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We start by examining the solvent accessibility for residues with significant B and C values from the three networks for BLIP. Fig 1 shows a scatter plot of the C z-score values versus the corresponding residue relative solvent accessibility RSA
values. A significance z-score value of 1 is chosen arbitrarily to give a representative
sample for each network. The average RSA values are 0.17, 0.17, and 0.37, for the
un-weighted, CSU-weighted, and JRP-weighted networks, respectively. Similarly, Fig. 2 shows a scatter plot of the B z-score values larger than 1 versus the corresponding residue RSA values for the
three networks. The average RSA values are 0.15, 0.18, and 0.40, for the un-weighted,
CSU-weighted, and JRP-weighted networks, respectively. The significant residues extracted
from the JRP-weighted network have mostly medium and high RSA values. Amitai et al. 9] reported that the optimal parameters for protein active site prediction for a set
consisting of 178 protein chains of enzymes with a total of 567 active sites were
C values???1.1, and RSA values of 4.5–40 %. However, they also reported a general tendency
for residues with high C to be unexposed. Del Sol et al. 50] considered only residues with RSA??20 % in their work to identify key residues.
To see if this is justified in the case of BLIP, a histogram of the RSA values for
the experimentally determined BLIP hotspot residues is shown in Fig. 3. The majority of these residues has RSA values larger than 20 %, and can thus be
regarded as being at least partially exposed 9]. In fact, the average RSA value for these hotspot residues is 31 %, ranging from
3 to 86 %. Thus, even though the conventional wisdom is to narrow the search for key
residues among buried or partially exposed residues, one should not generalize this
approach. Solvent exposed residues should be expected to play an important part in
the control and flow of information inside the protein network.

Fig. 1. The closeness centrality C versus the relative solvent accessibility RSA. This figure shows the C z-scores larger than 1 for the BLIP residues versus their RSA values for the un-weighted
network with a 7 Å cutoff threshold (?), the CSU weighted network (+), and the JRP
weighted network (?)

Fig. 2. The betweenness centrality B versus RSA. This figure shows the B z-scores larger than 1 for the BLIP residues versus their RSA values for the un-weighted
network with a 7 Å cutoff threshold (?), the CSU weighted network (+), and the JRP
weighted network (?)

Fig. 3. The relative solvent accessibility RSA histogram for the BLIP hotspot residues. This
figure shows the RSA value distribution for the experimentally determined hotspot
residues in BLIP

Figures 4 and 5 show the standardized B and C values, respectively, for the residues represented as nodes in each of the three
networks. The results are summarized in Tables 1, 2, and 3, for the un-weighted, CSU-weighted, and JRP-weighted networks, respectively. A z-score
cutoff threshold of 2 is chosen arbitrarily for the B values, and 1.5 for the C values, respectively, to get a representative significant sample. Each table lists
the significant nodes, and points out which ones are experimentally determined hotspots
or ion binding sites. It also lists the first degree neighbors for each node, and
points out if they are hotspot residues or ion binding sites as well.

Fig. 4. The standardized betweenness centrality B values for BLIP residues. This figure shows the standardized B values for the BLIP residues calculated from (a) un-weighted network, (b) CSU weighted network, and (c) JRP weighted network

Fig. 5. The standardized closeness centrality C values for BLIP residues. This figure shows the standardized C values for BLIP residues calculated from (a) un-weighted network, (b) CSU weighted network, and (c) JRP weighted network

Table 1. Betweenness centrality and closeness centrality results for significant nodes in the
un-weighted network

Table 2. Betweenness centrality and closeness centrality results for significant nodes in the
CSU-weighted network

Table 3. Betweenness centrality and closeness centrality results for significant nodes in the
JRP-weighted network

Table 1 lists residues with significant B and C values detected by the un-weighted network. This list contains five experimentally
determined hotspot residues: 53(C5), 71(C6), 74(C2), 112(C4), and 113(C6). The RSA
values for these hotspots range from 0.13 to 0.28. Five hotspot clusters, as well
as the sulfate ion and the ammonium ion binding sites, are among the first neighbors
for residues in this list. The only cluster missing is C1, which consists of the key
residue 49. Fig 6 shows the locations of these residues inside BLIP. In general, they are situated
in the middle of the concave shaped active site.

