Institute of Physics, University of Freiburg, Freiburg, Germany.
Freiburg Center for Data Analysis and Modeling, University of Freiburg, Freiburg, Germany.
PLoS Comput Biol. 2023 Sep 13;19(9):e1010867. doi: 10.1371/journal.pcbi.1010867. eCollection 2023 Sep.
Ordinary differential equations are frequently employed for mathematical modeling of biological systems. The identification of mechanisms that are specific to certain cell types is crucial for building useful models and to gain insights into the underlying biological processes. Regularization techniques have been proposed and applied to identify mechanisms specific to two cell types, e.g., healthy and cancer cells, including the LASSO (least absolute shrinkage and selection operator). However, when analyzing more than two cell types, these approaches are not consistent, and require the selection of a reference cell type, which can affect the results. To make the regularization approach applicable to identifying cell-type specific mechanisms in any number of cell types, we propose to incorporate the clustered LASSO into the framework of ordinary differential equation modeling by penalizing the pairwise differences of the logarithmized fold-change parameters encoding a specific mechanism in different cell types. The symmetry introduced by this approach renders the results independent of the reference cell type. We discuss the necessary adaptations of state-of-the-art numerical optimization techniques and the process of model selection for this method. We assess the performance with realistic biological models and synthetic data, and demonstrate that it outperforms existing approaches. Finally, we also exemplify its application to published biological models including experimental data, and link the results to independent biological measurements.
常微分方程常用于生物系统的数学建模。确定特定于某些细胞类型的机制对于构建有用的模型和深入了解潜在的生物学过程至关重要。已经提出并应用了正则化技术来识别两种细胞类型（例如健康细胞和癌细胞）特有的机制，包括 LASSO（最小绝对值收缩和选择算子）。然而，当分析超过两种细胞类型时，这些方法不一致，需要选择参考细胞类型，这可能会影响结果。为了使正则化方法适用于识别任意数量的细胞类型中的细胞类型特异性机制，我们建议通过惩罚不同细胞类型中特定机制的对数倍变化参数的对差异，将聚类 LASSO 纳入常微分方程建模框架中。这种方法引入的对称性使得结果与参考细胞类型无关。我们讨论了该方法所需的最先进数值优化技术的适应性和模型选择过程。我们使用现实的生物模型和合成数据评估了性能，并证明它优于现有方法。最后，我们还举例说明了它在包括实验数据的已发表生物模型中的应用，并将结果与独立的生物学测量结果联系起来。
