We used ultra-deep sequencing to obtain tens of thousands of HIV-1 sequences from regions targeted by CD8+ T lymphocytes from longitudinal samples from three acutely infected subjects, and modeled viral evolution during the critical first weeks of infection. Previous studies suggested that a single virus established productive infection, but these conclusions were tempered because of limited sampling; now, we have greatly increased our confidence in this observation through modeling the observed earliest sample diversity based on vastly more extensive sampling. Conventional sequencing of HIV-1 from acute/early infection has shown different patterns of escape at different epitopes; we investigated the earliest escapes in exquisite detail. Over 3–6 weeks, ultradeep sequencing revealed that the virus explored an extraordinary array of potential escape routes in the process of evading the earliest CD8 T-lymphocyte responses – using 454 sequencing, we identified over 50 variant forms of each targeted epitope during early immune escape, while only 2–7 variants were detected in the same samples via conventional sequencing. In contrast to the diversity seen within epitopes, non-epitope regions, including the Envelope V3 region, which was sequenced as a control in each subject, displayed very low levels of variation. In early infection, in the regions sequenced, the consensus forms did not have a fitness advantage large enough to trigger reversion to consensus amino acids in the absence of immune pressure. In one subject, a genetic bottleneck was observed, with extensive diversity at the second time point narrowing to two dominant escape forms by the third time point, all within two months of infection. Traces of immune escape were observed in the earliest samples, suggesting that immune pressure is present and effective earlier than previously reported; quantifying the loss rate of the founder virus suggests a direct role for CD8 T-lymphocyte responses in viral containment after peak viremia. Dramatic shifts in the frequencies of epitope variants during the first weeks of infection revealed a complex interplay between viral fitness and immune escape.

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Abstract. Existing stochastic models of unsaturated flow and transport are usually developed using the simple Gardner-Russo constitutive relationship though it is generally accepted that the more complex van Genuchten and Brooks-Corey relationships may perform better in describing experimental data. In this paper, we develop first-order stochastic models for gravity-dominated flow in second-order stationary media with both the Brooks-Corey and the Gardner-Russo constitutive relationships. These models also account for the spatial variability in effective water content, while the spatial variability is generally neglected in most existing stochastic models. Analytical solutions are obtained for the case of one-dimensional gravity-dominated flow. On the basis of the solutions, we illustrate the differences between results from these two constitutive models through some one-dimensional examples. It is found that the impacts of the constitutive models on the statistical moments of suction head, effective water content, unsaturated hydraulic conductivity, and velocity depend on the saturation ranges. For example, the mean head and the mean effective water content for the Brooks-Corey model differ in a great manner with their counterparts for the Gardner-Russo model near the dry and wet limits while the differences are small at the intermediate range of saturation. This finding is confirmed with some two-dimensional examples. It is also found that the Brook-Corey model has certain advantages over the Gardner-Russo model in analyzing unsaturated flow in heterogeneous media. For example, the stochastic model developed based on the BrooksCorey function requires the coefficient of variation of head and soil parameter "aac" to be small (<<1), whereas that based on the Gardner-Russo function assumes the one-point cross covariance of head and a• to be small (<<1). Illustrative examples reveal that the latter condition may be violated because the one-point covariance is found to increase rapidly to beyond unity as the soil becomes dry, whereas the former may be readily satisfied.

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