Multi-norm constrained optimization methods for calling copy number variants in single cell sequencing data

The revolutionary invention of single-cell sequencing technology carves out a new way to delineate intra tumor heterogeneity and the evolution of single cells at the molecular level. Since single-cell sequencing requires a special genome amplification step to accumulate enough samples, a large number of bias were introduced, making the calling of copy number variants rather challenging. Accurately modeling this process and effectively detecting copy number variations (CNVs) are the major roadblock for single-cell sequencing data analysis. Recent advances manifested that the underlying copy numbers are corrupted by noise, which could be approximated by negative binomial distribution. In this paper, we formulated a general mathematical model for copy number reconstruction from read depth signal, and presented its two specific variants, namely Poisson-CNV and NB-CNV to catering for various reads distribution. Efficient numerical solution based on the classical alternating direction minimization method was designed to solve the proposed models. Extensive experiments on both synthetic datasets and empirical single-cell sequencing datasets were conducted to compare the performance of the two models. The results show that the proposed model of NB-CNV achieved superior performance in calling the CNV for single-cell sequencing data.