Stochastic models of cell invasion with fluorescent cell cycle indicators

Abstract

Fluorescent cell cycle labelling in cell biology experiments provides real time information about the location of individual cells, as well as the phase of the cell cycle of individual cells. We develop a stochastic, lattice-based random walk model of a two-dimensional scratch assay where the total population is composed of three distinct subpopulations which we visualise as red, yellow and green subpopulations. Our model mimics FUCCI technology in which cells in the G1 phase of the cell cycle fluoresce red, cells in the early S phase fluoresce yellow, and cells in the S/G2/M phase fluoresce green. The model is an exclusion process so that any potential motility or proliferation event that would place an agent on an occupied lattice site is aborted. Using experimental images and previous experimental measurements we explain how to apply the stochastic model to simulate a scratch assay initialised with a low to moderate density monolayer of human melanoma cell line. We obtain additional mathematical insight by deriving an approximate partial differential equation (PDE) description of the stochastic model, leading to a novel system of three coupled nonlinear reaction diffusion equations. Comparing averaged simulation data with the solution of the continuum limit model confirms that the PDE description is accurate for biologically-relevant parameter combinations.

Microenvironment-Driven Dynamic Heterogeneity and Phenotypic Plasticity as a Mechanism of Melanoma Therapy Resistance

“…We have developed a 3D melanoma spheroid model, which recapitulates the in vivo tumor microenvironment and architecture ( 54 , 55 ), that combined with the fluorescent ubiquitination-based cell cycle indicator ( 56 ) is a useful tool to study the microenvironment in vitro ( 57 , 58 ). This model is being complemented constantly, e.g., by including DRAQ7 as a real-time cell death marker ( 59 ) or by applying mathematical algorithms to predict spatial and temporal patterns of cell density and cell cycle ( 60 , 61 ). Due to an oxygen and nutrient gradient, melanoma spheroids segregate into a continuously proliferating subpopulation in the periphery and a G1-arrested subpopulation in the center ( 12 ).…”

Synchronised oscillations in growing cell populations are explained by demographic noise

“…Due to recent technological advances, we are now able to access accurate data revealing the structure of dynamic cell populations [13, 14] using, amongst other tools, proliferation assays: an in vitro experimental protocol in which the growth of cell populations is monitored over time [15]. In particular, in recent work [16], we assayed the proliferation of melanoma cells labelled with FUCCI (Fluorescent Ubiquitination-based Cell Cycle Indicator [17, 18] - see Fig.…”

Examining go-or-grow using fluorescent cell-cycle indicators and cell cycle-inhibiting drugs

“…Our data consist of time-series images, acquired every 15 min for 48 h, from 2-D proliferation assays using the melanoma cell lines C8161, WM983C and 1205Lu [6,20,28,29], which have respective mean cell-cycle durations of approximately 21, 23 and 37 h [6]. The cell lines have very different ratios of durations in G1 to S/G2/M (Supplementary Material).…”