Rachel Timo, Brombacher Eva, Wöhrle Svenja, Groß Olaf, Kreutz Clemens
Institute of Medical Biometry and Statistics, Medical Center, Faculty of Medicine, University of Freiburg, Stefan-Meier-Str. 26, Freiburg, Baden-Württemberg, 79104, Germany.
Institute of Physics, University of Freiburg, Hermann-Herder-Straße 3, Freiburg, Baden-Württemberg, 79104, Germany.
Bioinformatics. 2024 Nov 28;40(12). doi: 10.1093/bioinformatics/btae683.
Mathematical modelling plays a crucial role in understanding inter- and intracellular signalling processes. Currently, ordinary differential equations (ODEs) are the predominant approach in systems biology for modelling such pathways. While ODE models offer mechanistic interpretability, they also suffer from limitations, including the need to consider all relevant compounds, resulting in large models difficult to handle numerically and requiring extensive data.
In previous work, we introduced the retarded transient function (RTF) as an alternative method for modelling temporal responses of signalling pathways. Here, we extend the RTF approach to integrate concentration or dose-dependencies into the modelling of dynamics. With this advancement, RTF modelling now fully encompasses the application range of ODE models, which comprises predictions in both time and concentration domains. Moreover, characterizing dose-dependencies provides an intuitive way to investigate and characterize signalling differences between biological conditions or cell types based on their response to stimulating inputs. To demonstrate the applicability of our extended approach, we employ data from time- and dose-dependent inflammasome activation in bone marrow-derived macrophages treated with nigericin sodium salt. Our results show the effectiveness of the extended RTF approach as a generic framework for modelling dose-dependent kinetics in cellular signalling. The approach results in intuitively interpretable parameters that describe signal dynamics and enables predictive modelling of time- and dose-dependencies even if only individual cellular components are quantified.
The presented approach is available within the MATLAB-based Data2Dynamics modelling toolbox at https://github.com/Data2Dynamics and https://zenodo.org/records/14008247 and as R code at https://github.com/kreutz-lab/RTF.
数学建模在理解细胞间和细胞内信号传导过程中起着至关重要的作用。目前，常微分方程（ODEs）是系统生物学中用于模拟此类信号通路的主要方法。虽然ODE模型提供了机制可解释性，但它们也存在局限性，包括需要考虑所有相关化合物，这导致模型规模庞大，难以进行数值处理且需要大量数据。
在之前的工作中，我们引入了延迟瞬态函数（RTF）作为模拟信号通路时间响应的替代方法。在此，我们扩展了RTF方法，将浓度或剂量依赖性整合到动力学建模中。通过这一进展，RTF建模现在完全涵盖了ODE模型的应用范围，其中包括在时间和浓度域的预测。此外，表征剂量依赖性提供了一种直观的方式，可基于生物条件或细胞类型对刺激输入的响应来研究和表征信号差异。为了证明我们扩展方法的适用性，我们使用了用尼日利亚菌素钠盐处理的骨髓来源巨噬细胞中时间和剂量依赖性炎性小体激活的数据。我们的结果表明，扩展的RTF方法作为细胞信号传导中剂量依赖性动力学建模的通用框架是有效的。该方法产生了描述信号动力学的直观可解释参数，即使仅对单个细胞成分进行量化，也能够对时间和剂量依赖性进行预测建模。
所提出的方法可在基于MATLAB的Data2Dynamics建模工具箱中获取，网址为https://github.com/Data2Dynamics和https://zenodo.org/records/14008247，也可作为R代码在https://github.com/kreutz-lab/RTF获取。
