; Borrow, P.; Ferrari, G.; Betts, M.R.; et al. Distinct kinetics of Gag-specific CD4(+) and CD8(+) T cell responses during acute HIV-1 infection. J. Immunol.
**2012**, 188, 2198–2206. [Google Scholar] [CrossRef] [PubMed] - Yue, L.; Pfafferott, K.J.; Baalwa, J.; Conrod, K.; Dong, C.C.; Chui, C.; Rong, R.; Claiborne, D.T.; Prince, J.L.; Tang, J.; et al. Transmitted virus fitness and host T cell responses collectively define divergent infection outcomes in two HIV-1 recipients. PLoS Pathog.
**2015**, 11, e1004565. [Google Scholar] [CrossRef] [PubMed] - Ndhlovu, Z.M.; Kamya, P.; Mewalal, N.; Klaverpris, H.N.; Nkosi, T.; Pretorius, K.; Laher, F.; Ogunshola, F.; Chopera, D.; Shekhar, K.; et al. Magnitude and Kinetics of CD8(+) T Cell Activation during Hyperacute HIV Infection Impact Viral Set Point. Immunity
**2015**, 43, 591–604. [Google Scholar] [CrossRef] [PubMed] - Miller, J.; van der Most, R.; Akondy, R.; Glidewell, J.; Albott, S.; Masopust, D.; Murali-Krishna, K.; Mahar, P.; Edupuganti, S.; Lalor, S.; et al. Human effector and memory CD8+ T cell responses to smallpox and yellow fever vaccines. Immunity
**2008**, 28, 710–722. [Google Scholar] [CrossRef] [PubMed] - Le, D.; Miller, J.D.; Ganusov, V.V. Mathematical modeling provides kinetic details of the human immune response to vaccination. Front. Cell. Infect. Microbiol.
**2015**, 4, 177. [Google Scholar] [CrossRef] [PubMed] - Davenport, M.P.; Ribeiro, R.M.; Chao, D.L.; Perelson, A.S. Predicting the impact of a nonsterilizing vaccine against human immunodeficiency virus. J. Virol.
**2004**, 78, 11340–11351. [Google Scholar] [CrossRef] [PubMed] - Davenport, M.P.; Ribeiro, R.M.; Perelson, A.S. Kinetics of virus-specific CD8+ T cells and the control of human immunodeficiency virus infection. J. Virol.
**2004**, 78, 10096–10103. [Google Scholar] [CrossRef] [PubMed] - Althaus, C.L.; De Boer, R.J. Dynamics of immune escape during HIV/SIV infection. PLoS Comput. Biol.
**2008**, 4, e1000103. [Google Scholar] [CrossRef] [PubMed] - Asquith, B.; Edwards, C.; Lipsitch, M.; McLean, A. Inefficient cytotoxic T lymphocyte-mediated killing of HIV-1-infected cells in vivo. PLoS Biol.
**2006**, 4, e90. [Google Scholar] [CrossRef] [PubMed] - De Boer, R.J. Understanding the failure of CD8+ T-cell vaccination against simian/human immunodeficiency virus. J. Virol.
**2007**, 81, 2838–2848. [Google Scholar] [CrossRef] [PubMed] - Ganusov, V.V.; De Boer, R.J. Estimating Costs and Benefits of CTL Escape Mutations in SIV/HIV Infection. PLoS Comput. Biol.
**2006**, 2, e24. [Google Scholar] [CrossRef] [PubMed] - Nowak, M.A.; Bangham, C.R.M. Population dynamics of immune responses to persistent viruses. Science
**1996**, 272, 74–79. [Google Scholar] [CrossRef] [PubMed] - Nowak, M.A.; Maya, R.M.; Sigmund, K. Immune responses against multiple epitopes. J. Theor. Biol.
**1995**, 175, 325–353. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Martyushev, A.P.; Petravic, J.; Grimm, A.J.; Alinejad-Rokny, H.; Gooneratne, S.L.; Reece, J.C.; Cromer, D.; Kent, S.J.; Davenport, M.P. Epitope-specific CD8+ T cell kinetics rather than viral variability determine the timing of immune escape in simian immunodeficiency virus infection. J. Immunol.
**2015**, 194, 4112–4121. [Google Scholar] [CrossRef] [PubMed] - van Deutekom, H.W.; Wijnker, G.; de Boer, R.J. The rate of immune escape vanishes when multiple immune responses control an HIV infection. J. Immunol.
**2013**, 191, 3277–3286. [Google Scholar] [CrossRef] [PubMed] - van der Most, R.G.; Concepcion, R.J.; Oseroff, C.; Alexander, J.; Southwood, S.; Sidney, J.; Chesnut, R.W.; Ahmed, R.; Sette, A. Uncovering subdominant cytotoxic T-lymphocyte responses in lymphocytic choriomeningitis virus-infected BALB/c mice. J. Virol.
**1997**, 71, 5110–5114. [Google Scholar] [PubMed] - Vijh, S.; Pilip, I.; Pamer, E. Noncompetitive Expansion of Cytotoxic T Lymphocytes Specific for Different Antigens during Bacterial Infection. Infect. Immun.
**1999**, 67, 1303–1309. [Google Scholar] [PubMed] - Kedl, R.M.; Rees, W.A.; Hildeman, D.A.; Schaefer, B.; Mitchell, T.; Kappler, J.; Marrack, P. T cells compete for access to antigen-bearing antigen-presenting cells. J. Exp. Med.
