In this study, we present a method of pattern mining based on network theory that enables the identification of protein structures or complexes from synthetic volume densities, without the knowledge of predefined templates or human biases for refinement. We hypothesized that the topological connectivity of protein structures is invariant, and they are distinctive for the purpose of protein identification from distorted data presented in volume densities. Three‐dimensional densities of a protein or a complex from simulated tomographic volumes were transformed into mathematical graphs as observables. We systematically introduced data distortion or defects such as missing fullness of data, the tumbling effect, and the missing wedge effect into the simulated volumes, and varied the distance cutoffs in pixels to capture the varying connectivity between the density cluster centroids in the presence of defects. A similarity score between the graphs from the simulated volumes and the graphs transformed from the physical protein structures in point data was calculated by comparing their network theory order parameters including node degrees, betweenness centrality, and graph densities. By capturing the essential topological features defining the heterogeneous morphologies of a network, we were able to accurately identify proteins and homo‐multimeric complexes from 10 topologically distinctive samples without realistic noise added. Our approach empowers future developments of tomogram processing by providing pattern mining with interpretability, to enable the classification of single‐domain protein native topologies as well as distinct single‐domain proteins from multimeric complexes within noisy volumes. Common scanning approaches for biological specimens include positron emission tomography  to detect topologically invariant features between spatially proximal amino acids in volume densities, and leverage the network theory order parameters that offer physically meaningful interpretations of known protein structures from the protein databank , identifies protein structures with high accuracy from simulated tomographic volumes lacking noise. To accelerate the identification of protein structures in tomograms, here we introduce a pipeline to test simulated samples with common defects that present challenges for the precise identification of protein structures within noisy volume density data. Our work here demonstrates that the foundation of GRIP‐Tomo is compatible with these defects such that future tuning and development can be performed to match the specific typical noise levels from different tomographic methods , regardless that they are covalently bonded or not, was presented by an adjacency matrix whose connectivity was determined with distance, Equation  in SectiEquation —when thedcut, values ranging from 6 Å to 10 Å with an increment of 1 Å were used to generate graphs from a set of five proteins of varying size and complexity. They include two single domain proteins, a beta barrel (PDB ID: 4RLC) in Figure To determine an appropriate length for Betweenness Centrality (BC)—the number of times that a node appears on the shortest path between two other nodes—as a representative feature to determine the structurally important alpha carbons by presenting a protein structure into a network . For example, dcut = 6 Å and dcut = 10 Å did not show sufficient cross‐chain interaction. dcut = 6 produced very sparse graph layouts, while dcut = 10 Å created very dense graph layouts. Both are inadequate to represent the underlying 3D backbone structure.As to other dcut = 8 Å is the most suitable choice of cutoff distance to define a connection between alpha carbons for identifying multimers, and dcut = 9 Å is most suited for identifying features in monomers. Our findings suggest that the connectivity of the graph network, as determined by the pairwise cutoff threshold dcut, can capture different levels of hierarchical structure of the target protein, and that 8 and 9 Å cutoffs are well suited for monomer and multimeric modeling, respectively. In the following sections, we created graphs using both dcut = 8 Å and dcut = 9 Å for identifying protein structures from volume densities.Based on our quantitative testing, we stated that 2.2dcut = 8 Å and dcut = 9 Å in Figure χ, from Equation  in a graph from the volume densities simulated with all‐atom protein models (Observable Graphs) in order to address whether the GRIP‐Tomo is capable of coarse‐graining the volume density data into a reduced representation. This set of simulated tomograms is the basis of every tested sample with minimal data deformation  between the Control Graphs and Observable Graphs, signifying high fidelity in identifying the correct protein structures using GRIP‐Tomo. Note that the graphs with dcut = 9 Å in Figure dcut = 8 Å correctly identified all except the single domain protein of a collapsed calmodulin (1PRW) with beta barrel (4RLC) in the red and yellow boxes in Figure Along the diagonal in Figure 2.3Our second attempt to test the efficacy of GRIP‐Tomo was to identify protein structures with only the connection of alpha carbons (Control Graphs) in a graph from the volume densities (Observable graphs) with data defects due to tumbled proteins. When taking a snapshot of a native cell environment via tomography, each protein molecule is randomly tumbled except in some limited cases of organelle or location‐ based preferential orientation. Thus, when trying to interpret tomograms one needs to account for tumbling, and involves random positioning and orientation of a sample.hypothesized that the application of network order parameters will advance the protein identification by revealing distinct hierarchies in the structural feature of a protein, avoiding the data deformation due to random orientations of samples. We emulated this tumbling effect in the volume densities by randomly rotating a protein in real space. The densities of a volume were constructed with back projections using a full range of rotational angles from 90° to −90° in an 0.5° increment. We then applied GRIP‐Tomo (with same threshold as the one used in previous section) for identification against the Control Graph and computed the similarity score  between the Control Graphs and Observable Graphs. Using dcut = 9 Å  in a graph from the volume densities (Observable graphs) with tumbled proteins and the “missing wedge effect.” The missing wedge effect is a known defect that results from tomographic reconstructions generated from datasets not spanning a full 180° tilt wedge. Cryo‐ET is one tomography method that is impacted by the missing wedge due to the limit of data acquisition typically in the range of −60° to 60° spanning a wedge of only 120°. The lack of data within the missing wedge means that reconstruction in Fourier space is not only discretely populated along the given tilt angles (with zero information between each tilt angle), but that the entire space from −90° to −60° and +60° to +90° also lack phase and amplitude information about the sample. The resulting defect appears as a blurring out or stretching of volume density perpendicular to the tilt axis with smaller wedges or wedges with smaller sampling  showing more exacerbated defects. Because the network theory order parameters obey rotational invariance as shown above, we hypothesized that the topological connectivity of protein structures is invariant with respect to rotation and translation, and they are distinctive for the purpose of protein identification from distorted data presented in volume densities.χ > 0.75) between the Control Graphs and Observable Graphs. We showed that both graphs at dcut = 8 Å  we computed the similarity score against those from the Control Graphs in Figure Å Figure  and dcuÅ Figure  have cor33.1Graph‐based representations of structurally complex biomolecules extend the learning of chemical and molecular data by transforming the connectivity and morphology of physical structures into graphical maps for advancing discoveries in protein‐ligand binding  that represent the minimalist model of a protein for probing the connectivity of their residues in space. We transformed 3D protein structures into 2D contact maps, and further present them into mathematical graphs. Cα‐only protein models have been commonly adopted in the coarse‐grained molecular dynamics simulations in the past decades  are highly interpretable. As demonstrated in Section dcut and d′cut was necessary to capture protein structural features and connectivity. A cutoff of 8 Å better captures short range interactions and protein features such as protein unit junctions, where as a cutoff of 9 Å better captures longer range interactions and protein features that are distant in sequence space but relatively close in physical space. Future work will explore how to integrate networks with different connectivity  in order to utilize the hierarchical information of the protein network features to improve classification and identification. Hence, GRIP‐Tomo achieves a relatively high accuracy of protein identification across various data distortions in network configurations such as missing data fullness  prove to be challenging to correctly classify. This can likely be remedied with more hyperparameter tuning as well as a greater emphasis on global or higher order hierarchical structure such as the number of communities and