Copy number variants calling for single cell sequencing data by multi-constrained optimization

Variations in DNA copy number carry important information on genome evolution and regulation of DNA replication in cancer cells. The rapid development of single-cell sequencing technology allows one to explore gene expression heterogeneity among single-cells, thus providing important cancer cell evolution information. Single-cell DNA/RNA sequencing data usually have low genome coverage, which requires an extra step of amplification to accumulate enough samples. However, such amplification will introduce large bias and makes bioinformatics analysis challenging. Accurately modeling the distribution of sequencing data and effectively suppressing the bias influence is the key to success variations analysis. Recent advances demonstrate the technical noises by amplification are more likely to follow negative binomial distribution, a special case of Poisson distribution. Thus, we tackle the problem CNV detection by formulating it into a quadratic optimization problem involving two constraints, in which the underling signals are corrupted by Poisson distributed noises. By imposing the constraints of sparsity and smoothness, the reconstructed read depth signals from single-cell sequencing data are anticipated to fit the CNVs patterns more accurately. An efficient numerical solution based on the classical alternating direction minimization method (ADMM) is tailored to solve the proposed model. We demonstrate the advantages of the proposed method using both synthetic and empirical single-cell sequencing data. Our experimental results demonstrate that the proposed method achieves excellent performance and high promise of success with single-cell sequencing data.