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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. Author summary: The way protein binding sites are arranged on DNA can influence the regulation and transcription of downstream genes. Areas with a high concentration of binding sites can enable complex interplay between transcription factors, a feature that is exploited by natural promoters. However, designing synthetic promoters that contain dense arrangements of binding sites is a challenge. The task involves overlapping many binding sites, each typically about 10 nucleotides long, within a constrained sequence area, which becomes increasingly difficult as sequence length decreases and binding site variety increases. We introduce an approach to design nucleotide sequences with optimally packed protein binding sites, which we call the nucleotide String Packing Problem (SPP). We show that the SPP can be solved efficiently using integer linear programming to identify the densest arrangements of binding sites for a specified sequence length. We show how adding additional constraints, like the inclusion of sequence elements with fixed positions, allows for the design of bacterial promoters. The presented approach enables the rapid design and study of nucleotide sequences with complex, dense binding site architectures. [ABSTRACT FROM AUTHOR]

Heteroresistance can allow otherwise drug-susceptible bacteria to survive and resume growth after antibiotic exposure. This temporary form of antibiotic tolerance can be caused by the upregulation of stress response genes or a decrease in cell growth rate. However, it is not clear how expression of multiple genes contributes to the tolerance phenotype. By using fluorescent reporters for stress related genes, we conducted real time measurements of expression prior to, during, and after antibiotic exposure. We first identified relationships between growth rate and reporter levels based on auto and cross correlation analysis, revealing consistent patterns where changes in growth rate were anticorrelated with fluorescence following a delay. We then used pairs of stress gene reporters and time lapse fluorescence microcopy to measure the growth rate and reporter levels in cells that survived or died following antibiotic exposure. Using these data, we asked whether combined information about reporter expression and growth rate could improve our ability to predict whether a cell would survive or die following antibiotic exposure. We developed a Bayesian inference model to predict how the combination of dual reporter expression levels and growth rate impact ciprofloxacin survival in Escherichia coli . We found clear evidence of the impact of growth rate and the gadX promoter activity on survival. Unexpectedly, our results also revealed examples where additional information from multiple genes decreased prediction accuracy, highlighting an important and underappreciated effect that can occur when integrating data from multiple simultaneous measurements.