Jamming state transition has been used in literature to describe migrating-to-resting cell state transition during collective cell migration without proper rheological confirmation. Yield stress often has been used as an indicator of a jamming state. Yield stress points to the liquid-to-solid state transition, but not a priori to jamming state transition. Various solid states such as elastic solid and viscoelastic solids can be considered in the context of their ability to relax. The relaxation time for (1) an elastic solid tends to zero, (2) Kelvin-Voigt viscoelastic solid is finite, and (3) jamming state tends to infinity. In order to clarify the meaning of jamming state from the rheological standpoint we formulated the constitutive model of this state based on following conditions (1) migration of the system constituents is much damped such that the diffusion coefficient tends to zero, (2) relaxation time tends to infinity, (3) storage and loss moduli satisfy the condition G '(ω)/G "(ω) = const > 1. Jamming state represents the non-linear viscoelastic solid state. The main characteristic of this state is that the system cannot relax. Jamming state transition of multicellular systems caused by collective cell migration is discussed on a model system such as cell aggregate rounding after uni-axial compression between parallel plates based on the data from the literature. Cell aggregate rounding occurs via successive relaxation cycles. Every cycle corresponds to a different scenario of cell migration. Three scenarios were established depending on the magnitude of mechanical and biochemical perturbations (1) ordered scenario with reduced perturbations corresponds to the case that most of the cells migrate, (2) disordered scenario corresponds to the case that some cell groups migrate while the others (at the same time) stay in resting state (corresponds to medium perturbations), and (3) highly suppressed cell migration under large perturbations corresponds to the viscoelastic solid under jamming state. If cells reach the jamming state in one cycle, they are able to overcome this undesirable state and start migrating again in the next cycle by achieving the first or second scenarios again.

中文翻译：

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干扰状态转换和集体细胞迁移。

干扰状态转换已在文献中用于描述集体细胞迁移过程中迁移到静止的细胞状态转变，而没有适当的流变学确认。屈服应力通常已被用作干扰状态的指标。屈服应力指向液态到固态的转变，而不是干扰态转变的先验。在其松弛能力的范围内，可以考虑各种固态，例如弹性固体和粘弹性固体。（1）弹性固体的松弛时间趋于零，（2）Kelvin-Voigt粘弹性固体是有限的，（3）阻塞态趋于无穷大。每个周期对应于细胞迁移的不同情况。根据机械和生物化学扰动的程度，建立了三种情况（1）扰动减小的有序情况对应于大多数细胞迁移的情况，（2）无序情况对应于某些细胞组迁移而其他细胞组（ （同时）保持静止状态（对应于中等扰动），并且（3）在大扰动下高度抑制的细胞迁移对应于处于阻塞状态的粘弹性固体。如果单元在一个周期内达到干扰状态，则它们能够克服这种不良状态，并通过再次实现第一或第二种情况在下一个周期再次开始迁移。根据机械和生物化学扰动的程度，建立了三种情况（1）扰动减小的有序情况对应于大多数细胞迁移的情况，（2）无序情况对应于某些细胞组迁移而其他细胞组（ （同时）保持静止状态（对应于中等扰动），并且（3）在大扰动下高度抑制的细胞迁移对应于处于阻塞状态的粘弹性固体。如果单元在一个周期内达到干扰状态，则它们能够克服这种不良状态，并通过再次实现第一或第二种情况在下一个周期再次开始迁移。根据机械和生物化学扰动的程度，建立了三种情况（1）扰动减小的有序情况对应于大多数细胞迁移的情况，（2）无序情况对应于某些细胞组迁移而其他细胞组（ （同时）保持静止状态（对应于中等扰动），并且（3）在大扰动下高度抑制的细胞迁移对应于处于阻塞状态的粘弹性固体。如果单元在一个周期内达到干扰状态，则它们能够克服这种不良状态，并通过再次实现第一或第二种情况在下一个周期再次开始迁移。（2）无序情况对应于某些细胞群迁移而其他细胞（同时）保持静止状态（对应于中等扰动）的情况，（3）在大扰动下高度抑制的细胞迁移对应于粘弹性固体在卡纸状态下。如果单元在一个周期内达到干扰状态，则它们能够克服这种不良状态，并通过再次实现第一或第二种情况在下一个周期再次开始迁移。（2）无序情况对应于某些细胞群迁移而其他细胞（同时）保持静止状态（对应于中等扰动）的情况，（3）在大扰动下高度抑制的细胞迁移对应于粘弹性固体在卡纸状态下。如果小区在一个周期内达到阻塞状态，则它们能够克服这种不良状态，并通过再次实现第一或第二种情况在下一个周期再次开始迁移。