Evaluation of HIV 2-LTR formation models using monotone system theory

An important question in HIV research is whether the combination Antiretroviral Therapy (cART) is capable of fully suppressing the replication of HIV virus. Recent experiments have tested whether this is the case by perturbing the virus dynamics in patients with apparently suppressed HIV replication, as measured by blood viremia levels, by adding an integrase inhibitor raltegravir to the existing cART regimen. Following the addition of raltegravir, a consistent spike followed by decay was observed in the concentrations of a HIV DNA artifact marker, the 2-LTR circle. In previous work, we have shown that a model of ongoing HIV replication explains this behavior, while a model of controlled or absent HIV replication does not. A recent paper by Angeli and Sontag (2012) describes a method of invalidating biological models with sign-definite interactions by considering the monotonicity of the observed outputs relative to the monotonicity of the network description of the model. In this paper, we use this method to evaluate alternative explanations of the observed 2-LTR behavior. We show via monotone system theory that models consistent with the observed non-monotonic response in measured 2-LTR are either biologically infeasible or contain ongoing viral replication.