群体细胞动力学现象广泛存在于胚胎发育、伤口愈合、肿瘤侵袭等生理或病理过程中，且对这些过程起着重要调控作用。群体细胞动力学涉及细胞骨架的自组装、生化信号转导的调控、细胞间以及细胞与微环境间的复杂相互作用，因而是力学与生物学交叉领域中一个具有挑战性的前沿课题。本文采用生物力学和统计力学方法，结合实验、理论和模拟，对细胞单层系统的群体动力学行为进行研究。 首先，发展了二维细胞单层系统群体动力学研究的实验观测和图像分析方法。阐明了群体细胞顶点模型的理论基础，讨论了模型的参数范围和适用性。分析并给出了细胞单层的弹性模量与细胞自身力学性质、细胞密度之间的解析表达式。 其次，基于实验测量与统计力学方法，研究了二维细胞单层系统群体运动的速度分布规律和能量特征。通过活细胞成像实验，发现群体细胞运动呈现出与传统高斯分布迥异的速度分布规律，满足q-高斯分布，并具有与传统湍流截然不同的能量特征。该速度分布与能量特征在细胞单层的拥堵转变过程中保持不变，对细胞类型和基底刚度无明显依赖性，即在一定程度上具有普适性。采用Tsallis熵理论揭示了群体细胞运动速度分布规律的统计物理基础。基于主动顶点模型探究了群体细胞运动能量特征的力学机制。 此外，研究了细胞在平面基底和曲面基底上的群体运动规律。揭示了两种典型的细胞间社会性相互作用—局部对齐和接触抑制迁移—对细胞单层系统的群体运动模式、特征尺度和密度波动的影响。从细胞单层系统本征涡尺度与空间约束尺度竞争的角度阐释了受限空间内群体细胞迁移模式转变的机理。类比传统的层流–湍流转捩过程，提出一个新的控制受限空间群体细胞迁移模式的无量纲数。建立了曲面基底上群体细胞运动的理论模型，分析了几种典型曲面基底上群体细胞运动模式和密度波动特征。 最后，研究了细胞单层群体形貌振荡的规律和机制。考虑细胞变形和细胞内肌球蛋白活性之间的负反馈调控，建立了描述细胞单层形貌动力学的力–化学耦合模型。据此揭示了群体细胞振荡的物理机制。以果蝇胚胎羊浆膜组织群体振荡现象为例，研究了群体细胞振荡的模式、极化、同步化等。利用Hopf分岔理论，分析了力载荷和边界约束对群体细胞振荡的调控。发现了力学信号调控群体细胞振荡的门控机制。进而考虑具体的信号转导通路，以RhoA效应器通路为例，建立了刻画细胞单层系统群体形貌演化的一般模型。
Collective cell dynamics exists extensively and plays key regulating roles in vast physiological or pathological processes including embryo development, wound healing, and tumor invasion. It involves the self-assembly of intracellular cytoskeleton, the regulation of biochemical signaling pathways, as well as the interactions among cells and those between cells and microenvironment, making it a challenging frontier topic in biomechanics. In this dissertation, via combining experiments, theory, and simulations, we study collective cell dynamics in confluent cell monolayer systems using the methods from biomechanics and statistical mechanics. Firstly, experimental and image analyzing methods for the study of collective cell dynamics in two-dimensional (2D) confluent cell monolayer systems are established. The theoretical foundation of the vertex model for mimicking collective cells, the model parameters and the model applicability are elaborated in details. Moreover, the analytical expression of the macroscopic elastic modulus of a cell monolayer is derived in the form of individual cells’ mechanical properties as well as cell density. Secondly, based on experimental measurements and statistical mechanics methods, the velocity distribution and energy landscape of collective cell migration in 2D cell monolayer systems are studied. Through live-cell imaging experiments, we find that collective cell migration exhibits a velocity distribution statistics that is distinctly different from the classic Gaussian distribution but rather q-Gaussian distribution. Besides, the energetic statistics is markedly different from that of the classical turbulence in passive fluids. Further, both the velocity distribution and energetic statistics keep invariant during the jamming transition of cell monolayers and have no apparent dependence on cell type and substrate stiffness, thus to some extent, revealing their universality. The Tsallis entropy theory is employed to account for the velocity distribution found in our experiments. Moreover, an active vertex model is established to probe the energetic statistics of collective cell migration. Thirdly, collective cell migration on both planar and curved substrates are studied theoretically. The regulating roles of two typical social interactions among cells -- local alignment and contact inhibition of locomotion -- on collective migration modes, characteristic scales, and density fluctuations are elucidated. The mechanism of the mode transition of collective cell migration in confined spaces is deciphered from the perspective of the competition between the intrinsic scale of cell monolayers and the scale of geometric confinements. Further, in analogy with the classic laminar-to-turbulent transition, a new dimensionless parameter is proposed to quantify the migration mode of collective cells in confined space. Besides, a theoretical model for collective cell migration on curved substrates is established. Based on this model, we investigate the modes and density fluctuations of collective cell migration on several typical curved substrates. Finally, the dynamic features and underlying mechanisms of collective shape oscillations in 2D cell monolayers are investigated. Considering the negative feedback between cell deformation and intracellular myosin activity, a chemomechanical model is established to describe the collective morphodynamics in cell monolayers. Taking the collective shape oscillations in Drosophila amnioserosa as an example, we study the pattern, polarization, and synchronization of collective cell oscillations. Employing the theory of Hopf bifurcation, we examine the regulating roles of mechanical forces and boundary constraints in collective cell oscillations, and reveal the gating mechanism of mechanical forces. Moreover, considering the detailed biochemical signaling pathway and taking the RhoA effector signaling pathway as an example, we establish a general model to depict collective morphodynamics in cell monolayer systems.
