Markov modelling of changes in HIV-specific cytotoxic T-lymphocyte responses with time in untreated HIV-1 infected patients

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Abstract
HIV‐specific cytotoxic CD8+ T‐lymphocytes (CTL) appear to be the cornerstone of the immune response to HIV infection. Recent studies show that CTL activity reflects patients' anti‐HIV immune status and slows disease progression. However, the dynamics of the diversity of this response also appears as a key parameter for immune control but the dynamics of this diversity is largely undocumented. We modelled changes in CTL responses against the seven principal HIV proteins over time. We also studied the influence of plasma viral load on temporal changes in HIV protein recognition by memory CTL. The generic model we developed is based on a continuous time homogeneous Markov process with reversible states. Those states are defined by the number of proteins recognized by memory CTL in a given patient at a given time. This approach was developed within a Bayesian framework. Full Bayesian inference is implemented using Markov chain Monte Carlo simulations (MCMC). The Gibbs sampling algorithm was used to estimate the marginal posterior distributions of the transition intensities between stages of CTL responses. We applied our model to data of 152 HIV‐infected patients included in the IMMUNOCO cohort. The model suggested that the diversity of HIV protein recognition by memory CTL in treatment‐naive patients decreases as the disease progresses. Namely, the loss of T cytotoxic responses is globally faster than their acquisition. Indeed, these patients' T cytotoxic responses were characterized by marked individual turnover and a gradual loss of multiple protein recognition over time, this loss accelerating as viral load increased. Copyright © 2003 John Wiley & Sons, Ltd.