An Algebraic Implicitization and Specialization of Minimum KL-Divergence Models

In this paper we study representation of KL-divergence minimization, in the cases where integer sufficient statistics exists, using tools from polynomial algebra. We show that the estimation of parametric statistical models in this case can be transformed to solving a system of polynomial equations. In particular, we also study the case of Kullback-Csiszar iteration scheme. We present implicit descriptions of these models and show that implicitization preserves specialization of prior distribution. This result leads us to a Grobner bases method to compute an implicit representation of minimum KL-divergence models.

Estimating the fraction of progeny virions that must incorporate APOBEC3G for suppression of productive HIV-1 infection

The contest between the host factor APOBEC3G (A3G) and the HIV-1 protein Vif presents an attractive target of intervention. The extent to which the A3G-Vif interaction must be suppressed to tilt the balance in favor of A3G remains unknown. We employed stochastic simulations and mathematical modeling of the within-host dynamics and evolution of HIV-1 to estimate the fraction of progeny virions that must incorporate A3G to render productive infection unsustainable. Using three different approaches, we found consistently that a transition from sustained infection to suppression of productive infection occurred when the latter fraction exceeded similar to 0.8. The transition was triggered by A3G-induced hypermutations that led to premature stop codons compromising viral production and was consistent with driving the basic reproductive number, R-o, below unity. The fraction identified may serve as a quantitative guideline for strategies targeting the A3G-Vif axis. (C) 2013 Elsevier Inc. All rights reserved.