title: Differentiated cell behavior: a multiscale approach using measure theory.
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 by 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.
authors.affiliation: Department of Mathematical Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Torino, Italy.
authors.forename: Annachiara
authors.initials: A
authors.lastname: Colombi
authors.affiliation: Department of Mathematical Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Torino, Italy.
authors.forename: Marco
authors.initials: M
authors.lastname: Scianna
authors.affiliation: Istituto per le Applicazioni del Calcolo "M. Picone", Consiglio Nazionale delle Ricerche, Via dei Taurini 19, 00185, Rome, Italy. a.tosin@iac.cnr.it.
authors.forename: Andrea
authors.initials: A
authors.lastname: Tosin
mesh_terms: D000818:Animals; D055592:Biophysical Phenomena; D002449:Cell Aggregation; D002454:Cell Differentiation; D002468:Cell Physiological Phenomena; D002633:Chemotaxis; D003198:Computer Simulation; D006801:Humans; D055641:Mathematical Concepts; D008954:Models, Biological
keywords: Cell populations; Discrete vs. continuous descriptions; Functional subsystems; Multiscale dynamics