細胞的集體運動在胚胎演化、腫瘤轉移等生物過程中扮演極其重要的角色。在細胞本身的自驅動能力與細胞連結(cell junction)的交互作用之下，細胞形成自主耦合多體系統（active coupled-many body system），並展現極為豐富的多尺度集體合作運動如團簇、漩渦運動、類紊流運動（turbulent-like motion）。在二元細胞混合體中(binary cell mixture)，因兩細胞物種間的差異性如運動力或黏著力的不同，細胞混合體可自我分離成細胞團簇，並展現更為複雜的集體運動行為。
此篇論文將探討在二元細胞混合系統中，均勻混合的癌細胞與血管內皮細胞間如何相互作用、如何聚合、及此系統中細胞團簇邊界的時空動力行為。癌細胞相較於血管內皮細胞有較強的運動力與較弱的細胞連結，隨著時間與細胞密度增加，此二元混合系統因細胞聚集而加速並緊接著減緩至冷液體相。在此動力學相轉移的過程中，癌細胞逐漸形成更大的團簇，並增強團簇中的類紊流運動，展現多尺度的群聚現象。在癌細胞的類紊流運動特性與內皮細胞的冷液相結構侷限的交互作用下，癌細胞團簇與血細管內皮細胞間形成多尺度的碎形邊界。藉由型態指標(shape index)和非整數維度(fractal dimension)的分析發現，碎形邊界的非整數維度與細胞團簇大小呈正比關係。細胞隨團簇邊界的速度差亦呈現自我相似的特性，隨著癌細胞團簇的增長，細胞團簇邊界可展現更長尺度的擾動，並導致更為快速的邊界速度差增長。此外，因細胞分裂造成的過擁擠與細胞動力減緩，非整數維度與團簇邊界的速度差隨著時間逐漸被抑制。

Fluctuating interfaces have been widely observed in various nonlinear media such as solid-liquid interfaces during solidification, paper burning fronts, and passive or active binary mixtures after segregation. Multiscale interface fluctuations are self-organized under the interplay of coherence generated by different mutual couplings on each side of the interface and the disorder generated by stochastic agitations or passive/active forces. In binary cell mixtures, due to different cell motilities and cell-cell couplings of two types of cells, two types of cells can segregate into clusters. Past studies on binary cell mixtures mainly focused on the temporal evolutions of segregated cluster size and the degree of segregation. Nevertheless, the generic behaviors of multiscale cluster aggregation and fluctuating cluster boundaries, and their correlation to the turbulent-like cell motion down to the microscopic scale, are still unexplored.
In this work, the above issues are experimentally unraveled by observing the cancer-endothelia cell mixture from the randomly distributed dilute state. It is found that, with increasing time, cancer cells (CCs) gradually aggregate into larger clusters exhibiting fractal cluster boundaries, associated with the transition to scale-free cluster size distributions. The interaction of multiscale turbulent-like CC motions in CC clusters and excluded volume constraints from surrounding endothelial cells (ECs) is the key for generating the fractal structure and multiscale spatial velocity fluctuations of CC cluster boundaries. Larger CC clusters allow stronger longer-scale fluctuations with increasing scaling exponents of position and velocity fluctuations of CC cluster boundaries, which can be suppressed by cell crowding through cell proliferation.

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