Dataset construction and extraction of metal-binding site point clouds

We obtain protein structures from the RCSB PDB via its REST API (accessed 2024-07-20) [23]. We query the PDB for entries containing chemical components with the target metal atoms listed in Table 1. Candidate MBSs are then defined from individual metal atom coordinates parsed from the associated PDBx/mmCIF files. Thus, metal-containing compounds are not treated as complete MBS centers; rather, each retained metal atom instance provides one candidate MBS and is subject to the following quality filter: We retain only crystallographic structures with reported overall resolution <3.0 Å. Coordinates are parsed from PDBx/mmCIF files and expanded into biological assemblies by applying the PDB-provided assembly generation operators using Biopython [24,25]. For entries with multiple biological assemblies, we process each assembly separately and track assembly identifiers to enable downstream de-duplication.

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Table 1. Metals used to identify MBSs. Elements used in the PDB query to retrieve metal-containing protein structures forming the basis for MBS point cloud extraction.

https://doi.org/10.1371/journal.pcbi.1014636.t001

To define a fixed-size representation for subsequent geometric comparison, we first calibrate the typical number of protein atoms in metal-centered neighborhoods. For a stratified random subset of metal-containing structures, we enumerate all protein atoms within a 7Å radius of each retained metal ion. This choice contrasts with the smaller cutoffs (e.g., 5Å) commonly used to delineate MBSs, which primarily emphasize atoms directly involved in metal coordination [26]. By adopting a larger radius, we include not only the immediate coordination environment but also nearby second-shell and local scaffold atoms. Such extended environments capture structural features that influence metal-site geometry, selectivity, and function [27]. Including this broader context also provides a more stringent structural comparison, because similarity must extend beyond the atoms closest to the metal ion and encompass a larger portion of the local three-dimensional environment.

The resulting atom-count distribution is centered at approximately 65 protein atoms, which is adopted as the fixed cardinality of the MBS point clouds. Each MBS is therefore represented by the N = 65 nearest protein atoms to the metal ion, allowing the effective radius to vary according to local protein-atom density. We subsequently quantify this effective radius as the distance between the metal ion and the 65th nearest protein atom.

For each biological assembly, we construct an MBS point cloud for every metal instance. Point clouds are built by ranking all protein atoms by Euclidean distance to the metal coordinate and selecting the N = 65 nearest atoms. This procedure yields a fixed-size set while permitting a variable effective radius across sites. Only atoms belonging to protein polymer entities are eligible for selection. Solvent molecules, including waters directly coordinating the metal ion, and other non-protein heteroatoms are excluded from the point cloud by construction. The polymer-chain entity contributing the largest fraction of atoms to a given point cloud is used to assign protein-specific metadata. Enzyme Commission (EC) numbers are obtained from the PDB when available. For missing EC assignments, we supplement annotations by cross-reference mapping PDB polymer chains to UniProt accessions and retrieving EC information from UniProt [28]. When multiple EC numbers map to a given chain, we retain the full set of candidate EC annotations and propagate this ambiguity rather than collapsing to a single label.

Robust ICP alignment of MBS point clouds

We use the iterative closest point (ICP) algorithm [22] to perform pairwise alignment of MBS point clouds. ICP computes a rigid spatial transformation that minimizes the squared distance between corresponding points in two point clouds and in [29]. The point registration problem can be formulated as finding an optimal transformation that produces a minimal alignment error :

(1)

where is a rotation matrix, is a translation vector, and is the Euclidean norm. In this study, all MBS point clouds are constructed with fixed cardinality, so m = n for all pairwise alignments. The ICP algorithm iteratively solves this minimization problem by alternating between two steps:

• Correspondence step: Given the transformation at iteration k of the algorithm, we determine the closest point in Q for each point by minimizing the distance

(2)

• Alignment step: We calculate the transformation matrices of the iteration by solving

(3)

We employ the Open3D library for representing point clouds and conducting the ICP alignments [30]. As residuals (i.e., the distances between point correspondences) are measured using squared distances (Eq. 1), the metric is sensitive to outliers due to the disproportionate influence of poorly aligned points. To reduce this sensitivity, we incorporate Tukey’s biweight function [31] as a loss function.

The correspondence and alignment steps are repeated until the relative change in root mean square deviation (RMSD) between successive iterations is below 10^-6, or until the maximum of 30 iterations is reached. The former is the convergence criterion, whereas the iteration limit is a stopping criterion. The relative-change threshold is dimensionless; RMSD values are expressed in Å. RMSD is defined in terms of the alignment error as:

(4)

Multi-start coarse-to-fine initialization for reliable ICP convergence

Because ICP optimizes a non-convex objective, it is only guaranteed to converge to a local minimum and is therefore sensitive to initialization [32]. In preliminary experiments on MBS point clouds, repeated runs on the same geometrically similar pairs yield a characteristic bimodal distribution of final RMSD values (Fig 1A), consistent with convergence either to a low-RMSD basin or to a higher-RMSD local minimum. Notably, the higher RMSD-mode overlap substantially with the RMSD distribution obtained from aligning unrelated point clouds with no meaningful geometric resemblance (Fig A in S1 File), motivating an explicit multi-start strategy to increase the probability of reaching the best-observed solution for a given pair.

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Fig 1. Performance of single-start and multi-start coarse-to-fine ICP alignment.