assortativity  by comparing the Control Graphs against each other for the 10 selected protein structures or complexes using dcut = 8 Å and dcut = 9 Å in Figure dcut in GRIP‐Tomo. We note that our sample size of proteins is limited. By expanding the data set of “Control Graphs” beyond the 10 proteins we used in this work, we aim to broaden the discovery of proteins in heterogeneous samples.We also showed the similarity scores  of the GRIP‐Tomo based particle classification under a range of different data conditions evaluating the effect of missing data fullness, tumbling, and missing wedge effect without noise. We demonstrate that graph properties from protein structure networks and 3D volume densities are topologically invariant and enable rapid protein identification from point cloud/tomogram datasets. While there is more work to be done in order to improve classification and identify proteins within experimental datasets, this study serves as a proof‐of‐concept for the near‐term application of topological data analysis to identify volumetric features from cryo‐ET, PET, MRI, or CT datasets, with applications across multiple disciplines for improved object detection and pattern mining.55.1G =  of a snapshot of a protein structural network is defined a set of nodes V, which correspond to the alpha‐carbon on each residue, and a set of edges E, which accounts for the relations between nodes. An edge exists between any two nodes if their two corresponding residues in the system are within a cutoff distance dcut. We define the distance d between nodes v and w to be the minimum Euclidean distance among all pairs of nodes. Mathematically, the graph representation of the proteins structural network is defined as an adjacency matrix.dcut is an important hyperparameter governing the connectivity of the graph  is V=Nresidues and the number of edges E varies depending on the spatial distribution of the residues. Topological measures of a graph can be used as order parameters at varying graininess from a “node,” a “local,” to a “community” viewpoint. The network theory order parameters are sorted into three vantage points: (a) the topology of a node, which is illustrated in Figure The number of vertices in the graph 5.2We developed a novel data science approach based on network theory to accelerate the accurate identification of proteins and protein complexes from idealized synthetic data . We created a pipeline shown in Figure 5.2.1G where V is each alpha carbon in the structure. The edges are E assigned based on a pairwise Euclidean distance between nodes less than dcut. Dcut is determined by the user based on domain knowledge, and we used both dcut of 8 and 9 Å for our analysis (see Section We converted known protein structures with atomic coordinates (.PDB file) into mathematical graphs. The alpha carbon atoms were used to capture a minimal representation of the protein structure. We parsed a PDB structure file and converted it into a mathematical graph To validate our pipeline against different types of data distortions, we selected 10 proteins  was converted to 3D grids of voxels  based on electron density using eman2 . The graphs generated from these 3D densities are Observable Graphs to be compared against the Control Graphs from Section We first removed the low intensity values in the 3D densities in simulated volumes by applying a threshold. We used a threshold cutoff that was determined empirically using ChimeraX  in Equation , wi is the weight of the ith graph feature , and Xi and Yi are the calculated values of the ith graph feature between the Observable Graph (from simulated 3D volumes) and the Control Graph (from atomic coordinates).To compute a similarity score ; data curation (supporting); investigation (supporting); methodology (supporting); software ; validation ; visualization ; writing – original draft ; writing – review and editing (supporting). Doo Nam Kim: Data curation (supporting); investigation (supporting); methodology (supporting); software ; validation (supporting); visualization (supporting); writing – review and editing (supporting). Trevor H. Moser: Data curation (supporting); methodology (supporting); software (supporting); writing – review and editing (supporting). Ian T. Gildea: Investigation (supporting); methodology (supporting); visualization (supporting). James E. Evans: Conceptualization ; funding acquisition (supporting); methodology (supporting); resources (supporting); software (supporting); writing – review and editing (supporting). Margaret S. Cheung: Conceptualization ; data curation (lead); formal analysis (lead); funding acquisition (lead); investigation (lead); methodology (lead); project administration (lead); resources (lead); software (lead); supervision (lead); validation (lead); writing – original draft (lead); writing – review and editing (lead).The authors declare that they have no conflict of interest.Figure S1. (a) The ribbon representation of space‐filling Ankyrin repeats (4RLY) (R1‐R9) model. The graph network representation of this structure at (b) dcut = 8 Å and (c) dcut = 9 Å. The highlighted nodes (residues) on (b) were located on the structural helices whereas those in (c) were located on the binding segments of the chain across the helical R repeats. The structural pairs corresponding to the high‐BC nodes on the graph with dcut = 9 Å are colored in (a), capturing a higher‐order complexity across repeated structural helices within a single domain.Figure S2.  The ribbon representation of a space‐filling four‐helix bundle protein . The graph network representation of  protein structures at (b) dcut = 7 Å and (d) dcut = 8 Å, respectively. (d) identified four residues with extremely high BC scores. The amino residues with the two highest scores were copies of PHE85, located on both the A and B chains. The third and fourth highest scoring residues were copies of ASN34 – another pair of identical aminos on the A and B chains in (c). 8 Å is the best choice of cutoff distance for identifying the cross‐helix and cross‐chain interaction, indicating the structural importance of the residues in the higher‐order complexity of dimer of dimer.Figure S3. (a) The ribbon representation of the space filling hemoglobin . The graph network representation of the tetramer at (b) dcut = 7 Å, (c) dcut = 8 Å, and (d) dcut = 9 Å. The graph with dcut = 8 Å contained the most distinct cluster of nodes (residues) with high BC. These clusters contained residues (colored in (a)) on multiple chains within proximity of each other, indicating cross‐chain interaction.Figure S4. (a) The ribbon representation of the Apoferritin complex, containing 24 units of the same chain (2W0O) in an octahedral symmetry. The graph network representation Apoferritin at (b) dcut = 7 Å, (c) dcut = 8 Å, and (d) dcut = 9 Å. These nodes on the graph with (c) dcut = 8 Å become more prominent with high BC than those in (b) dcut = 7 Å. (d) At dcut = 9 Å, residues with high BC appeared in the center part of each chain, instead of at the vertex that captures the cross‐unit interaction.Figure S5. Fundamental graph properties at a node level on two network models (a) and (b). Each model comprises five nodes, V = {A,B,C,D,E}. The difference between the network in (a) and the network in (b) is the set of edges connecting these nodes. Graph (a) has one triangle . While in graph (a) all nodes are connected, in graph (b) there are two separate components: {A,C} and {B,D,E}. In (a), the clique number, which is the largest subset of nodes that are all directly connected, is 3, and the largest clique is {A,B,C}. In contrast, the largest clique in graph (b) is {A,C}. The degree of a node is the number of edges connected to it. For example, in (a), the degree of node B equals 3. The shortest path between two nodes is the minimal number of edges one needs to hop over to reach from one node to the other. In graph (a), the shortest path between node D and node A is D ↔ E ↔ B ↔ A. Nodes that are disconnected, as in the case of D and A in (b), are said to be separated by an infinite path by definition. The betweenness of a node is the number of the shortest paths between any other nodes that go through this node. For example, in (a), the node B has the largest betweenness of 4, as the shortest path between D and A, between D and C, between E and A, and between E and C, all go through B.Figure S6i . The procedure to convert a 3D protein structure (.pdb) into a graph (.gexf). In Step 1, the protein structure with an all‐atomistic representation is coarse‐grained to a minimalist representation with only alpha carbons. The alpha carbons are assigned as vertices in a graph. In Step 2, for each pair of graph vertices  the Euclidean distance is calculated. If the distance is less than or equal to dcut (ie.g. 8 Angstroms), an edge is connected between the two vertices. The resulting graph is then saved as a graph exchange XML file (.gexf). The NetworkX package of Python was used to process and export the graph for further analysis.Figure S7. The similarity scores (χ) by comparing the Control Graphs against each other for the 10 selected protein structures or complexes using dcut = 8 Å for (a) and dcut = 9 Å for (b). As expected, graphs from proteins of similar size and complexity tend to have the largest similarity scores – with the same graphs having the maximum similarity score of 1.Click here for additional data file.


