Likelihood-based inference, identifiability and prediction using count data from lattice-based random walk models

TL;DR

This paper develops likelihood-based methods for parameter estimation and prediction in lattice-based random walk models of cell migration, introducing a new multinomial measurement error model that improves physical realism and computational efficiency.

Contribution

It introduces a novel multinomial measurement error model for linking noisy count data to PDE solutions in lattice-based models, enhancing inference accuracy and physical plausibility.

Findings

Multinomial error model yields physically meaningful predictions.

Both error models provide similar parameter estimates and identifiability.

The multinomial model has lower computational overhead.

Abstract

In vitro cell biology experiments are routinely used to characterize cell migration properties under various experimental conditions. These experiments can be interpreted using lattice-based random walk models to provide insight into underlying biological mechanisms, and continuum limit partial differential equation (PDE) descriptions of the stochastic models can be used to efficiently explore model properties instead of relying on repeated stochastic simulations. Working with efficient PDE models is of high interest for parameter estimation algorithms that typically require a large number of forward model simulations. Quantitative data from cell biology experiments usually involves non-negative cell counts in different regions of the experimental images, and it is not obvious how to relate finite, noisy count data to the solutions of continuous PDE models that correspond to noise-free density profiles. In this work we illustrate how to develop and implement likelihood-based methods for parameter estimation, parameter identifiability and model prediction for lattice-based models describing collective migration with an arbitrary number of interacting subpopulations. We implement a standard additive Gaussian measurement error model as well as a new physically-motivated multinomial measurement error model that relates noisy count data with the solution of continuous PDE models. Both measurement error models lead to similar outcomes for parameter estimation and parameter identifiability, whereas the standard additive Gaussian measurement error model leads to non-physical prediction outcomes. In contrast, the new multinomial measurement error model involves a lower computational overhead for parameter estimation and identifiability analysis, as well as leading to physically meaningful model predictions.