Distributions of final RMSD values for 10⁴ geometrically similar MBS point-cloud pairs (reference minimum RMSD <0.4 Å), aligned using either A. a single ICP run from one initialization or B. the two-stage, multi-start heuristic that screens T randomized coarse initializations and refines the top-scoring candidates. In this benchmark, a pair-specific reference minimum RMSD is defined as the lowest RMSD observed under an extensive multi-start protocol (). C. Success rate, defined as the fraction of pairs whose heuristic result falls within a tolerance of the reference minimum, and D. wall-clock runtime per pair, shown as functions of the number of coarse initializations T. The dashed line indicates the selected operating point T = 200.

https://doi.org/10.1371/journal.pcbi.1014636.g001

Although global point registration methods exist to generate ICP initializations [32], we found their performance to be inconsistent on these sparse, unordered point clouds, with a substantial fraction of alignments failing to reach the reference minimum achieved by repeated ICP (Fig B in S1 File). We therefore adopt a two-stage, multi-start coarse-to-fine ICP heuristic (Fig 1B) that screens a set of randomized initializations using a short ICP budget and then refines only the most promising candidates.

Before any restart, the point clouds are translated to a common origin by subtracting the centroid. All ICP runs in both stages use the same correspondence definition, correspondence-distance threshold, and robust loss settings as in the preceding subsection; only the iteration budget differs between stages. For each restart, the target point cloud is initialized by applying a random 3D rotation and then applying the fixed centering translation so that the initial translation is zero.

Representative MBS selection via RMSD-threshold clustering

Multiple PDB entries often capture the same protein in closely related conformations, and individual entries may provide several biological assemblies intended to reflect the functional oligomeric state. As a result, a single underlying MBS can appear multiple times in the extracted point-cloud dataset, inflating redundancy and increasing the likelihood of near-duplicate links in downstream network construction. To mitigate this effect, we apply a within-group redundancy reduction step to select a set of representative MBS point clouds prior to network assembly.

We first partition MBS point clouds into groups defined by shared UniProt accession and metal type. Within each group, we compute all pairwise MBS alignments using the two-stage ICP heuristic and obtain an RMSD score for each pair. We then construct a within-group similarity network in which nodes correspond to MBS point clouds and an undirected link is drawn between two nodes if their pairwise RMSD is below a fixed threshold (RMSD<0.5 Å). Representative point clouds are selected using a greedy network-pruning procedure applied independently to each connected component of the within-group similarity network. For a given connected component, we compute for each node the mean RMSD to its adjacent neighbors and select the node with the smallest mean neighbor RMSD as the component representative. We retain this representative and remove all of its immediate neighbors (and their incident links) from the component, thereby eliminating near-duplicate point clouds within the threshold neighborhood of the representative. We repeat this select-and-prune step until no links remain in the component. All remaining isolated nodes are retained as representatives. The resulting set of retained point clouds across all groups constitutes the representative, redundancy-reduced dataset used for subsequent network construction.

Network assembly from RMSD similarity with post hoc realignment

Given the redundancy-reduced MBS point-cloud set, we perform all-to-all pairwise alignments of the entire MBS dataset and form an undirected network in which each node corresponds to one MBS point cloud. A link is added between nodes i and j if their alignment score (i.e., RMSD) is below a global similarity threshold . We select in a data-driven manner by estimating how well low-RMSD outcomes separate from high-RMSD (misaligned) outcomes in empirical RMSD distributions. We stratify MBS pairs into bins defined by , and perform 10³ point cloud alignments to produce bin-wise empirical RMSD distributions. For each bin, we fit a two-component Gaussian mixture model and interpret the lower- and higher-RMSD components as representing geometry-consistent and misaligned or random-like outcomes, respectively. The two Gaussian components are defined as normal probability density functions

(5)

where denotes the Gaussian density with mean and variance , and and are the means and standard deviations of the low- and high-RMSD components, respectively. To quantify the separability of the two components, we compute an overlap statistic defined as the area under the pointwise minimum of the two modes:

(6)

where the integration bounds are chosen to capture the effective support of both distributions:

(7)

To define the global threshold , we track across bins where indicates cleanly separated modes, whereas marks the onset of overlap, rendering the demarcation of well-aligned and misaligned pairs unreliable. We set conservatively to the upper end of the last bin preceding this overlap transition.

Because ICP outcomes remain initialization-sensitive even under the proposed multi-start heuristic, some true geometry-similar pairs may be missed by this primary thresholding step. To selectively revisit such candidate false negatives without re-aligning all non-links, we apply a topology-guided screening based on topological overlap (TO). We compute TO for node pairs that are not directly connected, defined as

(8)

where is the number of common neighbors between node i and node j, denotes whether i and j are directly connected, and and are the degrees of nodes i and j, respectively. Pairs with TO are re-aligned using the same ICP objective and correspondence settings but with an increased number of random initial transformations (T = 300) to further reduce the probability of convergence to a poor local minimum. If the resulting RMSD falls below the original threshold , we add a link between i and j.

Metal ligand and functional co-occurrence

To quantify metal co-occurrence within the network, we test whether nodes annotated with metal i preferentially connect to nodes annotated with metal j relative to a permutation null. For each metal pair (i,j) among M metals, we compute the observed number of links whose incident nodes carry annotations i and j. We generate R = 10⁴ null networks by randomly permuting the node annotations while preserving the original network topology and degree sequence, and record the corresponding link counts . From these, we estimate and and compute the -score

(9)

We also compute the two-sided empirical p-values

(10)

and adjust for multiple testing across all tested pairs (i,j) using the Benjamini–Hochberg procedure [33]; pairs with FDR < 0.05 are considered significant.

We perform the same Z-score analysis for functional co-occurrence using the node’s EC numbers as categories, where the EC numbers are grouped at the third classification level.

