论文标题
具有多个时间尺度的生物网络的算法减少
Algorithmic Reduction of Biological Networks With Multiple Time Scales
论文作者
论文摘要
我们提出了一种符号算法方法，该方法允许计算不变的流形和相应的减少系统，用于模拟生物网络的微分方程，该方程组成了用于细胞生物化学的化学反应网络，以及用于药理学，流行病学和生态学的隔室模型。给定网络的多个时间尺度是基于热带几何形状来获得的。我们的减少在数学上是合理的，这是在单一的扰动设置中。不变歧管的存在受超血度条件的约束，为此，我们提出了基于Hurwitz标准的算法测试。我们最终获得了一系列嵌套不变的歧管和这些歧管上的减少系统。我们的理论结果通常伴随着严格的算法描述，适用于基于现有的现成软件系统，特别是符号计算库和满意度模型理论求解器的直接实现。我们介绍了使用我们自己的原型实现从著名的生物模型数据库中获取的计算示例。
We present a symbolic algorithmic approach that allows to compute invariant manifolds and corresponding reduced systems for differential equations modeling biological networks which comprise chemical reaction networks for cellular biochemistry, and compartmental models for pharmacology, epidemiology and ecology. Multiple time scales of a given network are obtained by scaling, based on tropical geometry. Our reduction is mathematically justified within a singular perturbation setting. The existence of invariant manifolds is subject to hyperbolicity conditions, for which we propose an algorithmic test based on Hurwitz criteria. We finally obtain a sequence of nested invariant manifolds and respective reduced systems on those manifolds. Our theoretical results are generally accompanied by rigorous algorithmic descriptions suitable for direct implementation based on existing off-the-shelf software systems, specifically symbolic computation libraries and Satisfiability Modulo Theories solvers. We present computational examples taken from the well-known BioModels database using our own prototypical implementations.
