Quantifying tissue growth, shape and collision via continuum models and Bayesian inference

Abstract

Although tissues are usually studied in isolation, this situation rarely occurs in biology, as cells, tissues and organs coexist and interact across scales to determine both shape and function. Here, we take a quantitative approach combining data from recent experiments, mathematical modelling and Bayesian parameter inference, to describe the self-assembly of multiple epithelial sheets by growth and collision. We use two simple and well-studied continuum models, where cells move either randomly or following population pressure gradients. After suitable calibration, both models prove to be practically identifiable, and can reproduce the main features of single tissue expansions. However, our findings reveal that whenever tissue–tissue interactions become relevant, the random motion assumption can lead to unrealistic behaviour. Under this setting, a model accounting for population pressure from different cell populations is more appropriate and shows a better agreement with experimental measurements. Finally, we discuss how tissue shape and pressure affect multi-tissue collisions. Our work thus provides a systematic approach to quantify and predict complex tissue configurations with applications in the design of tissue composites and more generally in tissue engineering.

Environmental stress level to model tumor cell growth and survival

“…13. This suggests that the model parameters used are practically identifiable [16,45,46] in the settings considered.…”

“…The methods mentioned so far are fully Bayesian, in the sense that they aim at sampling from the full posterior. Examples of their use for biological and medical applications are [15][16][17][18]. An alternative would be to aim at approximate posteriors, especially if we know some characteristics a priori, for example unimodality.…”

Parameter identifiability and model selection for partial differential equation models of cell invasion

“…It is built upon the maximum-likelihood estimator (MLE), and has often been compared with Markov chain Monte Carlo (MCMC)-based methods for Bayesian inference. MCMC methods are widely used for inferring parameters in mathematical biology [23][24][25]. These methods provide more detailed information on parameter values, but are more expensive to compute.…”

A new paradigm considering multicellular adhesion, repulsion and attraction represents diverse cellular tile patterns

“…Cell sorting mechanisms have been considered in mathematical biology since the formulation of the differential adhesion hypothesis (DAH) by Malcolm Steinberg [35,36,37,38] more than 50 years ago. Differential adhesion between different cell populations [20,42] is now understood as a fundamental mechanism for cellular patterns, confirmed by experiments [10,14,15,22,44,18,19] and by mathematical models that are able to identify suitable parameters [21,9,34,11,12]. Mathematical Population Models (MPM) of cell sorting by differential adhesion are derived from Agent Based Models (ABM) by a coarse graining procedure usually referred as the mean-field approximation [8,6,9,26].…”