A hybrid modeling environment to describe aggregates of cells heterogeneous for genotype and behavior with possible phenotypic transitions

Biological systems are typically composed of cells heterogeneous for genotype and phenotype, the latter being time-evolving in response to internal or external stimuli. In order to take these aspects into account, we here propose a modeling framework in which a discrete structuring variable distinguishes cells according to their genotype while a specific mathematical representation (i.e., individual/pointwise vs. collective/density-based) is assigned to each individual on the basis of its phenotypic hallmarks. A coherent procedure is then set to reproduce mechanisms of phenotypic plasticity: based on the definition of a bubble function, which gives the spatial distribution of the mass of a single cell, it possibly accounts the role played by stochasticity and environmental conditions. The proposed modeling environment is then enriched with the inclusion of further cell behavior, such as migratory dynamics and duplication/apoptotic processes, as well as with chemical kinetics. The resulting multiscale hybrid approach is finally applied to the scenario of a heterogeneous tumor aggregate cultured in vitro.