Monte Carlo simulations of VEGF binding to cell surface receptors in vitro.

The vascular endothelial growth factor (VEGF) family binds multiple endothelial cell surface receptors. Our goal is to build comprehensive models of these interactions for the purpose of simulating angiogenesis. In view of low concentrations of growth factors in vivo and in vitro, stochastic modeling of molecular interactions may be necessary. Here, we compare Monte Carlo simulations of the stochastic binding of VEGF and two of its major receptors on cells in vitro to equivalent deterministic simulations. In the range of typical VEGF concentrations, the stochastic and deterministic models are in agreement. However, we observe significant variability in receptor binding, which may be linked to biological stochastic events, e.g., blood vessel sprout initiation. We study patches of cell surface of varying sizes to investigate spatial integration of the signal by the cell, which impacts directly the variability of binding, and find significant variability up to the single-cell level. Dimerization of VEGF receptors does not significantly alter the variability in ligand binding. A 'sliding window' approach demonstrated no reduction in the variability of binding by temporal integration. The variability is expected to be more prominent in in vivo situations where the number of ligand molecules available for binding is less.