Network measures for protein folding state discrimination

The protein folding rate and the geometry and topology of the native state

Proteins fold in 3-dimensional conformations which are important for their function. Characterizing the global conformation of proteins rigorously and separating secondary structure effects from topological effects is a challenge. New developments in applied knot theory allow to characterize the topological characteristics of proteins (knotted or not). By analyzing a small set of two-state and multi-state proteins with no knots or slipknots, our results show that 95.4% of the analyzed proteins have non-trivial topological characteristics, as reflected by the second Vassiliev measure, and that the logarithm of the experimental protein folding rate depends on both the local geometry and the topology of the protein’s native state.

Network theory reveals principles of spliceosome structure and dynamics

Cryoelectron microscopy has revolutionized spliceosome structural biology, and structures representing much of the splicing process have been determined. Comparison of these structures is challenging due to extreme dynamics of the splicing machinery and the thousands of changing interactions during splicing. We have used network theory to analyze splicing factor interactions by constructing structure-based networks from protein-protein, protein-RNA, and RNA-RNA interactions found in eight different spliceosome structures. Our analyses reveal that connectivity dynamics result in step-specific impacts of factors on network topology. The spliceosome's connectivity is focused on the active site, in part due to contributions from nonglobular proteins. Many essential factors exhibit large shifts in centralities during splicing. Others show transiently high betweenness centralities at certain stages, thereby suggesting mechanisms for regulating splicing by briefly bridging otherwise poorly connected network nodes. These observations provide insights into organizing principles of the spliceosome and provide frameworks for comparative analysis of other macromolecular machines.

Network-based strategies for protein characterization

Protein structure characterization is fundamental to understand protein properties, such as folding process and protein resistance to thermal stress, up to unveiling organism pathologies (e.g., prion disease). In this chapter, we provide an overview on how the spectral properties of the networks reconstructed from the Protein Contact Map (PCM) can be used to generate informative observables. As a specific case study, we apply two different network approaches to an example protein dataset, for the aim of discriminating protein folding state, and for the reconstruction of protein 3D structure.

Validation and quality assessment of macromolecular structures using complex network analysis

Validation of three-dimensional structures is at the core of structural determination methods. The local validation criteria, such as deviations from ideal bond length and bonding angles, Ramachandran plot outliers and clashing contacts, are a standard part of structure analysis before structure deposition, whereas the global and regional packing may not yet have been addressed. In the last two decades, three-dimensional models of macromolecules such as proteins have been successfully described by a network of nodes and edges. Amino acid residues as nodes and close contact between the residues as edges have been used to explore basic network properties, to study protein folding and stability and to predict catalytic sites. Using complex network analysis, we introduced common network parameters to distinguish between correct and incorrect three-dimensional protein structures. The analysis showed that correct structures have a higher average node degree, higher graph energy, and lower shortest path length than their incorrect counterparts. Thus, correct protein models are more densely intra-connected, and in turn, the transfer of information between nodes/amino acids is more efficient. Moreover, protein graph spectra were used to investigate model bias in protein structure.