Detailed mechanistic models of biological processes can pose significant challenges for analysis and parameter estimations due to the large number of equations used to track the dynamics of all distinct configurations in which each involved biochemical species can be found. Model reduction can help tame such complexity by providing a lower-dimensional model in which each macro-variable can be directly related to the original variables. We present CLUE, an algorithm for exact model reduction of systems of polynomial differential equations by constrained linear lumping. It computes the smallest dimensional reduction as a linear mapping of the state space such that the reduced model preserves the dynamics of user-specified linear combinations of the original variables. Even though CLUE works with nonlinear differential equations, it is based on linear algebra tools, which makes it applicable to high-dimensional models. Using case studies from the literature, we show how CLUE can substantially lower model dimensionality and help extract biologically intelligible insights from the reduction. An implementation of the algorithm and relevant resources to replicate the experiments herein reported are freely available for download at https://github.com/pogudingleb/CLUE.

中文翻译：

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CLUE：通过微分方程的约束集总精确最大程度地减少动力学模型

由于大量方程用于跟踪所有不同配置的动力学，其中可以找到每个涉及的生化物种，因此生物过程的详细机械模型可能对分析和参数估计构成重大挑战。模型简化可以通过提供一个低维模型来帮助控制这种复杂性，其中每个宏变量都可以与原始变量直接相关。我们提出了 CLUE，这是一种通过约束线性集总对多项式微分方程组进行精确模型简化的算法。它将最小降维计算为状态空间的线性映射，从而使缩减模型保留原始变量的用户指定线性组合的动态。尽管 CLUE 适用于非线性微分方程，它基于线性代数工具，适用于高维模型。使用文献中的案例研究，我们展示了 CLUE 如何显着降低模型维度并帮助从减少中提取生物学上可理解的见解。用于复制本文报告的实验的算法和相关资源的实现可在 https://github.com/pogudingleb/CLUE 免费下载。