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The autoxidation of triglyceride (or triacylglycerol, TAG) is a poorly understood complex system. It is known from mass spectrometry measurements that, although initiated by a single molecule, this system involves an abundance of intermediate species and a complex network of reactions. For this reason, the attribution of the mass peaks to exact molecular structures is difficult without additional information about the system. We provide such information using a graph theory-based algorithm. Our algorithm performs an automatic discovery of the chemical reaction network that is responsible for the complexity of the mass spectra in drying oils. This knowledge is then applied to match experimentally measured mass spectra with computationally predicted molecular graphs. We demonstrate this methodology on the autoxidation of triolein as measured by electrospray ionization-mass spectrometry (ESI-MS). Our protocol can be readily applied to investigate other oils and their mixtures.

Several systems in organic chemistry are so large and complex that formulating the rate equations for their kinetics is difficult. Examples include polymerization of bio-derived materials, such as natural oils and resins, and metabolic oxidation reactions, as in the Krebs cycle. The challenge lies in the diversity of reaction products and their growth in size, which may be unbounded due to the polymerization-like reactions. Here we demonstrate an algorithm that formulates the kinetics of chemical systems of unlimited size in terms of a fine number of fragment species, and therefore, renders such structures tractable for kinetic modelling. We study a complex system of ethyl linoleate polymerization using such an algorithm. Additionally, we show that the algorithm may assist interpreting experimental measurements from electrospray ionization mass spectrometry.

In every network, a distance between a pair of nodes can be defined as the length of the shortest path connecting these nodes, and therefore one may speak of a ball, its volume, and how it grows as a function of the radius. Spatial networks tend to feature peculiar volume scaling functions, as well as other topological features, including clustering, degree-degree correlation, clique complexes, and heterogeneity. Here we investigate a nongeometric random graph with a given degree distribution and an additional constraint on the volume scaling function. We show that such structures fall into the category of m -colored random graphs and study the percolation transition by using this theory. We prove that for a given degree distribution the percolation threshold for weakly connected components is not affected by the volume growth function. Additionally, we show that the size of the giant component and the cyclomatic number are not affected by volume scaling. These findings may explain the surprisingly good performance of network models that neglect volume scaling. Even though this paper focuses on the implications of the volume growth, the model is generic and might lead to insights in the field of random directed acyclic graphs and their applications.

Additional file 1. Imaging ATR-FTIR data showing the formation of zinc soaps over time and the formation of zinc soaps close to the pLOC17 layer.