**2000**, 192, 1105–1113. [Google Scholar] [CrossRef] [PubMed] - Grayson, J.M.; Harrington, L.E.; Lanier, J.G.; Wherry, E.J.; Ahmed, R. Differential sensitivity of naive and memory CD8(+) T cells to apoptosis in vivo. J. Immunol.
**2002**, 169, 3760–3770. [Google Scholar] [CrossRef] [PubMed] - Brehm, M.; Pinto, A.; Daniels, K.; Schneck, J.; Welsh, R.; Selin, L. T cell immunodominance and maintenance of memory regulated by unexpectedly cross-reactive pathogens. Nat. Immunol.
**2002**, 3, 627–634. [Google Scholar] [CrossRef] [PubMed] - Kedl, R.M.; Kappler, J.W.; Marrack, P. Epitope dominance, competition and T cell affinity maturation. Curr. Opin. Immunol.
**2003**, 15, 120–127. [Google Scholar] [CrossRef] - Andreansky, S.S.; Stambas, J.; Thomas, P.G.; Xie, W.; Webby, R.J.; Doherty, P.C. Consequences of immunodominant epitope deletion for minor influenza virus-specific CD8+-T-cell responses. J. Virol.
**2005**, 79, 4329–4339. [Google Scholar] [CrossRef] [PubMed] - D’Souza, W.; Hedrick, S. Cutting edge: Latecomer CD8 T cells are imprinted with a unique differentiation program. J. Immunol.
**2006**, 177, 777–781. [Google Scholar] [CrossRef] [PubMed] - Badovinac, V.; Haring, J.; Harty, J. Initial T cell receptor transgenic cell precursor frequency dictates critical aspects of the CD8(+) T cell response to infection. Immunity
**2007**, 26, 827–841. [Google Scholar] [CrossRef] [PubMed] - Gruta, N.L.L.; Rothwell, W.T.; Cukalac, T.; Swan, N.G.; Valkenburg, S.A.; Kedzierska, K.; Thomas, P.G.; Doherty, P.C.; Turner, S.J. Primary CTL response magnitude in mice is determined by the extent of naive T cell recruitment and subsequent clonal expansion. J. Clin. Investig.
**2010**, 120, 1885–1894. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Farrington, L.A.; Smith, T.A.; Grey, F.; Hill, A.B.; Snyder, C.M. Competition for antigen at the level of the APC is a major determinant of immunodominance during memory inflation in murine cytomegalovirus infection. J. Immunol.
**2013**, 190, 3410–3416. [Google Scholar] [CrossRef] [PubMed] - Fryer, H.R.; Scherer, A.; Oxenius, A.; Phillips, R.; McLean, A.R. No evidence for competition between cytotoxic T-lymphocyte responses in HIV-1 infection. Proc. Biol. Sci.
**2009**, 276, 4389–4397. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Robb, M.L.; Eller, L.A.; Kibuuka, H.; Rono, K.; Maganga, L.; Nitayaphan, S.; Kroon, E.; Sawe, F.K.; Sinei, S.; Sriplienchan, S.; et al. Prospective Study of Acute HIV-1 Infection in Adults in East Africa and Thailand. N. Engl. J. Med.
**2016**, 374, 2120–2130. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Jones, N.A.; Wei, X.; Flower, D.R.; Wong, M.; Michor, F.; Saag, M.S.; Hahn, B.H.; Nowak, M.A.; Shaw, G.M.; Borrow, P. Determinants of human immunodeficiency virus type 1 escape from the primary CD8+ cytotoxic T lymphocyte response. J. Exp. Med.
**2004**, 200, 1243–1256. [Google Scholar] [CrossRef] [PubMed] - De Boer, R.J.; Oprea, M.; Antia, R.; Murali-Krishna, K.; Ahmed, R.; Perelson, A.S. Recruitment times, proliferation, and apoptosis rates during the CD8(+) T-cell response to lymphocytic choriomeningitis virus. J. Virol.
**2001**, 75, 10663–10669. [Google Scholar] [CrossRef] [PubMed] - Jenkins, M.K.; Moon, J.J. The role of naive T cell precursor frequency and recruitment in dictating immune response magnitude. J. Immunol.
**2012**, 188, 4135–4140. [Google Scholar] [CrossRef] [PubMed] - De Boer, R.J.; Homann, D.; Perelson, A.S. Different dynamics of CD4+ and CD8+ T cell responses during and after acute lymphocytic choriomeningitis virus infection. J. Immunol.
**2003**, 171, 3928–3935. [Google Scholar] [CrossRef] [PubMed] - Barton, J.P.; Goonetilleke, N.; Butler, T.C.; Walker, B.D.; McMichael, A.J.; Chakraborty, A.K. Relative rate and location of intra-host HIV evolution to evade cellular immunity are predictable. Nat. Commun.
**2016**, 7, 11660. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Bodine, E.; Lenhart, S.; Gross, L. Mathematics for the Life Sciences; Princeton University Press: Princeton, NJ, USA, 2014. [Google Scholar]
- Haas, G.; Samri, A.; Gomard, E.; Hosmalin, A.; Duntze, J.; Bouley, J.M.; Ihlenfeldt, H.G.; Katlama, C.; Autran, B. Cytotoxic T-cell responses to HIV-1 reverse transcriptase, integrase and protease. AIDS
