Atmospheric reaction systems as null-models to identify structural traces of evolution in metabolism

Abstract

The metabolism is the motor behind the biological complexity of an organism. One problem of characterizing its large-scale structure is that it is hard to know what to compare it to. All chemical reaction systems are shaped by the same physics that gives molecules their stability and affinity to react. These fundamental factors cannot be captured by standard null-models based on randomization. The unique property of organismal metabolism is that it is controlled, to some extent, by an enzymatic machinery that is subject to evolution. In this paper, we explore the possibility that reaction systems of planetary atmospheres can serve as a null-model against which we can define metabolic structure and trace the influence of evolution. We find that the two types of data can be distinguished by their respective degree distributions. This is especially clear when looking at the degree distribution of the reaction network (of reaction connected to each other if they involve the same molecular species). For the Earth's atmospheric network and the human metabolic network, we look into more detail for an underlying explanation of this deviation. However, we cannot pinpoint a single cause of the difference, rather there are several concurrent factors. By examining quantities relating to the modular-functional organization of the metabolism, we confirm that metabolic networks have a more complex modular organization than the atmospheric networks, but not much more. We interpret the more variegated modular arrangement of metabolism as a trace of evolved functionality. On the other hand, it is quite remarkable how similar the structures of these two types of networks are, which emphasizes that the constraints from the chemical properties of the molecules has a larger influence in shaping the reaction system than does natural selection.

Figure 1. Degree distributions of substance and reaction graphs of the human metabolism and Earth's atmospheric reaction system.

Panel A shows the probability mass-function of the degree of the substance graph of the reaction system of the Earth's atmosphere and the human metabolic networks. B shows the same as A, but for the reaction network. The similar behavior in A is drastically different in B. The plots are log-binned and plotted on double logarithmic scales.

Figure 2. Ridiculograms of the human metabolism and Earth's atmospheric reaction system in bipartite, substance and reaction graph representations.

The areas of the vertices are proportional to their degree. White vertices are reaction vertices; black vertices are currency vertices. For the other vertices the color represent different network modules. The colors of the edges are the same as their vertex of largest degree.

Figure 3. Deeper investigations of the degree distributions.

Panel A displays the degree distribution of substances in a bipartite representation of the reaction system, i.e. the probability distribution of the number of reactions a substance participates in. Panel B shows the corresponding plot for reactions and also the average degree of neighbors. The dashed line is a linear-regression line to highlight the trend in κ. C and G displays the values of the three bipartite-network terms of k—S (the sum of the degrees of neighbors), K (the degree) and X (the number of four-cycles the vertex participates in). The diagonal line shows the k-value (so if you subtract the values of circles and squares from the values of crosses you would get this line). Panel D and H shows the average degrees of nodes with certain values of the three terms that contribute to the degree in the projected reaction networks. is averaged over logarithmic bins of S, K, and X values. The dashed line is a reference corresponding to a linear -dependence. Panels A–D are for the human metabolic reaction networks, E–H show the corresponding plots for the Earth atmospheric reaction networks.

Figure 4. Relative modularity and the number of currency vertices separate networks of metabolism from networks of planetary atmospheres more than their sizes do.

To show that the maximal relative modularity separates metabolism from reaction systems of planetary atmospheres, we display (panel A) the relative modularity Δ as a function of the number of vertices N. The shaded areas indicate the standard deviation and means of the respective quantities. Similarly, in B, we show another quantity related to the functional organization, the number of currency vertices c, as a function of the number of edges M in the network. Note that axes are linear and logarithmic respectively.