Computing network modules

To identify densely interconnected communities within components of the MBS similarity network, we perform community detection using the Leiden algorithm [34]. Community partitions are computed on the weighted, undirected network, where link weights encode geometric similarity (i.e., RMSD scores) and thus emphasize stronger MBS–MBS similarity relationships. We used the leidenalg implementation [35] with resolution parameter .

Global structural alignment

We perform global structural alignments between protein structures using TM-align [36] via the RCSB PDB web interface (https://www.rcsb.org/alignment). Alignments are executed using default parameters, with individual PDB entries and chain identifiers specified as input. TM-scores are used as the primary metric for assessing global fold similarity, where values above 0.5 generally indicate similar global folds, and values below 0.3 are typically observed for unrelated structures [36].

Joint analysis of local metal-binding site geometry and sequence context

We apply a two-stage sequence-similarity screening to protein-chains of connected MBS pairs in the network in order to characterize MBS similarity in the context of global and local sequence concordance. For each protein-chain pair, we compute an optimal global alignment using the Needleman-Wunsch algorithm [37] as implemented in Biopython [24] with the BLOSUM62 substitution matrix and affine gap penalties. Pairs with global identity <25% are retained for local-homology screening.

For these pairs, we test for statistically significant local sequence similarity using Smith-Waterman local alignment computed with ssearch36 (FASTA v36.1.1) [38]. Alignments are run with composition-preserving shuffled-sequence controls enabled (-k 1000) and the BLOSUM62 matrix (-s BP62). Statistical significance is estimated from the shuffle-based null returned by ssearch36. To account for multiple testing and to express significance relative to the scale of our pairwise screen, we set the effective database size to the total number of local sequence alignments. MBS pairs with proteins exhibiting statistically significant local sequence similarity (E < 10⁻³) are excluded from further analysis.

To assess whether the geometry-conserved, sequence-divergent links identified by this screen are dispersed across the network or concentrated within locally dense regions, we compute the average clustering coefficient of the node-induced subgraph spanned by all MBS nodes incident to at least one retained candidate link. We evaluate this statistic against a permutation null by sampling, for R = 10⁴ replicates, link sets of identical size uniformly at random from the full MBS network, constructing the corresponding node-induced subgraph for each replicate, and recomputing its average clustering coefficient. A one-sided empirical p-value is then obtained as the fraction of null replicates with clustering coefficient greater than or equal to the observed value.

Drug off-target inference from MBS-network enrichment and structural proximity evidence

This section describes the pipeline for identifying candidate drug off-target interactions supported by (i) enrichment of within-drug connectivity among known target MBS nodes in the MBS network and (ii) structural proximity evidence of drug binding near metal sites.

Drug-target interactions are obtained from DrugBank (v5.1.13). Targets are mapped to network nodes by UniProt accession, assigning each drug d the set of MBS nodes corresponding to its annotated protein targets. Drugs associated with at least two MBS-containing target proteins are retained for analysis, designated as interactor drugs. If a target protein contributed multiple MBS nodes, all corresponding nodes are included in .

For each interactor drug, we quantify target interconnectivity as the number of links in the induced subnetwork over its target-node set, . Statistical significance is assessed against a null distribution generated from R = 10⁴ degree-preserving randomizations of drug–MBS annotations. For each randomization r, we compute , and derive a one-sided empirical p-value

(11)

Empirical p-values are adjusted for multiple testing across all interactor drugs using the Benjamini–Hochberg procedure; drugs with FDR < 0.05 are considered connectivity-enriched.

For each connectivity-enriched interactor drug, we restrict the set of starting nodes to the subset of its target-associated MBS nodes that exhibit structural proximity evidence for that drug. Specifically, an MBS node is retained as a high-confidence starting point if the bound drug is observed within 5 Å of the node’s metal coordinate in the associated structure, or if the same proximity criterion is satisfied for any 1-hop neighbor of that node in the MBS network. Putative off-targets are then defined by expanding from these high-confidence starting nodes to their 1-hop neighbors that are not annotated as known targets of the drug in DrugBank.

Software and data availability

All network construction and analyses are implemented in Python using NetworkX [39]. Network visualizations are generated in Cytoscape [40] and accessed programmatically via its REST API using py4cytoscape. Source code for reproducing all analyses and figures is available at https://github.com/AlmaasLab/MBSNetwork.

MBS dataset overview and impact of redundancy filtering

We assemble an initial metalloprotein dataset by parsing PDB entries containing any of the queried metals (Table 1) and extracting, for each metal ligand, an MBS point cloud from surrounding protein atoms (see Methods). Because closely related structures are frequently deposited multiple times (often with multiple biological assemblies), we apply a redundancy reduction procedure that clusters highly similar sites within protein- and metal-matched groups and retains representative point clouds. This filtering reduces the number of MBSs from 130,151–23,342, thus significantly decreasing structural redundancy, while retaining coverage of the same set of proteins (6,868). Key properties of both the retrieved and filtered datasets are summarized in Table 2.

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Table 2. Summary of the properties of the retrieved and filtered MBS datasets.

https://doi.org/10.1371/journal.pcbi.1014636.t002

We further characterize the spatial extent of the fixed-cardinality representation by measuring the distance from each metal atom to the nearest protein atom. Across retained MBSs, this distance has a median of 7.14 Å (IQR Å; 5th–95th percentiles Å), indicating that the N = 65 point clouds capture local protein neighborhoods centered near the initially calibrated 7 Å scale while allowing the effective radius to vary according to local packing density. The representation therefore generally extends beyond the immediate coordination sphere while retaining equal point-cloud cardinality across sites.

