Differentiated cell behavior: a multiscale approach using measure theory

TL;DR

This paper develops a multiscale model of cell populations using measure theory, allowing flexible representation of cells as discrete or continuous entities based on their biological roles.

Contribution

It introduces a novel measure-theoretic framework for multiscale cell modeling, enabling adaptive microscopic or macroscopic representations based on cell function.

Findings

Hybrid system behavior depends on key biological parameters.

Discrete and continuous representations can be combined in a unified model.

Numerical simulations reveal parameter influence on cell population dynamics.

Abstract

This paper deals with the derivation of a collective model of cell populations out of an individual-based description of the underlying physical particle system. By looking at the spatial distribution of cells in terms of time-evolving measures, rather than at individual cell paths, we obtain an ensemble representation stemming from the phenomenological behavior of the single component cells. In particular, as a key advantage of our approach, the scale of representation of the system, i.e., microscopic/discrete vs. macroscopic/continuous, can be chosen a posteriori according only to the spatial structure given to the aforesaid measures. The paper focuses in particular on the use of different scales based on the specific functions performed by cells. A two-population hybrid system is considered, where cells with a specialized/differentiated phenotype are treated as a discrete population of point masses while unspecialized/undifferentiated cell aggregates are represented with a continuous approximation. Numerical simulations and analytical investigations emphasize the role of some biologically relevant parameters in determining the specific evolution of such a hybrid cell system.