Quantitative method to study the network formation of endothelial cells in response to tumor angiogenic factors

To study the network formation of endothelial cells (ECs) in an extracellular matrix (ECM) environment, we have devised an EC aggregation-type model based on a diffusion limited cluster aggregation model (DLCA), where clusters of particles diffuse and stick together upon contact. We use this model to quantify EC differentiation into cord-like structures by comparing experimental and simulation data. Approximations made with the DLCA model, when combined with experimental kinetics and cell concentration results, not only allow us to quantify cell differentiation by a pseudo diffusion coefficient, but also measure the effects of tumor angiogenic factors (TAFs) on the formation of cord-like structures by ECs. We have tested our model by using an in vitro assay, where we record EC aggregation by analysing time-lapse images that provide us with the evolution of the fractal dimension measure through time. We performed these experiments for various cell concentrations and TAFs (e.g. EVG, FGF-b, and VEGF). During the first six hours of an experiment, ECs aggregate quickly. The value of the measured fractal dimension decreases with time until reaching an asymptotic value that depends solely on the EC concentration. In contrast, the kinetics depend on the nature of TAFs. The experimental and simulation results correlate with each other in regards to the fractal dimension and kinetics, allowing us to quantify the influence of each TAF by a pseudo diffusion coefficient. We have shown that the shape, kinetic aggregation, and fractal dimension of the EC aggregates fit into an in vitro model capable of reproducing the first stage of angiogenesis. We conclude that the DLCA model, combined with experimental results, is a highly effective assay for the quantification of the kinetics and network characteristics of ECs embedded in ECM proteins. Finally, we present a new method that can be used for studying the effect of angiogenic drugs in in vitro assays.