The filtered dataset largely preserves the relative metal and enzyme-class composition of the retrieved dataset, with a few notable exceptions (Fig 2). The most prominent change is a redistribution between Fe- and Zn-containing sites: Fe decreases from 39.8% of MBSs in the retrieved dataset to 26.0% after filtering, whereas Zn increases from 27.4% to 35.4% and becomes the most prevalent metal in the filtered dataset. The remaining metals show comparatively modest changes in relative abundance (e.g., Mn remains near 14%, and Cu remains near 8–9%). At the level of EC first-level classes, oxidoreductases (EC 1) remain the dominant class but decrease from 54.8% to 38.1% after filtering, accompanied by increases in transferases (EC 2; 9.8% to 16.0%) and hydrolases (EC 3; 24.4% to 33.8%).

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Fig 2. Distribution of metals and enzyme classes before and after redundancy filtering.

Relative frequencies of A. metals and B. EC first-level classes (EC 1–6) in the retrieved dataset (all MBSs prior to redundancy filtering) and in the filtered dataset. EC-class frequencies are computed over MBSs with an assigned EC annotation.

https://doi.org/10.1371/journal.pcbi.1014636.g002

MBS network assembly with topology-guided link recovery

Using our two-stage point registration heuristic, we perform all-to-all pairwise alignment of the filtered MBS point cloud dataset (N = 23,342), corresponding to pairwise registrations and totaling approximately 14,250 CPU hours. We use the empirically observed bimodality of alignment RMSD values, reflecting separable regimes of good and poor alignment quality (Fig 1A & 1B), to guide selection of a conservative similarity threshold for network link formation.

To calibrate this threshold, we quantify the separation between the low- and high-RMSD modes across bins of increasing reference-minimum RMSD using the mode-overlap statistic (Eq. 6). As mode overlap increases, the distinction between the two regimes becomes less reliable. Based on the onset of appreciable overlap (Fig 3A), we select a global similarity cutoff of Å, corresponding to the upper end of the last bin preceding the overlap transition. The resulting global RMSD distribution from all pairwise alignments, with the selected cutoff indicated, is shown in Fig 3B. Applying yields a similarity network with 274,563 links (mean degree ).

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Fig 3. RMSD mode overlap and selection of the network similarity threshold.

A. Mode-overlap metric estimated from two-component Gaussian mixture model fits to RMSD distributions computed from 10³ point cloud alignments per bin; bins are defined by increasing reference-minimum RMSD. B. Probability density of RMSD scores from all-to-all pairwise alignments of filtered MBS point clouds. The dashed line at Å marks the RMSD threshold used for network link creation.

https://doi.org/10.1371/journal.pcbi.1014636.g003

As a targeted refinement to reduce potential false negatives due to the initialization sensitivity of ICP, we perform a post hoc realignment step on a restricted set of initially disconnected node pairs with TO (Eq. 8). These candidates are re-aligned using an increased number of randomized initializations (T = 300). Pairs meeting the original cutoff after re-alignment are added as links, contributing an additional 37,510 links and increasing the network to 312,073 links (mean degree ).

To assess whether network links were sensitive to the selected point-cloud size, we re-aligned stratified subsets of MBS pairs after reconstructing the corresponding point clouds with N = 55 and N = 75 atoms (see Fig C in S1 File). RMSD values obtained at N = 55 and N = 75 were strongly correlated with the original N = 65 scores (Spearman’s and , respectively), approaching the independent N = 65 re-alignment baseline (). Binary link classification under the Å threshold was retained for 90.4% of pairs at N = 55 and 87.9% of pairs at N = 75. Classification changes were concentrated near the similarity threshold, indicating that the bulk of high-confidence links and non-links is robust to moderate variation in point-cloud size.

Network connectivity reflects metal ligand type and functional co-occurrence

We next test whether connectivity in the MBS similarity network aligns with biologically interpretable node annotations, focusing on (i) metal identity and (ii) enzymatic function. If local geometric similarity is captured faithfully by the network links, we expect its topology to reflect both metal-specific coordination chemistry and shared functional properties of the associated proteins. Specifically, MBSs of the same metal should preferentially connect due to recurring coordination motifs, while MBSs from enzymes with related catalytic roles should exhibit enriched connectivity.

Visualizing the network at the selected similarity threshold (Fig 4) reveals a compartmentalized topology comprising 8,255 connected components. Despite this fragmentation, connectivity is locally dense (mean degree ; average clustering coefficient ), and overall modularity is high (Q = 0.92), consistent with MBS point clouds forming tightly connected neighborhoods separated by comparatively fewer between-neighborhood links. Inspection of the network further suggests that metal (Fig 4) and enzymatic function (Fig D in S1 File) composition appears structured across many components. This metal-based assortativity is particularly evident in the largest component (Fig 4), in the fourth largest component, and across many of the intermediate-sized components, where links predominantly connect MBS nodes sharing the same metal ligand. In contrast, a few components, such as the second, third, and sixth largest component, display seemingly more heterogeneous compositions, with more frequent connections between MBSs of different metal types. Computing the relative distribution of metal-pair link composition across the entire network, we observe that for most metals the majority of links occur between nodes of the same metal (Fig 5A).

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Fig 4. The MBS network colored by metal type.

Connected components of size in the MBS network. Nodes are colored by the bound metal with the following coloring scheme: Co (blue), Cu (orange), Fe (dark green), Mn (red), Mo (purple), Ni (brown), V (pink), W (grey), and Zn (light green).

https://doi.org/10.1371/journal.pcbi.1014636.g004

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Fig 5. Metal-to-metal connectivity and enrichment.

