protein and far in the chain according to the sequence ordering
(that is with at least with 7 amino acids in the sequence between the
two considered amino acids). The Long Range Network codes for
the 3D structure.
The HSN, IHSN, and LRN are sub-networks of the PCN
modeling the contacts involved in the different structural levels of
a protein. We investigate if these networks have different topological properties, considering the connected components, the degree
distribution, and the assortativity, which suggest the different
structural levels have some specificity, coding, and structural
independency.
The chapter is divided in five sections. The first describes the
proteins of the dataset and the networks; the second defines the
four networks; the connected components, the degree distribution,
and the assortativity are provided in the third, fourth, and fifth
sections.
2 Proteins and Networks
In this chapter, we focus on oligomeric proteins, which are composed of k times the same chain of amino acids (k is called the
quaternary structure of a protein). The amino acid residues of
different chains, called Hot Spots, are connected together by chemical and physical interactions to form the atomic interfaces that
build the oligomer. Thus usually we name the k chains by distinct
letters in an alphabetic order (for a pentamer the names of the five
chains could be A, B, C, D, E or D, E, F, G, H or other combinations of consecutive letters in an alphabetic order). Each chain is
formed by a sequence of amino acids, which corresponds to the
order in which the amino acids are covalently attached to one
another (1D structure). The ordering from the sequence which is
encoded at the DNA level gives a natural ordering of the amino
acids in each chain; this ordering is given by a sequence of consecutive integers (thus we could speak of the amino acid number 50 in
the chain B and for short we use the notation 50:B [or B50 in this
chapter] for this amino acid with the concatenation of the name of
the chain with the position of the amino acid in the chain). The
20 amino acids with special chemical and geometrical properties are
constituted by a set of covalent atoms. In order to understand the
construction of oligomeric proteins, we propose to define formally
several networks and investigate their topology. Thus, we use
mathematical tools and theory of networks to study biological
constructions and coding.
The main mathematical tool for our study is a network (also
called graph) G ¼ (N, L) with nodes (also called vertices) noted N
and links (also called edges) noted L. This graph is constructed by a
Protein Data Base file associated with a given protein (Fig. 1) from
Topology Results on Adjacent Amino Acid Networks of Oligomeric Proteins
115
(that is with at least with 7 amino acids in the sequence between the
two considered amino acids). The Long Range Network codes for
the 3D structure.
The HSN, IHSN, and LRN are sub-networks of the PCN
modeling the contacts involved in the different structural levels of
a protein. We investigate if these networks have different topological properties, considering the connected components, the degree
distribution, and the assortativity, which suggest the different
structural levels have some specificity, coding, and structural
independency.
The chapter is divided in five sections. The first describes the
proteins of the dataset and the networks; the second defines the
four networks; the connected components, the degree distribution,
and the assortativity are provided in the third, fourth, and fifth
sections.
2 Proteins and Networks
In this chapter, we focus on oligomeric proteins, which are composed of k times the same chain of amino acids (k is called the
quaternary structure of a protein). The amino acid residues of
different chains, called Hot Spots, are connected together by chemical and physical interactions to form the atomic interfaces that
build the oligomer. Thus usually we name the k chains by distinct
letters in an alphabetic order (for a pentamer the names of the five
chains could be A, B, C, D, E or D, E, F, G, H or other combinations of consecutive letters in an alphabetic order). Each chain is
formed by a sequence of amino acids, which corresponds to the
order in which the amino acids are covalently attached to one
another (1D structure). The ordering from the sequence which is
encoded at the DNA level gives a natural ordering of the amino
acids in each chain; this ordering is given by a sequence of consecutive integers (thus we could speak of the amino acid number 50 in
the chain B and for short we use the notation 50:B [or B50 in this
chapter] for this amino acid with the concatenation of the name of
the chain with the position of the amino acid in the chain). The
20 amino acids with special chemical and geometrical properties are
constituted by a set of covalent atoms. In order to understand the
construction of oligomeric proteins, we propose to define formally
several networks and investigate their topology. Thus, we use
mathematical tools and theory of networks to study biological
constructions and coding.
The main mathematical tool for our study is a network (also
called graph) G ¼ (N, L) with nodes (also called vertices) noted N
and links (also called edges) noted L. This graph is constructed by a
Protein Data Base file associated with a given protein (Fig. 1) from
Topology Results on Adjacent Amino Acid Networks of Oligomeric Proteins
115