Spectral reconstruction of protein contact networks

Enrico Maiorino, Antonello Rizzi, Alireza Sadeghian, Alessandro Giuliani

Research output: Contribution to journalArticle

Abstract

In this work, we present a method for generating an adjacency matrix encoding a typical protein contact network. This work constitutes a follow-up to our recent work (Livi et al., 2015), whose aim was to estimate the relative contribution of different topological features in discovering of the unique properties of protein structures. We perform a genetic algorithm based optimization in order to modify the matrices generated with the procedures explained in (Livi et al., 2015). Our objective here is to minimize the distance with respect to a target spectral density, which is elaborated using the normalized graph Laplacian representation of graphs. Such a target density is obtained by averaging the kernel-estimated densities of a class of experimental protein maps having different dimensions. This is possible given the bounded-domain property of the normalized Laplacian spectrum. By exploiting genetic operators designed for this specific problem and an exponentially-weighted objective function, we are able to reconstruct adjacency matrices representing networks of varying size whose spectral density is indistinguishable from the target. The topological features of the optimized networks are then compared to the real protein contact networks and they show an increased similarity with respect to the starting networks. Subsequently, the statistical properties of the spectra of the newly generated matrices are analyzed by employing tools borrowed from random matrix theory. The nearest neighbors spacing distribution of the spectra of the generated networks indicates that also the (short-range) correlations of the Laplacian eigenvalues are compatible with those of real proteins.

Original languageEnglish
Pages (from-to)804-817
Number of pages14
JournalPhysica A: Statistical Mechanics and its Applications
Volume471
DOIs
Publication statusPublished - Apr 1 2017

Fingerprint

Contact
proteins
Protein
Spectral Density
Adjacency Matrix
matrices
Target
Laplacian Spectrum
Graph Laplacian
Laplacian Eigenvalues
Genetic Operators
Random Matrix Theory
matrix theory
Protein Structure
genetic algorithms
Statistical property
Spacing
Averaging
Bounded Domain
Nearest Neighbor

Keywords

  • Genetic algorithm
  • Graph laplacian
  • Graph spectra
  • Protein contact network
  • Random matrix theory

ASJC Scopus subject areas

  • Statistics and Probability
  • Condensed Matter Physics

Cite this

Spectral reconstruction of protein contact networks. / Maiorino, Enrico; Rizzi, Antonello; Sadeghian, Alireza; Giuliani, Alessandro.

In: Physica A: Statistical Mechanics and its Applications, Vol. 471, 01.04.2017, p. 804-817.

Research output: Contribution to journalArticle

Maiorino, Enrico ; Rizzi, Antonello ; Sadeghian, Alireza ; Giuliani, Alessandro. / Spectral reconstruction of protein contact networks. In: Physica A: Statistical Mechanics and its Applications. 2017 ; Vol. 471. pp. 804-817.
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