Wang Jin | Search bioRxiv

bioRxiv2016

Logistic proliferation of cells in scratch assays is delayed

Scratch assays are used to study how a population of cells re-colonises a vacant region on a two-dimensional substrate after a cell mono-layer is scratched. These experiments are used in many applications including drug design for the treatment of cancer and chronic wounds. To provide insights into the mechanisms that drive scratch assays, solutions of continuum reaction-diffusion models have been calibrated to data from scratch as-says. These models typically include a logistic source term to model carrying capacity-limited proliferation, however the choice of using a logistic source term is often made without examining whether it is valid. Here we study the proliferation of PC-3 prostate cancer cells in a scratch assay, and we focus on the proliferation of these cells far away from the scratch. All experimental results for the scratch assay are compared with equivalent results from a proliferation assay where the cell monolayer is not scratched. Visual inspection of the evolution of the cell density as a function of time reveals a series of sigmoid curves that could be naively calibrated to the solution of the logistic growth model. However, careful analysis of the per capita growth rate as a function of density reveals several key differences between the proliferation of cells in scratch and proliferation assays. The per capita growth rate in the proliferation assay decreases, approximately linearly, with density in the proliferation assay suggesting that the logistic growth model is valid for the entire duration of the proliferation assay. However, the per capita growth rate in the scratch assay increases with density when the density is sufficiently small in the scratch assay, suggesting that the logistic growth model does not apply. Instead, guided by data, we find that there are two phases of proliferation in a scratch assay. At short time we have a disturbance phase where proliferation is not logistic, and this is followed by a growth phase where proliferation appears to be logistic. Accounting for the differences in the growth and disturbance phase, we obtain biologically realistic estimates of the proliferation rate and carrying capacity density. In contrast, simply calibrating the solution of the logistic growth equation to all data from the scratch assays, we obtain an excellent match between the data and the model, but the parameter estimates vary wildly and are not biologically realistic. Overall our study shows that simply calibrating the solution of a continuum model to a scratch assay might produce misleading parameter estimates, and this issue can be resolved by making a distinction between the disturbance and growth phases. Repeating our procedure for other scratch assays will provide insight into the roles of the disturbance and growth phases for different cell lines and scratch assays performed on different substrates.

Biophysics↗

bioRxiv2016

Stochastic simulation tools and continuum models for describing two-dimensional collective cell spreading with universal growth functions

Two-dimensional collective cell migration assays are used to study cancer and tissue repair. These assays involve combined cell migration and cell proliferation processes, both of which are modulated by cell-to-cell crowding. Previous discrete models of collective cell migration assays involve a nearest-neighbour proliferation mechanism where crowding effects are incorporated by aborting potential proliferation events if the randomly chosen target site is occupied. There are two limitations of this traditional approach: (i) it seems unreasonable to abort a potential proliferation event based on the occupancy of a single, randomly chosen target site; and, (ii) the continuum limit description of this mechanism leads to the standard logistic growth function, but some experimental evidence suggests that cells do not always proliferate logistically. Motivated by these observations, we introduce a generalised proliferation mechanism which allows non-nearest neighbour proliferation events to take place over a template of r [≥] 1 concentric rings of lattice sites. Further, the decision to abort potential proliferation events is made using a crowding function, f (C), which accounts for the density of agents within a group of sites rather than dealing with the occupancy of a single randomly chosen site. Analysing the continuum limit description of the stochastic model shows that the standard logistic source term, {lambda}C(1 - C), where {lambda} is the proliferation rate, is generalised to a universal growth function, {lambda}Cf (C). Comparing the solution of the continuum description with averaged simulation data indicates that the continuum model performs well for many choices of f (C) and r. For nonlinear f (C), the quality of the continuum-discrete match increases with r.

Biophysics↗