  In this study, we present a method of pattern mining based on network theory
that enables the identification of protein structures or complexes from
synthetic volume densities, without the knowledge of predefined templates or
human biases for refinement. We hypothesized that the topological connectivity
of protein structures is invariant, and they are distinctive for the purpose of
protein identification from distorted data presented in volume densities.
Three-dimensional densities of a protein or a complex from simulated
tomographic volumes were transformed into mathematical graphs as observables.
We systematically introduced data distortion or defects such as missing
fullness of data, the tumbling effect, and the missing wedge effect into the
simulated volumes, and varied the distance cutoffs in pixels to capture the
varying connectivity between the density cluster centroids in the presence of
defects. A similarity score between the graphs from the simulated volumes and
the graphs transformed from the physical protein structures in point data was
calculated by comparing their network theory order parameters including node
degrees, betweenness centrality, and graph densities. By capturing the
essential topological features defining the heterogeneous morphologies of a
network, we were able to accurately identify proteins and homo-multimeric
complexes from ten topologically distinctive samples without realistic noise
added. Our approach empowers future developments of tomogram processing by
providing pattern mining with interpretability, to enable the classification of
single-domain protein native topologies as well as distinct single-domain
proteins from multimeric complexes within noisy volumes.