A. Observed relative distribution of metal-to-metal connectivity across network links. B. Heatmap of permutation-based Z-scores for metal-to-metal link counts, standardized against 10⁴ randomized label permutations. Significance is assessed using two-sided empirical p-values with Benjamini–Hochberg correction (FDR < 0.05). Significant enrichments are shown in color; non-significant cells are shown in black; metal pairs with no observed links are shown in white.

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To rigorously quantify this pattern and account for differences in metal abundance and node degree that can inflate raw link fractions, we determine whether MBSs of the same metal are connected more frequently than expected by chance by performing a metal enrichment analysis. Specifically, we compute Z-scores for the number of links connecting nodes with metal i to those with metal j, using a null distribution generated from 10⁴ randomized networks. The resulting enrichment map (Fig 5B) is strongly diagonal, while most off-diagonal entries are significantly depleted relative to the null, indicating that network links largely connect MBSs of the same metal. In particular, Fe and Cu exhibit strong within-metal enrichment (Fe: Z = 120, ; Cu Z = 134, ), reflecting distinctive interaction profiles and suggesting limited structural compatibility with MBSs of other metal types. In contrast, between-metal enrichment is observed for W and V, and W and Mo. This is consistent with known cases where these metals can substitute in related enzyme families [41], but the network-based enrichment alone does not distinguish substitution from other sources of shared local geometry. Notably, Ni is the only metal to show a statistically significant within-metal depletion (, ), whereas Co displays no statistically significant enrichment (Z = 0.6, ), hinting at broader geometric heterogeneity among their MBSs.

We next test whether network connectivity is similarly structured by enzymatic function. Using EC annotations grouped at the third level (a.b.c.*), we compute EC-pair link enrichment under the same topology-preserving label-permutation null used for metal enrichment and assess significance using two-sided empirical p-values with Benjamini–Hochberg correction (FDR < 0.05). The resulting Z-score heatmap (Fig 6) shows a prominent diagonal, indicating that MBS nodes assigned to the same EC subclass are connected more frequently than expected by chance. Compared to the metal-based analysis, the EC-based enrichment exhibits a larger number of significant off-diagonal associations, particularly among oxidoreductase (EC 1) subclasses. These cross-subclass associations suggest that some local metal-site geometries recur across distinct functional annotations, although attributing specific drivers (e.g., shared cofactor-binding motifs [42]) would require additional annotation of bound cofactors or domain context beyond the EC labels used here.

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Fig 6. Enrichment of EC subclass co-occurrence among network links.

Heatmap of permutation-based Z-scores for EC-pair link counts, with EC numbers grouped at the third level (a.b.c.*). Significance is assessed using two-sided empirical p-values followed by Benjamini–Hochberg correction (FDR < 0.05). Significant enrichments are shown in color; non-significant cells are shown in black.

https://doi.org/10.1371/journal.pcbi.1014636.g006

Recurrent motifs drive modularity of structural Zn-binding sites

The largest connected component of the MBS network (component in Fig 4; N = 1,167 nodes) is enriched for Zn-binding sites. Many nodes in this component exhibit residue compositions characteristic of tetrahedral coordination environments dominated by cysteine and/or histidine, consistent with common structural Zn-binding architectures such as zinc-finger-like motifs [43–45].

To characterize internal structure within this component, we partition the component into modules using the Leiden community detection algorithm applied to the weighted network. We embed the component using a link-weighted spring-embedded layout, in which more similar MBS pairs exert stronger attractive forces (Fig 7), and summarize local residue environments by assigning each MBS a four-residue signature defined by the identities of the four residues closest to the metal coordinate (closest by minimum heavy-atom distance).

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Fig 7. Modules of the largest connected component.

Eight largest () Leiden modules within component of the MBS network, visualized using a link-weighted spring-embedded layout (link weights proportional to geometric similarity). Nodes are colored by the bound metal ion: Co (blue), Fe (dark green), Mn (red), Ni (brown), and Zn (light green).

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Focusing on the eight largest modules (A–H), each containing at least 50 nodes (Table 3), we find that four-residue signatures are strongly cysteine/histidine-enriched and align with canonical tetrahedral coordination patterns. Three modules (A, B, and E) are dominated by a Cys₄ signature, with the dominant motif accounting for of sites within each module, consistent with recurrent tetrahedral Cys-rich coordination environments. Three additional modules are enriched for mixed Cys/His coordination signatures (modules F, G, and H; Cys₃His at 75.0%, 80.3%, and 52.5%, respectively), capturing common variants of Cys/His tetrahedral coordination. A further module (module C) is characterized by the canonical Cys motif, albeit with a lower dominant-motif frequency (56.0%), indicating greater within-module heterogeneity in residue composition despite tight geometric clustering. Metal identity is not perfectly aligned with module structure: module D is entirely Fe-associated (100%) yet exhibits a highly coherent Cys motif (91.8%), demonstrating that similar residue-level coordination architectures can place non-Zn sites within the same geometric neighborhoods as Zn-binding sites.

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Table 3. Coordination signatures of modules in the largest connected component. Each MBS is summarized by the identities of the four amino acid residues closest to the metal coordinate. Motifs are reported as unordered residue multisets (e.g., Cys), with the dominant motif defined as the most frequent four-residue signature within the module.

https://doi.org/10.1371/journal.pcbi.1014636.t003

These network components also include additional non-Zn sites embedded within otherwise Zn-enriched neighborhoods of the network. For example, module B contain several rubredoxin-like sites, in which an Fe ion is tetrahedrally coordinated by four cysteine residues (Cys₄), a coordination geometry previously noted to resemble certain Zn-binding folds [46]. Module D also contains sites consistent with Fe-S cluster coordination patterns that have previously been misassigned as Zn-binding in sequence-based analyses [47]. More generally, the occurrence of non-Zn nodes within Zn-like modules supports the interpretation that recurrent coordination environments—captured here by local residue signatures and geometric similarity—can underlie module structure even when the annotated metal identity differs.

