Detailed dynamical systems models used in life sciences may include dozens or even hundreds of state variables. Models of large dimension are not only harder from the numerical perspective (e.g., for parameter estimation or simulation), but it is also becoming challenging to derive mechanistic insights from such models. Exact model reduction is a way to address this issue by finding a self-consistent lower-dimensional projection of the corresponding dynamical system. A recent algorithm CLUE allows one to construct an exact linear reduction of the smallest possible dimension such that the fixed variables of interest are preserved. However, CLUE is restricted to systems with polynomial dynamics. Since rational dynamics occurs frequently in the life sciences (e.g., Michaelis-Menten or Hill kinetics), it is desirable to extend CLUE to the models with rational dynamics. In this paper, we present an extension of CLUE to the case of rational dynamics and demonstrate its applicability on examples from literature. Our implementation is available in version 1.5 of CLUE at https://github.com/pogudingleb/CLUE.
翻译:生命科学中使用的详细动态系统模型可能包括数十个甚至数百个州变量。从数字角度看,大维模型不仅难度更大(例如参数估计或模拟),而且从这些模型中获取机械洞见也越来越具有挑战性。精确模型的减少是解决这一问题的一种方法,办法是找到一个自相一致的对相应的动态系统进行低维预测的方法。最近的CLUE算法允许一个人对最小的可能的维度进行精确的线性缩小,以便保存感兴趣的固定变量。然而,CLUE局限于具有多元动态的系统。由于理性动态在生命科学中经常发生(例如Michaelis-Menten或Hill 动能学),因此有必要将CLUE扩大到具有理性动态的模型。在本文中,我们介绍了CLUE对合理动态的延伸,并展示其对文献实例的适用性。我们的实施情况见于https://github.com/pogudingleb/CLUE。