Chapter 8
Topology Results on Adjacent Amino Acid Networks
of Oligomeric Proteins
Claire Lesieur and Laurent Vuillon
Abstract
In this chapter, we focus on topology measurements of the adjacent amino acid networks for a data set of
oligomeric proteins and some of its subnetworks. The aim is to present many mathematical tools in order to
understand the structures of proteins implicitly coded in such networks and subnetworks. We mainly
investigate four important networks by computing the number of connected components, the degree
distribution, and assortativity measures. We compare each result in order to prove that the four networks
have quite independent topologies.
Key words Adjacent amino acid network, Topology of graphs associated with proteins, Subnetworks,
Protein contact network, Long range network, Hot spot network, Induced hot spot network,
Connected components, Degree distribution, Assortativity measures
1 Introduction
The main goal of this chapter is to present mathematical tools to
investigate the structure of protein using network topology. It is
well known that proteins, oligomeric proteins in our case study,
have geometrical control over their shapes (folding) and functions
(dynamics) based on four structural levels, so-called 1D, 2D, 3D,
and 4D structural levels [1, 2]. Proteins have a 1D structure which
is the sequence of amino acids involved in each chain; this sequence
is by definition one-dimensional and has an intrinsic ordering coming from the addition upon protein synthesis, of the amino acids
one by one via peptide bonds. The next remarkable geometrical
structure comes from the 2D structure of the protein that is the
ability of constructing local geometrical structures like alpha helix
or beta sheet; these structures are rather local and involve nearest
amino acids of the 1D structure. The folding mechanism is also
crucial to construct the 3D (tridimensional) structure by bringing
into contacts amino acids, which are far in the 1D structure but
become close in space. By this step, the 2D structures are connected
Luisa Di Paola and Alessandro Giuliani (eds.), Allostery: Methods and Protocols, Methods in Molecular Biology, vol. 2253,
https://doi.org/10.1007/978-1-0716-1154-8_8, © Springer Science+Business Media, LLC, part of Springer Nature 2021
113
Topology Results on Adjacent Amino Acid Networks
of Oligomeric Proteins
Claire Lesieur and Laurent Vuillon
Abstract
In this chapter, we focus on topology measurements of the adjacent amino acid networks for a data set of
oligomeric proteins and some of its subnetworks. The aim is to present many mathematical tools in order to
understand the structures of proteins implicitly coded in such networks and subnetworks. We mainly
investigate four important networks by computing the number of connected components, the degree
distribution, and assortativity measures. We compare each result in order to prove that the four networks
have quite independent topologies.
Key words Adjacent amino acid network, Topology of graphs associated with proteins, Subnetworks,
Protein contact network, Long range network, Hot spot network, Induced hot spot network,
Connected components, Degree distribution, Assortativity measures
1 Introduction
The main goal of this chapter is to present mathematical tools to
investigate the structure of protein using network topology. It is
well known that proteins, oligomeric proteins in our case study,
have geometrical control over their shapes (folding) and functions
(dynamics) based on four structural levels, so-called 1D, 2D, 3D,
and 4D structural levels [1, 2]. Proteins have a 1D structure which
is the sequence of amino acids involved in each chain; this sequence
is by definition one-dimensional and has an intrinsic ordering coming from the addition upon protein synthesis, of the amino acids
one by one via peptide bonds. The next remarkable geometrical
structure comes from the 2D structure of the protein that is the
ability of constructing local geometrical structures like alpha helix
or beta sheet; these structures are rather local and involve nearest
amino acids of the 1D structure. The folding mechanism is also
crucial to construct the 3D (tridimensional) structure by bringing
into contacts amino acids, which are far in the 1D structure but
become close in space. By this step, the 2D structures are connected
Luisa Di Paola and Alessandro Giuliani (eds.), Allostery: Methods and Protocols, Methods in Molecular Biology, vol. 2253,
https://doi.org/10.1007/978-1-0716-1154-8_8, © Springer Science+Business Media, LLC, part of Springer Nature 2021
113