Alterations in epidermal growth factor receptor (EGFR) dynamics can influence tumor initiation by changing receptor abundance, ligand-dependent activation, and downstream proliferative signaling. Mathematically linking these receptor-scale processes to population-level tumor growth remains challenging because they couple molecular, cellular, and tissue-scale dynamics. Here, we develop multiscale models that explicitly captures receptor-ligand dynamics. We analyze the dynamics of a refined version of a 3D stochastic multicellular model with explicit EGFR-EGF interactions to derive a receptor-structured continuum model in which cells are organized by active receptor clusters. This model is further reduced into a population dynamics model that tracks the mean number of active receptors. It captures the main qualitative behaviours of the higher-dimensional models while enabling analytical and numerical characterization of model-derived thresholds for sustained growth. After calibration and comparison with available textit{in vivo} tumor-growth data under EGFR overexpression, we use the model hierarchy to quantify how initiation thresholds depend on EGF availability, EGFR abundance, receptor-ligand unbinding, and genetic potential. The models predict that EGFR overexpression, stronger receptor-ligand binding, and more aggressive cell phenotypes each lower the EGF molecular counts required for sustained tumor growth. Overall, the proposed framework provides a flexible mathematical approach for connecting receptor-ligand kinetics with population-level tumor-initiation dynamics.
Qasim, R., BOUCHNITA, A.
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