to one another to form a 3D shape. The last important structuration is related to the construction of interfaces between chains in
order to construct a protein oligomer; the 4D structure is the
number of copies of a chain, which composed the oligomer (see
the tiling theory for proteins in [3]). Not all proteins have a 4D
structure.
We propose to investigate these geometrical structures by considering adjacent amino acid properties and networks. This transformation from geometrical structure to networks using a cutoff
allows us to ignore geometrical positions and focus only on the
topology of the proteins, that is, the connectivity of amino acids
given by the network of adjacent amino acids, distant by a cutoff of
5 A ˚ . In network theory, many measurements exist to investigate
topology, among which we will use the following:
l
The Connected Components of the network or any
sub-networks relevant to the structural hierarchy considering
the Stoichiometry (4D structure) (see [4]),
l
The Degree Distribution of the nodes of the network (see [4]),
l
The Assortativity gives a global measurement for the local topology of the networks and is linked to folding rates in protein
networks and more generally is involved in the spreading rates of
error propagation or of diseases (see [4, 5, 6, 7, 8]).
The different structural levels that compose a protein can be
respectively modeled by different networks of adjacent amino acids.
The most studied network is the Adjacent Amino Acid Network
(also called in the literature Protein Contact Network or protein
structure network) (see DPB, [2, 9, 10]) where the nodes are amino
acids and the links between two amino acids are when amino acid
are at distant less or equal to a cutoff value (here we use 5 A ˚ )
[11]. This network gives information on the whole structure of
the protein and we use PCN to denote the Adjacent Amino Acid
Network.
In addition, we investigate three other networks: the HSN, the
IHSN, and the LRN. The Hot Spot Network (HSN) represents the
amino acids involved in the interface between chains in oligomeric
proteins codes for the 4D structure (see [2, 12] and references
within (we call a Hot Spot, an amino acid, which is linked to at
least one amino acid from another chain). The Induced Hot Spot
Network (IHSN) constructed from the Hot Spots and all amino
acids in contact with hot spots in the chain (with distant less or
equal to 5 A ˚ ). The IHSN gives the contacts of the hot spots with
other hot spots (contacts between chains) and with amino acids
within a chain. Thus HSN provides only the 4D contacts of the
interface while IHSN provides all contacts information of the hot
spots. The Long Range Network (LRN), which is constructed for
each chain considering two amino acids in spatial contact in the
114
Claire Lesieur and Laurent Vuillon
order to construct a protein oligomer; the 4D structure is the
number of copies of a chain, which composed the oligomer (see
the tiling theory for proteins in [3]). Not all proteins have a 4D
structure.
We propose to investigate these geometrical structures by considering adjacent amino acid properties and networks. This transformation from geometrical structure to networks using a cutoff
allows us to ignore geometrical positions and focus only on the
topology of the proteins, that is, the connectivity of amino acids
given by the network of adjacent amino acids, distant by a cutoff of
5 A ˚ . In network theory, many measurements exist to investigate
topology, among which we will use the following:
l
The Connected Components of the network or any
sub-networks relevant to the structural hierarchy considering
the Stoichiometry (4D structure) (see [4]),
l
The Degree Distribution of the nodes of the network (see [4]),
l
The Assortativity gives a global measurement for the local topology of the networks and is linked to folding rates in protein
networks and more generally is involved in the spreading rates of
error propagation or of diseases (see [4, 5, 6, 7, 8]).
The different structural levels that compose a protein can be
respectively modeled by different networks of adjacent amino acids.
The most studied network is the Adjacent Amino Acid Network
(also called in the literature Protein Contact Network or protein
structure network) (see DPB, [2, 9, 10]) where the nodes are amino
acids and the links between two amino acids are when amino acid
are at distant less or equal to a cutoff value (here we use 5 A ˚ )
[11]. This network gives information on the whole structure of
the protein and we use PCN to denote the Adjacent Amino Acid
Network.
In addition, we investigate three other networks: the HSN, the
IHSN, and the LRN. The Hot Spot Network (HSN) represents the
amino acids involved in the interface between chains in oligomeric
proteins codes for the 4D structure (see [2, 12] and references
within (we call a Hot Spot, an amino acid, which is linked to at
least one amino acid from another chain). The Induced Hot Spot
Network (IHSN) constructed from the Hot Spots and all amino
acids in contact with hot spots in the chain (with distant less or
equal to 5 A ˚ ). The IHSN gives the contacts of the hot spots with
other hot spots (contacts between chains) and with amino acids
within a chain. Thus HSN provides only the 4D contacts of the
interface while IHSN provides all contacts information of the hot
spots. The Long Range Network (LRN), which is constructed for
each chain considering two amino acids in spatial contact in the
114
Claire Lesieur and Laurent Vuillon