A mathematical model of rna3 recruitment in the replication cycle of brome mosaic virus

Abstract

Positive-strand RNA viruses, such as the brome mosaic virus (BMV) and hepatitis C virus, utilize a replication cycle which involves the re- cruitment of RNA genomes from the cellular translation machinery to the viral replication complexes. Here, we coupled mathematical modeling with a statisti- cal inverse problem methodology to better understand this crucial recruitment process. We developed a discrete-delay differential equation model that de- scribes 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 sta- tistical 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 experi- mental designs and found that we could improve our data collection procedure in future experiments to increase the confidence in our parameter estimates.