**1998**, 12, 1427–1436. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Radebe, M.; Gounder, K.; Mokgoro, M.; Ndhlovu, Z.M.; Mncube, Z.; Mkhize, L.; van der Stok, M.; Jaggernath, M.; Walker, B.D.; Ndung’u, T. Broad and persistent Gag-specific CD8+ T-cell responses are associated with viral control but rarely drive viral escape during primary HIV-1 infection. AIDS
**2015**, 29, 23–33. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Radebe, M.; Nair, K.; Chonco, F.; Bishop, K.; Wright, J.K.; van der Stok, M.; Bassett, I.V.; Mncube, Z.; Altfeld, M.; Walker, B.D.; et al. Limited immunogenicity of HIV CD8+ T-cell epitopes in acute Clade C virus infection. J. Infect. Dis.
**2011**, 204, 768–776. [Google Scholar] [CrossRef] [PubMed] - Ganusov, V.V.; Goonetilleke, N.; Liu, M.K.; Ferrari, G.; Shaw, G.M.; McMichael, A.J.; Borrow, P.; Korber, B.T.; Perelson, A.S. Fitness costs and diversity of the cytotoxic T lymphocyte (CTL) response determine the rate of CTL escape during acute and chronic phases of HIV infection. J. Virol.
**2011**, 85, 10518–10528. [Google Scholar] [CrossRef] [PubMed] - Ganusov, V.V.; Barber, D.L.; De Boer, R.J. Killing of targets by CD8 T cells in the mouse spleen follows the law of mass action. PLoS ONE
**2011**, 6, e15959. [Google Scholar] [CrossRef] [PubMed] - Mellors, J.W.; Munoz, A.; Giorgi, J.V.; Margolick, J.B.; Tassoni, C.J.; Gupta, P.; Kingsley, L.A.; Todd, J.A.; Saah, A.J.; Detels, R.; et al. Plasma viral load and CD4+ lymphocytes as prognostic markers of HIV-1 infection. Ann. Intern. Med.
**1997**, 126, 946–954. [Google Scholar] [CrossRef] [PubMed] - Mothe, B.; Llano, A.; Ibarrondo, J.; Daniels, M.; Miranda, C.; Zamarreño, J.; Bach, V.; Zuniga, R.; Pérez-Álvarez, S.; Berger, C.T.; et al. Definition of the viral targets of protective HIV-1-specific T cell responses. J. Transl. Med.
**2011**, 9, 208. [Google Scholar] [CrossRef] [PubMed] - Geldmacher, C.; Gray, C.; Nason, M.; Currier, J.R.; Haule, A.; Njovu, L.; Geis, S.; Hoffmann, O.; Maboko, L.; Meyerhans, A.; et al. A high viral burden predicts the loss of CD8 T-cell responses specific for subdominant gag epitopes during chronic human immunodeficiency virus infection. J. Virol.
**2007**, 81, 13809–13815. [Google Scholar] [CrossRef] [PubMed] - Ribeiro, R.M.; Qin, L.; Chavez, L.L.; Li, D.; Self, S.G.; Perelson, A.S. Estimation of the initial viral growth rate and basic reproductive number during acute HIV-1 infection. J. Virol.
**2010**, 84, 6096–6102. [Google Scholar] [CrossRef] [PubMed] - Alanio, C.; Lemaitre, F.; Law, H.K.; Hasan, M.; Albert, M.L. Enumeration of human antigen-specific naive CD8+ T cells reveals conserved precursor frequencies. Blood
**2010**, 115, 3718–3725. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Murali-Krishna, K.; Altman, J.; Suresh, M.; Sourdive, D.; Zajac, A.; Miller, J.; Slansky, J.; Ahmed, R. Counting antigen-specific CD8+ T cells: A re-evaluation of bystander actiation during viral infection. Immunity
**1998**, 8, 177–187. [Google Scholar] [CrossRef] - Homann, D.; Teyton, L.; Oldstone, M. Differential regulation of antiviral T-cell immunity results in stable CD8+ but declining CD4+ T-cell memory. Nat. Med.
**2001**, 7, 913–919. [Google Scholar] [CrossRef] [PubMed] - Obar, J.J.; Khanna, K.M.; Lefrancois, L. Endogenous naive CD8+ T cell precursor frequency regulates primary and memory responses to infection. Immunity
**2008**, 28, 859–869. [Google Scholar] [CrossRef] [PubMed] - Akondy, R.S.; Johnson, P.L.F.; Nakaya, H.I.; Edupuganti, S.; Mulligan, M.J.; Lawson, B.; Miller, J.D.; Pulendran, B.; Antia, R.; Ahmed, R. Initial viral load determines the magnitude of the human CD8 T cell response to yellow fever vaccination. Proc. Natl. Acad. Sci. USA
**2015**, 112, 3050–3055. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Sergeev, R.A.; Batorsky, R.E.; Rouzine, I.M. Model with two types of CTL regulation and experiments on CTL dynamics. J. Theor. Biol.
