nbCNV: a multi-constrained optimization model for discovering copy number variants in single-cell sequencing data

Variations in DNA copy number have an important contribution to the development of several diseases, including autism, schizophrenia and cancer. Single-cell sequencing technology allows the dissection of genomic heterogeneity at the single-cell level, thereby providing important evolutionary information about cancer cells. In contrast to traditional bulk sequencing, single-cell sequencing requires the amplification of the whole genome of a single cell to accumulate enough samples for sequencing. However, the amplification process inevitably introduces amplification bias, resulting in an over-dispersing portion of the sequencing data. Recent study has manifested that the over-dispersed portion of the single-cell sequencing data could be well modelled by negative binomial distributions.

We developed a read-depth based method, nbCNV to detect the copy number variants (CNVs). The nbCNV method uses two constraints-sparsity and smoothness to fit the CNV patterns under the assumption that the read signals are negatively binomially distributed. The problem of CNV detection was formulated as a quadratic optimization problem, and was solved by an efficient numerical solution based on the classical alternating direction minimization method.

Extensive experiments to compare nbCNV with existing benchmark models were conducted on both simulated data and empirical single-cell sequencing data. The results of those experiments demonstrate that nbCNV achieves superior performance and high robustness for the detection of CNVs in single-cell sequencing data.