Quantifying uncertainty in parameter estimates for stochastic models of collective cell spreading using approximate Bayesian computation

Abstract

<p>Wound healing and tumour growth involve collective cell spreading, which is driven by individual motility and proliferation events within a population of cells. Mathematical models are often used to interpret experimental data and to estimate the parameters so that predictions can be made. Existing methods for parameter estimation typically assume that these parameters are constants and often ignore any uncertainty in the estimated values. We use approximate Bayesian computation (ABC) to estimate the cell diffusivity, <i>D</i>, and the cell proliferation rate, <i>λ</i>, from a discrete model of collective cell spreading, and we quantify the uncertainty associated with these estimates using Bayesian inference. We use a detailed experimental data set describing the collective cell spreading of 3T3 fibroblast cells. The ABC analysis is conducted for different combinations of initial cell densities and experimental times in two separate scenarios: (i) where collective cell spreading is driven by cell motility alone, and (ii) where collective cell spreading is driven by combined cell motility and cell proliferation. We find that <i>D</i> can be estimated precisely, with a small coefficient of variation (CV) of 2-6%. Our results indicate that <i>D</i> appears to depend on the experimental time, which is a feature that has been previously overlooked. Assuming that the values of <i>D</i> are the same in both experimental scenarios, we use the information about <i>D</i> from the first experimental scenario to obtain reasonably precise estimates of <i>λ</i>, with a CV between 4 and 12%. Our estimates of <i>D</i> and <i>λ</i> are consistent with previously reported values; however, our method is based on a straightforward measurement of the position of the leading edge whereas previous approaches have involved expensive cell counting techniques. Additional insights gained using a fully Bayesian approach justify the computational cost, especially since it allows us to accommodate information from different experiments in a principled way.</p>