Waldeland Jahn O, Evje Steinar
University of Stavanger, Faculty of Science and Technology, 4068 Stavanger, Norway.
University of Stavanger, Faculty of Science and Technology, 4068 Stavanger, Norway.
J Biomech. 2018 Nov 16;81:22-35. doi: 10.1016/j.jbiomech.2018.09.011. Epub 2018 Sep 17.
In the seminal work by Swartz and collaborators (Shields et al., 2007) it was discovered that autologously secreted or activated (ECM-bound) chemokine forms local pericellular diffusion gradients skewed by fluid convection, and the cells subsequently chemotact up the flow-directed gradient. However, in (Polacheck et al., 2011) Kamm and collaborators found that there is a competing downstream and upstream migration transport mechanism. Their study showed that both mechanisms are present at the same time and the relative strength of these two stimuli governs the directional bias in migration for a cell population and is a function of cell density, interstitial flow rate, and CCR7 receptor availability. The main objective of this work is to give a possible explanation of these two different concurrent cell migration mechanisms by means of a theoretical model. Relying on multiphase modelling, separate momentum balance equations are formulated, respectively, for the cell phase and the interstitial fluid (IF) phase. In order to represent proteolytic activity and autologous chemotaxis a non-moving ECM component is included, as well as proteases secreted by the cancer cells and chemokine that can be released from ECM. The cell and IF momentum balance equations include cell-ECM and fluid-ECM resistance force terms (i.e., classical Darcy's equation terms), but also a cell-fluid interaction term that can account for a more indirect effect that fluid-generated stress may have on cancer cells. We illustrate how the cancer cells can work through this term and effectively avoid being pushed in the flow direction, and even create upstream migration by controlling its magnitude and sign. We think of this as the mathematical interpretation of the experimental observation by Kamm and collaborators that the fluid generated matrix adhesion tension on the upstream side of cells activates integrin adhesion complexes, resulting in activation of focal adhesion (FA) proteins. The model predicts that generally the strength of the upstream migration mechanism is sensitive to the cell volume fraction: a lower density of cells is subject to a weaker upstream migration effect; a higher density of cancer cells can more effectively generate upstream migration. This behavior is a result of the nonlinear coupling between cell-ECM, fluid-ECM, and cell-fluid interaction terms that naturally are involved in the mathematical expression for the net cell velocity.
在施瓦茨及其合作者的开创性研究（希尔兹等人，2007年）中发现，自体分泌或激活的（与细胞外基质结合的）趋化因子会形成局部的细胞周扩散梯度，该梯度因流体对流而发生偏移，随后细胞会沿流向梯度进行趋化运动。然而，在（波拉切克等人，2011年）的研究中，卡姆及其合作者发现存在一种相互竞争的下游和上游迁移运输机制。他们的研究表明，这两种机制同时存在，并且这两种刺激的相对强度决定了细胞群体迁移的方向偏向，它是细胞密度、间质流速和CCR7受体可用性的函数。这项工作的主要目标是通过一个理论模型对这两种不同的同时存在的细胞迁移机制给出一种可能的解释。基于多相建模，分别为细胞相和间质液（IF）相建立了单独的动量平衡方程。为了表示蛋白水解活性和自体趋化作用，纳入了一个不移动的细胞外基质成分，以及癌细胞分泌的蛋白酶和可从细胞外基质释放的趋化因子。细胞和IF动量平衡方程包括细胞 - 细胞外基质和流体 - 细胞外基质阻力项（即经典的达西方程项），但也包括一个细胞 - 流体相互作用项，该项可以解释流体产生的应力可能对癌细胞产生的更间接的影响。我们说明了癌细胞如何通过该项起作用，并有效地避免被推向流动方向，甚至通过控制其大小和符号来产生上游迁移。我们将此视为对卡姆及其合作者实验观察结果的数学解释，即细胞上游侧流体产生的基质黏附张力激活整合素黏附复合物，导致黏着斑（FA）蛋白的激活。该模型预测，一般来说，上游迁移机制的强度对细胞体积分数敏感：细胞密度较低时，上游迁移效应较弱；癌细胞密度较高时，能更有效地产生上游迁移。这种行为是细胞 - 细胞外基质、流体 - 细胞外基质和细胞 - 流体相互作用项之间非线性耦合的结果，这些项自然地包含在净细胞速度的数学表达式中。