Fig. 6. The locations of the significant un-weighted network residues inside BLIP. This figure
shows the locations of significant BLIP residues with B z-score values larger than 2, and C z-score values larger than 1.5. The black colored spheres are experimentally determined
hotspots. The red colored spheres are experimentally determined hotspots detected
by this network. The green colored spheres are significant residues determined by
this network

Table 2 lists significant residues detected by the CSU-weighted network. This list contains
eight experimentally determined hotspot residues: 41(C5), 53(C5), 71(C6), 74(C2),
112(C4), 113(C6), 143(C2), and 148(C3). The RSA values for these hotspot residues
range between 0.03 and 0.28. Five hotspot clusters, as well as the sulfate ion and
the ammonium ion binding sites, are among the first neighbors for the residues in
this list. Cluster C1 is again not detected. Fig 7 shows the locations of these residues in BLIP. They are situated at the edge and
the center of the active site.

Fig. 7. The locations of the significant CSU-weighted network residues inside BLIP. This figure
shows the locations of significant BLIP residues with B z-score values larger than 2, and C z-score values larger than 1.5. The black colored spheres are experimentally determined
hotspots. The red colored spheres are experimentally determined hotspots detected
by this network. The green colored spheres are significant residues determined by
this network

Table 3 lists significant residues in the JRP-weighted network. This list contains four experimentally
determined hotspot residues: 49(C1), 50(C5), 142(C2), and 162(C4). The RSA values
for these hotspot residues range from 0.25 to 0.86. Five hotspot clusters, including
C1(49), as well as the sulfate ion and the ammonium ion binding sites, are among the
first neighbors for the residues in this list. Only cluster C6 (71,113) is not detected.
Most notably, the two “anchor” hotspot residues 49(C1) and 142(C2) are detected by
the JRP-weighted network 51], while the two other networks fail to detect these important residues. Fig 8 shows the locations of these residues in BLIP. In clear contrast to the results in
the un-weighted and CSU-weighted networks, these residues are located at the periphery
of the protein interface surface.

Fig. 8. The locations of the significant JRP-weighted network residues inside BLIP. This figure
shows the locations of significant BLIP residues with B z-score values larger than 2, and C z-score values larger than 1.5. The black colored spheres are experimentally determined
hotspots. The red colored spheres are experimentally determined hotspots detected
by this network. The green colored spheres are significant residues determined by
this network

Five BLIP residues are regarded as consensus hotspots for binding with the TEM-1,
SHV-1, SME-1, and Bla1 enzymes: 36, 41, 49, 53, and 150. The residues 148, 160, and
162 are hotspots when BLIP binds all of the above enzymes with the exception of SHV-1
40], 41]. The residues 73, 74, and 50, are considered binding specificity determinants 52],53]. The un-weighted network detects residue 53(C5, RSA?=?0.22) from the first group,
and residue 74(C2, RSA?=?0.13) from the third group. It does not detect any of the
residues from the second group. The CSU-weighted network detects residues 41(C5, RSA?=?0.03)
and 53(C5, RSA?=?0.22) from the first group, residue 148(C3, RSA?=?0.15) from the
second group, and residue 74(C2, RSA?=?0.13) from the third group. The JRP-weighted
network detects residue 49(C1, RSA?=?0.25) from the first group, residue 162(C4, RSA?=?0.42)
from the second group, and residue 50(C5, 0.35) from the third group. Again, the hotspots
detected by the JRP-weighted network tend to have higher RSA values. This should be
noteworthy since the significant hydration of the BLIP interface surface, has been
proposed as a major factor in its “promiscuity”, and ability to bind multiple enzymes
37],48]. It is also worth noting that a significant number of the residues with large B and C values extracted from the JRP weighted network, lie in the flexible loop regions
between the secondary structure elements of the protein. It is also interesting that
even though the hotspot residue 49 has a relatively low RSA value of 0.25, it was
not detected directly by the un-weighted or the CSU-weighted networks.