Biology Reference
In-Depth Information
bacteriorhodopsin, bovine rhodopsin, sensory rhodopsin, and squid rhodopsin. Fi-
nally, the normalization factor for water (i.e., 27) was computed on the crystal struc-
tures of rhodopsin and four G
a
proteins (PDB codes: 1GZM, 1CIP, 1CUL, 1TAG,
and 1TND).
Thus,
I
ij
are generally calculated for all node pairs, excluding those made of ad-
jacent nodes. An interaction strength cutoff
I
min
is then chosen and any residue pair
ij
for which
I
ij
I
min
is considered to be interacting and hence is connected in the PSG.
Therefore, it is possible to obtain different PSGs for the same protein structure
depending on the selected
I
min
. Consequently,
I
min
can be varied to obtain graphs
with strong or weak interactions forming the edges between the residues. The resi-
dues making zero edges are termed as orphans and those that make at least four edges
are referred to as hubs at that particular
I
min
.
As previously demonstrated (
Vishveshwara et al., 2009
), the optimal
I
min
is the
one at which the size of the largest cluster of nodes at
I
min
0% halves. Incidentally, a
node cluster is a set of connected nodes in a graph. We approximate the
I
min
value to
the second decimal place. In the case study shown herein, the
I
min
cutoffs are 4.33%
for dark rhodopsin and 3.98% for MII.
With the PSN-ENM method, all edges at the selected
I
min
are considered in the
PSG, whereas with the PSN-MD method, only edges occurring in a given fraction of
the trajectory frames, that is, link frequency, enter in the PSG (
Angelova et al., 2011;
Fanelli & Felline, 2011; Fanelli & Seeber, 2010; Mariani, dell'Orco, Felline,
Raimondi, & Fanelli, 2013; Raimondi, Felline, Portella, et al., 2013; Raimondi,
Felline, et al., 2013
).
Different states of a molecular system, for example, free or bound, wild type or
mutated, inactive or active, and monomeric or oligomeric, can be compared in terms
of PSGs; PSG differences can be either plotted in histograms or mapped onto the 3D
structure (
Table 3.1
and
Figs. 3.3 and 3.4
).
3.2.3
Search for the shortest communication paths
The search for the shortest path(s) between pairs of nodes as implemented in the
PSN-PATH module of Wordom relies on the Dijkstra's algorithm (
Dijkstra,
1959
). Paths are searched by combining PSN data with cross correlation of atomic
motions calculated by using the LMI method, for PSN-MD, or by the covariance
matrix inferred from ENM-NMA, for the PSN-ENM method (
Raimondi, Felline,
Seeber, et al., 2013
). When dealing with GPCRs, pathways are worth searching be-
tween all possible residues in the intracellular and extracellular portions (
Angelova
et al., 2011; Fanelli & Felline, 2011
) or between all residue pairs in the protein except
those at sequence distance
5. The latter setup has been employed in the case study
shown herein leading to 52,003 investigated pairs (i.e., the first and last amino acids
in the path).
Following calculation of the PSG and of correlated motions, the procedure to
search for the shortest path(s) between each residue pair consists of (a) searching
for the shortest path(s) between each selected amino acid pair based upon the
