Simplified motif background model provides significant speed-up for regulatory activity inference

Regulatory microRNA activity can be inferred from mRNA data by evaluating the clustering of its target motif across expression-ranked mRNA sequences. Sequence-specific motif probabilities (SSPs) are required to distinguish functional motif enrichment from random motif occurrence driven by sequence length and nucleotide composition; however, current exact background Markov models scale poorly with k-mer motif size. Here, we introduce a binomial approximation parameterized by a single-site motif probability and sequence length for scalable SSP computation, which is at least 9-fold faster for k-mer screens while generating closely matching SSP values used for downstream Bayesian activity inference. The approximation is further extended to a 1st-order di-nucleotide background model, improving correction for compositionally biased sequences leading to better separation of AT- and GC-rich motif expectations for longer k-mers in AT-biased mRNA sequences. Applied to liver cancer samples, the binomial background approximation preserve downstream microRNA activity estimates, making it a better option for large-scale applications such as single-cell regulatory profiling.