Protein complexes are essential for biologists to understand cell organization and function effectively. In recent years, predicting complexes from protein–protein interaction (PPI) networks through computational methods is one of the current research hotspots. Many methods for protein complex prediction have been proposed. However, how to use the information of known protein complexes is still a fundamental problem that needs to be solved urgently in predicting protein complexes.To solve these problems, we propose a supervised learning method based on network representation learning and gene ontology knowledge, which can fully use the information of known protein complexes to predict new protein complexes. This method first constructs a weighted PPI network based on gene ontology knowledge and topology information, reducing the network's noise problem. On this basis, the topological information of known protein complexes is extracted as features, and the supervised learning model SVCC is obtained according to the feature training. At the same time, the SVCC model is used to predict candidate protein complexes from the protein interaction network. Then, we use the network representation learning method to obtain the vector representation of the protein complex and train the random forest model. Finally, we use the random forest model to classify the candidate protein complexes to obtain the final predicted protein complexes. We evaluate the performance of the proposed method on two publicly PPI data sets.Experimental results show that our method can effectively improve the performance of protein complex recognition compared with existing methods. In addition, we also analyze the biological significance of protein complexes predicted by our method and other methods. The results show that the protein complexes predicted by our method have high biological significance. As the material basis of life, protein plays a crucial role in cell life activities and participates in almost all life activities. Proteins do not act alone but form complexes with other proteins. Therefore, predicting protein complexes is very important to comprehensively and deeply understand cell composition and life processes. Many methods exist to predict protein complexes, such as tandem affinity purification (TAP) and mass spectrometry. However, this experimental method costs a lot of human resources. Therefore, quickly and efficiently predicting protein complexes from the protein–protein interaction network has become a fundamental problem. With the rapid development of high-throughput technology, much protein–protein interaction (PPI) data  has beenBased on the idea of converting large-scale protein–protein interaction data into a network structure, many methods have been proposed to predict protein complexes in the PPI network. Bader et al. proposed a protein complex prediction algorithm MCODE , which wRecently, supervised learning methods have been successfully applied in protein complex prediction, which can use the information of known protein complexes to predict new protein complexes. Yu et al. proposed the SLPC  method. In this paper, we propose a protein complex prediction method based on supervised learning, which can fully use the information of known protein complexes. Moreover, to reduce the noise problem in the network and mine the biological information contained in the protein network, we introduce gene ontology (GO) knowledge  to constWe detail our protein complex prediction method in this section. Our method mainly includes four parts: 1) weighted PPI network using GO knowledge; (2) generating supervised features for protein complex prediction; (3) the first stage of protein complex candidate recognition; (4) the second stage of final protein complex classification. Figure  weightedA protein interaction network is a basis for using computational methods to predict protein complexes. However, due to the limitations of technology and the flow characteristics of the protein interaction network, protein interaction data sets generated by high-throughput experiments often contain many a lot of noisy data –25. TherHOCN proposed by Wang 3], Clust formula . After fytoscape . The parTable method, the obtained F-score is 0.5213. After using the RF model to classify the candidate protein complexes identified by SVCC, the experimental performance improved by about 10%. It can be seen from the above experiment that using a trained RF model to classify candidate protein complexes predicted by SVCC can significantly improve the performance of the experiment. In summary, our method achieves good performance on both the yeast PPI network and the human PPI network. Especially in the human PPI network, our method is significantly better than other methods. Therefore, our method is superior to the existing protein complex prediction methods.We also note that the precision is much higher than recall on DIP network, but vice-versa on HPRD network. This maybe because the scale of HPRD is much larger than that of DIP , logistic regression (LR), KNN, XGBoost, AdaBoost, and gradient boosted tree GBDT six supervised learning models and compared their experimental results with the random forest model RF. We conducted parameter tuning experiments on these supervised learning models. We selected the best test parameters which are shown in Table It can be seen from Fig. In this study, we applied the network representation learning method node2vec to obtain the vector representation of the protein. Then, according to the protein vector representation, the protein complex vector is calculated as the feature of the protein complex. Finally, the candidate protein complexes are classified through the feature vector training model. To verify the effect of node2vec for our method, we also evaluate four other network representation learning methods, including DeepWalk , HOPE 3, LINE 3, and SDNAs shown in Figs. The training set data we selected when training the SVC model and the RF model is the same, including positive and negative examples. The positive data is a standard protein complex data set. The negative data is generated by randomly selecting nodes from the PPI network according to the ratio of the standard protein complexes. Many researchers used multiple classification labels to train supervised learning models in the existing research on protein complex prediction based on supervised learning. To verify the effectiveness of the two-class training set data selected, we also used the three-class training set data to train the supervised learning model for experiments on the DIP and HPRD protein interaction relationship network. The three-category training set data we choose mainly consists of three parts: positive examples, intermediate examples, and negative examples. Among them, the positive and negative data are the same as the binary classification. For the intermediate data, we chose to use the COACH algorithm to identify protein complexes from the PPI network. This is mainly because the possibility of the complexes identified by COACH being real complexes is higher than that of negative sample data but lower than that of positive sample data, which can effectively increase the richness of training sample data. And in order to ensure the accuracy of the experiment, the protein complexes matching the positive example were filtered out. The results of the experimental comparison of the two-class and three-class data on the yeast PPI network DIP and the human PPI network HPRD are shown in Table As shown in Table In this section we validate the biological significance of protein complexes based on Gene Ontology GO. In previous complex identification methods, many researchers used sed LAGO  to calcused LAGO , which cTables  formula ), suggesFor these complexes with low We also found that some predicted complexes did not match the standard protein complexes, but they still had very low We proposed a supervised protein complex prediction method with network representation and gene ontology knowledge. We weight the PPI network through the GO knowledge and topological information. Then we extract the topological information of the protein complex according to the weighted PPI network and the unweighted PPI network as its features and construct a training set. Through the constructed training set, the SVCC model is obtained. The SVCC model is used to predict candidate protein complexes from the protein interaction relationship network. Finally, we use the network representation learning method node2vec to obtain the vector representation of the protein complex and train the RF model. The RF model is used to classify the candidate protein complexes. The candidate protein complexes marked as positive by the RF model are the final predicted protein complexes. We evaluate the experimental performance of our method and seven other existing methods on the yeast PPI network DIP and the human PPI network HPRD. The experimental results show that our method effectively detects protein complexes from the PPI network compared with the existing protein complex identification methods. We also analyzed the biological significance of protein complexes predicted by different methods. The results show that the protein complexes predicted by our method have higher biological significance.Since GO term simlilarity is used in training SVC model in our method, using GO terms to evaluate the predicted complexes has certain limitations. As a future study, we will explore another way than GO terms to evaluate the biological significance of protein complexs.


