Abstract

Fluorescent ubiquitination-based cell cycle indicator, known as FUCCI , enables the visualisation of the G1 and S/G2/M cell cycle phases of individual cells. FUCCI consists of two fluorescent probes, so that cells in the G1 phase fluoresce red and cells in the S/G2/M phase fluoresce green. FUCCI reveals real-time information about cell cycle dynamics of individual cells, and can be used to explore how the cell cycle relates to the location of individual cells, local cell density, and different cellular microenvironments. In particular, FUCCI is used in experimental studies examining cell migration, such as malignant invasion and wound healing. Here we present simple mathematical models which can describe cell migration and cell cycle dynamics as indicated by FUCCI . We present experimental data from scratch assays using FUCCI -transduced melanoma cells, and show that the predictions of spatial and temporal patterns of cell density in the experiments can be described by our mathematical model. We obtain numerical solutions of both the model, which can take the form of travelling waves. These solutions are mathematically interesting because they are a combination of moving wavefronts and moving pulses. We derive and confirm a simple analytical expression for the minimum wave speed, and conclude by outlining future directions of our work in this area.