Positive-strand RNA viruses, such as the brome mosaic virus (BMV) and hepatitis C virus, utilize a replication cycle which involves the recruitment of RNA genomes from the cellular translation machinery to the viral replication complexes. Here, we coupled mathematical modeling with a statistical inverse problem methodology to better understand this crucial recruitment process. We developed a discrete-delay differential equation model that describes the production of BMV protein 1a and BMV RNA3, and the effect of protein 1a on RNA3 recruitment. We validated our model with experimental data generated in duplicate from a yeast strain that was engineered to express protein 1a and RNA3 under the control of inducible promoters. We used a statistical model comparison technique to test which biological assumptions in our model were correct. Our results suggest that protein 1a expression is governed by a nonlinear phenomenon and that a time delay is important for modeling RNA3 recruitment. We also performed an uncertainty analysis of two experimental designs and found that we could improve our data collection procedure in future experiments to increase the confidence in our parameter estimates.

This research was supported in part by grant number NIAID R01 AI071915-09 from the National Institute of Allergy and Infectious Diseases, in part by the Undergraduate Biomathematics grant number NSF DBI-1129214 from the National Science Foundation and in part by a grant from the Spanish Ministerio de Ciencia e Innovación (BFU2010-20083