In response to the practical needs of structure-based analysis, we have created a Mapiya web server. The Mapiya integrates four main functionalities: (i) generation of contact maps – intramolecular and intermolecular—for proteins, nucleic acids, and their complexes; (ii) characterization of the interactions physicochemical nature, (iii) interactive visualization of biomolecular conformations with automatic zoom on selected contacts using Molstar and (iv) additional sequence- and structure-based analyses performed with third-party software and in-house algorithms combined into an easy-to-use interface. Thus, Mapiya offers a highly customized analysis of the molecular interactions' in various biological systems. The web server is available at:   Contact maps provide a useful framework for uncovering the principles of complex network of biomolecular interactions . ContactIn this work, we present Mapiya, an interactive and easy-to-use web service for biomolecular structure analysis of proteins and their complexes (protein-protein and protein with RNA and/or DNA). The Mapiya combines some of the functionalities of the tools described above with additional structure- and sequence-based analyses. It integrates numerous practical visualization features and centers them around contact maps.http://mapiya.lcbio.pl/about/.The only required input is a biomolecular structure file in PDB format. Providing the input structure is marked as the fourth step on the main Mapiya page. The first three steps are optional and allow to modify default Mapiya settings as well as to invoke additional calculations. The optional steps include: (i) ‘Select options’ section allowing for modification of default Mapiya settings including contact cutoff value; (ii) ‘Fix structure’ section giving access to PDBfixer package  for fixiMapiya handles both intramolecular and intermolecular interactions between various biomolecules: proteins, peptides, and nucleic acids . Single-state and multi-model PDBs are supported. The structure can be loaded into the Mapiya web server from the file system on the user's local machine and fetched directly from the Protein Data Bank. Mapiya, within an internal analytical framework, integrates several well-established open-source third-party tools which support the robustness of highly-specialized analyses and high-quality results. On default settings, a widely used PDBfixer package  repairs The analysis of core structural features are also performed automatically, including (i) identification of hydrogen bonding networks (EDHB ), assignEach project has two analytical views: an interaction network diagram and a contact map. The contact maps are integrated interactively with Molstar Viewer for 3D structure visualization . It allointramolecular’ option or a bulge in the discrete color will load the internal contact map for the matching chain. Selecting the ‘intermolecular’ option or one of the gray ribbons will load the map of the contact interface between two molecules. When the submitted PDB has multiple models, the user can display the results for the particular model by clicking on the corresponding button at the top of the screen.When preliminary calculations  for a given project are ready, Mapiya loads the interaction diagram . The CM provides a simplified and useful 2D representation to investigate complex protein interaction networks  and distance maps (DM), see examples in Figure networks . Such a Mapiya's unique features include filtering and coloring contacts on the map based on the physicochemical nature of the driving interactions  Kyte-Doolittle hydropathy  along the sequence, for which contacts are excluded.The characterization of the physicochemical nature of interactions is available through interactive labels and numerous filters, which use various coloring schemes to discriminate molecular contacts. Using the ‘dropathy  (hydrophdropathy ). AdditiDisplay 1D data along sequence’ section of settings  chosen by the user , including interaction network diagram, contact map, and a section for viewing and downloading raw data, were implemented in a python framework using modern Dash (widgets) and Plotly (graphing) libraries and custom client-side javascript functions.2NDRY structure’ option available in ‘Display 1D data along the sequence’ and setting the ‘Interactive structure coloring’ to ‘using 1D features’  and RNA PDB ID: 1C9S). TRAP is a central regulator in the expression of tryptophan biosynthetic genes  and bindC9S. TRAP’ Figure , B. The ’ Figure , C.The use of Mapiya in understanding the structural mechanisms of the biological process can be further illustrated with the example of RNA-dependent RNA polymerase (RdRp) (PDB ID: 6YYT). The active form of RNA-dependent RNA polymerase (RdRp) from SARS-CoV-2 mimics the replication enzyme. In this example, the macromolecular assembly consists of the viral non-structural protein 12 (nsp12), nsp8 and nsp7, along with more than two turns of RNA template-product duplex . The nspcontacts’ are used in the ‘Interactive structure coloring’ option, along with ‘electrostatics’ as a ‘Contact Filter’, then the molecular visualizer will display the interaction interface between the protein and nucleotide chains (top right panel). Most of these contacts are stabilized by attractive electrostatic interactions . Suppose we want to find out which contacts are bound by the salt bridge. For this purpose, we selected ‘charged’ from the options available for protein-A (a feature for the X-axis) in the ‘Display 1D data’ section of settings. The bar-chart displayed on the top of the zoomed-in contact map (bottom left panel) shows the pattern of positively (dark red) and negatively (dark blue) charged amino acids along the sequence of protein chain A. Since nucleic acid is strongly negatively charged, salt bridges can be formed with positively charged amino acids such as Arg, Lys and His. For a better view (and a higher resolution in the preview), we zoomed in the interactive graph (using the mouse) to the 218–262 fragment along the protein-A sequence. We found an isolated contact between ARG:258 and DG:9 (marked with a black frame). Clicking on a selected point invokes two actions:The last example provides a practical tutorial of applying the Mapiya's analysis for a Human DNA polymerase beta complexed with gapped DNA (PDB ID: 1BPY). The following steps correspond to Figure displays an interactive label with details describing the contact ,automatically zooms the Molstar viewer window (bottom right panel) on the residues that are in contact, revealing the atomic details of the interaction.The analysis of biomolecular interactions is the basis for understanding how biomolecules perform their function. Nowadays there is a great need for readily available tools for the analysis of biomolecule structures, also thanks to the high availability of new protein structures ,35. Ideahttps://mapiya.lcbio.pl. An extended Mapiya descriptions and online tutorials are available at the Mapiya About page http://mapiya.lcbio.pl/about/.This website is free and open to all users and there is no login requirement. The web server is available at


Many biomedical applications, such as classification of binding specificities or bioengineering, depend on the accurate definition of protein binding interfaces. Depending on the choice of method used, substantially different sets of residues can be classified as belonging to the interface of a protein. A typical approach used to verify these definitions is to mutate residues and measure the impact of these changes on binding. Besides the lack of exhaustive data this approach generates, it also suffers from the fundamental problem that a mutation introduces an unknown amount of alteration into an interface, which potentially alters the binding characteristics of the interface. In this study we explore the impact of alternative binding site definitions on the ability of a protein to recognize its cognate ligand using a pharmacophore approach, which does not affect the interface. The study also provides guidance on the minimum expected accuracy of interface definition that is required to capture the biological function of a protein. The residue level description or prediction of protein interfaces is a critical input for protein engineering and classification of function. However, different parametrizations of the same methods and especially alternative methods used to define the interface of a protein can return substantially different sets of residues. Typical experimental or computational methods employ mutational studies to verify interface definitions, but all these approaches inherently suffer from the problem that in order to probe the importance of any one position of an interface, an unknown amount of alteration is introduced into the very interface being studied. In this work, we employ a pharmacophore-based approach to computationally explore the consequences of defining alternative binding sites. The pharmacophore generates a hypothesis for the complementary protein binding interface, which then can be used in a search to identify the corresponding ligand from a library of candidates. The accurate ranking of cognate ligands can inform us about the biological accuracy of the interface definition. This study also provides a guideline about the minimum required accuracy of protein interface definitions that still provides a statistically significant recognition of cognate ligands above random expectation, which in turn sets a minimum expectation for interface prediction methods. Protein-protein interactions are key players in many biological processes including metabolism, development, and regulation. Residue level descriptions of protein binding interfaces are essential for explaining, classifying, and modulating the formation of specific protein complexes. The biological function of a protein binding interface critically relies on its specificity, the ability to selectively recognize its cognate binding partners. However, the question of what exactly comprises a biological interface does not have a clear answer. Many interface prediction approaches exist. Some of these employ a radial distance cutoff-based approach , 2, whicA major strategy, both computationally –25 and eIn this paper, we computationally explore various protein interface definitions by probing the minimum interface necessary to successfully recognize its cognate ligand. Through this analysis we quantitatively investigate how much overlap alternative receptor interface patches must share with their true biological interface to still recognize their cognate partner reliably. Similarly, we investigate how many true interface residues can be lost without diminishing a proteins ability to accurately recognize its cognate partners.The analysis presented here does not perturb the integrity of the protein structure with mutations. Instead, we utilize a computational approach, ProtLID , to obtaIn this work, we study three protein interfaces: PD1:PD-L1, CTLA4:CD80, and CTLA4:CD86. These interactions are critical in regulating cellular functions. PD1 and PD-L1 form a co-inhibitory complex that can limit the development of T-cell response. PD1-PD-L1 interaction helps ensure that the immune system is activated only at the appropriate time to minimize autoimmune inflammation . CTLA4, Our results show that, on average, one can misdefine a protein interface by about 20–30% while still preserving its ability to recognize its cognate partner with statistically significant results. These results suggest that methods that predict protein interfaces should achieve above 70% accuracy to be useful. Our results also show that receptors with higher binding affinity (CTLA4:CD80) compared to receptors with lower binding affinity (CTLA4:CD86) are harder to destroy by removing true interface residues and adding false interface residues.The goal of this work is to assess the impact of alternative interface definitions for a protein receptor by monitoring how well each alternatively defined interface can recognize its cognate binding partner(s) from an ensemble of candidates. We consider the receptor-ligand interactions in three protein-protein complexes: PD1:PD-L1, where the interface on PD1 comprises 14 residues, and CTLA4:CD86/CD80, with a smaller interface on CTLA4 of 9 and 10 residues, respectively . CTLA4 wth percentile for the PD1 receptor when we consider interface patches with gradually reduced degree of overlap with the original interface. The original interface . nterface ), was abnterface . If we cIt is interesting to consider protein receptor interfaces with a smaller number of known cognate ligands as well. We consider two CTLA4 interfaces in complex with CD80 and CD86. We collected all the docked poses of CTLA4:CD80 and CTLA4:CD86 