Accelerated enumeration of extreme rays through a positive-definite elementarity test.

Wannes Mores, Satyajeet S Bhonsale, Filip Logist, Jan F M Van Impe
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Abstract

Motivation: Analysis of metabolic networks through extreme rays such as extreme pathways and elementary flux modes has been shown to be effective for many applications. However, due to the combinatorial explosion of candidate vectors, their enumeration is currently limited to small- and medium-scale networks (typically <200 reactions). Partial enumeration of the extreme rays is shown to be possible, but either relies on generating them one-by-one or by implementing a sampling step in the enumeration algorithms. Sampling-based enumeration can be achieved through the canonical basis approach (CBA) or the nullspace approach (NSA). Both algorithms are very efficient in medium-scale networks, but struggle with elementarity testing in sampling-based enumeration of larger networks.

Results: In this paper, a novel elementarity test is defined and exploited, resulting in significant speedup of the enumeration. Even though NSA is currently considered more effective, the novel elementarity test allows CBA to significantly outpace NSA. This is shown through two case studies, ranging from a medium-scale network to a genome-scale metabolic network with over 600 reactions. In this study, extreme pathways are chosen as the extreme rays, but the novel elementarity test and CBA are equally applicable to the other types. With the increasing complexity of metabolic networks in recent years, CBA with the novel elementarity test shows even more promise as its advantages grows with increased network complexity. Given this scaling aspect, CBA is now the faster method for enumerating extreme rays in genome-scale metabolic networks.

Availability and implementation: All case studies are implemented in Python. The codebase used to generate extreme pathways using the different approaches is available at https://gitlab.kuleuven.be/biotec-plus/pos-def-ep.

通过正定初等检验的极值射线的加速枚举。
动机:通过极端路径和基本通量模式等极端射线分析代谢网络已被证明对许多应用是有效的。然而,由于候选向量的组合爆炸,它们的枚举目前仅限于中小型网络(通常少于200个反应)。极端射线的部分枚举被证明是可能的,但要么依赖于一个接一个地生成它们,要么依赖于在枚举算法中实现采样步骤。基于抽样的枚举可以通过规范基方法(CBA)或零空间方法(NSA)来实现。这两种算法在中等规模的网络中都非常有效,但在基于抽样的大型网络枚举中却难以进行基本测试。结果:本文定义并开发了一种新的基本检验方法,使枚举速度显著提高。尽管NSA目前被认为更有效,但新的基础测试使CBA明显超过NSA。这是通过两个案例研究来证明的,从中等规模的网络到基因组规模的代谢网络,有超过600个反应。本研究选择极端路径作为极端射线,但其他类型的极端射线同样适用于新颖的初等检验和CBA。近年来,随着代谢网络复杂性的不断增加,具有新颖初等检验的CBA随着网络复杂性的增加,其优势也越来越有前景。考虑到这种缩放方面,CBA现在是在基因组尺度代谢网络中枚举极端射线的更快方法。可用性和实现:所有案例研究都是用Python实现的。使用不同方法生成极端路径的代码库可在https://gitlab.kuleuven.be/biotec-plus/pos-def-ep.Supplementary information上获得;补充数据可在Bioinformatics在线上获得。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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