Modeling and estimation of replication fitness of human immunodeficiency virus type 1 in vitro experiments by using a growth competition assay

Growth competition assays have been developed to quantify the relative fitnesses of human immunodeficiency virus (HIV-1) mutants. In this article we develop mathematical models to describe viral/cellular dynamic interactions in the assay experiment, from which new competitive fitness indices or parameters are defined. These indices include the log fitness ratio (LFR), the log relative fitness (LRF), and the production rate ratio (PRR). From the population genetics perspective, we clarify the confusion and correct the inconsistency in the definition of relative fitness in the literature of HIV-1 viral fitness. The LFR and LRF are easier to estimate from the experimental data than the PRR, which was misleadingly defined as the relative fitness in recent HIV-1 research literature. Calculation and estimation methods based on two data points and multiple data points were proposed and were carefully studied. In particular, we suggest using both standard linear regression (method of least squares) and a measurement error model approach for more-accurate estimates of competitive fitness parameters from multiple data points. The developed methodologies are generally applicable to any growth competition assays. A user-friendly computational tool also has been developed and is publicly available on the World Wide Web at http://www.urmc.rochester.edu/bstools/vfitness/virusfitness.htm.