**2010**, 263, 369–384. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Kemp, R.A.; Powell, T.J.; Dwyer, D.W.; Dutton, R.W. Cutting edge: Regulation of CD8+ T cell effector population size. J. Immunol.
**2004**, 173, 2923–2927. [Google Scholar] [CrossRef] [PubMed] - Badovinac, V.P.; Harty, J.T. Manipulating the rate of memory CD8+ T cell generation after acute infection. J. Immunol.
**2007**, 179, 53–63. [Google Scholar] [CrossRef] [PubMed] - Bocharov, G.; Ludewig, B.; Bertoletti, A.; Klenerman, P.; Junt, T.; Krebs, P.; Luzyanina, T.; Fraser, C.; Anderson, R.M. Underwhelming the immune response: Effect of slow virus growth on CD8+-T-lymphocyte responses. J. Virol.
**2004**, 78, 2247–2254. [Google Scholar] [CrossRef] [PubMed] - Davenport, M.P.; Belz, G.T.; Ribeiro, R.M. The race between infection and immunity: How do pathogens set the pace? Trends Immunol.
**2009**, 30, 61–66. [Google Scholar] [CrossRef] [PubMed] - Kastenmuller, W.; Gasteiger, G.; Gronau, J.H.; Baier, R.; Ljapoci, R.; Busch, D.H.; Drexler, I. Cross-competition of CD8+ T cells shapes the immunodominance hierarchy during boost vaccination. J. Exp. Med.
**2007**, 204, 2187–2198. [Google Scholar] [CrossRef] [PubMed] - Smith, A.L.; Wikstrom, M.E.; Fazekas de St Groth, B. Visualizing T cell competition for peptide/MHC complexes: A specific mechanism to minimize the effect of precursor frequency. Immunity
**2000**, 13, 783–794. [Google Scholar] [CrossRef] - Probst, H.C.; Dumrese, T.; van den Broek, M.F. Cutting edge: Competition for APC by CTLs of different specificities is not functionally important during induction of antiviral responses. J. Immunol.
**2002**, 168, 5387–5391. [Google Scholar] [CrossRef] [PubMed] - Owen, R.E.; Heitman, J.W.; Hirschkorn, D.F.; Lanteri, M.C.; Biswas, H.H.; Martin, J.N.; Krone, M.R.; Deeks, S.G.; Norris, P.J.; NIAID Center for HIV/AIDS Vaccine Immunology. HIV+ elite controllers have low HIV-specific T-cell activation yet maintain strong, polyfunctional T-cell responses. AIDS
**2010**, 24, 1095–1105. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Halsey, L.G.; Curran-Everett, D.; Vowler, S.L.; Drummond, G.B. The fickle P value generates irreproducible results. Nat. Methods
**2015**, 12, 179–185. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Martin, G.E.; Gossez, M.; Williams, J.P.; Stöhr, W.; Meyerowitz, J.; Leitman, E.M.; Goulder, P.; Porter, K.; Fidler, S.; Frater, J.; et al. Post-treatment control or treated controllers? Viral remission in treated and untreated primary HIV infection. AIDS
**2017**, 31, 477–484. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Lanzavecchia, A. Lack of fair play in the T cell response. Nat. Immunol.
**2002**, 3, 9–10. [Google Scholar] [CrossRef] [PubMed] - Tilman, D. Resource Competition and Community Structure; Princeton University Press: Princeton, NJ, USA, 1982. [Google Scholar]
- Amanna, I.J.; Carlson, N.E.; Slifka, M.K. Duration of humoral immunity to common viral and vaccine antigens. N. Engl. J. Med.
**2007**, 357, 1903–1915. [Google Scholar] [CrossRef] [PubMed] - Althaus, C.L.; Ganusov, V.V.; De Boer, R.J. Dynamics of CD8+ T cell responses during acute and chronic lymphocytic choriomeningitis virus infection. J. Immunol.
**2007**, 179, 2944–2951. [Google Scholar] [CrossRef] [PubMed] - Fiebig, E.W.; Wright, D.J.; Rawal, B.D.; Garrett, P.E.; Schumacher, R.T.; Peddada, L.; Heldebrant, C.; Smith, R.; Conrad, A.; Kleinman, S.H.; et al. Dynamics of HIV viremia and antibody seroconversion in plasma donors: Implications for diagnosis and staging of primary HIV infection. AIDS
**2003**, 17, 1871–1879. [Google Scholar] [CrossRef] [PubMed] - Giorgi, E.E.; Funkhouser, B.; Athreya, G.; Perelson, A.S.; Korber, B.T.; Bhattacharya, T. Estimating time since infection in early homogeneous HIV-1 samples using a poisson model. BMC Bioinform.
**2010**, 11, 532. [Google Scholar] [CrossRef] [PubMed] - McMichael, A.J.; Haynes, B.F. Lessons learned from HIV-1 vaccine trials: New priorities and directions. Nat. Immunol.
**2012**, 13, 423–427. [Google Scholar] [CrossRef] [PubMed]

