Natural-abundance stable isotope compositions are powerful tools for understanding complex processes across myriad scientific disciplines. However, quantitative interpretation of these signals often requires equally complex models. Previous stable isotope models have treated isotopic compositions as intrinsic properties of molecules or atoms (e.g. $\delta$¹³C, ¹³R, etc.). This has proven to be a computationally efficient but inflexible approach. Here, we present a new isotope modelling software tool that combines computational strategies used in metabolic modeling with an understanding of natural isotope fractionations from the geosciences, called Quantifying Isotopologue Reaction Networks (QIRN, “churn”). QIRN treats isotopic properties as distributions of discrete isotopologues, i.e. molecules with different numbers and distributions of isotopic substitutions. This approach is remarkably generalizable and computationally tractable, enabling models of reaction networks with unprecedented complexity. QIRN parameterizes reactions as rate law equations with distinct isotopologues as the reactants and products. Isotope effects are implemented as small changes to the relevant isotopologues’ rate constants. Running this model forward in time gives the numerical solution for steady state isotopologue abundances. Different subsets of the isotopologue population can then be sampled to quantify numerous isotopic proprieties simultaneously (i.e. compound-specific, site-specific, and multiply-substituted isotope compositions). Furthermore, QIRN can model any physical, chemical or biological process as reversible or irreversible. As such, it incorporates both kinetic and equilibrium isotope effects. It can be readily applied to any isotope system (i.e. C, N, O, etc.), though at present can only track two isotopes of one element at a time. Given its generalizability, QIRN has a diverse range of applications. To demonstrate the flexibility and efficiency of QIRN, we reconstructed previous (intrinsic-property) models of sulfate reduction, abiotic amino acid synthesis, lipid biosynthesis, and photosynthesis. In these examples, QIRN consistently reproduced outputs from prior models and predicted isotopic anomalies that have been measured in nature. With its new approach to isotope modelling, QIRN will expand the potential complexity of modelled reaction networks, help predict isotopic signals that can direct experimental efforts, and provide a more efficient means of modeling emerging isotopic properties such as ‘clumped isotopes’.

天然丰度的稳定同位素组成是理解众多科学学科中复杂过程的有力工具。然而，这些信号的定量解释通常需要同样复杂的模型。以前的稳定同位素模型将同位素组成视为分子或原子的固有特性（例如$\delta$¹³ C, ¹³R 等）。这已被证明是一种计算效率高但不灵活的方法。在这里，我们提出了一种新的同位素建模软件工具，该工具将代谢建模中使用的计算策略与地球科学中对天然同位素分馏的理解相结合，称为 Quantifying Isotopologue Reaction Networks (QIRN, “churn”)。QIRN 将同位素特性视为离散同位素体的分布，即具有不同数量和同位素取代分布的分子。这种方法具有显着的泛化性和计算上的可处理性，使反应网络模型具有前所未有的复杂性。QIRN 将反应参数化为速率定律方程，其中不同的同位素异构体作为反应物和产物。同位素效应是通过对相关同位素体的速率常数的微小变化来实现的。及时运行该模型给出了稳态同位素体丰度的数值解。然后可以对同位素体群的不同子集进行采样，以同时量化多种同位素特性（即化合物特异性、位点特异性和多取代同位素组成）。此外，QIRN 可以将任何物理、化学或生物过程建模为可逆或不可逆。因此，它结合了动力学和平衡同位素效应。它可以很容易地应用于任何同位素系统（即 C、N、O 等），尽管目前一次只能跟踪一种元素的两种同位素。鉴于其普遍性，QIRN 具有广泛的应用范围。为了证明 QIRN 的灵活性和效率，我们重建了以前的（固有）硫酸盐还原模型，非生物氨基酸合成、脂质生物合成和光合作用。在这些示例中，QIRN 始终如一地再现了先前模型的输出并预测了在自然界中测量的同位素异常。凭借其新的同位素建模方法，QIRN 将扩展建模反应网络的潜在复杂性，帮助预测可以指导实验工作的同位素信号，并提供一种更有效的方法来模拟新兴同位素特性，例如“聚集同位素”。