Small-sample estimation of the mutational support and the distribution of mutations in the SARS-Cov-2 genome

The problem of estimating unknown features of viral species using a limited collection of observations is of great relevance in computational biology. We consider one such particular problem, concerned with determining the mutational support and distribution of the SARS-Cov-2 viral genome and its open reading frames (ORFs). The mutational support refers to the unknown number of sites that is expected to be eventually mutated in the SARS-Cov-2 genome. It may be used to assess the virulence of the virus or guide primer selection for real-time RT-PCR tests during the early stages of an outbreak. Estimating the unknown distribution of mutations in the genome of different subpopulations while accounting for the unseen may aid in discovering adaptation mechanisms used by the virus to evade the immune system. To estimate the mutational support in the small-sample regime, we use GISAID sequencing data and new state-of-the-art polynomial estimation techniques based on weighted and regularized Chebyshev approximations. For distribution estimation, we adapt the well-known Good-Turing estimator. We also perform a differential analysis of mutations and their sites across different populations. Our analysis reveals several findings: First, the mutational supports exhibit significant differences in the ORF6 and ORF7a regions (older vs younger patients), ORF1b and ORF10 regions (females vs males) and as may be expected, in almost all ORFs (for Asia versus Europe and North America). Second, despite the fact that the N region of SARS-Cov-2 has a predicted 10% mutational support, almost all observed mutations fall outside of the two regions of paired primers recommended for testing by the CDC.