Constructing lower-bounds for CTL escape rates in early SIV infection

Highlights

• In HIV and SIV infections, the viral population repeatedly escapes from CTL response.

• We develop inference methods to estimate the rate of the first CTL escape.

• Using frequency data, we construct estimators which serve as lower bounds for the escape rate.

• The early part of the first CTL escape proceeds quicker than later parts.

• The rate of the first CTL escape diers across dierent infected compartments.

Abstract

Intrahost human and simian immunodeficiency virus (HIV and SIV) evolution is marked by repeated viral escape from cytotoxic T-lymphocyte (CTL) response. Typically, the first such CTL escape starts around the time of peak viral load and completes within one or two weeks. Many authors have developed methods to quantify CTL escape rates, but existing methods depend on sampling at two or more timepoints. Since many datasets capture the dynamics of the first CTL escape at a single timepoint, we develop inference methods applicable to single timepoint datasets. To account for model uncertainty, we construct estimators which serve as lower bounds for the escape rate. These lower-bound estimators allow for statistically meaningful comparison of escape rates across different times and different compartments. We apply our methods to two SIV datasets, showing that escape rates are relatively high during the initial days of the first CTL escape and drop to lower levels as the escape proceeds.

Introduction

During HIV and SIV infections, the viral population repeatedly escapes from selective pressure exerted by cytotoxic T-lymphocytes (CTLs), a type of immune system cell. Each CTL targets a specific peptide, referred to as an epitope, associated with a locus on the viral genome. Mutation at the locus may change the epitope, making it partially or completely unrecognisable by existing CTLs. Viruses possessing such mutations are at a selective advantage, leading to a selective sweep referred to as a CTL escape. See Goulder and Watkins (2004) for a review of CTL escape in both HIV and SIV infections.

In this work, we consider the first CTL escape to occur during an infection. In SIV and HIV infections, CTL response initiates roughly at 14 and 21 days after infection, respectively, just prior to peak viral load (Borrow et al., 1994, Cohen et al., 2011, Goulder and Watkins, 2004, McMichael et al., 2010). In the week or two following the initiation of CTL response, CTL escape often occurs at a single targeted epitope (Boutwell et al., 2010, McMichael et al., 2010, Goonetilleke et al., 2009, Henn et al., 2012, Allen et al., 2000). T-cell tetramer studies suggest that this escape is driven by an especially focused CTL response in comparison to subsequent responses and escapes (Turnbull et al., 2009, Yasutomi et al., 1994, Veazey et al., 2003).

Many authors have attempted to quantify the strength of CTL response by measuring the rate at which CTL escape occurs. A commonly used method (e.g. Goonetilleke et al., 2009, Love et al., 2008, Loh et al., 2008, Asquith and McLean, 2007, Ganusov et al., 2011), introduced in Fernandez et al. (2005), Asquith et al. (2006), fits escape mutation frequencies at two timepoints to a differential equation model. The model fit is determined by a parameter, known as the escape rate, which is used to quantify the strength of CTL response at a given epitope. Since this approach requires frequency data at two timepoints, we call it the two-point method.

Using the two-point method to analyze the first CTL escape is difficult because rarely do both sampled timepoints capture the escape. For example, the first two timepoints available in HIV studies of acute infection are typically in the range of days 30 and 50, e.g. Fisher et al. (2010) and Goonetilleke et al. (2009). Using the two-point method on such data estimates escape rates between days 30 and 50, while CTL response is likely strongest prior to day 30. The situation is different for SIV studies. Since the time of infection can be controlled, sampling timepoints can be chosen that straddle day 14, the approximate time of CTL response; for example sampling can occur at days 7 and 21. But usually the CTL escape has not started at day 7, so the two-point method must be applied using data collected at day 21 and a later timepoint, leading to the same difficulties seen in HIV datasets.

Other authors (e.g. Mandl et al., 2007, Althaus and de Boer, 2008, Petravic et al., 2008, Monteiro et al., 2000) have developed methods based on the standard model of viral dynamics (Perelson, 2002, Nowak and May, 2000). These methods depend on models with many parameters, in contrast the two-point method depends only on the escape rate and the mutation frequencies at the two timepoints. Further, fitting the standard model and its variants requires multiple timepoints, so the time period to which such escape rate estimates apply is often unclear. Recently, haplotype data has been used to estimate escape rates, but this method is more applicable to later timepoints in infection, when the viral population possesses significant genetic diversity (Messer and Neher, 2012).

The rate of CTL escape can be defined in different ways. For example, some authors measure the timespan from initiation of CTL response to the time when mutant frequencies reach a prescribed level (Liu et al., 2006, Palmer et al., 2013). In the two-point method, using the underlying model, the escape rate is the difference between the average CTL kill rate and the fitness cost of mutation (Asquith et al., 2006, Fernandez et al., 2005). We take this as our definition of the escape rate.

In this work, we develop inference methods for estimating the rate of the first CTL escape using frequency data from a single timepoint. We apply these methods to SIV datasets, a setting in which inference is slightly easier because infection time is typically known, but our methods extend to HIV escape as well. For SIV infection, we have in mind frequency data collected somewhere between days 14 and 28, times that capture the first CTL escape when the mutation frequency is substantial, but before escape at other epitopes has developed. Single timepoint methods have been used to infer early growth rates for cytomegalovirus, a situation in which immune response and viral mutation are less important (Cromer et al., 2013).

The price we pay for using a single timepoint is the need for an underlying model describing viral dynamics and evolution in the early stages of infection, prior to peak viral load. Specifying such a model is difficult because the dynamics of early SIV and HIV infections are poorly understood. We solve this difficulty by introducing a model that allows for a range of assumptions on early viral dynamics depending on the parameters chosen. Then, in order to cope with the resulting large parameter space, we derive estimators which serve as lower bounds for the escape rate over a large range of possible models.

We apply our methods to the two SIV datasets presented in Bimber et al. (2009) and Vanderford et al. (2011). By combining lower-bound estimators and the two-point method, we are able to compare escape rates between early and late time periods during the first CTL escape, as well as across different compartments. Our results also clarify the role of different modeling assumptions on escape rate inference.