The dynamics of cellular pattern formation is 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. The orientational alignment occurs primarily when cells reach a high density near confluence. Therefore, for accurate modeling, it is crucial to take into account both the cell-cell interaction term and the influence from the substrate, acting as a one-body external potential term. To fill in this gap, we develop a hybrid procedure that utilizes statistical learning approaches to extend the state-of-the-art physics models for quantifying both effects. We develop a more efficient way to perform feature selection that avoids testing all feature combinations through simulation. 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 quantitatively reproduce the key system-level parameters--the temporal progression of the velocity orientational order parameters and the variability of velocity vectors, whereas models missing any of the features fail to capture these temporally dependent parameters.

翻译：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，在分子排列基底的弱引导作用下，培养于液晶弹性体上的人真皮成纤维细胞会随时间推移展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形成的全面理解仍 largely unknown。这一认知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性模型。定向排列主要发生在细胞达到接近汇合的高密度时。因此，为了精确建模，必须同时考虑细胞-细胞相互作用项以及基底作为单体外势能项的影响。为填补这一空白，我们开发了一种混合程序，利用统计学习方法扩展最先进的物理模型以量化这两种效应。我们提出了一种更高效的特征选择方法，避免通过模拟测试所有特征组合。模型的极大似然估计量被推导出来，并实现了计算可扩展的算法用于模型校准和模拟。通过纳入这些特征（如非高斯各向异性涨落，以及仅对具有相同速度方向的邻近细胞施加定向排列相互作用），该模型定量重现了关键系统级参数——速度定向序参数的时间演进和速度向量的变异性，而缺失任何特征的模型均无法捕捉这些时间依赖参数。