We argue in favor of representing living cells as automata and review demonstrations that autonomous cells can form patterns by responding to local variations in the strain fields that arise from their individual or collective motions. An autonomous cell's response to strain stimuli is assumed to be effected by internally-generated, internally-powered forces, which generally move the cell in directions other than those implied by external energy gradients. Evidence of cells acting as strain-cued automata have been inferred from patterns observed in nature and from experiments conducted in vitro. Simulations that mimic particular cases of pattern forming share the idealization that cells are assumed to pass information among themselves solely via mechanical boundary conditions, i.e., the tractions and displacements present at their membranes. This assumption opens three mechanisms for pattern formation in large cell populations: wavelike behavior, kinematic feedback in cell motility that can lead to sliding and rotational patterns, and directed migration during invasions. Wavelike behavior among ameloblast cells during amelogenesis (the formation of dental enamel) has been inferred from enamel microstructure, while strain waves in populations of epithelial cells have been observed in vitro. One hypothesized kinematic feedback mechanism, “enhanced shear motility”, accounts successfully for the spontaneous formation of layered patterns during amelogenesis in the mouse incisor. Directed migration is exemplified by a theory of invader cells that sense and respond to the strains they themselves create in the host population as they invade it: analysis shows that the strain fields contain positional information that could aid the formation of cell network structures, stabilizing the slender geometry of branches and helping govern the frequency of branch bifurcation and branch coalescence (the formation of closed networks). In simulations of pattern formation in homogeneous populations and network formation by invaders, morphological outcomes are governed by the ratio of the rates of two competing time dependent processes, one a migration velocity and the other a relaxation velocity related to the propagation of strain information. Relaxation velocities are approximately constant for different species and organs, whereas cell migration rates vary by three orders of magnitude. We conjecture that developmental processes use rapid cell migration to achieve certain outcomes, and slow migration to achieve others. We infer from analysis of host relaxation during network formation that a transition exists in the mechanical response of a host cell from animate to inanimate behavior when its strain changes at a rate that exceeds 10⁻⁴–10⁻³ s⁻¹. The transition has previously been observed in experiments conducted in vitro.

我们主张将活细胞表示为自动机，并回顾证明自主细胞可以通过响应因其个体或集体运动而产生的应变场中的局部变化来形成模式。假定自主细胞对应变刺激的响应受内部产生的，内部提供动力的影响，该力通常使细胞朝外部能量梯度所暗示的方向以外的方向移动。根据自然界中观察到的模式和体外实验，可以推断出细胞作为应变自动机的证据。。模仿图案形成的特定情况的模拟具有理想化的条件，即假定细胞仅通过机械边界条件（即，其膜上存在的牵引力和位移）在它们之间传递信息。该假设为大型细胞群体中的模式形成打开了三种机制：波状行为，细胞运动中的运动反馈（可能导致滑动和旋转模式）以及入侵过程中的定向迁移。从釉质的微观结构推断出成釉细胞（牙釉质形成）过程中成釉细胞之间的波状行为，而体外观察到上皮细胞群中的应变波。一种假设的运动学反馈机制，“增强的剪切运动性”，成功地解释了在小鼠门牙的牙釉质形成过程中分层模式的自发形成。定向迁移以入侵细胞理论为例，入侵细胞在入侵时会感知并响应它们自身在宿主群体中产生的菌株：分析表明，菌株场中含有位置信息，可以帮助细胞网络结构的形成，从而稳定细胞。分支的几何形状细长，有助于控制分支分叉和分支合并的频率（闭合网络的形成）。在模拟同质种群中的模式形成和入侵者形成网络的过程中，形态学结果受两个竞争性时间依赖性过程的速率之比控制，一个是迁移速度，另一个是与应变信息传播有关的弛豫速度。弛豫速度对于不同的物种和器官大约是恒定的，而细胞迁移速率则变化了三个数量级。我们推测，发育过程使用快速的细胞迁移来实现某些结果，而使用缓慢的迁移来实现其他结果。我们从网络形成过程中宿主松弛的分析中推断，当其应变以超过10的速率变化时，宿主细胞的机械响应会从有生命行为转变为无生命行为 我们推测，发育过程使用快速的细胞迁移来实现某些结果，而使用缓慢的迁移来实现其他结果。我们从网络形成过程中宿主松弛的分析推断出，当其应变以超过10的速率变化时，宿主细胞的机械响应会从有生命行为转变为无生命行为 我们推测，发育过程使用快速的细胞迁移来实现某些结果，而使用缓慢的迁移来实现其他结果。我们从网络形成过程中宿主松弛的分析推断出，当其应变以超过10的速率变化时，宿主细胞的机械响应会从有生命行为转变为无生命行为^-4 –10 ^-3  s ^-1。这种转变以前在体外实验中已经观察到。