Mathematical models of RNA silencing: Unidirectional amplification limits accidental self-directed reactions

Abstract

RNA silencing, found broadly throughout the eukaryotes, post-transcriptionally suppresses the expression of aberrant genes including those of many viruses and transposons. Similar to the specific immune system of vertebrates, RNA silencing works by generating specific responses against foreign elements and rapidly amplifying these responses to clear or otherwise inactivate the threat. Also like the vertebrate immune system, RNA silencing systems risk making mistakes and mounting undesirable responses against the self. We develop a set of mathematical models of RNA silencing. We show that current models of RNA silencing do little to explain what prevents mistaken reactions from silencing vital organismal genes. We extend the basic models to show that the presumed unidirectional nature of the amplification process (namely, unidirectional RNA-directed RNA polymerase-mediated synthesis of secondary double-stranded RNA as observed in Caenorhabditis elegans) serves as a safety mechanism that safeguards against accidental generation of damaging self-directed reactions.