Ferrenq I, Tranqui L, Vailhé B, Gumery P Y, Tracqui P
Laboratoire TIMC-IMAG, UMR CNRS 5525, Faculté de Médecine, La Tronche, France.
Acta Biotheor. 1997 Nov;45(3-4):267-93. doi: 10.1023/a:1000684025534.
Traction forces developed by most cell types play a significant role in the spatial organisation of biological tissues. However, due to the complexity of cell-extracellular matrix interactions, these forces are quantitatively difficult to estimate without explicitly considering cell properties and extracellular mechanical matrix responses. Recent experimental devices elaborated for measuring cell traction on extracellular matrix use cell deposits on a piece of gel placed between one fixed and one moving holder. We formulate here a mathematical model describing the dynamic behaviour of the cell-gel medium in such devices. This model is based on a mechanical force balance quantification of the gel visco-elastic response to the traction forces exerted by the diffusing cells. Thus, we theoretically analyzed and simulated the displacement of the free moving boundary of the system under various conditions for cells and gel concentrations. This model is then used as the theoretical basis of an experimental device where endothelial cells are seeded on a rectangular biogel of fibrin cast between two floating holders, one fixed and the other linked to a force sensor. From a comparison of displacement of the gel moving boundary simulated by the model and the experimental data recorded from the moving holder displacement, the magnitude of the traction forces exerted by the endothelial cell on the fibrin gel was estimated for different experimental situations. Different analytical expressions for the cell traction term are proposed and the corresponding force quantifications are compared to the traction force measurements reported for various kind of cells with the use of similar or different experimental devices.
大多数细胞类型产生的牵引力在生物组织的空间组织中起着重要作用。然而，由于细胞与细胞外基质相互作用的复杂性，如果不明确考虑细胞特性和细胞外机械基质反应，这些力在定量上很难估计。最近为测量细胞在细胞外基质上的牵引力而设计的实验装置，利用放置在一个固定支架和一个移动支架之间的一块凝胶上的细胞沉积物。我们在此建立一个数学模型，描述此类装置中细胞 - 凝胶介质的动态行为。该模型基于对凝胶粘弹性响应于扩散细胞施加的牵引力的机械力平衡量化。因此，我们从理论上分析并模拟了在细胞和凝胶浓度的各种条件下系统自由移动边界的位移。然后，该模型被用作一种实验装置的理论基础，在内皮细胞接种在两个浮动支架（一个固定，另一个连接到力传感器）之间浇铸的纤维蛋白矩形生物凝胶上。通过比较模型模拟的凝胶移动边界的位移与从移动支架位移记录的实验数据，估计了在不同实验情况下内皮细胞对纤维蛋白凝胶施加的牵引力大小。提出了细胞牵引力项的不同解析表达式，并将相应的力量化结果与使用类似或不同实验装置报道的各种细胞的牵引力测量结果进行了比较。