Conserved metalloenzyme families form cohesive components in the MBS network

Given the enrichment of within-function connectivity observed at the EC-subclass level, we next ask whether this organization persists at the level of conserved metalloprotein families. Many metalloenzyme families retain highly similar local metal coordination environments across members, even when global sequence identity is low and overall fold context varies [48]. If the MBS similarity network captures these conserved local architectures, then MBSs derived from a single family should preferentially connect, forming cohesive network structure.

As a case study, we examine the ureohydrolase domain superfamily, a well-characterized group of binuclear metalloenzymes with conserved active-site geometry and reaction chemistry [49]. Members catalyze hydrolysis of non-peptide C–N bonds (EC 3.5.-.-) and employ a binuclear center in which two metals are coordinated by conserved aspartate and histidine residues within the active-site cleft of a three-layer fold [50]. We extract all ureohydrolase-associated MBS nodes in the network and examine their induced subnetworks, together with their immediate neighbors. Because each binuclear enzyme contributes two metal-centered MBS nodes (one per metal coordinate), we anticipate the selected ureohydrolase-associated MBS nodes to segregate into two components — one per metal-centered site in the binuclear catalytic center.

Consistent with these expectations, the ureohydrolase-associated MBS nodes partition into two distinct, highly connected network components (components and in Fig 4) that correspond to the two metal-sites of the binuclear catalytic center (Fig 8). These components exhibit high internal connectivity and are functionally coherent, consisting primarily of MBSs (82 of 119) from arginase (EC 3.5.3.1) and agmatinase (EC 3.5.3.11), along with related ureohydrolase-domain enzymes such as formimidoylglutamase (EC 3.5.3.8) and N()-hydroxy-L-arginine amidinohydrolase (EC 3.5.3.25). The components also display heterogeneity in metal identity, encompassing MBSs annotated with Mn, Ni, Cu, Co, and Zn within the same components, thereby providing another concrete example of between-metal connectivity in the network.

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Fig 8. Ureohydrolase domain superfamily components in the MBS network.

Shown are the two connected components formed by ureohydrolase-associated MBS nodes and immediate neighborhoods; each component corresponds to one metal-centered site of the binuclear catalytic center (i.e., one MBS node per coordinated metal ion). Node positions are computed using a force-directed layout with link weights derived from geometric similarity, so that more similar MBSs are placed closer together.

https://doi.org/10.1371/journal.pcbi.1014636.g008

Beyond canonical ureohydrolases, these same components include atypical enzymes reported to preserve ureohydrolase-like binuclear site geometry. For example, MBSs from the recently characterized metformin hydrolase subunit A (MfmA) of Ectopseudomonas mendocina appear in both components, consistent with maintenance of a ureohydrolase-like local metal-site architecture despite only moderate sequence similarity to canonical ureohydrolases [51]. A similar pattern is observed for the atypical peptide arginase from Kamptonema sp. implicated in post-translational arginine-to-ornithine modification: although this system differs in sequence context and quaternary organization [52], its MBS point clouds align closely with ureohydrolase-family MBSs and localize within the same two components. Together, these observations indicate that MBS-network connectivity can recover conserved local metal-site architectures within a metalloenzyme family, including relationships that are not readily implied by sequence- or fold-based similarity alone.

Recurrent metal-binding site geometries across sequence-divergent proteins

As demonstrated, our point cloud alignment framework enables the identification of cases where highly similar MBS geometries occur in proteins with little sequence similarity. Another such example is provided in cluster 3 of component (Fig 7). Within this cluster, an MBS of the phosphotyrosine-binding domain of the Hakai protein (CBLL1) contains an atypical Zn site in which a cysteine residue (Cys61) from the adjacent protomer completes the Cys coordination sphere [53]. Aligning this site (PDB 3VK6) to a canonical Cys zinc finger (PDB 4M9E) yields a closely matching local geometry (RMSD 0.47 Å), despite low global sequence identity (20.1%) and poor global fold similarity (TM-score 0.22) (Fig 9). More generally, the occurrence of closely matching MBS geometries in proteins with little detectable sequence similarity is consistent with two non-exclusive scenarios: (i) divergent evolution from a remote common ancestor, in which the local MBS architecture is conserved while surrounding sequence and/or overall fold context diverges, or (ii) convergent evolution, in which similar coordination geometries and/or associated catalytic environments arise independently under shared physicochemical and functional constraints [54].

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Fig 9. Structural alignment of Zn-binding sites from CBLL1 and a canonical Cys zinc finger.

The Zn-binding site of the phosphotyrosine binding domain from E3 ubiquitin-protein ligase CBLL1 (PDB entry 3VK6, green) superimposed on a canonical Cys zinc finger domain from Krüppel-like factor 4 of Mus musculus (PDB entry 4M9E, cyan) using the optimal transformation obtained from the point cloud alignment (RMSD 0.47 Å). The inset shows the protein structures that constitute the corresponding MBS point clouds and highlights the conserved tetrahedral coordination geometry of Zn (grey spheres).

https://doi.org/10.1371/journal.pcbi.1014636.g009

To assess how frequently local geometry and sequence context decouple at network scale, we systematically compare protein sequence and MBS geometry across all network links. Specifically, we compute for each connected MBS pair in the network the global sequence identity of the corresponding proteins and compare these to the ICP-derived geometric similarity (max-normalized RMSD). Global sequence identity and local geometric similarity exhibit a moderate correlation (Spearman’s , ), indicating that higher sequence identity is generally associated with lower geometric divergence. However, inspection of the sequence–structure landscape reveals that this relationship is heterogeneous (Fig 10): the correlation is driven largely by MBS pairs with low sequence identity and only moderate geometric similarity, whereas strongly geometry-similar MBS pairs appear across a wide range of sequence identities. The latter includes regimes where sequence identity is minimal, motivating a targeted analysis of links where MBS geometry is conserved even at low sequence resemblance of the associated proteins.

