Skipping and sliding to optimize target search on protein-bound DNA and RNA

Rapidly finding a specific nucleic-acid sequences in a large pool of competing off-targets is a fundamental challenge overcome by all living systems. To optimize the search and beat the diffusion limit, it is known that searchers should spend time sliding along the nucleic-acid substrate. Still, such sliding generally has to contend with high levels of molecular crowding on the substrate, and it remains unclear what effect this has on optimal search strategies. Using mechanistic modelling informed by single-molecule data, we show how sliding combined with correlated short-ranged skips allow searchers to maintain search speed on densely crowded substrates. We determine the conditions of optimal search, which show that an optimized searchers always spend more than half its time skipping and sliding along the substrate. Applying our theory to single-molecule data, we determine that both human and bacterial Argonaute proteins alternate between sliding 10 nt and skipping 30 nt along the substrate. We show that this combination of skipping and sliding lengths allows the searcher to maintain search speeds largely unaffected by molecular roadblocks covering up to 70% of the substrate. Our novel combination of experimental and theoretical approach could also help elucidate how other systems ensure rapid search in crowded environments.