The impact of experimental design choices on parameter inference for models of growing cell colonies

Abstract

To better understand development, repair and disease progression it is useful to quantify the behaviour of proliferative and motile cell populations as they grow and expand to fill their local environment. Inferring parameters associated with mechanistic models of cell colony growth using quantitative data collected from carefully designed experiments provides a natural means to elucidate the relative contributions of various processes to the growth of the colony. In this work we explore how experimental design impacts our ability to infer parameters for simple models of the growth of proliferative and motile cell populations. We adopt a Bayesian approach, which allows us to characterise the uncertainty associated with estimates of the model parameters. Our results suggest that experimental designs that incorporate initial spatial heterogeneities in cell positions facilitate parameter inference without the requirement of cell tracking, whilst designs that involve uniform initial placement of cells require cell tracking for accurate parameter inference. As cell tracking is an experimental bottleneck in many studies of this type, our recommendations for experimental design provide for significant potential time and cost savings in the analysis of cell colony growth.

A free boundary model of epithelial dynamics

“…Substitution of equations (19) and (20), and a simple rearrangement (multiplying by q and differentiating with respect to x, identical to earlier arguments), results in a PDE for the cell density of the form…”

“…Changing variables from (i, t) to (x, τ ), as before, with a simple substitution of terms from equations (19) and (20) into equation (82) we obtain the PDE…”

“…Depending on the biological context, there are many different kinds of individual-based models that can be used to simulate cell biology processes including random walk frameworks involving point particles [2,3] or random walk frameworks based on an exclusion process that explicitly account for excluded volume effects as well as the shape and size of the individuals in the system [9,19]. While discrete models based on point particles and exclusion processes have been successfully applied to study many cell biology phenomena, these models do not include any mechanical effects that are known to be important in a host of applications.…”