Link between the numbers of particles and variants founding new HIV-1 infections depends on the timing of transmission

Abstract

Understanding which HIV-1 variants are most likely to be transmitted is important for vaccine design and predicting virus evolution. Since most infections are founded by single variants, it has been suggested that selection at transmission has a key role in governing which variants are transmitted. We show that the composition of the viral population within the donor at the time of transmission is also important. To support this argument, we developed a probabilistic model describing HIV-1 transmission in an untreated population, and parameterised the model using both within-host next generation sequencing data and population-level epidemiological data on heterosexual transmission. The most basic HIV-1 transmission models cannot explain simultaneously the low probability of transmission and the non-negligible proportion of infections founded by multiple variants. In our model, transmission can only occur when environmental conditions are appropriate (e.g. abrasions are present in the genital tract of the potential recipient), allowing these observations to be reconciled. As well as reproducing features of transmission in real populations, our model demonstrates that, contrary to expectation, there is not a simple link between the number of viral variants and the number of viral particles founding each new infection. These quantities depend on the timing of transmission, and infections can be founded with small numbers of variants yet large numbers of particles. Including selection, or a bias towards early transmission (e.g. due to treatment), acts to enhance this conclusion. In addition, we find that infections initiated by multiple variants are most likely to have derived from donors with intermediate set-point viral loads, and not from individuals with high set-point viral loads as might be expected. We therefore emphasise the importance of considering viral diversity in donors, and the timings of transmissions, when trying to discern the complex factors governing single or multiple variant transmission.

Keywords: HIV-1 vaccine; mathematical modelling; selection bottleneck; transmitted HIV-1 variants; viral evolution; virus transmission.

Figure 1.

Schematic illustrating how the number of viral particles and number of variants founding a new infection were described by our model. The viral load and the proportion of each variant in the donor (potentially accounting for selection at transmission, as described in Section 4) were used to determine the number of particles of each variant available for transmission in the donor’s genital tract. When a successful transmission act occurred, the particles that successfully founded the new infection were sampled at random from those in the genital tract.

Figure 2.

Viral loads in donors. (A) Proportions of infected individuals with different SPVLs. (B) Viral load profiles assumed in our model. Viral load profiles shown in (B) appear in the population of donors according to the proportions shown in (A). Some of the SPVL values from (A) are omitted in (B) for clarity, but all values in (A) are included in our analyses.

Figure 3.

Distribution of variants in donors during the course of untreated infection. All data are for integrase. In the left column, the x-axis represents the xth most common variant at the time of sampling, whereas in the right column the x-axis represents xth most common variant after adjusting for selection ($\alpha$_s = 3). Note that the xth variant in one subfigure does not necessarily correspond to the xth variant in another subfigure. Bars represent the model fit to all the data using a discretised gamma distribution (see Section 4), and the red dots represent the data from one of the individuals (individual 3). We displayed data from this individual because of their long duration of infection and approximately equally spaced sampling time points. (A) 0.4 years since infection; (B) 2.2 years since infection; (C) 4 years since infection; (D) 6.4 years since infection; (E) 8.4 years since infection. Data from other infected individuals, and other regions of the viral genome, are shown in Supplementary Figs S10–S12.

Figure 4.

Distributions of transmitted numbers of particles and variants. (A) No selection and no weighting to early infection. The top left panel gives the distributions of the numbers of particles (teal) and numbers of distinct variants (grey) founding new infections in the population. The top middle panel shows the joint probability distribution of the numbers of particles and variants founding new infections; the area of each circle is proportional to the probability that exactly n particles and N variants were transmitted. The top right panel gives the distribution of the numbers of particles (teal) and numbers of distinct variants (grey) founding new infections in the population, from donors in early infection only (infected for less than 2 years). The bottom panels are the joint probability distributions that n particles and N variants are transmitted, conditioned on the donor being in primary (bottom left), chronic (bottom middle), and pre-AIDS (bottom right) infection. (B) Figures analogous to the top row of (A), with selection at transmission ($\alpha$_s = 3). (C) Figures analogous to the top row of (A), with no selection at transmission but with a bias towards early transmission. The right panel is omitted since the bias towards early infection is assumed to change the proportion of infections in early infection (before 2 years), but not the composition of transmissions occurring during early infection, and so the result is identical to the top right panel of (A). In the case with selection, due to the reduced diversity of variants available for transmission, some infections must be with large numbers of particles so that Prob(transmit multiple variants) = 0.3. Because of these large numbers of particles, the ranges on the x-axes in all panels of (B) and the y-axes of the middle panel of (B) are larger than in the equivalent subfigures in (A) and (C). For parameter values, see Tables 1 and 2 of Supplementary Text S1. In (C), the same parameter values as (A) were used but with infection w = 10 times more likely at times when donors have been infected for less than τ_crit = 2 years.

Figure 5.

Relationship between number of T/F variants and donor SPVL. (A) No selection and no weighting to early infection. Left: The joint probability distribution of the number of distinct variants initiating a randomly chosen infection and the SPVL of the donor. The area of each circle is proportional to the probability of a randomly chosen infection both originating from a donor with SPVL V_c and being founded by N variants. Centre: Conditional on transmission, the probability that an individual with SPVL V_c transmits multiple variants. Right: Probability that a randomly chosen infection initiated by multiple variants arose from a donor with SPVL V_c. (B) Figures analogous to (A), but with selection at transmission ($\alpha$_s = 3). (C) Figures analogous to (A), but with a bias towards early transmission. For parameter values, see Tables 1 and 2 of Supplementary Text S1. In (C), the same parameter values as (A) were used but with infection w = 10 times more likely at times when each donor has been infected for less than 2 years.