### 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 language | English |
---|---|

Pages (from-to) | 804-817 |

Number of pages | 14 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 471 |

DOIs | |

Publication status | Published - Apr 1 2017 |

### Fingerprint

### 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

*Physica A: Statistical Mechanics and its Applications*,

*471*, 804-817. https://doi.org/10.1016/j.physa.2016.12.046

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

Research output: Contribution to journal › Article

*Physica A: Statistical Mechanics and its Applications*, vol. 471, pp. 804-817. https://doi.org/10.1016/j.physa.2016.12.046

}

TY - JOUR

T1 - Spectral reconstruction of protein contact networks

AU - Maiorino, Enrico

AU - Rizzi, Antonello

AU - Sadeghian, Alireza

AU - Giuliani, Alessandro

PY - 2017/4/1

Y1 - 2017/4/1

N2 - 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.

AB - 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.

KW - Genetic algorithm

KW - Graph laplacian

KW - Graph spectra

KW - Protein contact network

KW - Random matrix theory

UR - http://www.scopus.com/inward/record.url?scp=85008479955&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85008479955&partnerID=8YFLogxK

U2 - 10.1016/j.physa.2016.12.046

DO - 10.1016/j.physa.2016.12.046

M3 - Article

AN - SCOPUS:85008479955

VL - 471

SP - 804

EP - 817

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

ER -