In this paper, we study the structure of three types of biochemical networks: protein contact networks , metabolic networks, and gene regulatory networks, together with simulated archetypal models acting as probes. We consider both classical topological descriptors, such as the modularity and statistics of the shortest paths, and different interpretations in terms of diffusion provided by the well-known discrete heat kernel  . A principal component analysis shows high discrimination among the network types, either by considering the topological and heat kernel based  characterizations. Furthermore, a canonical correlation analysis demonstrates the strong agreement among those two characterizations, providing thus an important justification in terms of interpretability for the heat kernel. Finally, and most importantly, the focused analysis of the heat kernel provides a way to yield insights on the fact that proteins have to satisfy specific structural design constraints that the other considered biochemical networks do not need to obey. Notably, the heat trace decay of the protein ensemble denotes subdiffusion, a peculiar property of proteins.
In this paper, we study the structure and dynamical properties of protein contact networks with respect to other biological networks, together with simulated archetypal models acting as probes. We consider both classical topological descriptors, such as the modularity and statistics of the shortest paths, and different interpretations in terms of diffusion provided by the discrete heat kernel , which is elaborated from the normalized graph Laplacians . A principal component analysis shows high discrimination among the network types, either by considering the topological and heat kernel based vector characterizations. Furthermore, a canonical correlation analysis demonstrates the strong agreement among those two characterizations, providing thus an important justification in terms of interpretability for the heat kernel. Finally, and most importantly, the focused analysis of the heat kernel provides a way to yield insights on the fact that proteins have to satisfy specific structural design constraints that the other considered networks do not need to obey. Notably, the heat trace decay of an ensemble of varying-size proteins denotes subdiffusion, a peculiar property of proteins.
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of three types of biochemical networks:
and dynamical properties of
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, metabolic networks, and gene regulatory networks,
with respect to other biological networks,
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well-known
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, which is elaborated from the normalized graph Laplacians
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vector
D
biochemical
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the protein ensemble
an ensemble of varying-size proteins