A coherent modeling procedure to describe cell activation in biological systems

Biological systems are typically formed by different cell phenotypes, characterized by specific biological properties and behaviors. In particular, cells are able to undergo phenotypic transitions (i.e., activation or differentiation) upon internal or external stimuli. In order to take these phenomena into account, we here propose a modelling framework in which cell ensembles can be described collectively (i.e., through a distributed mass density) or individually (i.e., as a group of pointwise/concentrated particles) according to their biological determinants. A set of suitable rules involving the introduction of a cell shape function then defines a coherent procedure to model cell activation mechanisms, which imply a switch between the two mathematical representations. The theoretical environment describing cell transition is then enriched by including cell migratory dynamics and duplication/apoptotic processes, as well as the kinetics of selected diffusing chemicals influencing the system evolution. Remarkably, our approach provides consistency of the same modeling framework across all types of cell representation, as it is suitable to cope with the often ambiguous translation of individual cell arguments (i.e., cell dimensions and interaction radii) into collective cell descriptions. Biologically relevant numerical realizations are also presented: in particular, they deal with phenotypic transitions within cell colonies and with the growth of a tumor spheroid. These phenomena constitute biological systems particularly suitable to assess the advantages of the proposed model and to analyze the role on cell dynamics both of relevant parameters and of the specific form given to the cell shape function.