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Fig 10. Sequence-geometry decoupling highlights recurrent metal-binding site geometries across sequence-divergent proteins.

(A) Joint distribution of global sequence identity and normalized geometric similarity for all network-connected MBS pairs. The colorbar indicates the log-scaled density of MBS pairs in each bin. The red dashed box highlights MBS pairs combining low global sequence identity (<25%) with high local geometric similarity (RMSD <0.5 Å). (B) Relationship between local MBS geometric similarity and global fold similarity for candidate pairs that remain after local sequence-similarity filtering. Global fold similarity is quantified as the maximum TM-score reported by TM-align for each corresponding protein-chain pair. Dashed horizontal lines mark TM-score thresholds commonly used to distinguish globally unrelated structures (<0.3), ambiguous structural similarity (), and substantial fold similarity ().

https://doi.org/10.1371/journal.pcbi.1014636.g010

Accordingly, we compile MBS pairs that combine high geometric similarity with pronounced sequence divergence. We focus on network-connected MBS pairs (19,293) with low global sequence identity (<25%) and high geometric similarity (RMSD <0.5 Å) (red dashed box in Fig 10A). To enrich for cases without detectable local sequence homology, we further filter these pairs using pairwise local sequence alignment of the associated protein sequences; pairs with statistically significant local similarity at an expectation value threshold of E = 10^-3 are excluded (Fig E in S1 File). In total, this yield 7,237 MBS pairs spanning 1,159 unique proteins that exhibit high local geometric similarity with low global sequence identity and no detectable local sequence similarity under the chosen significance threshold. We then asked whether these sequence-divergent, geometry-conserved pairs also occur across globally dissimilar protein structures by performing TM-align on the corresponding protein-chain pairs (Fig 10B). Of the 7,221 candidate pairs with available structural data (16 pairs were excluded due to unparseable CIF files), 685 (9.5%) had a maximum TM-score <0.3, 2,271 (31.5%) had a score between 0.3 and 0.5, and 4,265 (59.1%) had a score . Thus, most sequence-divergent, geometry-conserved pairs occur between proteins sharing substantial global fold similarity, consistent with remote divergent evolution in which local MBS architecture is retained despite extensive sequence divergence. Conversely, the subset with TM-score <0.3 provides the strongest candidates for convergent emergence of similar local coordination geometries across globally unrelated folds, while pairs in the intermediate TM-score range remain ambiguous with respect to fold-level relatedness. The full list of pairs, including their associated proteins, metals, TM-scores, and geometric and sequence similarity scores, is provided in S2 File.

Across the 7,237 candidate links, metal identity matches for most pairs (5,327; 74%), while 1,910 pairs (26%) connect sites annotated with different metals. The overall metal composition of the candidate set resembles that of the full dataset (Fig F in S1 File), indicating that geometry-conserved links across sequence-divergent proteins are not confined to a single metal chemistry. Functionally, 1,190 pairs share at least one EC annotation at the third classification level, thus constituting interesting cases of related catalytic activity despite lacking any appreciable sequence similarity under our filters. We further test whether the candidate links concentrate in locally cohesive regions of the MBS network by computing the average clustering coefficient of the node-induced subgraph spanned by their incident MBS nodes and comparing it to a permutation null generated by sampling link sets of identical size uniformly from the full network. The candidate-induced subnetwork shows a higher average clustering coefficient than expected under this null (, p = 10⁻³), indicating that these links are enriched within densely interconnected neighborhoods rather than being uniformly distributed across the network. Together, these candidate pairs identify recurring metal-site architectures among proteins with low detectable sequence similarity, but the TM-score analysis indicates that many occur within globally similar folds. They therefore provide a prioritized set for follow-up analyses, with the strongest convergence candidates concentrated among pairs with low TM-scores.

Network-driven drug off-target prediction

Misregulation of metalloproteins is a major contributor to human disease, and many drugs are designed specifically to target MBSs [55]. Since drug–target interactions depend on structural compatibility, we posit that the topology of the MBS network can be leveraged to identify potential drug off-target interactions: If a drug is developed to bind to an MBS-containing protein, it may unintentionally bind to its target’s nearest MBS network neighbors owing to their similar MBS geometry. To investigate this possibility, we first map DrugBank drug-target interactions onto the MBS network, yielding 3,657 drugs with at least one MBS-containing target protein, collectively associated with 4,020 MBS nodes across the network. Among these, 800 drugs are linked to multiple MBS-encoding protein targets—hereafter referred to as interactor drugs—enabling a network-based assessment of whether a drug’s annotated targets occupy a coherent region of MBS space.

