A mathematical model for eph/ephrin-directed segregation of intermingled cells.

Eph receptors, the largest family of receptor tyrosine kinases, control cell-cell adhesion/de-adhesion, cell morphology and cell positioning through interaction with cell surface ephrin ligands. Bi-directional signalling from the Eph and ephrin complexes on interacting cells have a significant role in controlling normal tissue development and oncogenic tissue patterning. Eph-mediated tissue patterning is based on the fine-tuned balance of adhesion and de-adhesion reactions between distinct Eph- and ephrin-expressing cell populations, and adhesion within like populations (expressing either Eph or ephrin). Here we develop a stochastic, Lagrangian model that is based on Eph/ephrin biology: incorporating independent Brownian motion to describe cell movement and a deterministic term (the drift term) to represent repulsive and adhesive interactions between neighbouring cells. Comparison between the experimental and computer simulated Eph/ephrin cell patterning events shows that the model recapitulates the dynamics of cell-cell segregation and cell cluster formation. Moreover, by modulating the term for Eph/ephrin-mediated repulsion, the model can be tuned to match the actual behaviour of cells with different levels of Eph expression or activity. Together the results of our experiments and modelling suggest that the complexity of Eph/ephrin signalling mechanisms that control cell-cell interactions can be described well by a mathematical model with a single term balancing adhesion and de-adhesion between interacting cells. This model allows reliable prediction of Eph/ephrin-dependent control of cell patterning behaviour.

Creation and biophysical characterization of a high-affinity, monomeric EGF receptor ectodomain using fluorescent proteins.

X-ray structural studies revealed two conformations of the epidermal growth factor receptor (EGFR) ectodomain (ECD): a compact, tethered conformation in the absence of EGF and an untethered or extended conformation in the presence of EGF. An EGFR-ECD derivative with a monomeric red fluorescent protein (mRFP) at the N-terminus and an enhanced green fluorescent protein (eGFP) at the C-terminus (dual-tag-EGFR-ECD) was created and characterized. The dual-tag-EGFR-ECD construct was shown to have high affinity (nanomolar range) for both EGF and EGFR monoclonal antibody (mAb528). The dual-tag-EGFR-ECD was further characterized by fluorescence-detected analytical ultracentrifugation, lifetime FRET, and fluorescence anisotropy. We found no evidence of a tethered unliganded conformation, nor did we observe a large shape change upon ligand binding as predicted by the crystal models. Increases in steady-state anisotropy upon binding of EGF to the dual-tag-EGFR-ECD were observed and interpreted as changes in the protein flexibility and dynamics. We conclude the fluorescent protein tags perturb the EGFR-ECD structure, making it extended with a 50-fold higher affinity for EGF relative to that of the nontagged EGFR-ECD.