**Figure 1.**Schematic representation of the ${T}_{\mathrm{on}}/{T}_{\mathrm{off}}$ mathematical model fitted to the epitope-specific CD8${}^{+}$ T-cell response kinetics data [86]. In this model, ${E}_{0}$ epitope-specific naive CD8${}^{+}$ T cells become activated at time $t={T}_{\mathrm{on}}$ and start proliferating at rate $\rho $. At $t={T}_{\mathrm{off}}$, T-cell response peaks and declines at rate $\alpha $. We refer to ${E}_{0}$ as the predicted initial frequency of epitope-specific CD8${}^{+}$ T cells [87]. Evidently, ${E}_{0}$ may over- or under-estimate the response precursor frequency depending on exactly when the T cells became activated and how adequate the mathematical model is for describing immune response data during the expansion phase.

**Figure 2.**Most HIV proteins were recognized by CD8${}^{+}$ T-cell responses. We calculated the frequency at which HIV proteins were recognized by CD8${}^{+}$ T cells; overall, 50% of responses were directed against Env or Gag (

**A**). $m=8$ CD8${}^{+}$ T cell responses were detected in this cohort of 22 patients at any given time point after infection (

**B**). In B (and other figures in the paper), $\mu $ denotes the average, m is the median, and $\sigma $ is the standard deviation. The distributions are shown for the first 100 days after symptom onset but, overall, distributions changed little over the course of 400 days of infection. Patient SUMA0874 was excluded from the analysis in B due to a lack of measurements of all T-cell responses at all time points.

