LazySampling and LinearSampling: Fast Stochastic Sampling of RNA Secondary Structure with Applications to SARS-CoV-2.

Many RNAs fold into multiple structures at equilibrium. The classical stochastic sampling algorithm can sample secondary structures according to their probabilities in the Boltzmann ensemble, and is widely used. However, this algorithm, consisting of a bottom-up partition function phase followed by a top-down sampling phase, suffers from three limitations: (a) the formulation and implementation of the sampling phase are unnecessarily complicated; (b) the sampling phase repeatedly recalculates many redundant recursions already done during the partition function phase; (c) the partition function runtime scales cubically with the sequence length. These issues prevent stochastic sampling from being used for very long RNAs such as the full genomes of SARS-CoV-2. To address these problems, we first adopt a hypergraph framework under which the sampling algorithm can be greatly simplified. We then present three sampling algorithms under this framework, among which the LazySampling algorithm is the fastest by eliminating redundant work in the sampling phase via on-demand caching. Based on LazySampling, we further replace the cubic-time partition function by a linear-time approximate one, and derive LinearSampling, an end-to-end linear-time sampling algorithm that is orders of magnitude faster than the standard one. For instance, LinearSampling is 176Ã- faster (38.9s vs. 1.9h) than Vienna RNAsubopt on the full genome of Ebola virus (18,959 ). More importantly, LinearSampling is the first RNA structure sampling algorithm to scale up to the full-genome of SARS-CoV-2 without local window constraints, taking only 69.2 seconds on its reference sequence (29,903 ). The resulting sample correlates well with the experimentally-guided structures. On the SARS-CoV-2 genome, LinearSampling finds 23 regions of 15 with high accessibilities, which are potential targets for COVID-19 diagnostics and drug design. See code: https://github.com/LinearFold/LinearSampling.