generated by ZDOCK that have the same interface size as CTLA4 in complex with its respective cognate binding partners . BecauseThe large degree of overlap between the two CTLA4 interfaces , defined using the CTLA4:CD80 complex or the CTLA4:CD86 complex, enables us to assess the ability of the CTLA4:CD80 interface to recognize CD86, and the CTLA4:CD86 interface to recognize CD80. As shown in Fig. S1, the ability of the CTLA4:CD80 interface to recognize CD86 as a cognate ligand is poorer than the average ability of it to recognize its own cognate ligands. In contrast, as shown in Fig. S2, the ability of the CTLA4:CD86 interface to recognize CD80 as a cognate ligand is better than the average ability of it to recognize its own cognate ligands. This suggests that CD80 has greater specificity than CD86 for recognizing the CTLA4 interface.In general, we find that the performance of the CTLA4:CD80 interface is better on average than that of the CTLA4:CD86 interface in recognizing cognate partners. This observation possibly implies that the binding affinity of CTLA4 for CD80 is markedly higher than the affinity for CD86 –49. The In an alternative approach, we explored what happens when we gradually eliminate residues in a combinatorial way from the original interface, without replacing them with non-interface residues (thereby reducing the size of the interface). We systematically removed residues in cohorts  from the residues comprising the rs-pharmacophore to assess the ability of the reduced rs-pharmacophore to recognize its cognate ligands. Protein interfaces can be defined using various approaches, which include using radial cutoffs, monitoring change in solvent accessible surface areas, or employing Voronoi polyhedra calculations. The disagreement among the results of these methods can be traced back to the fact that these approaches aim at identifying interfaces from a physical point of view using alternative criteria. In contrast, in this work we tried to assess the impact of alternative interface definitions from a biological point of view, from the perspective of a protein to maintain its ability to selectively recognize its cognate binding partner. The central question we ask in this work is how imperfect can the interface definition be whilst retaining the ability to recognize the cognate ligand(s). We assessed this by pursuing alternative interface patches that had decreasing overlap with the original biological interface. In this work, none of the alternative interfaces sampled produced higher accuracy results than the original definition obtained from CSU. This does not validate CSU as a uniformly accurate approach, but simply reflects the fact that we picked well performing cases, where the pharmacophore reliably identified the cognate ligand partners from a set of decoys. This means that the original definition of the interface had to be reasonably good to start with.ab-initio methods , CTLA4:CD80 (PDB code: 1I8L), and CTLA4:CD86 (PDB code: 1I85). A rs-pharmacophore is calculated with ProtLID treating PD1 , CTLA4 , and CTLA4  as receptor proteins. Each receptor rs-pharmacophore is screened against a library of 103 structures of the immunoglobulin superfamily (Suppl. Table 1). There are 24 available structures of the cognate ligand of receptor PD1   was usedProtein Ligand Interface Design,  is a comskewness = (Pm3/ Psd3) where Pm3 is the third moment of a ProtLID score distribution, and Psd is the standard deviation of ProtLID scores. Once a pharmacophore for a given protein interface is generated, we enumerate all possible 5-mer combinations of the calculated residue preferences to screen a ligand structure database. This results in a certain number of matches for each potential ligand out of all combinatorial possibilities. For instance, for a 15-residue large rs-pharmacophore, the number of 5-mer enumerations is 3003 (15C5). The ProtLID score is the number of 5-mer hits for a particular ligand. Skewness is calculated over the distribution or scores obtained for all possible ligands. Only interface patches for which the skewness is above 2.5 are deemed reliable (Mathematical skewness of ProtLID scores assesses the reliability of the rs-pharmacophore generated by ProtLID . Skewnesreliable , while o


Protein interactions are key in vital biological processes. In many cases, particularly in regulation, this interaction is between a protein and a shorter peptide fragment. Such peptides are often part of larger disordered regions in other proteins. The flexible nature of peptides enables the rapid yet specific regulation of important functions in cells, such as their life cycle. Consequently, knowledge of the molecular details of peptide-protein interactions is crucial for understanding and altering their function, and many specialized computational methods have been developed to study them. The recent release of AlphaFold and AlphaFold-Multimer has led to a leap in accuracy for the computational modeling of proteins. In this study, the ability of AlphaFold to predict which peptides and proteins interact, as well as its accuracy in modeling the resulting interaction complexes, are benchmarked against established methods. We find that AlphaFold-Multimer predicts the structure of peptide-protein complexes with acceptable or better quality (DockQ ≥0.23) for 66 of the 112 complexes investigated—25 of which were high quality (DockQ ≥0.8). This is a massive improvement on previous methods with 23 or 47 acceptable models and only four or eight high quality models, when using energy-based docking or interaction templates, respectively. In addition, AlphaFold-Multimer can be used to predict whether a peptide and a protein will interact. At 1% false positives, AlphaFold-Multimer found 26% of the possible interactions with a precision of 85%, the best among the methods benchmarked. However, the most interesting result is the possibility of improving AlphaFold by randomly perturbing the neural network weights to force the network to sample more of the conformational space. This increases the number of acceptable models from 66 to 75 and improves the median DockQ from 0.47 to 0.55 (17%) for first ranked models. The best possible DockQ improves from 0.58 to 0.72 (24%), indicating that selecting the best possible model is still a challenge. This scheme of generating more structures with AlphaFold should be generally useful for many applications involving multiple states, flexible regions, and disorder. Protein-protein interactions are central to all biological process; knowledge of the molecular details of these interactions is crucial to understanding and altering their function. Up to 40% of protein-protein interactions are considered peptide-protein interactions, with many of these responsible for vital functions such as cell life-cycle regulation . These aThe unprecedented accuracy of AlphaFold  and the Despite the fact that AlphaFold was trained on monomeric structures, it has demonstrated an impressive ability and stability to allow manipulation of its input to predict protein complexes—for instance, using a 200 residue gap to infer a chain break  or usingAlthough AlphaFold expertly implements several state-of-the-art neural network concepts and contributes its own with the Evoformer layers, the common bioinformatics concept of simple increased sampling of the conformational space with more lenient energy terms in search of a global optimum has not been explored. Repeated sampling of predictions with different random seeds or parameters is commonly utilized in bioinformatics methods; examples include Rosetta and ZDOCK . For manHere, we demonstrate that AlphaFold-Multimer, which has been so successful in the prediction of complexes of globular structures, can also be used to advance the field of peptide-protein complex modeling and interaction prediction. Without any modifications, AlphaFold-Multimer performs much better than state-of-the-art on both peptide-protein complex modeling and interaction prediction. We also show that AlphaFold can be improved by randomly perturbing the neural network weights to force it to sample a larger variety of conformations. By generating a large pool of models and using the excellent scoring function in AlphaFold, it is possible to select much better models than the default setting.A test set was constructed for the benchmarking of peptide-protein complex modeling which could also be used for peptide-protein interaction prediction. The samples of observed peptide-protein interaction complexes in the test set were based on the state-of-the art paper for peptide-protein interaction prediction, CAMP, by A negative set was created for peptide-protein interaction prediction in the same manner as in This scheme results in a dataset which can be used to both evaluate the docking performance on the positive set as well as be used for benchmarking the capacity to predict whether peptide-protein pairs interact or not. Both the positive and negative sets are available as AF-gap: This is an input-adapted version using AlphaFold (• lphaFold  monomer.lphaFold . The modAFmulti-: This is AlphaFold-Multimer version 2.1.0 (ranking_confidence score and rank 1 was selected. ranking_confidence is a linear combination of the interface score ipTM (interface predicted Template Modeling score) and overall structural score pTM: 0.8ipTM + 0.2pTM. AlphaFold multimer was run with one or several options from the list below:• on 2.1.0 . The modreduced_dbs: using the reduced database setting.– full_dbs: using the large sequence databases, BFD, and Uniclust30.– template: allowing templates as input into AlphaFold. To ensure that the target protein or very close homologs were not used as a template, templates were filtered with BLAST E-values better than 10–20 when searching with the target against PDBSEQ or for the peptides – v2: AlphaFold-Multimer version 2.2.0 .