**Figure 3.**Modest yet statistically significant increase in the average normalized T-cell response breadth over the course of the first year of HIV infection. We divided the observations into different time bins ((

**A**) 50-day intervals; (

**B**) 100-day intervals) and calculated the relative breadth for the corresponding interval. The relative breadth was calculated as the number of HIV-specific CD8${}^{+}$ T-cell responses detected in a given time period divided by the number of all responses measured for that patient in all time periods; data were averaged to simplify presentation. Averaging did not influence the statistical significance of conclusions. Colors and symbols represent the data from different patients as shown in Figure S5 in Supplementary Material. Black horizontal bars denote the mean relative breadth for that time interval for all patients. There was a statistically significant increase in relative breadth (Spearman’s rank correlation coefficient $\rho $ and p values indicated on panels). There was no change in the average total immune response in all patients (Figure S6). Detailed analysis of the relative number of CD8${}^{+}$ T-cell responses in individual patients revealed variable patterns: constant breadth, increasing breadth, decreasing breadth, and breadth changing non-monotonically over time (Figure S7). Also, no overall change in the average breadth (un-normalized) was observed (Figure S5). We observed a similarly modest but significant increase in $SE$ and $EI$ of HIV-specific CD8${}^{+}$ T-cell response with time (Figure S8).

