Mathematical Modelling of Stochastic Gene Expression Quantifies mRNA Heterogeneity in Cancer Cell Populations with Extrachromosomal DNA

Oncogene amplification on circular extrachromosomal DNA (ecDNA) has been linked to poor prognosis and higher treatment resistance in multiple types of human cancer. ecDNA are mobile genetic elements lacking centromeres that are partitioned unevenly into daughter cells at mitosis. While random segregation of ecDNA contributes to gene-copy-number heterogeneity among tumour cells, how ecDNA contribute to phenotypic heterogeneity, via mRNA and proteins, and how this affects targeted therapy outcomes is still not understood. In fact, cancer cell populations with ecDNA show remarkable heterogeneity in mRNA concentrations, which is not explained by gene-copy-number heterogeneity alone. In this paper, we use a stochastic model of gene transcription to mathematically model mRNA production and decay in cancer cells with ecDNA, extending a method that has been used to study phenotypic heterogeneity in eurokaryotic and prokaryotic cells. Using our model, we explore the space of possible mRNA distributions from a given ecDNA distribution, under different model parameter regimes. Our model is able to produce realistic mRNA distributions and we use it to estimate transcriptional parameters from single-cell measurements of ecDNA and mRNA counts in cell-line data. We discover a remarkable similarity in estimated parameters across cell lines and amplification types, indicating similar processes underlying transcription in ecDNA and chromosomal amplifications. We also model genotoxic therapy and use our model to predict the mRNA composition of persisting cells, showing the usefulness of such a modelling framework to understanding the origins of treatment resistance in ecDNA-containing cancers.