Quantitative dynamical models facilitate the understanding of biological processes and the prediction of their dynamics. These models usually comprise unknown parameters, which have to be inferred from experimental data. For quantitative experimental data, there are several methods and software tools available. However, for qualitative data the available approaches are limited and computationally demanding. Here, we consider the optimal scaling method which has been developed in statistics for categorical data and has been applied to dynamical systems. This approach turns qualitative variables into quantitative ones, accounting for constraints on their relation. We derive a reduced formulation for the optimization problem defining the optimal scaling. The reduced formulation possesses the same optimal points as the established formulation but requires less degrees of freedom. Parameter estimation for dynamical models of cellular pathways revealed that the reduced formulation improves the robustness and convergence of optimizers. This resulted in substantially reduced computation times. We implemented the proposed approach in the open-source Python Parameter EStimation TOolbox (pyPESTO) to facilitate reuse and extension. The proposed approach enables efficient parameterization of quantitative dynamical models using qualitative data.

定量动力学模型有助于理解生物学过程并预测其动力学。这些模型通常包含未知参数，必须从实验数据中推断出这些参数。对于定量实验数据，有几种可用的方法和软件工具。但是，对于定性数据，可用的方法是有限的，并且在计算上要求很高。在这里，我们考虑最优分类法，该方法已在分类数据的统计中开发，并已应用于动态系统。这种方法将定性变量转换为定量变量，并考虑了它们之间的关系约束。我们为定义最佳缩放比例的优化问题导出了简化的公式。简化的公式具有与已建立的公式相同的最佳点，但所需的自由度较小。细胞途径动力学模型的参数估计表明，减少的配方提高了优化程序的鲁棒性和收敛性。这导致计算时间大大减少。我们在开源Python参数估计工具栏（pyPESTO）中实现了所建议的方法，以方便重用和扩展。所提出的方法使得能够使用定性数据对定量动力学模型进行有效的参数化。我们在开源Python参数估计工具栏（pyPESTO）中实现了所建议的方法，以方便重用和扩展。所提出的方法使得能够使用定性数据对定量动力学模型进行有效的参数化。我们在开源Python参数估计工具栏（pyPESTO）中实现了所建议的方法，以方便重用和扩展。所提出的方法使得能够使用定性数据对定量动力学模型进行有效的参数化。