**Figure 4.**Breadth of HIV-specific CD8${}^{+}$ T-cell response in a patient does not correlate significantly with average viral load. We calculated the average number of HIV-specific (

**A**–

**C**), Gag-specific (

**D**–

**F**), and Env-specific (

**G**–

**I**) CD8${}^{+}$ T-cell responses over the whole observation period (

**A**,

**D**,

**G**), during acute infection ($t\le 100$ days since symptom onset; (

**B**,

**E**,

**H**)), or during chronic infection ($t>100$ days since symptom onset; (

**C**,

**F**,

**I**)) and ${log}_{10}$ average viral load in that time period. The average viral load during infection was not dependent on the breadth of the Gag-specific CD8${}^{+}$ T-cell response during the infection (

**D**–

**F**). Patient SUMA0874 was excluded from the analysis in (

**A**–

**C**) due to insufficient measurements of all T-cell responses at all time points.

**Figure 5.**Expanding CD8${}^{+}$ T-cell responses were negatively correlated with viral load before T-cell numbers reached their peak values. We calculated Spearman’s correlation coefficients between longitudinal changes in viral load and epitope-specific CD8${}^{+}$ T-cell responses in each patient during the whole period (

**A**), and before (

**B**) and after (

**C**) the peak of CD8${}^{+}$ T-cell response. The $f(cc<0)$ value denotes the fraction of negative correlation coefficients ($cc$), and p values are indicated for the binomial test of equal distribution of positive and negative correlations.

**Figure 6.**Differences in the kinetics of early and late HIV-specific CD8${}^{+}$ T-cell responses. We fitted the ${T}_{\mathrm{on}}/{T}_{\mathrm{off}}$ model (Equation (1)) to the data on the dynamics of epitope-specific CD8${}^{+}$ T-cell response in each patient and plotted the distribution of the estimated parameters. The results are presented separately for T cell responses that started expanding (or contracting) from the first observation (“early” responses, about 80% of all responses; black) or delayed responses, which were undetectable at one or several initial time points (“late” responses; red). Panels show distributions for (

**A**) time of expansion of T-cell response (${T}_{\mathrm{on}}$), (

**B**) time to peak of each T-cell response (${T}_{\mathrm{off}}$), (

**C**) initial predicted frequency of epitope-specific CD8${}^{+}$ T cells (${E}_{0}$), (

**D**,

**E**) expansion ($\rho $) and contraction ($\alpha $) rates of T-cell responses, respectively, and (

**F**) proteins recognized by late CD8${}^{+}$ T-cell responses. In (

**A**–

**E**), n represents the number of fitted responses, and $\mu $, m and $\sigma $ represent mean, median and standard deviation, respectively (${\mu}_{10}$, ${m}_{10}$, and ${\sigma}_{10}$ are mean, median, and standard deviation for ${log}_{10}$-scaled parameters). Late responses were predicted to have a higher expansion rate $\rho $ (Mann–Whitney, $p<0.001$) and smaller frequency ${E}_{0}$ (Mann–Whitney, $p<0.001$) than early responses.

**Figure 7.**Correlations between major parameters determining dynamics of HIV-specific CD8${}^{+}$ T-cell responses in acute infection. For all epitope-specific CD8${}^{+}$ T-cell responses in all 22 patients (circles) or the total HIV-specific CD8${}^{+}$ T-cell response per patient (stars), we estimated the initial frequency of epitope-specific CD8${}^{+}$ T cells (${E}_{0}$), rate of expansion of T-cell populations ($\rho $), time of the peak of the response (${T}_{\mathrm{off}}$), rate of contraction of the immune response after the peak ($\alpha $), predicted peak values reached by the epitope-specific CD8${}^{+}$ T-cell response (${E}_{\mathrm{peak}}=E\left({T}_{\mathrm{off}}\right)$), and the average viral load (${V}_{E}$). Solid lines denote regression lines; regression equations and p values are indicated on individual panels for all epitope-specific CD8${}^{+}$ T-cell responses. The total HIV-specific CD8${}^{+}$ T-cell response showed a similar trend to all epitope-specific CD8${}^{+}$ T-cell responses. Panels show correlations between the timing of the immune response peak ${T}_{\mathrm{off}}$ and predicted frequency ${E}_{0}$ (

