Computational model of mesenchymal migration in 3D under chemotaxis

Cell chemotaxis is an important characteristic of cellular migration, which takes part in crucial aspects of life and development. In this work, we propose a novel <i>in silico</i> model of mesenchymal 3D migration with competing protrusions under a chemotactic gradient. Based on recent experimental observations, we identify three main stages that can regulate mesenchymal chemotaxis: chemosensing, dendritic protrusion dynamics and cell–matrix interactions. Therefore, each of these features is considered as a different module of the main regulatory computational algorithm. The numerical model was particularized for the case of fibroblast chemotaxis under a PDGF-bb gradient. Fibroblasts migration was simulated embedded in two different 3D matrices – collagen and fibrin – and under several PDGF-bb concentrations. Validation of the model results was provided through qualitative and quantitative comparison with <i>in vitro</i> studies. Our numerical predictions of cell trajectories and speeds were within the measured <i>in vitro</i> ranges in both collagen and fibrin matrices. Although in fibrin, the migration speed of fibroblasts is very low, because fibrin is a stiffer and more entangling matrix. Testing PDGF-bb concentrations, we noticed that an increment of this factor produces a speed increment. At 1 ng mL⁻¹ a speed peak is reached after which the migration speed diminishes again. Moreover, we observed that fibrin exerts a dampening behavior on migration, significantly affecting the migration efficiency.

细胞趋化性（Cell chemotaxis）是细胞迁移的重要特征，参与生命活动与发育过程中的关键环节。本研究提出一种全新的虚拟（in silico）模型，用于描述趋化梯度环境下存在竞争性突起的间充质三维迁移过程。基于近期的实验观测结果，我们明确了可调控间充质细胞趋化性的三大核心阶段：化学传感、树突状突起动力学以及细胞-基质相互作用。因此，我们将上述三大特征分别作为主调控计算算法的不同模块进行建模。本数值模型针对血小板衍生生长因子BB（PDGF-bb）梯度环境下的成纤维细胞趋化场景进行了定制化适配。我们模拟了成纤维细胞在两种不同三维基质——胶原蛋白与纤维蛋白——中，以及不同浓度PDGF-bb环境下的迁移过程。通过与体外（in vitro）实验研究的定性与定量对比，完成了模型结果的验证。在胶原蛋白与纤维蛋白两种基质中，模型对细胞迁移轨迹与迁移速度的数值预测结果，均处于体外实验测得的数值范围内。但在纤维蛋白基质中，成纤维细胞的迁移速度普遍较低，这是因为纤维蛋白基质刚度更高且缠结性更强。通过测试不同浓度的PDGF-bb，我们发现该因子的浓度升高会使迁移速度提升；当浓度达到1 ng·mL⁻¹时，迁移速度达到峰值，此后迁移速度会再次下降。此外，我们发现纤维蛋白基质会对细胞迁移产生抑制作用，显著降低迁移效率。