We next identify the set of MBS nodes targeted by the same interactor drug that are preferentially connected with each other in the network. Such topological enrichments indicate that multiple drug targets occupy closely related regions of MBS space, suggesting that the drug can engage a broader range of geometrically similar binding sites. When a drug’s MBS targets form these densely interconnected clusters, this pattern could also hint at reduced molecular specificity and an increased likelihood of cross-reactivity among structurally related metalloproteins. To delineate the subset of interactor drugs exhibiting significant target interconnectivity, we compute, for each drug, the number of network links among its target-associated MBS nodes and evaluate significance against a degree-preserving permutation null (see Methods). In total, we identify 326 interactor drugs with significantly enriched within-drug target connectivity after multiple-testing correction (FDR < 0.05; Fig 11), demonstrating that for a substantial subset of interactor drugs, the topology of the MBS network reflects known patterns of drug promiscuity.

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Fig 11. Network enrichment and structural proximity filters for drug off-target prediction.

Volcano plot showing enrichment of interactor drugs, defined as compounds with MBS–associated targets. The x-axis reports the enrichment ratio of within-drug target interconnectivity (number of network links among the drug’s target-associated MBS nodes) and the y-axis shows the Benjamini–Hochberg–adjusted empirical p-value obtained from the permutation test (R = 10⁴). Drugs passing FDR < 0.05 are considered connectivity-enriched. Square markers denote drugs with independent structural evidence of proximity, defined as at least one predicted binding pose located within 5 Å of a metal coordinate for at least one high-confidence starting node (or its 1-hop neighbor). IBMX, 3-isobutyl-1-methylxanthine; CF2A, 5-(2-chlorophenyl)-2-furoic acid.

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To refine this signal toward higher-confidence off-target predictions, we next incorporate a complementary source of drug information. We define proximal drugs as those structurally observed to bind in the vicinity of an MBS, as curated from structural data (see Methods for details). This criterion confines enrichment to drug–MBS interactions that are consistent with metal-site proximity in available structures, rather than from coincidental binding to separate structural motifs that happen to co-occur with MBSs elsewhere in the protein. In total, we identify 1,233 proximal drugs associated with 6,363 MBS nodes in our dataset, and we focus on the subset of significantly enriched interactor drugs that also show proximal binding (135) near their associated MBSs. For these cases, geometric compatibility, as captured by the MBS network, is corroborated by independent experimental support of direct drug-to-MBS interaction (Fig 11). For each such drug, we infer putative off-targets by expanding from its high-confidence starting nodes to their 1-hop network neighbors that are not annotated as targets of that drug in DrugBank, restricting to human proteins to focus the analysis on clinically relevant off-target hypotheses.

Among the 135 connectivity-enriched interactor drugs with structural evidence of proximal binding, network expansion yields at least one candidate human off-target for 88 drugs. Across these 88 drugs, the analysis prioritizes 528 candidate drug–off-target combinations spanning 151 unique human proteins. For each predicted pair, S3 File reports the high-confidence starting node(s), the inferred off-target neighbor, and the intermediate network relationships used for inference. Several predictions correspond to drug–protein interactions previously reported in the literature but not annotated for the corresponding drug in DrugBank, providing case-level support that the MBS-network and proximity filters can recover independently observed off-target relationships. We therefore highlight a set of illustrative, high-ranking drugs for which multiple predicted off-targets have prior experimental support (Table 4).

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Table 4. Selected network-prioritized candidate off-targets for connectivity-enriched drugs. Predicted human drug off-targets inferred from integration of MBS network topology and structural evidence of proximal drug binding. Predicted off-targets are categorized by level of supporting evidence: Validated — experimentally confirmed interactions reported in independent studies; Inactive — targets reported to exhibit no measurable activity against the drug; Proposed — targets hypothesized in prior literature based on indirect evidence (e.g., known target homologues); and Predicted-only — novel targets based on our network-driven approach. Evidence categories reflect targeted literature review of these examples; the full candidate set was not systematically classified.

https://doi.org/10.1371/journal.pcbi.1014636.t004

The prediction of 3-isobutyl-1-methylxanthine (IBMX) as an inhibitor of phosphodiesterase (e.g., PDE4C and PDE10A) aligns with experimental evidence of inhibitory activity [57,83,84]. Likewise, among the predicted off-targets of the matrix metalloproteinase (MMP) inhibitors Marimastat, Ilomastat, and Batimastat, we recover multiple members of the ADAM and ADAMTS protein families, many of which have been proposed or experimentally validated as alternative targets [61,85]. Notably, the predicted off-targets for Ilomastat also include dipeptidyl peptidase III (DPP3) and neprilysin (MME), both having been identified as Ilomastat-sensitive metalloproteases by activity-based proteomic profiling [71]. Known for their broad selectivity, these synthetic hydroxamate-type inhibitors have produced adverse effects during clinical trials, most notably musculoskeletal syndrome (MSS) [86]. Although the mechanisms underlying MSS remain unresolved [87], the inhibition of non-MMP-members such as ADAM, ADAMTS, and related metalloproteases, including DPP3 and MME, represents a plausible contributing factor, consistent with their roles in extracellular matrix remodeling and inflammatory signaling [88].

Beyond cross-reactivity among human drug targets, our analysis also reveals potential off-target interactions for compounds originally developed against microbial protein targets. Notably, the antimicrobial agent 5-(2-chlorophenyl)-2-furoic acid (CF2A) is predicted to interact with several human metalloproteins, including type I methionine aminopeptidases METAP1 and METAP1D (Table 4). Given that CF2A was designed specifically to inhibit bacterial MetAP homologs, these findings suggest that its binding determinants are sufficiently conserved to permit interaction with the human isoenzymes. Such cross-species similarity highlights the importance of metal-site-aware similarity screening of metalloprotein-targeting antimicrobials, as inadvertent engagement of human metalloproteins could impact selectivity and safety profiles.