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Analysis of heat kernel highlights the strongly modular and heat-preserving structure of proteins

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  • Livi, Lorenzo
  • Maiorino, Enrico
  • Pinna, Andrea
  • Sadeghian, Alireza
  • Rizzi, Antonello
  • Giuliani, Alessandro

Abstract

In this paper, we study the structure and dynamical properties of protein contact networks with respect to other biological networks, together with simulated archetypal models acting as probes. We consider both classical topological descriptors, such as modularity and statistics of the shortest paths, and different interpretations in terms of diffusion provided by the discrete heat kernel, which is elaborated from the normalized graph Laplacians. A principal component analysis shows high discrimination among the network types, by considering both the topological and heat kernel based vector characterizations. Furthermore, a canonical correlation analysis demonstrates the strong agreement among those two characterizations, providing thus an important justification in terms of interpretability for the heat kernel. Finally, and most importantly, the focused analysis of the heat kernel provides a way to yield insights on the fact that proteins have to satisfy specific structural design constraints that the other considered networks do not need to obey. Notably, the heat trace decay of an ensemble of varying-size proteins denotes subdiffusion, a peculiar property of proteins.

Suggested Citation

  • Livi, Lorenzo & Maiorino, Enrico & Pinna, Andrea & Sadeghian, Alireza & Rizzi, Antonello & Giuliani, Alessandro, 2016. "Analysis of heat kernel highlights the strongly modular and heat-preserving structure of proteins," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 441(C), pages 199-214.
    • Handle: RePEc:eee:phsmap:v:441:y:2016:i:c:p:199-214
    DOI: 10.1016/j.physa.2015.08.059
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    References listed on IDEAS

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    1. Guifeng Li & Donny Magana & R. Brian Dyer, 2014. "Anisotropic energy flow and allosteric ligand binding in albumin," Nature Communications, Nature, vol. 5(1), pages 1-7, May.
    2. Chaoming Song & Shlomo Havlin & Hernán A. Makse, 2005. "Self-similarity of complex networks," Nature, Nature, vol. 433(7024), pages 392-395, January.
    3. Andrea Pinna & Nicola Soranzo & Alberto de la Fuente, 2010. "From Knockouts to Networks: Establishing Direct Cause-Effect Relationships through Graph Analysis," PLOS ONE, Public Library of Science, vol. 5(10), pages 1-8, October.
    4. Amir Bashan & Ronny P. Bartsch & Jan. W. Kantelhardt & Shlomo Havlin & Plamen Ch. Ivanov, 2012. "Network physiology reveals relations between network topology and physiological function," Nature Communications, Nature, vol. 3(1), pages 1-9, January.
    5. H. Jeong & B. Tombor & R. Albert & Z. N. Oltvai & A.-L. Barabási, 2000. "The large-scale organization of metabolic networks," Nature, Nature, vol. 407(6804), pages 651-654, October.
    6. Bagler, Ganesh & Sinha, Somdatta, 2005. "Network properties of protein structures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 346(1), pages 27-33.
    7. Martin Rosvall & Alcides V. Esquivel & Andrea Lancichinetti & Jevin D. West & Renaud Lambiotte, 2014. "Memory in network flows and its effects on spreading dynamics and community detection," Nature Communications, Nature, vol. 5(1), pages 1-13, December.
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    Cited by:

    1. Kohestani, Havva & Totonkuban, Mahbubeh & Di Paola, Luisa & Todde, Virginia & Giuliani, Alessandro, 2018. "The basic principles of topology-dynamics relations in networks: An empirical approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 584-594.
    2. Maiorino, Enrico & Rizzi, Antonello & Sadeghian, Alireza & Giuliani, Alessandro, 2017. "Spectral reconstruction of protein contact networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 804-817.

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