The dynamics of cellular pattern formation are crucial for understanding embryonic development and tissue morphogenesis. Recent studies have shown that human dermal fibroblasts cultured on liquid crystal elastomers can exhibit an increase in orientational alignment over time, accompanied by cell proliferation, under the influence of the weak guidance of a molecularly aligned substrate. However, a comprehensive understanding of how this order arises remains largely unknown. This knowledge gap may be attributed, in part, to a scarcity of mechanistic models that can capture the temporal progression of the complex nonequilibrium dynamics during the cellular alignment process. To fill in this gap, we develop a hybrid procedure that utilizes statistical learning approaches to select individual-level features for extending the state-of-art physics models. The maximum likelihood estimator of the model was derived and implemented in computationally scalable algorithms for model calibration and simulation. By including these features, such as the non-Gaussian, anisotropic fluctuations, and limiting alignment interaction only to neighboring cells with the same velocity direction, this model is able to reproduce system-level parameters: the temporal progression of the velocity orientational order parameters and the variability of velocity vectors. Unlike other data-driven approaches, we do not rely on a loss function to tune model parameters to match these system-level characteristics. Furthermore, we develop a computational toolbox for automating model construction and calibration that can be applied to other systems of active matter.

翻译：摘要：细胞模式形成的动力学对于理解胚胎发育和组织形态发生至关重要。近期研究表明，在分子排列基底弱引导作用下，培养于液晶弹性体上的人真皮成纤维细胞可随时间推移表现出定向排列的增加，并伴随细胞增殖。然而，关于这种有序性如何产生的全面理解仍基本未知。这一知识空白部分归因于缺乏能够捕捉细胞排列过程中复杂非平衡动力学时间演进的机制模型。为填补这一空白，我们开发了一种混合方法，利用统计学习方法选择个体层面特征以扩展最先进的物理模型。我们推导了模型的最大似然估计量，并采用计算可扩展的算法进行模型校准与模拟。通过纳入非高斯各向异性涨落等特征，并将排列相互作用限制于具有相同速度方向的相邻细胞，该模型能够再现系统层面参数：速度定向有序参数的时间演进及速度向量的变异性。与其他数据驱动方法不同，我们无需依赖损失函数调整模型参数以匹配这些系统层面特征。此外，我们开发了一套计算工具包，用于自动化模型构建与校准，可应用于其他活性物质系统。