Implications of phase transitions in knockdown networks of transitive RNAi

Gene silencing by RNA interference (RNAi) has been observed even in the presence of imperfect complementarity in the siRNA-mRNA hybridization. Since more permissive mismatches gives rise to higher chances of off-target gene silencing, the number of mismatched nucleotides allowed by nature becomes an important quantity in characterizing RNAi specificity and RNAi design. To estimate the allowable flexibility, we use scale-free graphs to model the knockdown interactions among genes by examining transitive RNAi (tRNAi), which amplifies siRNA and cyclically silences targets. We removed inefficient siRNA sequences using the commonly used siRNA efficacy rules, avoided redundant siRNAs using barcoding techniques, and employed both contiguous and scattered mismatches to emulate the siRNA-mRNA binding. Simulations in multiple organisms indicate that the fraction of the transcriptome silenced by tRNAi rises drastically with increased number of allowed mismatches and eventually tRNAi became self-destructive rather than defensive. At the phase transition, the number of mismatches implies a critical value beyond which tRNAi would cause the transcription of an organism to be instable. This critical value suggests an upper limit of no more than 6 nt mismatches in the hybridization in general.