Estimating cell diffusivity and cell proliferation rate by interpreting IncuCyte ZOOM™ assay data using the Fisher-Kolmogorov model

Abstract

BackgroundStandard methods for quantifying IncuCyte ZOOM™ assays involve measurements that quantify how rapidly the initially-vacant area becomes re-colonised with cells as a function of time. Unfortunately, these measurements give no insight into the details of the cellular-level mechanisms acting to close the initially-vacant area. We provide an alternative method enabling us to quantify the role of cell motility and cell proliferation separately. To achieve this we calibrate standard data available from IncuCyte ZOOM™ images to the solution of the Fisher-Kolmogorov model.ResultsThe Fisher-Kolmogorov model is a reaction-diffusion equation that has been used to describe collective cell spreading driven by cell migration, characterised by a cell diffusivity, D, and carrying capacity limited proliferation with proliferation rate, λ, and carrying capacity density, K. By analysing temporal changes in cell density in several subregions located well-behind the initial position of the leading edge we estimate λ and K. Given these estimates, we then apply automatic leading edge detection algorithms to the images produced by the IncuCyte ZOOM™ assay and match this data with a numerical solution of the Fisher-Kolmogorov equation to provide an estimate of D. We demonstrate this method by applying it to interpret a suite of IncuCyte ZOOM™ assays using PC-3 prostate cancer cells and obtain estimates of D, λ and K. Comparing estimates of D, λ and K for a control assay with estimates of D, λ and K for assays where epidermal growth factor (EGF) is applied in varying concentrations confirms that EGF enhances the rate of scratch closure and that this stimulation is driven by an increase in D and λ, whereas K is relatively unaffected by EGF.ConclusionsOur approach for estimating D, λ and K from an IncuCyte ZOOM™ assay provides more detail about cellular-level behaviour than standard methods for analysing these assays. In particular, our approach can be used to quantify the balance of cell migration and cell proliferation and, as we demonstrate, allow us to quantify how the addition of growth factors affects these processes individually.

Concepts for the Production of Viruses and Viral Vectors in Cell Cultures

“…WST-1 assay). In small scale, microscopy-based cell counting devices for static cultivation systems are also available [83]. Typically online, these data are collected by indirect inline measurement, e.g.…”

Investigating the Reproducibility of In Vitro Cell Biology Assays Using Mathematical Models

“…They also find that with different initial cell numbers, the estimated parameter values are not the same [115]. Johnston et al use the Fisher-Kolmogorov model and the edge detection method to quantify the cell diffusivity, proliferation rate, and carrying capacity of prostate cancer cells from IncuCyte ZOOM TM assays [54]. Mort et al apply a lattice-based discrete model to investigate the formation of diffusion clones, chimeric stripes and belly spots in a mice model [80].…”

“…Generalisations of the Fisher-Kolmogorov model, such as the Porous-Fisher model, in which cell migration is modelled by a nonlinear diffusion term, have also been applied to study cases in which cell diffusivity increases with local cell density. It is interesting to note that for proliferation assays in which cells are uniformly distributed, Equation (1.1) simplifies to the logistic growth equation [54], given by…”

“…Cell proliferation is considered one of the key factors that drive collective cell spreading in in vitro cell biology assays [54,71]. The continuum reaction-diffusion models that mimic certain features of cell biology assays normally include a logistic source term to model the carrying-capacity limited proliferation [100,109,115].…”

“…The logistic growth model is often used to study carrying-capacity limited population growth, such as cell proliferation in scratch assays and proliferation assays [14,54,76,77,98,100,118].…”