School of Mathematical Sciences, University of Adelaide, Adelaide, SA, 5005, Australia.
J Math Biol. 2022 Mar 16;84(5):31. doi: 10.1007/s00285-022-01730-6.
Biological tissues are composed of cells surrounded by the extracellular matrix (ECM). The ECM can be thought of as a fibrous polymer network, acting as a natural scaffolding to provide mechanical support to the cells. Reciprocal mechanical and chemical interactions between the cells and the ECM are crucial in regulating the development of tissues and maintaining their functionality. Hence, to maintain in vivo-like behaviour when cells are cultured in vitro, they are often seeded in a gel, which aims to mimic the ECM. In this paper, we present a mathematical model that incorporates cell-gel interactions together with osmotic pressure to study the mechanical behaviour of biological gels. In particular, we consider an experiment where cells are seeded within a gel, which gradually compacts due to forces exerted on it by the cells. Adopting a one-dimensional Cartesian geometry for simplicity, we use a combination of analytical techniques and numerical simulations to investigate how cell traction forces interact with osmotic effects (which can lead to either gel swelling or contraction depending on the gel's composition). Our results show that a number of qualitatively different behaviours are possible, depending on the composition of the gel (i.e. its chemical potentials) and the strength of the cell traction forces. A novel prediction of our model is that there are cases where the gel oscillates between swelling and contraction; to our knowledge, this behaviour has not been reported in experiments. We also consider how physical parameters like drag and viscosity affect the manner in which the gel evolves.
生物组织由细胞组成，细胞周围是细胞外基质（ECM）。可以将 ECM 视为纤维聚合物网络，作为为细胞提供机械支撑的天然支架。细胞与 ECM 之间的相互机械和化学作用对于调节组织的发育和维持其功能至关重要。因此，为了使细胞在体外培养时保持类似于体内的行为，通常将其接种在凝胶中，以模拟 ECM。在本文中，我们提出了一个数学模型，该模型将细胞-凝胶相互作用与渗透压结合在一起，以研究生物凝胶的力学行为。具体而言，我们考虑了一个实验，其中细胞接种在凝胶中，由于细胞对其施加的力，凝胶逐渐变稠。为了简单起见，采用一维笛卡尔几何形状，我们使用了分析技术和数值模拟的组合来研究细胞牵引力如何与渗透压相互作用（这取决于凝胶的组成，可以导致凝胶膨胀或收缩）。我们的结果表明，根据凝胶的组成（即化学势）和细胞牵引力的强度，可能存在许多定性不同的行为。我们模型的一个新预测是，在某些情况下，凝胶会在膨胀和收缩之间振荡；据我们所知，这种行为在实验中尚未报道过。我们还考虑了诸如阻力和粘度等物理参数如何影响凝胶的演化方式。