–20 was filtered. This filtered the target protein and very close homologs. Note that it is fine to use homologs and that the main purpose of this filter is to avoid using the target protein. The random forest-predicted suitability of the top-ranking template is used as the score for interaction prediction.InterPep2  is a temInterPep2 was run without the more computationally intensive refinement protocols, generating only coarse unrefined models. This will result in a lower number of sub-Ångström decoys but will have only minor to no effect on the positioning of the peptide at the correct binding site .PIPER-FlexPepDock is a state-of-the-art free modeling peptide-protein docking method which combines FFT-based rigid-body docking with high-resolution refinement . It is bCABS-dock utilizes a simulation search with flexible peptide and receptor for peptide-protein docking . In CABSZDOCK is a fast and accurate FFT-based rigid-body docking method which utilizes pairwise statistical potentials; it is a staple method for benchmarking protein–protein docking performance . In thisCAMP is a new deep learning-based method that can predict binary peptide-protein interactions . It usesThe DockQ program was used to assess the quality of docked peptide-protein complexes . DockQ aTPR = Recall = TP/P . FPR = FP/N . The ROC area under the curve (AUC) is frequently used as a measure of classification method performance  versus false positive rate (FPR) for different threshold cutoffs. formance .average precision) should be used instead (Precision = TP/(TP + FP). Recall = TPR = TP/P. F1 is the harmonic mean between precision and recall, defined as F1 = /.With an unbalanced dataset, TPR-FPR ROC curves and AUC can be used to benchmark methods against each other; however, it fails to capture the actual absolute performance of the methods, for which precision-recall curves and AUCPR  are consistently superior. However, running AlphaFold without template information seems better than running it with template information, especially when also run with a reduced database size. Previous work has shown that, although AlphaFold is fully capable of accurately judging the quality of structures derived from template information without any MSA information at all, it cannot efficiently sample the folding landscape without MSAs; if given template information with no MSA information, AlphaFold will essentially copy the template . As the By examining the quality in more detail, it can be seen that AlphaFold-Multimer version 2.2.0 (AFmulti-v2_full_dbs) produces more medium quality models than the other methods: 54 compared to only 43 and 30 for AF-gap, and InterPep2, respectively—see Two different methods were employed to force the best versions of AlphaFold-Multimer tested so far to sample more of the conformation space than the standard settings allow. Firstly, the number of recycling steps was incrementally increased from the default three to explore AlphaFold’s own ability to improve its sampling by refining its predictions. Secondly, the dropout layers used during AlphaFold training were activated at inference and the network was run several times with different random seeds, producing many structures for final comparison and evaluation. Similar schemes have been used in the past to create ensemble methods from single trained models and have been used with classifiers to estimate model variance .As can be seen in Dropout and increased recycles consistently lead AlphaFold to generate more varied models, including both worse models but also better models than a single run without dropout. The difference between the best and worst DockQ is shown in Additionally, combining dropout with increased recycles seems to restore the ranking performance in terms of the correlation of AlphaFold-Multimer version 2.2.0 back up to correlation R of 0.71. For version 2.1.0, the improved method seems to simply generate more high-quality structures without any significant change in the scoring correlation to DockQ . Note, hFor the remainder of this study, AlphaFold-Multimer run with dropout produces 200 structures per neural network model . Whenever AlphaFold-Multimer-v1 is referenced as being run with additional recycles, it is run with 21 recycles unless otherwise specified. Similarly, AlphaFold-Multimer-v2 is run with nine recycles. Note that the base behavior of AlphaFold is to run three recycles unless otherwise specified. These specific versions of AlphaFold-Multimer were selected based on the median DockQ score of their predictions .Even though running AlphaFold-Multimer with dropout active at inference improved the quality of final predicted docked peptide complexes, the correlation between AlphaFold predicted confidence and DockQ became worse . This isdropout_noSM for dropout but no dropout in the structure module (SM).To test this hypothesis, AlphaFold-Multimer versions 2.1.0 and 2.2.0 were run again on the entire dataset, using the best combination of hyper-parameters such as number of recycles and dropout seen in previous tests. This time, dropout was applied selectively to all parts of the network except the structure module, in the hope that the correlation between confidence score and DockQ would be retained in relation to running without dropout, thereby also improving the selection between generated structures and thus improving AlphaFold-Multimer for peptides overall. These versions are denoted with The same table also shows that AlphaFold-Multimer version 2.2.0 has no benefit from no dropout in the structure module at all: the performance drops from 0.51 to 0.50 and 0.53 to 0.50 for three and nine recycles, respectively, and the correlation does not change. We speculate that the reason version 2.1.0 seems to be more affected by increased sampling compared to 2.2.0 may be the increased loss term for clashing models that was introduced in 2.2.0 . Of courWhile both AlphaFold-Multimer versions 2.1.0 and 2.2.0 show higher performance with the increased sampling through dropout—with 2.1.0 seeing a larger improvement but 2.2.0 already starting at a higher performance level—the two versions show differences in their overall behavior. Version 2.1.0 performs better at high numbers of recycles and when the structure module is not subjected to dropout. Version 2.2.0, on the other hand, seems to require dropout in all layers to perform optimally, and a generally lower number of recycles is better.Since both versions produce predictions in the same predicted score range and both correlate their scores well with DockQ, it is simple to construct combination predictors by allowing the different versions to generate 100 structures each and then selecting the structure with the overall highest predicted score . Such different combinations can be compared to the versions of AlphaFold-Multimer investigated so far in While the performance of AlphaFold-Multimer, especially with the improvements described in this study, is far above the template-based method InterPep2, both AlphaFold-Multimer and InterPep2 have scores that correlate well with DockQ. In addition, AlphaFold-Multimer does not use its templates for the multimer interaction but only for folding the individual chains. Thus, if AlphaFold-Multimer is uncertain in its prediction, it is possible that a template for the interaction found by InterPep2 can be used. A combination method can be constructed, using the scores for confident predictions by AlphaFold-Multimer (ranking_confidence>0.70)  and Inte>0.40) , to seleThe results for the AlphaFold + InterPep2 combo predictor for peptide-protein docking can be found in To analyze potential trends in factors that contribute to the performance of AlphaFold, we correlated the performance with physiochemical and evolutionary factors that might influence the results—see p-value Sc for the native peptide-protein interfaces follows a skewed Gaussian distribution where the majority of the targets have Sceff < 100, as expected, but there are also some poor predictions with Neff > 1,000—see p-value As in previous reports , we coulp-value p-value Only 16% of the peptides in the test set are predicted to be almost completely disordered when unbound (more than 75% of the residues predicted as disordered). The average DockQ scores for complexes with peptides predicted as disordered when unbound are lower than the average DockQ score for the targets with peptides predicted as ordered when unbound—0.32 vs. 0.43—but the difference is not significant . For AlphaFold-Multimer, additional methods based on the median score of the generated models rather than the best score were added, suffixed with The precision-recall-AUC (PR-AUC) is 0.64 for AFm_v1_r3+_v2_r3_median + IP2 compared to 0.61 for AFm_v1_r3+_v2_r3_median and the best single AlphaFold-Multimer version (AFmulti-v2_full_dbs_median). Using the median score improves the PR-AUC from 0.57 to 0.61 for AFmulti-v2_full_dbs, indicating that picking the median predicted score rather than the highest predicted score seems to yield slightly better performance .To assess the significance of the PR-AUC values, a bootstrap procedure in which targets were selected with replacement and the PR-AUC was recalculated was used. Methods were compared pairwise and the process was repeated 10,000 times. The bootstrap values (percentage of times in which one method has a PR-AUC better than the other) are presented in Performance for interaction prediction needs to be assessed at low FPR to enable all-vs-all comparisons with high confidence predictions without too many false positives. At FPR = 0.01, the best methods recall around 0.26–0.29 (TPR) of the positive examples with a precision of 0.82–0.85—see Cases where AlphaFold failed were examined to understand why AlphaFold fails for certain samples as well as why forced sampling through dropout and the template-based method InterPep2 can help with prediction quality in these cases. One such example can be seen in In this particular case, increased sampling through forced dropout with AlphaFold-Multimer version 2.1.0 could also result in the correct conformation being sampled and selected, as AlphaFold samples were more nearby the conformational space, including the reverse direction of the peptide . In fact, the increased sampling for version 2.2.0 also samples a few high-DockQ conformations, although none of these are scored high enough to be selected .In 33% of improved cases, AlphaFold positioned the peptide at the binding site of a non-peptide binding partner, either for a co-factor or another protein chain . AlphaFold seems able to model the receptor protein regardless of the presence of any other binding chains or co-factors . HoweverWe have shown that AlphaFold-Multimer achieves state-of-the-art performance in both peptide-protein docking and peptide-protein interaction prediction without modification. Most interesting, however, is the discovery that forcing increased sampling of the conformational space by increasing the number of recycles of the final layers of the network or adding dropout at inference and running the protocol several times can significantly improve the performance of AlphaFold.The improvement median DockQ score when using the improved sampling strategy is dramatic, from 0.40/0.42 to 0.55/0.53 for AlphaFold-Multimer versions v1 and v2, respectively. By combining both versions v1 and v2, it possible to raise the median DockQ to 0.56; adding a template-based method (InterPep2) for complexes where AlphaFold produces low confidence predictions raises the median DockQ as high as 0.60.These results reinforce the previous findings that AlphaFold is well-suited for the peptide-protein docking problem which requires a wider sampling of conformations, especially with our modifications to improve sampling. It should be noted that the improved sampling protocol presented here is not limited to the peptide-protein docking problem and should be useful in many AlphaFold applications. Examples are, for investigating multiple stable conformations, for larger and more difficult targets, or for larger assemblies. Additionally, more variations in the application of dropout at inference could be investigated, such as different rates of dropout.Finally, while the improvements presented here are significant, there is still a large gap between the quality of the best model generated and the one ranked highest by AlphaFold’s predicted score. As such, protein model quality assessment remains an important field of research in protein structure prediction with AlphaFold.


