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Dense arrangements of binding sites within nucleotide sequences can collectively influence downstream transcription rates or initiate biomolecular interactions. For example, natural promoter regions can harbor many overlapping transcription factor binding sites that influence the rate of transcription initiation. Despite the prevalence of overlapping binding sites in nature, rapid design of nucleotide sequences with many overlapping sites remains a challenge. Here, we show that this is an NP-hard problem, coined here as the nucleotide String Packing Problem (SPP). We then introduce a computational technique that efficiently assembles sets of DNA-protein binding sites into dense, contiguous stretches of double-stranded DNA. For the efficient design of nucleotide sequences spanning hundreds of base pairs, we reduce the SPP to an Orienteering Problem with integer distances, and then leverage modern integer linear programming solvers. Our method optimally packs sets of 20–100 binding sites into dense nucleotide arrays of 50–300 base pairs in 0.05–10 seconds. Unlike approximation algorithms or meta-heuristics, our approach finds provably optimal solutions. We demonstrate how our method can generate large sets of diverse sequences suitable for library generation, where the frequency of binding site usage across the returned sequences can be controlled by modulating the objective function. As an example, we then show how adding additional constraints, like the inclusion of sequence elements with fixed positions, allows for the design of bacterial promoters. The nucleotide string packing approach we present can accelerate the design of sequences with complex DNA-protein interactions. When used in combination with synthesis and high-throughput screening, this design strategy could help interrogate how complex binding site arrangements impact either gene expression or biomolecular mechanisms in varied cellular contexts. 

Abstract Recent molecular analyses of transcriptome data from 94 species across 92 genera of North American Plecoptera identified the genus Kathroperla Banks, 1920 as sister group to Chloroperlidae + Perlodidae. Given that the genus Kathroperla has historically been included as a member of the family Chloroperlidae, this discovery indicated further investigation of the genus and the subfamily Paraperlinae was needed. Both transcriptome and genome sequencing datasets were generated from 32 species of the infraorder Systellognatha, including all described species of the Paraperlinae, to test the phylogenetic placement of these taxa. From these datasets, a large phylogenomic data matrix of 800 orthologous genes was produced, and multiple analyses were conducted, including both concatenated and coalescent analyses. Morphological comparisons were made among all Paraperlinae using light microscopy. All molecular results support a monophyletic Kathroperla, which is supported as sister taxon to the remaining Perloidea by five of six molecular analyses. Postocular head length is determined to be a distinct morphological character of this genus. Combined molecular and morphological evidence support the designation of Kathroperlidae, fam. n., as the seventeenth family of extant Plecoptera.