Travelling Waves in Gene Expression: A Mathematical Model of Cell-State Dynamics in Melanoma

Melanoma is a cancer of the melanocyte, known to have an ability to readily<br/>switch between different transcriptional cell states that convey different phenotypic properties (e.g. hyper-differentiated, neural crest-like). This ability is<br/>believed to underpin intratumour heterogeneity and plastic adaptation, which<br/>contributes to resistance to therapy and immune evasion of the tumour. Therefore,<br/>understanding the mechanisms underlying acquisition of transcriptional cell<br/>states and cell-state switching is crucial for the development of therapies. We<br/>model a minimal gene regulatory network comprising three key transcription<br/>factors, whose varying gene expression encodes different melanoma cell states,<br/>and use deterministic spatiotemporal differential-equation models to study gene expression dynamics. We exploit an approximation, based on cooperative binding of transcription factors, in which the models are piecewise-linear. We classify stable states of the local model in a biologically relevant manner and, using a naïve model of intercellular communication, we explore how a population of cells can take on a shared characteristic through travelling waves of gene expression. We derive a condition determining which characteristic will become dominant, under sufficiently strong cell-cell signalling, which creates a partition of parameter<br/>space.