Protein–protein interactions (PPIs) have emergedin thepast years as significant pharmacological targets in the developmentof new therapeutics due to their key roles in determining pathologicalpathways. Herein, we present fragments on energy surfaces, a simpleand general design strategy that integrates the analysis of the dynamicand energetic signatures of proteins to unveil the substructures involvedin PPIs, with docking, selection, and combination of drug-like fragmentsto generate new PPI inhibitor candidates. Specifically, structuralrepresentatives of the target protein are used as inputs for the blindphysics-based prediction of potential protein interaction surfacesusing the matrix of low coupling energy decomposition method. Thepredicted interaction surfaces are subdivided into overlapping windowsthat are used as templates to direct the docking and combination offragments representative of moieties typically found in active drugs.This protocol is then applied and validated using structurally diverse,important PPI targets as test systems. We demonstrate that our approachfacilitates the exploration of the molecular diversity space of potentialligands, with no requirement of prior information on the locationand properties of interaction surfaces or on the structures of potentiallead compounds. Importantly, the hit molecules that emerge from ourab initio design share high chemical similarity with experimentallytested active PPI inhibitors. We propose that the protocol we describehere represents a valuable means of generating initial leads againstdifficult targets for further development and refinement. Indeed, blocking PPI malfunctioning in transformed cells could represent an optimalstrategy for the treatment of many pathological conditions.2, making them complicated to engage them with smallmolecules.14 Moreover, a feature that distinguishesthese targets from classical active or binding site proteins is theabsence of well-defined pockets and cavities, which would facilitatethe design of ad hoc molecules, using established methods . Finally,because these large surfaces are largely apolar, the interactionsthat a ligand could form could expectedly be hydrophobic and thuspotentially weak or even a-specific.18However, PPIs are challenging targets for pharmacologicalinterventions.They are in fact characterized by the heterogeneity of their sizesand shapes: typically, the areas involved in interactions exceed 4000ÅFor all these reasons,there are currently a limited number ofactive ligands for PPIs, and these targets have often been defined“undruggable”.25To overcome the hurdles describedabove, the preferred approachto interact with large surfaces has involved the use of oligopeptidesand peptidomimetics. Recent years have witnessed the impact of PROTACs,a new class of bidentate drugs able to recruit (often undruggable)proteins to the unfolded protein response machinery of the cell.28 Their 3D binding mode can bedetermined via X-ray crystallography and NMR spectroscopy.Fragment-based drug design (FBDD) also recently emerged asan attractivestrategy to design ligands able to engage the large protein surfacesinvolved in PPIs. In this approach, the target is probed with low-molecular-weightligands (∼150 Da).30 This can be achieved either bygrowing a larger molecule out of a binding fragment or by connectingdifferent fragments that bind to distinct areas of the interactionsurface. A successful example of this approach is represented by thedesign of Venetoclax, drug approved by the FDA in 2016.31Informationon the fragments identified to bind productively isthen used to guide their evolution into optimized molecules with drug-likeproperties.36In the last few years, computational approacheshave made a significantcontribution to PPI targeting. In general terms, they encompass methodsfor the prediction of the PPI to be targeted and for the evaluationof the potential binding of candidate HITS. The former includes coevolutionanalyses, homology modeling, and multiple sequence alignment: manyof these are currently being coupled to machine learning approaches.The latter entails mainly docking methods to search for potentialligands from databases and define their putative binding modes usingphysics-based energy functions or geometric models. Many of thesemethods are based on the use of pre-existing information on the proteinor sequence to be targeted. Docking methods, on the other hand, maybe limited in their efficiency by the extension and complexity ofthe surfaces that need to be scanned. In this context, it is worthunderlining that computational methods have been developed that couplethe selection of possible fragments to the exploration of the potentialbinding surface using molecular dynamics (MD) simulations and enhancedsampling techniques.40 Next, the putative binding surface is subdivided into overlappingwindows , a simpleand straightforward (ab initio) approach that facilitates the identificationof new hit molecules to engage specific PPIs, independent of pre-existinginformation on the target and possible ligands. To this end, we useas input only the 3D structure in isolation of one of the PPI-formingpartners to target and a small library of fragments. As a test set,we choose several structurally different disease-related proteinswhich are known to carry out their activity via the assembly of specificPPIs. First, knowledge on the 3D structure of the target protein isused to predict the location of potential interaction regions usingour recently introduced energy-based method for PPI interface identification.windows 1:each wUpon analyzing the generated compounds and benchmarkingagainstexperimental complexes containing PPI-targeting ligands, we show thata high degree of similarity with known actives naturally emerges fordesigned HITS. Importantly, this is achieved with no prior informationon the chemistry of the ligands or on the location of the surfaces.The HITs identified through FOES are clearly non-optimized and canrepresent valuable starting points for ad hoc medicinal chemistrycampaigns.FOES is fully general and immediately applicableto new targetsin the context of PPI studies. Furthermore, we expect it to be usefulto unveil possible hits for orphan proteins, often very importantfor disease, but generally difficult to treat.45 The method has been described at large previouslyand tested experimentally in various settings. Here, we provide abrief overview. First, MLCE computes the non-bonded part of the potential E  via a MM/GBSA calculation, obtaining, for a protein of N residues, a N × N symmetric interaction matrix ijM. Thismatrix can be expressed in terms of its eigenvalues and eigenvectorsasK isthe kth eigenvalue and ikw is the ith component of the correspondingeigenvector. The eigenvector associated with the most negative eigenvaluecontains information on the most and least stabilizing interactionsin the system.The prediction of binding regions on selectedproteins was carried out using the matrix of low coupling energy (MLCE)method. MLCE starts from the analysis of the pair-interaction energiesof all the amino acids in a protein.M̃ij asIt was previously shown that the first eigenvectorcontains most of the relevant energetic information on interactionsof the system, and we can define an approximated interaction matrix v1, are not prone to adaptation, change of conformation,and dynamic behavior, we consider the binding interaction to a potentialpartner as a local phenomenon involving regions not directly dedicatedto structural stabilization. From this point of view, we can filterthe approximated interaction matrix M̃ij to contain only the pairs of residues thatare in geometric proximity in the analyzed structure, obtaining theMLCE. Namely,ijC is the residue contact matrix, which is equal to 1 if theresidues i and j are closer to 6.5Å  and 0 otherwise, and ⊗ is theHadamard product .39Under the assumptionthat residues involved in structural stability,corresponding to the components with highest values in ij matrix, weselect the residues that have an interaction energy with respect tothe other residues that are smaller than a threshold. In practice,with a threshold of 15% , we select the residuesinvolved in the 15% of non-zero interactions that are less energetic.This threshold value proved to be a key parameter for specificity/sensitivityof the approach. The residues obtained are then merged in patchesthat are sets of residues that are close to each other and constitutethe predicted protein–protein binding regions.39Starting from the MLCESpecifically, MLCE calculations are applied to structuralrepresentativesobtained from the MD simulations of Bcl, VHL, and HIV integrase (videinfra). The setup of MD simulations and the selection of structuralrepresentatives via clustering are described in the next paragraphs.46 This tool assigns correct bond orders, addsmissing hydrogens, and creates disulfide bonds where needed/possible.During the process, the pH used was set between 6 and 8. The protonationstate of acidic/basic residues was assigned using the PROPKA toolat pH 7. The resulting structures were subjected to a gentle backbone-restrainedminimization.The proteins were downloaded fromthe Protein Data Bank with the following PDB codes: Bcl, 1GJH.pdb;VHL, 4AJY.pdb; HIV, 3L3U.pdb. Possible detergent molecules, ligands,etc., were removed before entering the preparation protocol. The structuresof the proteins were first refined using the Protein Preparation Wizardtool of Maestro suite of programs (www.schrodinger.com).The resulting structure for each proteinwas used as the input for a 1 μs MD simulation. All MD simulationswere carried out with the DESMOND module of the Maestro suite. First,a cubic box was used as a solvation box: in all cases, the boxes werebuilt large enough to allow a distance of 1 nm between the edge ofthe box and the surface atoms of the minimized structure of the protein.The box was filled with the solvent TIP3P water molecules, and thecomplex was brought to neutrality by the addition of sodium or chlorineions depending on the total charge of the protein.1.NVT environment, at a temperature of 10 K with a timestepof 1 femtosecond and restraints on solute heavy atoms. The total durationof this step is 100 picoseconds.A Brownian dynamic was run, in an 2.NVT environmentwas run at a temperature of 10 K with a timestep of1 femtoseconds and restraints on solute backbone heavy atoms. Thistime the duration was 12 picoseconds.A subsequent step in an 3.NPT environment,starting at a temperature of 10 K and restraints onsolute heavy atoms, for 12 picoseconds. In this step, the temperatureis gently raised to 100 K.This step was run in an 4.The same as step 3, but the temperatureis progressively raised to 300 K.5.NPT environment withno restraints is used for 24 picoseconds to allowthe system to smoothly adapt to the 300 K temperature condition.In this step, the 6.Starting from the finalstructure obtainedat the previous step, the production MD simulation is run for 1 microsecondfor each system.The simulationwas next prepared as follows:47 withthe S-OPLS force field.The velocities and coordinates of each simulation weregeneratedrandomly, the simulation was run in a periodic system, the barostatused was the Langevin barostat (1 Bar), and the thermostat was theNose–Hoover chain (300 K). All simulations were carried outwith DESMOND (www.schrodinger.com),A clustering analysis using the hierarchicalclustering algorithm (implemented in MAESTRO) was carried out on eachof the resulting trajectories for each of the systems. We selectedthe representative structures from the six most populated clusters.For each protein, the binding region was considered as the