of atomic motion. More generally, we could compare IHSN with
PCN to test the hypothesis that there is a mechanism (topological
mechanism) that protects the interface: prevent perturbations from
reaching it (mutations of non-hotspot amino acids) or allow correcting errors introduced by mutations of hotspots.
The Long Range Network codes for the 3D structure and
could be compared to the HSN to see if the 4D and the 3D
topologies are independent. We could test different assembly
mechanisms such as the fly casting mechanism where interface
formation and folding happen concomitantly while the induce-fit
mechanism folding occurs first ([16] and references within, [17]).
The Long Range Network topology is known to have a strong
correlation with the folding rate of the protein (see [5]) and remark
that in the paper they consider amino acids in the sequence with
distance greater than 11 while in our construction we use a distance
greater than 7).
4 Stoichiometry and Connected Components
First of all, we investigate the stoichiometry and the number of
connected components of the four networks in order to understand
the topology of proteins in the data set. In fact, the stoichiometry is
an information on the number of chains used for the protein
construction. A connected component of a network is the set of
nodes that are connected together by paths following the links. By
definition PCN has only one connected component because an
oligomeric protein is composed of a single protein. HSN could
have only one connected component; that means that all the interfaces are connected together by paths following the links. More
interestingly if there are 2 or more connected components in HSN
this means that some interfaces are relatively far from each other in
the protein.
In our data set, we study 750 oligomeric proteins with stoichiometry (the number of chains) from 2 up to 20 (see [15]). In fact, in
the PDB sometimes the protein appears with copy of itself, and thus
the number of chains and connected components increases numerically; thus, we just discard these cases and reduce the number of
cases. Only 714 PDB files appear with 1 connected component for
PCN; this means with a single protein in the PDB, 30 PDB files
with two copies of itself and 2 PDB files with three copies of itself. If
we restrict to the 714 PDB files with a description of a single
protein, we notice that 218 proteins have 4 chains, 168 proteins
have 2 chains, 116 proteins have 3 chains, 70 proteins have 6 chains,
46 proteins have 6 chains, 30 proteins have 12 chains, 23 proteins
have 5 chains, and so on (Fig. 8). Remember that the number of
divisors of the stoichiometry k is important because if k is composed by many divisors the combinatorics give more proteins than
Topology Results on Adjacent Amino Acid Networks of Oligomeric Proteins
121
PCN to test the hypothesis that there is a mechanism (topological
mechanism) that protects the interface: prevent perturbations from
reaching it (mutations of non-hotspot amino acids) or allow correcting errors introduced by mutations of hotspots.
The Long Range Network codes for the 3D structure and
could be compared to the HSN to see if the 4D and the 3D
topologies are independent. We could test different assembly
mechanisms such as the fly casting mechanism where interface
formation and folding happen concomitantly while the induce-fit
mechanism folding occurs first ([16] and references within, [17]).
The Long Range Network topology is known to have a strong
correlation with the folding rate of the protein (see [5]) and remark
that in the paper they consider amino acids in the sequence with
distance greater than 11 while in our construction we use a distance
greater than 7).
4 Stoichiometry and Connected Components
First of all, we investigate the stoichiometry and the number of
connected components of the four networks in order to understand
the topology of proteins in the data set. In fact, the stoichiometry is
an information on the number of chains used for the protein
construction. A connected component of a network is the set of
nodes that are connected together by paths following the links. By
definition PCN has only one connected component because an
oligomeric protein is composed of a single protein. HSN could
have only one connected component; that means that all the interfaces are connected together by paths following the links. More
interestingly if there are 2 or more connected components in HSN
this means that some interfaces are relatively far from each other in
the protein.
In our data set, we study 750 oligomeric proteins with stoichiometry (the number of chains) from 2 up to 20 (see [15]). In fact, in
the PDB sometimes the protein appears with copy of itself, and thus
the number of chains and connected components increases numerically; thus, we just discard these cases and reduce the number of
cases. Only 714 PDB files appear with 1 connected component for
PCN; this means with a single protein in the PDB, 30 PDB files
with two copies of itself and 2 PDB files with three copies of itself. If
we restrict to the 714 PDB files with a description of a single
protein, we notice that 218 proteins have 4 chains, 168 proteins
have 2 chains, 116 proteins have 3 chains, 70 proteins have 6 chains,
46 proteins have 6 chains, 30 proteins have 12 chains, 23 proteins
have 5 chains, and so on (Fig. 8). Remember that the number of
divisors of the stoichiometry k is important because if k is composed by many divisors the combinatorics give more proteins than
Topology Results on Adjacent Amino Acid Networks of Oligomeric Proteins
121