Abstract
The rates of escape and reversion in response to selection pressure arising from the host immune system, notably the cytotoxic T-lymphocyte (CTL) response, are key factors determining the evolution of HIV. Existing methods for estimating these parameters from cross-sectional population data using ordinary differential equations (ODEs) ignore information about the genealogy of sampled HIV sequences, which has the potential to cause systematic bias and overestimate certainty. Here, we describe an integrated approach, validated through extensive simulations, which combines genealogical inference and epidemiological modelling, to estimate rates of CTL escape and reversion in HIV epitopes. We show that there is substantial uncertainty about rates of viral escape and reversion from cross-sectional data, which arises from the inherent stochasticity in the evolutionary process. By application to empirical data, we find that point estimates of rates from a previously published ODE model and the integrated approach presented here are often similar, but can also differ several-fold depending on the structure of the genealogy. The model-based approach we apply provides a framework for the statistical analysis and hypothesis testing of escape and reversion in population data and highlights the need for longitudinal and denser cross-sectional sampling to enable accurate estimate of these key parameters.
Highlights
Cytotoxic T-lymphocytes (CTLs) are implicated in the control of human immunodeficiency virus 1 (HIV-1)
Epitopes are presented to CTLs by human leukocyte antigen (HLA) class I proteins at the surface of almost all nucleated cells in the body
By altering the nucleotide substitution rate, we find that a lack of information about the genealogy can dramatically affect escape and reversion rate estimations using our integrated approach, though we find that the rates of substitution found in HIV are sufficiently large for this effect to be considered negligible
Summary
Cytotoxic T-lymphocytes (CTLs) are implicated in the control of human immunodeficiency virus 1 (HIV-1). Simple ordinary differential equation (ODE)-based models have been used to estimate the expected time to escape and reversion by using cross-sectional data across hosts Such estimates make use of only a small portion of the available data, namely presence or absence of an escape mutation and the HLA type of the sampled hosts (which we denote E), and disregard any remaining sequence information. We apply dynamic programming in combination with existing software to combine phylogenetic and statistical approaches with well-studied, ODE-based modelling to integrate available sequence data By combining these two frameworks we determine more informed estimates and credible regions of population-level escape and reversion rates, (lesc, lrev) which incorporate the underlying dependency structure present in the viral genealogy. Our model provides evidence for the hypothesis that rates of escape and reversion within host are slower than published estimates generated experimentally from individual case studies [20], and highlights the large amount of uncertainty inherent in estimates that make use of cross-sectional population data
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