A moving-boundary model of epidermal growth factor receptor trafficking predicts the basis of cell-to-cell heterogeneity in mitogenic signaling

Introduction: Receptor trafficking via endocytosis regulates the localization and persistence of activated growth factor receptors, and defects in receptor endocytosis arise frequently in cancer. Despite its clear physiological importance, the role of endocytosis in regulating downstream signaling is still debated and poorly understood. In particular, cell biologists lack an explanation for how sustained downstream signaling is possible when endocytosed receptors physically separate from membrane-retained signaling intermediates, including the RAS GTPase, within the first several minutes after growth factor ligation. In this work, we aim to determine if a hypothesized reaction-diffusion mechanism involving receptor-driven complexes of signaling intermediates can functionally connect endocytosed receptors to obligate membrane-bound signaling molecules to drive and prolong downstream signaling. Previous work from our lab suggested that the dynamic regulation of reversible association of functional complexes of signaling proteins and the activity of phosphatases regulates the ability of receptors to continue signaling from endosomes, remotely from the plasma membrane. We predicted that this regulatory mechanism would be significantly affected by cell-to-cell heterogeneity in the numbers, sizes, and rates of movement of EGFR-containing endosomes. We further hypothesized that intercellular heterogeneity in this mechanism explains the natural observed variance in the ability of cells to activate RAS effectors in response to growth factor receptor activation.

Materials and

Methods: To test our hypothesis, we built a reaction-diffusion model based on the epidermal growth factor receptor (EGFR)-extracellular signal-regulated kinase (ERK) pathway. The model is comprised of 31 ordinary and 20 partial differential equations written in MATLAB that describe how EGF binding to EGFR activates the canonical RAS-ERK pathway via membrane recruitment of GRB2 and SOS and parallel activation of the SH2 domain-containing tyrosine phosphatase SHP2 by complexation with the adaptor GRB2-associated binder 1 (GAB1). Src family kinases (SFKs), which phosphorylate GAB1 and enable its binding to SHP2, were modeled as a diffusible EGFR-activated intermediary kinase, and RAS-specific GTPase-activating proteins (RASGAP) were included as negative regulators of RAS and diffusible binding partners of GAB1, whose dephosphorylation is regulated by SHP2. Importantly, this model features a novel ability to solve the species conservation equations for a geometry including a prescribed number of moving endosomes, a capability that is absent in existing platforms for computational analysis of biochemical networks. The model was trained on experimental signaling data measured in gene-edited HeLa cells wherein 65 model parameters were fitted over many iterations of global optimization to minimize the difference between model predictions and data on a 40-core computing cluster. To validate model predictions, we used indirect iterative immunofluorescence imaging (4i) of EGFR-ERK signaling in lung adenocarcinoma cells.

Results, Conclusions, and Discussions: The trained model was used to predict changes in time-integrated amounts of active RAS and ERK molecules in the presence of 1-16 endosomes per cell, a typical range observed in HeLa cells. Upon endocytosis, the model distributes active EGFR molecules among the specified numbers of endosomes evenly. Cells with more endosomes exhibited stronger predicted activation RAS and ERK activity (Fig. 1A). Parameter sensitivity analysis nominated variation in the distribution of the active, diffusible protein tyrosine phosphatase SHP2 and SFKs as a candidate mechanism explaining the elevated ERK activity for cells with more EGFR-containing endosomes (Fig. 1B). More endosomes allowed larger numbers of active SHP2 to reach the plasma membrane and promote RAS activity by dephosphorylating RASGAP binding sites.

To validate model predictions, we used 4i to compare ERK activity of cells with different numbers of EGFR-containing endosomes. The number of colocalized EGFR-EEA1 puncta (i.e., endocytosed EGFR) positively correlated with phosphorylated ERK intensity and negatively correlated with variance in cytosolic SFK activity after substantial amounts of EGFR have endocytosed for the reaction-diffusion mechanisms to be at play (Fig. 1C,D), as predicted by our model. Experimental comparisons against the model are also being made among cells with similar numbers but disparate intracellular spatial distributions of EGFR-containing endosomes to test for correlations between variance in GAB1-SHP2 complex distribution with ERK activity. Our findings demonstrate that heterogeneity in ERK activation among cells can arise through spatial variation in the activity of cytosolic SFK and SHP2, which can be targeted by FDA-approved small-molecule inhibitors. Our analysis also provides an explanation for a previously described paradox in EGFR-ERK signaling by demonstrating that ERK activity can be sustained by moving, receptor-containing endosomes that promote the distribution of active SFK and SHP2 over the entire intracellular length scale via a reaction-diffusion mechanism.

The novel computational model we developed provides a new quantitative platform for predicting the impact of largely neglected biophysical effects on the ubiquitously important EGFR-ERK signaling pathway. The insights gained provide improved understanding of the most critical nodes to target pharmacologically for the efficient antagonism of pathological receptor-mediated signaling.

Acknowledgements (Optional): This work was supported by U54-CA274499 and NSF MCB 1716537.