Identifying memory gene expression from single sample scRNA-seq data using power law signatures

Genes with expression levels that fluctuate on time scales longer than cell division times are associated with cancer drug tolerance. However, current methods for identifying such memory genes rely on variants of the Luria-Delbruck experiment and require either multiple replicates or lineage information, limiting their use to model systems or in-vitro settings. We develop a new conceptual approach using recent results in Random Matrix Theory to demonstrate that the existence of memory genes results in a power-law signature in the cell covariance matrix eigenspectrum. Utilizing this theoretical framework, we develop Power-Seek, an algorithm to discover memory genes from a single time point scRNA-seq dataset. Without using prior information on lineages or cell-cycle times, Power-Seek correctly identifies memory genes in a melanoma cell line. Our results open up the possibility of identifying expression states driving drug tolerance in real-world scenarios, as we demonstrate using data from a human breast cancer tissue sample.