Chen Shaohua, Xu Wenxiang, Kim Jihan, Nan Hanqing, Zheng Yu, Sun Bo, Jiao Yang
Materials Science and Engineering, Arizona State University, Tempe AZ 85287, United States of America.
Phys Biol. 2019 Mar 8;16(3):036002. doi: 10.1088/1478-3975/ab0463.
Accurately resolving the traction forces on active cells in 3D extra-cellular matrix (ECM) is crucial to understanding stress homeostasis in cellularized ECM systems and the resulting collective cellular behavior. The majority of 3D traction force microscopy techniques, which compute the stress distribution in ECM as well as cellular traction forces from experimentally measured deformation field in the ECM using dispersed tracing particles or fluorescently-tagged matrix proteins, have assumed a spatially homogeneous ECM with constant material properties at every location in the system. Recent studies have shown that ECM can exhibit significant heterogeneity due to the disordered nature of collagen network as well as cell remodeling. In this paper, we develop a novel inverse finite-element formulation for accurately resolving the cellular traction forces by explicitly reconstructing the relative local elastic modulus values of the heterogeneous ECM containing an arbitrary shaped cell from a measured displacement field in the ECM. Our formulation does not require any a priori knowledge of the boundary conditions, and simultaneously results in the distribution of the heterogeneous modulus values and stress field in the ECM, as well as the traction forces on the cell, given experimentally measured average modulus of the ECM. We first validate our procedure in artifical model cell-ECM systems, and then employ the procedure to compute the distribution of elastic modulus in a heterogeneous type-I collagen gel as well as the traction force on a rounded breast cancer cell in the gel, based on the deformation field data obtained via 3D reflectance force microscopy. Our results indicate that the majority part of the cell is in a tensile state, while a local region on the cell is in a tri-axial compressive state, indicating the possible development of a local protrusion in this region. This is further verified by tracking the subsequent evolution of the cell morphology.
准确解析三维细胞外基质（ECM）中活细胞上的牵引力，对于理解细胞化ECM系统中的应力稳态以及由此产生的集体细胞行为至关重要。大多数三维牵引力显微镜技术，通过使用分散的示踪颗粒或荧光标记的基质蛋白，根据在ECM中实验测量的变形场来计算ECM中的应力分布以及细胞牵引力，这些技术都假定ECM在空间上是均匀的，系统中每个位置的材料属性都是恒定的。最近的研究表明，由于胶原网络的无序性质以及细胞重塑，ECM可能表现出显著的异质性。在本文中，我们开发了一种新颖的逆有限元公式，通过从ECM中测量的位移场明确重建包含任意形状细胞的异质ECM的相对局部弹性模量值，来准确解析细胞牵引力。我们的公式不需要任何关于边界条件的先验知识，并且在给定ECM的实验测量平均模量的情况下，同时得出ECM中异质模量值和应力场的分布以及细胞上的牵引力。我们首先在人工模型细胞-ECM系统中验证了我们的方法，然后基于通过三维反射力显微镜获得的变形场数据，使用该方法计算异质I型胶原凝胶中弹性模量的分布以及凝胶中圆形乳腺癌细胞上的牵引力。我们的结果表明，细胞的大部分处于拉伸状态，而细胞上的一个局部区域处于三轴压缩状态，这表明该区域可能会出现局部突起。通过跟踪细胞形态的后续演变进一步验证了这一点。
