细胞生长速率决定了在进化的细胞集落中玻璃状到流体状转变和长时间超扩散的开始
Cell growth rate dictates the onset of glass to fluid-like transition and long time super-diffusion in an evolving cell colony
摘要：
集体迁移支配着许多现象，从生命系统中的细胞运动到非生物的自我推进粒子。聚焦于肿瘤演变的早期阶段，我们阐明了细胞动力学中涉及的原则，并强调了它们在理解看似无关的软玻璃状材料中的类似行为和可能的趋化因子诱导的CD 8 $^{+}$ T细胞迁移中的意义。我们使用最小的三维模型进行了肿瘤侵袭的模拟，考虑了细胞弹性和粘附性细胞-细胞相互作用以及细胞出生和死亡，以建立细胞生长速率依赖性肿瘤扩张导致出现不同的拓扑小生境。边缘细胞垂直于肿瘤边界以较高的速度运动，而内部细胞的运动较慢且各向同性。细胞的均方位移$Δ(t)$在与细胞周期时间相当的时间表现出玻璃态行为，而在更长的时间表现出超扩散行为$Δ(t) \approx t^α$（$α> 1$）。我们推导出的值$α\approx 1.33$使用基于随机量子化的场论方法。在此过程中，我们建立了超扩散在一类看似无关的非平衡系统中的普适性。只有当细胞出生率和死亡率之间存在不平衡时，才会出现长时间的超扩散。我们对集体迁移的发现，也表明肿瘤演变以极化方式发生，与{ \it in vitro}实验定量一致。尽管是在肿瘤侵袭的背景下，这些发现也应该适用于描述生长细胞和活性系统中的集体运动，在活性系统中，粒子的产生和湮灭起着作用。
英文摘要：
Collective migration dominates many phenomena, from cell movement in living systems to abiotic self-propelling particles. Focusing on the early stages of tumor evolution, we enunciate the principles involved in cell dynamics and highlight their implications in understanding similar behavior in seemingly unrelated soft glassy materials and possibly chemokine-induced migration of CD8$^{+}$ T cells. We performed simulations of tumor invasion using a minimal three dimensional model, accounting for cell elasticity and adhesive cell-cell interactions as well as cell birth and death to establish that cell growth rate-dependent tumor expansion results in the emergence of distinct topological niches. Cells at the periphery move with higher velocity perpendicular to the tumor boundary, while motion of interior cells is slower and isotropic. The mean square displacement, $Δ(t)$, of cells exhibits glassy behavior at times comparable to the cell cycle time, while exhibiting super-diffusive behavior, $Δ(t) \approx t^α$ ($α> 1$), at longer times. We derive the value of $α\approx 1.33$ using a field theoretic approach based on stochastic quantization. In the process we establish the universality of super-diffusion in a class of seemingly unrelated non-equilibrium systems. Super diffusion at long times arises only if there is an imbalance between cell birth and death rates. Our findings for the collective migration, which also suggests that tumor evolution occurs in a polarized manner, are in quantitative agreement with {\it in vitro} experiments. Although set in the context of tumor invasion the findings should also hold in describing collective motion in growing cells and in active systems where creation and annihilation of particles play a role.
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