Analysis of X-ray structures of matrix metalloproteinases via chaotic map clustering

Abstract

Background: Matrix metalloproteinases (MMPs) are well-known biological targets implicated in tumour progression, homeostatic regulation, innate immunity, impaired delivery of pro-apoptotic ligands, and the release and cleavage of cell-surface receptors. With this in mind, the perception of the intimate relationships among diverse MMPs could be a solid basis for accelerated learning in designing new selective MMP inhibitors. In this regard, decrypting the latent molecular reasons in order to elucidate similarity among MMPs is a key challenge.

Results: We describe a pairwise variant of the non-parametric chaotic map clustering (CMC) algorithm and its application to 104 X-ray MMP structures. In this analysis electrostatic potentials are computed and used as input for the CMC algorithm. It was shown that differences between proteins reflect genuine variation of their electrostatic potentials. In addition, the analysis has been also extended to analyze the protein primary structures and the molecular shapes of the MMP co-crystallised ligands.

Conclusions: The CMC algorithm was shown to be a valuable tool in knowledge acquisition and transfer from MMP structures. Based on the variation of electrostatic potentials, CMC was successful in analysing the MMP target family landscape and different subsites. The first investigation resulted in rational figure interpretation of both domain organization as well as of substrate specificity classifications. The second made it possible to distinguish the MMP classes, demonstrating the high specificity of the S1' pocket, to detect both the occurrence of punctual mutations of ionisable residues and different side-chain conformations that likely account for induced-fit phenomena. In addition, CMC demonstrated a potential comparable to the most popular UPGMA (Unweighted Pair Group Method with Arithmetic mean) method that, at present, represents a standard clustering bioinformatics approach. Interestingly, CMC and UPGMA resulted in closely comparable outcomes, but often CMC produced more informative and more easy interpretable dendrograms. Finally, CMC was successful for standard pairwise analysis (i.e., Smith-Waterman algorithm) of protein sequences and was used to convincingly explain the complementarity existing between the molecular shapes of the co-crystallised ligand molecules and the accessible MMP void volumes.

Figure 1

Choice of the parameter ϑ controlling the resolution at which the data are processed. (a) Plot of cluster entropy as a function of the mutual information (I). (b) Size of the three largest clusters obtained by the CMC algorithm as a function of the mutual information (I) whose value ranges from 0 to ln2 with a bin-width equal to 0.01.

Figure 2

MMP target family landscape. Dendrogram obtained from the partition data relative to the electrostatic analysis of the entire protein structures. Different background colour boxes distinguished MMP allocations classified according to the domain organization. Stable clusters at ϑ = 0.06 and K = 16 are labelled with their corresponding MMP class. Singletons are indicated with the PDB codes.

Figure 3

Analysis of the S₁' specificity pocket. Dendrogram obtained from the partition data relative to the electrostatic analysis of the S₁' subsite. Different background colour boxes were used to distinguish the main stable groups at ϑ = 0.08, by setting K = 10. Singletons are indicated with the PDB codes.

Figure 4

Representation of global electrostatic similarity at the S₁' subsites. The intra-class and inter-class levels are indicated by the blue-coloured bars and solid red line, respectively. Specificity of S1' subsite demonstrated by its higher level of intra-class similarity compared with inter-class similarity.

Figure 5

High electrostatic similarity of S₃-S₁-S₃' stretches apart from gelatinases subfamily. (a) Heat map relative to the pairwise electrostatic distances for S₃-S₁-S₃' analysis. Colours ranging from red to blue indicate shifts from high to low similarity values. (b) Spy plot of the similarity values lower than 0.93; those greater than the threshold were dropped to zero.

Figure 6

Induced fit phenomena differentiates structures belonging to the same MMP class. Elucidation of differences between PDB:1CGL with PDB:1CGE and PDB:1CGF when comparing S₃-S₁-S₃' regions. The Asn80 residue is coloured yellow for the apo-proteins (PDB:1CGF and PDB:1CGE) and cyan for the complex (PDB:1CGL) co-crystallised with a peptide inhibitor rendered as green sticks. The coordination of zinc with the three catalytic histidines and carboxylic group of the ligand is highlighted.

Figure 7

CMC analysis of MMP sequences. Sequence-based clustering of the MMP family. The level of sequence distance is indicated by the colour shift from blue to red. Proteins classes were labelled, PDB codes were referred to those sequences assigned as singletons during CMC analysis.

Figure 8

Analysis of co-crystallised ligands via molecular shape similarity. Dendrogram obtained from the partition data relative to shape similarity analysis of the 84 co-crystallised ligand molecules. Different colours were used to distinguish the main stable groups at ϑ = 0.08, by setting K = 2.