**A**), ${T}_{\mathrm{off}}$ and $\rho $ (

**B**), expansion rate $\rho $ and average viral load ${V}_{E}$ (

**C**), $\rho $ and ${E}_{0}$ (

**D**), peak immune response ${E}_{\mathrm{peak}}$ and ${E}_{0}$ (

**E**), and ${E}_{\mathrm{peak}}$ and ${V}_{E}$ (

**F**). For a given patient, we calculated the total HIV-specific CD8${}^{+}$ T-cell response as the sum of all epitope-specific CD8${}^{+}$ T-cell responses at the same time point (i.e., by ignoring “nd”). For patient MM42, we could not fit the ${T}_{\mathrm{on}}/{T}_{\mathrm{off}}$ model to the dynamics of total CD8${}^{+}$ T cell response data because of wide oscillations in the data. Identified relationships did not change if estimates for responses with unphysiological initial frequencies (${E}_{0}\le {10}^{-2}$) were excluded from the analysis.

**Figure 8.**Evidence of interclonal competition between epitope-specific CD8${}^{+}$ T cell responses. We calculated Spearman’s rank correlation coefficients between longitudinal changes of pairs of epitope-specific CD8${}^{+}$ T cell responses in a given patient (see individual panels) and plotted the distribution of these coefficients. Panels show the number of correlations (n), fraction of negative correlation coefficients ($f\left(cc\right)<0$), and p values for the deviance of the distribution from uniform, found using the binomial test with null being the equal fraction of positive and negative correlations. We found that the majority of CD8${}^{+}$ T-cell populations expand and contract in unison and therefore do not appear to compete during the infection. Overall, discordant dynamics (negative correlation coefficients) were observed for 18% of all responses irrespective of the stage of infection (acute or chronic). Patients MM38 and MM40 were excluded from the analysis for having too few correlation pairs (two or three).

**Figure 9.**Average size of epitope-specific CD8${}^{+}$ T-cell response is unrelated to the number of HIV-specific T-cell responses. For every patient, we calculated the average number of HIV-specific CD8${}^{+}$ T-cell responses and the average density of epitope-specific T cells in a given observation period. To exclude the contribution of viral load to this relationship, we divided all 22 patients into three groups according to their mean viral load (low ${log}_{10}$ viral load: 3.40–4.44 (disks) (

**A**); intermediate viral load: 4.60–5.03 (stars) (

**B**); high viral load: 5.25–6.83 (diamonds) (

**C**)). Groups were estimated using the Manhattan Distance with the FindClusters function in Mathematica. Regression lines and corresponding p values are indicated on individual panels. Overall, results varied by time period and most correlations were not statistically significant (Figure S12).

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Yang, Y.; Ganusov, V.V.
Defining Kinetic Properties of HIV-Specific CD8^{+} T-Cell Responses in Acute Infection. *Microorganisms* **2019**, *7*, 69.
https://doi.org/10.3390/microorganisms7030069

**AMA Style**

Yang Y, Ganusov VV.
Defining Kinetic Properties of HIV-Specific CD8^{+} T-Cell Responses in Acute Infection. *Microorganisms*. 2019; 7(3):69.
https://doi.org/10.3390/microorganisms7030069

**Chicago/Turabian Style**

Yang, Yiding, and Vitaly V. Ganusov.
2019. "Defining Kinetic Properties of HIV-Specific CD8^{+} T-Cell Responses in Acute Infection" *Microorganisms* 7, no. 3: 69.
https://doi.org/10.3390/microorganisms7030069