Tumors exhibit phenotypic heterogeneity in proliferation rates, affecting growth, therapy response, and relapse risk. Faster-proliferating cells dominate untreated growth but face fitness costs like increased susceptibility to DNA damage or metabolic stress. Proliferation capacity is a core tumor characteristic, and capturing its heterogeneity is key to understanding tumor evolution and...
Biological tissues exhibit heterogeneity across multiple scales, from genetic to non-genetic. In epithelial layers, variability in mechanical properties such as adhesion and motility, together with differences in cellโcell interactions, strongly influences collective dynamics and tissue organization.
We present a 3D multiphase-field model \cite{monfared2025multiphase} of confluent cell...
The coexistence of diverse phenotypic traits within a population - such as variations in cell movement, growth, or signalling - can profoundly shape collective dynamics of cell populations. To capture these complexities, classical PDE models for cell migration can be extended to include phenotypic structuring, giving rise to a powerful class of non-local models: phenotype-structured partial...
Population models commonly use discrete structure classes to capture trait heterogeneity among individuals (e.g. age, size, phenotype, intracellular state). Upscaling these discrete models into continuum descriptions can improve analytical tractability and scalability of numerical solutions. Common upscaling approaches based solely on Taylor expansions may, however, introduce ambiguities in...
Cell-proliferation dynamics shape the spatiotemporal organisation of developing and regenerating tissues, yet collective growth often emerges from heterogeneous cell-cycle behaviour at the single-cell level. In early animal embryos, initially synchronous divisions progressively lose synchrony after a well-characterised number of cycles, providing a setting to study how individual variability...
The control of gene expression by epigenetic factors, along with gene expression noise, results in a distribution of cell states amongst genetically identical cells. Previous studies have explored the role of gene expression in proliferation and vice versa, which, in turn, shapes cellular heterogeneity within a population. However, in these studies, the population was assumed to be well-mixed....
Cellular automaton models have long been used to study cellular processes, but may be challenging for incorporating heterogeneity, migratory, and high-density effects. In this work, we introduce an extension of the classic lattice-gas cellular automata, a framework which allows to consider changes in cell numbers, cellโcell interactions, migration, and evolution of genotypic and phenotypic...
Melanoma cells can transition between cell states, contributing to therapy resistance and immune evasion. These state changes involve dynamic and reversible shifts in gene expression, making it essential to understand the underlying regulatory mechanisms for developing effective therapies. We present a mathematical model of a minimal gene regulatory network comprising key transcription factors...
Heterogeneity in cell behaviour plays a central role in the spatiotemporal organisation of cell populations, such as in the formation of bacterial biofilms, tissues, and tumour invasion. Mathematical modelling provides a framework for understanding how emergent collective behaviours arise from dynamic interactions within heterogeneous cell populations. The nature of this heterogeneity, as well...
