Amyot F, Camphausen K, Siavosh A, Sackett D, Gandjbakhche A
Section on Biomedical Stochastic Physics, Laboratory of Integrative and Medical Biophysics, National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, MD 20892, USA.
Syst Biol (Stevenage). 2005 Jun;152(2):61-6. doi: 10.1049/ip-syb:20045036.
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.
为了研究细胞外基质（ECM）环境中内皮细胞（ECs）的网络形成，我们基于扩散限制簇聚集体模型（DLCA）设计了一种EC聚集型模型，其中颗粒簇扩散并在接触时粘在一起。我们使用该模型通过比较实验数据和模拟数据来量化EC分化为索状结构的过程。当DLCA模型与实验动力学和细胞浓度结果相结合时，所做的近似不仅使我们能够通过伪扩散系数量化细胞分化，还能测量肿瘤血管生成因子（TAFs）对ECs形成索状结构的影响。我们通过体外试验测试了我们的模型，在该试验中，我们通过分析延时图像来记录EC聚集，这些图像为我们提供了分形维数随时间的演变。我们针对各种细胞浓度和TAFs（如EVG、FGF-b和VEGF）进行了这些实验。在实验的前六个小时内，ECs迅速聚集。测量的分形维数值随时间下降，直到达到仅取决于EC浓度的渐近值。相比之下，动力学取决于TAFs的性质。实验和模拟结果在分形维和动力学方面相互关联，使我们能够通过伪扩散系数量化每种TAF的影响。我们已经表明，EC聚集体的形状、动力学聚集和分形维数符合能够再现血管生成第一阶段的体外模型。我们得出结论，DLCA模型与实验结果相结合，是一种用于量化嵌入ECM蛋白中的ECs的动力学和网络特征的高效检测方法。最后，我们提出了一种可用于在体外试验中研究血管生成药物作用的新方法。
