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. 2015 Jan 13:5:661.
doi: 10.3389/fimmu.2014.00661. eCollection 2014.

The Effect of Interference on the CD8(+) T Cell Escape Rates in HIV

Victor Garcia  1 , Roland Robert Regoes  1
Affiliations

The Effect of Interference on the CD8(+) T Cell Escape Rates in HIV

Victor Garcia et al. Front Immunol. .

Abstract

In early human immunodeficiency virus (HIV) infection, the virus population escapes from multiple CD8(+) cell responses. The later an escape mutation emerges, the slower it outgrows its competition, i.e., the escape rate is lower. This pattern could indicate that the strength of the CD8(+) cell responses is waning, or that later viral escape mutants carry a larger fitness cost. In this paper, we investigate whether the pattern of decreasing escape rates could also be caused by genetic interference among different escape strains. To this end, we developed a mathematical multi-epitope model of HIV dynamics, which incorporates stochastic effects, recombination, and mutation. We used cumulative linkage disequilibrium measures to quantify the amount of interference. We found that nearly synchronous, similarly strong immune responses in two-locus systems enhance the generation of genetic interference. This effect, combined with a scheme of densely spaced sampling times at the beginning of infection and sparse sampling times later, leads to decreasing successive escape rate estimates, even when there were no selection differences among alleles. These predictions are supported by empirical data from one HIV-infected patient. Thus, interference could explain why later escapes are slower. Considering escape mutations in isolation, neglecting their genetic linkage, conceals the underlying haplotype dynamics and can affect the estimation of the selective pressure exerted by CD8(+) cells. In systems in which multiple escape mutations appear, the occurrence of interference dynamics should be assessed by measuring the linkage between different escape mutations.

Keywords: HIV dynamics; cytotoxic T lymphocytes; escape; interference; mathematical modeling; theoretical biology.

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Figures

Figure 1
Figure 1
Pattern of ERD emerging from repeated application of logistic model fits in an interference scenario. (A) Population frequencies of two-locus system haplotypes display interference. The wildtype ab (green area) gives rise to two beneficial single mutants Ab and aB (yellow and violet areas, respectively). (B) Fixation patterns of the beneficial alleles A (orange line) and B (green line). Samples of frequencies of A and B are taken at times 10, 20, and 50 days (blue points). Logistic model fits (red lines) are laid through sample points with an added noise (green points). (C) From each logistic model fit the escape time and escape rate are calculated. A pattern of ERD is generated due to interference.
Figure 2
Figure 2
Example for a simulation run showing sequential escapes in a scaled down two-locus two-allele system. (A) Time course of the number of non-productively infected cells by strain types show sequential transitions from the wildtype to a single escape mutant to a double mutant. (B) Analogous situation for the time courses of productively infected cells. Productively infected cells are cleared by epitope-specific CD8+ T cell action. The mounted immune response leads to a transitory decrease of the total number of productively infected cells. (C) The CD8+ functions E1 and E2 start at 0 and 15 days, respectively, with a final value of 107. The mounting of the immune response coincides with the temporary reduction of infected and productively infected cell numbers. (D) The killing of productively infected cells causes the transitory reduction of produced virions, temporarily reducing net new infections, and releasing target cells. Parameters are as given in Table 1.
Figure 3
Figure 3
Three HIV dynamics scenarios and the cumulative LD. (A) The wildtype population is replaced by a double mutant. A positive LD is generated during the replacement leading to positive cumulative LD. (B) Succession of wildtype, single mutant, and double mutant. LD remains zero for each transition. (C) Wildtype is replaced by two single mutants, which are in turn outcompeted by the double mutant. The longer the single mutants coexist, the more negative the cumulative LD value will be.
Figure 4
Figure 4
Cumulative LD values for simulation runs of a downsized two-locus system (a = 10−4) differing in CD8+ T cell function strength and timing. The x-axis denotes the time delay the second immune response has to the first. The black line is the median of 100 simulations, the upper and lower end of the blue-shaded area are the 75 and 25 percentiles of all measured simulation runs, respectively. K1 and K2 denote the final values for the first and the second immune responses, respectively. (A) Little cumulative LD is generated for K1 < K2. Pronounced negative cumulative LD values are attained for nearly equally spaced CD8+ T cell curves in (B,C). (D) Shows an increase in interference at a delay of 5 days.
Figure 5
Figure 5
Density plot of negative cumulative LD versus ERD values for 1000 simulations runs for equal CD8+ T cell final values of K1 = K2 = 7 ⋅ 106 and zero time delay between the elicitation of the CD8+ T cell functions. Positive cumulative LD values were ignored. Black line: base line through the origin. Red line: Theil–Sen estimator fit on data. The density distribution is compressed along a line of positive slope, indicating a positive association between interference and ERD values.
Figure 6
Figure 6
A possible instance of interference generating ERD in Ref. (16). (A) The fits of the logistic escape model as used in Ref. (15) to the sample points of escape mutant frequency. Escape mutations appear in the epitopes Nef A24-RW8 and Vif B38-WI9 as a consequence of two, nearly equally potent CTL responses specific to these epitopes. (B) The LD between Nef A24-RW8 and Vif B38-WI9 becomes negative at one of the time points sampled (connected by blue line). To calculate LD, we constructed a contingency table with the frequencies of wildtype (no mutations in any epitope), single mutants (escape mutation in one epitope) and the double mutant (escape mutations in both Nef and Vif) reconstructed in Ref. (28) and measured D as defined above. (C) The inferred escape rates of the escape mutations in Nef and Vif show ERD.
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