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Conformational energy variations and the way in which the fluctuation is distributed within the internal modes have been recognized to be of crucial importance for ligand binding [65]. At this purpose we used two standard and complementary analyses: the rootmean-square fluctuation (RMSF) of the enzyme Ca atoms and the ED on the same subset of atoms. All the simulations show a comparable RMSF (Figure 4) with largest fluctuations occurring in the unstructured regions, with ahelices and b-strands remaining essentially unaltered. Consistently with this observation, it is also important to note that the secondary structural elements, analysed by the DSSP methods [66] and whose results are not reported for the sake of brevity, are maintained during all simulations. As shown in Figure 4 the binding of the ligands to the MMP-2 active site does not induce dramatic changes in the global enzyme fluctuation. However some localized modifications in the RMSF pattern might be worth of further attention. A dramatic reduction of fluctuation (i.e. increase of mechanical stability) was found for the S19 site (see residues 131?44 in Figure 4) in the case of allFigure 3. Best docking poses in the MMP-2 binding site of 1a (A), 1b (B) and 2 (C). MMP-2 is represented as solid ribbon; the zinc ion as a purple sphere. H-bond interactions are depicted as yellow dashed lines. Figure 4. Root-mean-square fluctuations (RMSF, nm) of the MMP-2 Ca atoms. RMSF is reported for the free enzyme (blue curve), the complex with 1a (black curve), with 1b (red curve) and 2 (green curve). The baseline indicates b-strands (red line), a-helix (orange line) and loops (cyan line). complexes, and for the S39 site (see residues 74?6 in Figure 4) for MMP-2:1a and MMP-2:1b. To get more insight on this aspect we investigated the effect on the average enzyme structure upon binding. This has been accomplished by comparing the single-residue (single Ca) RMSD of each complex with the corresponding RMSD of the free enzyme. An ideal value of 0.0, hereafter termed as DRMSD, implies that the presence of the inhibitor does not significantly alter the structure of the enzyme. The result reported in Figure 5A shows that the lowest DRMSD is found for MMP-2:2, indicating that the insertion of this inhibitor produces the lowest structural perturbation on the enzyme structure. On the other hand MMP2:1a and MMP-2:1b, showing a very similar DRMSD, undergo sharp variations in correspondence to the residues Tyr223, Tyr228 e Lys230 all belonging to the S19specificity loop. Interestingly, occurrence of intra-molecular H-bonds for residues belonging to the S19 site has revealed that in MMP-2:1a (1761 number of contacts) and MMP-2:1b (16+1 number of contacts) this number is larger than the one found for the apo (1561 number of contacts) and MMP-2:2 (1361). This result implies that the inhibitor 1, in both the tautomeric forms, produces structural modifications essentially concentrated in the S19 site, enhancing the number of H-bonds. This stabilization could be taken into account as determining the observed differences in the enzyme-inhibitor affinity. Further information was derived from ED analysis [54]. Figure 6 reports a significant portion of the covariance matrix spectrum of eigenvalues from the diagonalization of the covariance matrix for the apo and complexed MMP-2. The trace of the covariance matrix, which quantifies the extent of the whole enzyme fluctuation, turned out to be rather similar (within the error) in all of the investigated cases (2.460.2 nm2, 2.060.2 nm2 and 2.060.2 nm2 for MMP-2:1a, MMP-2:1b and MMP-2:2 respectively and 1.960.2 nm2 for the apo MMP-2). However different steepness emerged in the eigenvalues spectrum (Figure 6).

In particular, in the case of MMP-2:2 only the first
Figure 5. Perturbation on the enzyme structure. A) DRMSD for the three simulated complexes. DRMSD stands for RMSDatom-i-complexRMSDatom-i-apo. The atoms of the S19 pocket are numbered from 1 to 240; B) Schematic representation of the S19 pocket. Described residues are represented as sticks. Figure 6. Eigenvalues (nm2) of the covariance matrix of MMP-2 Ca positional fluctuations. Eigenvalues are reported for the free enzyme (blue triangles) and after complexation with 1a (black circles), 1b (red square) and 2 (green diamonds). Estimated standard error, using three subportion of the trajectories, does not exceed the 10% of the reported values. X-axis contains the eigenvector index. Note that only the first 20 eigenvalues are shown.eigenvector turns out to significantly contribute to the whole fluctuation. On the other hand, in the apo, MMP-2:1a and MMP2:1b also the second eigenvector shows not negligible eigenvalues. The above findings imply that the presence of the ligand, although not producing relevant variations in the extent of the whole enzyme internal fluctuation, alters the repertoire of enzyme conformational space which can be visualized by considering the structures extracted by ED analysis on the whole enzyme (see Figure S1 for details) reported in Figure 7. Major differences emerge in particular in the unstructured regions (grey loops), in the C-terminal coil (green) which is particularly mobile in MMP-2:1a, in the V-loop (blue) and S39 loop (red), whose conformational repertoire appears rather different for the four systems. Moreover, comparing the diverse conformations of complexed enzymes with the apo form, greater differences concern the S19 loop. In the apo form, the S19 pocket adopts a closed state, while in the complexed forms an open state, differently from what described in previous articles [67], [68]. This conformational change is in agreement with the above results and might depend on the ligand dimensions: the S19 site assumes a tunnel-like shape in the complexes MMP-2:1a and MMP-2:1b, while it enlarges in the MMP-2:2. This behaviour of the MMP-2 binding site can represent an example of induced-fit effect, where the apo form of the protein is not able to explore conformations that can be sampled by the ligand, as expected on the basis of the conformational selection theory [69]. In conclusion the analyses of the enzyme fluctuation confirm the role of the S19 site motion in the interaction with non-zinc-binding inhibitors [20]. The next step concerns the use of the same computational strategy for determining whether the inclusion into MMP-2 induces, at a similar extent, the same changes into the inhibitor.Dynamical-mechanical features of the free and bound inhibitors. In Figure 8 and in Table 1 we compared the all-
the free and bound inhibitors. In general, the interaction with the enzyme systematically lowers the fluctuation of the inhibitors. However, slight but significant differences between the ligand 1a, 1b and 2 are worthy of remark.

Figure 7. Most sampled Ca configurations obtained from ED analysis. A) Free enzyme, B) MMP-2:1a, C) MMP-2:1b, D) MMP-2:2. The V-loop is represented in blue, the S39 loop in red and the C-terminal loop in green.Figure 8. All-atoms RMSF of 1a (black), 1b (red) and 2 (green) in aqueous solution (full line) and bound to MMP-2 (dashed line). Estimated error does not exceed 10% in all the systems.

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