Mathematical Model for the Effects of Epidermal Growth Factor Receptor Trafficking Dynamics on Fibroblast Proliferation Responses

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Abstract
We apply a mathematical model for receptor-mediated cell uptake and processing of epidermal growth factor (EGF) to analyze and predict proliferation responses to fibroblastic cells transfected with various forms of the EGF receptor (EGFR) to EGF. The underlying conceptual hypothesis is that the mitogenic signal generated by EGF/EGFR binding on the cell surface, via stimulation of receptor tyrosine kinase activity, is attenuated when the receptors are downregulated and growth factor is depleted by endocytic internalization and subsequent intracellular degradation. Hence, the cell proliferation rate ought to depend on receptor/ligand binding and trafficking parameters as well as on intrinsic receptor signal transduction properties. The goal of our modeling efforts is to formulate this hypothesis in quantitative terms. The mathematical model consists of kinetic equations for binding, internalization, degradation, and recycling of EGF and EGFR, along with an expression relating DNA synthesis rate to EGF/EGFR complex levels. Parameter values have been previously determined from independent binding and trafficking kinetic experiments on B82 fibroblasts transfected with wild-type and mutant EGFR. We show that this model can successfully interpret literature data for EGF-dependent growth of NR6 fibroblasts transfected with wild-type EGFR. Moreover, it successfully predicts the literature observation that NR6 cells transfected with a delta 973 truncation mutant EGFR, which is kinase-active but internalization-deficient, require an order of magnitude lower EGF concentration than cells with wild-type EGFR for half-maximal proliferation rate. This result demonstrates that it may be feasible to genetically engineer mammalian cell lines with reduced growth factor requirements by a rational, nonempirical approach. We explore by further model computations the possibility of exploiting other varieties of EGFR mutants to alter growth properties of fibroblastic cells, based on relationships between changes in the primary structure of the EGF receptor and the rates of specific receptor/ligand binding and trafficking processes. Our studies show that the ability to predict cell proliferation as a function of serum growth factors such as EGF could lead to the designed development of cells with optimized growth responses. This approach may also aid in elucidation of mechanisms underlying loss of normal cell proliferation control in malignant transformation, by demonstrating that receptor trafficking dynamics may in some cases play as important a role as intrinsic signal transduction in determining the overall resulting mitogenic response.