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Potential energy of complex networks: a quantum mechanical perspective.

ABSTRACT: We propose a characterization of complex networks, based on the potential of an associated Schrödinger equation. The potential is designed so that the energy spectrum of the Schrödinger equation coincides with the graph spectrum of the normalized Laplacian. Crucial information is retained in the reconstructed potential, which provides a compact representation of the properties of the network structure. The median potential over several random network realizations, which we call ensemble potential, is fitted via a Landau-like function, and its length scale is found to diverge as the critical connection probability is approached from above. The ruggedness of the ensemble potential profile is quantified by using the Higuchi fractal dimension, which displays a maximum at the critical connection probability. This demonstrates that this technique can be successfully employed in the study of random networks, as an alternative indicator of the percolation phase transition. We apply the proposed approach to the investigation of real-world networks describing infrastructures (US power grid). Curiously, although no notion of phase transition can be given for such networks, the fractality of the ensemble potential displays signatures of criticality. We also show that standard techniques (such as the scaling features of the largest connected component) do not detect any signature or remnant of criticality.

SUBMITTER: Amoroso N

PROVIDER: S-EPMC7592062 | biostudies-literature | 2020 Oct

REPOSITORIES: biostudies-literature

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Potential energy of complex networks: a quantum mechanical perspective.

Amoroso Nicola N Bellantuono Loredana L Pascazio Saverio S Lombardi Angela A Monaco Alfonso A Tangaro Sabina S Bellotti Roberto R

Scientific reports 20201027 1

We propose a characterization of complex networks, based on the potential of an associated Schrödinger equation. The potential is designed so that the energy spectrum of the Schrödinger equation coincides with the graph spectrum of the normalized Laplacian. Crucial information is retained in the reconstructed potential, which provides a compact representation of the properties of the network structure. The median potential over several random network realizations, which we call ensemble potentia ...[more]

PMID: 33110089

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Project description:DNA bases can adopt energetically unfavorable tautomeric forms that enable the formation of Watson-Crick-like (WC-like) mispairs, which have been proposed to give rise to spontaneous mutations in DNA and misincorporation errors in DNA replication and translation. Previous NMR and computational studies have indicated that the population of WC-like guanine-thymine (G-T) mispairs depends on the environment, such as the local nucleic acid sequence and solvation. To investigate these environmental effects, herein G-T mispair tautomerization processes are studied computationally in aqueous solution, in A-form and B-form DNA duplexes, and within the active site of a DNA polymerase λ variant. The wobble G-T (wG-T), WC-like G-T*, and WC-like G*-T forms are considered, where * indicates the enol tautomer of the base. The minimum free energy paths for the tautomerization from the wG-T to the WC-like G-T* and from the WC-like G-T* to the WC-like G*-T are computed with mixed quantum mechanical/molecular mechanical (QM/MM) free energy simulations. The reaction free energies and free energy barriers are found to be significantly influenced by the environment. The wG-T→G-T* tautomerization is predicted to be endoergic in aqueous solution and the DNA duplexes but slightly exoergic in the polymerase, with Arg517 and Asn513 providing electrostatic stabilization of G-T*. The G-T*→G*-T tautomerization is also predicted to be slightly more thermodynamically favorable in the polymerase relative to these DNA duplexes. These simulations are consistent with an experimentally driven kinetic misincorporation model suggesting that G-T mispair tautomerization occurs in the ajar polymerase conformation or concertedly with the transition from the ajar to the closed polymerase conformation. Furthermore, the order of the associated two proton transfer reactions is predicted to be different in the polymerase than in aqueous solution and the DNA duplexes. These studies highlight the impact of the environment on the thermodynamics, kinetics, and fundamental mechanisms of G-T mispair tautomerization, which plays a role in a wide range of biochemically important processes.

Dataset Information

Potential energy of complex networks: a quantum mechanical perspective.

Publications

Potential energy of complex networks: a quantum mechanical perspective.

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