Summary: To construct gene co-expression networks based on single-cell RNA-Sequencing data, we present an algorithm called LEAP, which utilizes the estimated pseudotime of the cells to find gene co-expression that involves time delay. Availability and Implementation: R package LEAP available on CRAN. Contact: [email protected]. Supplementary information: Supplementary data are available at Bioinformatics online.

Synonymous rare codons are considered to be sub-optimal for gene expression because they are translated more slowly than common codons. Yet surprisingly, many protein coding sequences include large clusters of synonymous rare codons. Rare codons at the 5' terminus of coding sequences have been shown to increase translational efficiency. Although a general functional role for synonymous rare codons farther within coding sequences has not yet been established, several recent reports have identified rare-to-common synonymous codon substitutions that impair folding of the encoded protein. Here we test the hypothesis that although the usage frequencies of synonymous codons change from organism to organism, codon rarity will be conserved at specific positions in a set of homologous coding sequences, for example to tune translation rate without altering a protein sequence. Such conservation of rarity-rather than specific codon identity-could coordinate co-translational folding of the encoded protein. We demonstrate that many rare codon cluster positions are indeed conserved within homologous coding sequences across diverse eukaryotic, bacterial, and archaeal species, suggesting they result from positive selection and have a functional role. Most conserved rare codon clusters occur within rather than between conserved protein domains, challenging the view that their primary function is to facilitate co-translational folding after synthesis of an autonomous structural unit. Instead, many conserved rare codon clusters separate smaller protein structural motifs within structural domains. These smaller motifs typically fold faster than an entire domain, on a time scale more consistent with translation rate modulation by synonymous codon usage. While proteins with conserved rare codon clusters are structurally and functionally diverse, they are enriched in functions associated with organism growth and development, suggesting an important role for synonymous codon usage in organism physiology. The identification of conserved rare codon clusters advances our understanding of distinct, functional roles for otherwise synonymous codons and enables experimental testing of the impact of synonymous codon usage on the production of functional proteins.