consensusresult by applying MLCE to the minimized X-ray structure and the sixstructures identified by the clustering analysis.39 This division into windows is intended to divide very large portionsof surfaces into smaller portions in order to sample the entire regionwith fragments as exhaustively as possible . Eventually, only the best poseis saved as output.Docking was carried out with the Glide module of theMaestro suiteof programs. We used the same setup for each case:At the end, another docking study was doneon the raw HITs moleculesto verify that they were akin to the chosen interaction site usingthe same settings.1.In the case of VHL and HIV, the selectedfragments were all treated the same way: automatic “directjoining” (random) was done between the fragments considered.2.In the case of Bcl, consideringa muchlarger surface to cover, a core was created with the two fragmentsthat bound to the mid-low portion of the helix of interest. First,these two fragments were prepared with LigPrep individually to seewhich were the most likely stereoisomers. After that, the four resultstructures of the two starting fragments were combined with the CombineFragments tool. The result of this core (having decine of differentstarting cores available) was used with the starting structure forthe construction of the final molecules: using the “linking”option, and entering the cores, two “number of trials”were made by adding from one to three fragments.After selecting only those fragmentsthat interacted with the protein in the identified region and gaveinteractions characteristic of small-molecule–protein bonds,the Combine Fragments tool was used to achieve fully computationaland automated linkage between fragments. To do this, different strategieswere used depending on the case study:For both strategies used, settings were used to allowall the chosen fragments to be considered. To do this, allowed distancesand angles were adjusted specifically according to the protein beingstudied.49 as implemented in Maestro. The following settings wereused for this analysis:64-bit precisionFingerprinttype atom pairsAtom typing scheme 4Similarity metric TanimotoAs a final analysis,a similarity study was done using the Tanimoto metric50 force field was used consideringa pH between 6 and 8 using Epik.The fragment library was taken from Schrödinger’ssite and prepared with the latest force field through the LigPreptool using the default settings. A preparation step was first run,and the OPLS451 VHL,27 and HIV integrase.52 These proteins arestructurally different and are involved in distinct disease pathways.For all targets, we started from the experimental (X-ray or NMR) structureof the protein in isolation and removed possible bound ligands, detergentmolecules, trapped solvents, etc. Each protein was then simulatedfor 1 μs using all-atom MD simulations. This step is intendedto relax the structure and remove biases/correlations with the initialstructure. From the resulting trajectory, the six most representativestructures are extracted as the centers of the six most populatedconformational clusters. These were then used together with the initialminimized structure as the basis for the blind prediction of potential protein interactionsurfaces.In this study, we consideredseveral structurally unrelated proteins that are known to carry outtheir functional activity via the formation of complexes with otherprotein partners and to be important pharmacological targets. We studiedBcl,40 In this framework, we analyze the energetics of residue-pair interactionsas this can unveil key information on the structural organizationand localization of interacting areas of the molecule. The workinghypothesis is that specific networks of residues may be dedicatedto fold stabilization, while others may deal with establishing interactionswith partners. Evolutionary pressure has in fact selected protein–proteinbinding sites favoring those chemical and conformational propertiesthat guarantee the correct function. Internal energetics accountsfor the interactions that each residue establishes with all otherresidues of the protein it belongs to: in this context, strong pairinteractions identify internal residues related to the stabilizationof the folding core, while weaker pair interactions, combined withthe localization of residues in continuous patches on the proteinsurface, highlight substructures that are not internally optimizedand are thus prone (or in other words preorganized) to interact witha potential partner.To this end, we used the MLCE approach.N residues, a N × N symmetric interaction matrix ijM. Theeigenvalue decomposition of the matrix highlights the regions of strongestand weakest couplings: the fragments that are on the surface, contiguousin space and weakly coupled to the protein core, define the potentialinteraction regions. Putative interaction patches can be consideredfrustrated (non-optimized) in terms of intramolecular interactionsand open to stabilization by partners. MLCE has been extensively validated,also in experimental contexts.54In this spirit, MLCE analyses of the interactionenergies of allthe amino acids in a protein compute the non-bonded part of the potential via aMM/GBSA calculation, obtaining, for a protein composed of The seven representative structures for each protein are thusanalyzedwith MLCE, and the consensus results highlighting non-optimized substructuresthat are consistently found in distinct clusters were selected asthe regions that could aptly be targeted by small drug-like fragments.As the predicted surfaces are expectedly large, they are first subdividedinto overlapping regions, or windows 1, to redThrough the analysis of thelocation, energetics, and interactionpatterns of the fragments with their respective target areas, themost promising ones are selected.2 or with two CH2 bridgingmoieties. The aim here was to simplify the construction process asmuch as possible.Once the most relevant fragmentsare selected, they are joinedin the simplest way possible using the Combine Fragments tool see  of the S49 was used  ligandsfor the respective proteins was calculated. To do this, the Tanimoto similarity metricwas used 2 based owas used .In this context, one should keep in mind that akey problem incomparing the generated HIT and the experimentally tested ligand residesin the different size of the molecules being compared. Specifically,the reference molecule may have a different number of features fromeither the fragments or the fully reconstructed HITs. As a consequence,even if the main features were correctly captured by the fragment-basedapproaches, since they would likely represent a subset of the featurespresent in the benchmark molecule, one may expect to obtain low similaritycoefficients. Moreover, in our approach, we use no information onthe cryptographically determined binding region: to identify the locationof the interaction surface, we indeed use structures that are generatedby MD simulations. In this framework, the actual shapes and conformationsdisplayed by the protein for interactions may differ from the onesobserved in the structures we use as benchmarks, favoring the generationof HITs with conformations that are different from the ones observedfor X-ray characterized experimental ligands in complex with the proteinused as benchmarks. To overcome these potential limitations, we useda variant of the Tanimoto similarity score implemented in the MAESTROsuite, which compares atom pairs taking their relative distances inspace into account, coupled to “atom typing scheme 4”which takes into account functional groups and their bonding hybridization.The scores obtained are reported in the form of graphs and tablesthroughout the paper (vide infra).Finally, we ran a dockingstudy using designed HITs to characterizethe potential affinity of the molecules for their respective targetprotein. Strikingly, the Hits with the highest calculated affinitieswere shown to belong to the ensemble of structures with the highersimilarity coefficients to known active ligands.55 This family of proteins forms an extensive interactionsnetwork within the cytosol and membranes.56Bcl proteins are a family of proteins involvedin the regulation of programmed cell death (apoptosis). Alterationof their expression in cancer makes them oncogenic promoters as theirtask of switching on the programmed death of cancer cells is suppressed.31 The two fragments in window 3 of the helix were then defined asthe starting moieties onto which the different fragments selectedfor the other portions were connected with simple bridging groups(see We first applied MLCE to identify possible interaction surfaceson Bcl 3a.The coupssee .Table S1). Importantly, thegroup of 30 molecules with the best docking scores contained a largenumber of molecules with a Tanimoto similarity with Venetoclax higherthan 0.5 , a transcriptionfactor with a key role in the regulation of gene expression by oxygen.Importantly, the VHL protein is the substrate receptor subunit ofthe (RING)-VHL (CRL2VHL) multi-subunit E3 ligase, an enzymeof the ligase family, essential for guiding intracellular proteindegradation via the ubiquitin–proteasome system (UPS).27 VHL has been targeted with small molecules withthe aims of disrupting its deranged interactions with HIFs and hijackingthe protein to form complexes with non-native neo-substrate proteinsusing proteolysis targeting chimeras (PROTACs) and induce the UPSdegradation of pathologic proteins. The discovery of VHL ligands entailedboth HTS campaigns and rational design efforts initially based onmimicking the critical PPIs of the HIF-1α/VHL complex.58The von Hippel–Lindau (VHL) protein playsa key role as the tumor suppressor by forming protein complexes withother proteins within the cell.Tables S2–S5).From the structural point of view, thisprotein turned out to be the most complex: MLCE analysis identifieda large interaction surface spanning residues 14–19, 47–51,and 89–93. This predicted interaction area is composed of threeβ-sheets spanning approximately 27.0 Å in length and 12Å in width 4. Consid59 and known ligands from PDB structures  K, 4W9H) 5b,c.Overall, the best scoring designer hits can aptly representa viablestarting point for the development of drug-like molecules targetinga difficult, but important, PPI surface 5d,e.60HIV integrase is one of the main pharmacologicaltargets, along with reverse DNA polymerase and HIV protease, whichare pursued in the search for anti-AIDS therapies. The protein catalyzesthe entry of viral DNA into the host DNA. This protein consists ofthree domains: N-terminal, C-terminal, and the central binding domain.61First, MLCE analysis identified the threehelices that constitute the binding site as a possible zone of interaction6a. This Supporting Information).To test our integrated PPI identification and FBDDapproach, wefirst subdivided the predicted binding region in three overlappingdocking windows as described above. Additionally, given the more compactnature of the interaction area, we examined the performance of usingone single window spanning the three α-helices that enclosethe predicted region of interest were considered 6a. In boA challengingaspect of HIV integrase as a target is that knownactive ligands are highly drug like: given the nature of our designprotocol, based on combining fragments that span potentially extendedregions, emerging molecules could be expected to be large and flexible.Notably, the physicochemical characteristics of the designs matchedwell with those of experimentally tested ligands. Indeed, good similarityscores were obtained for all ligands tested 6b.Tables S6–S8).Importantly, the final dockinganalysis on the target site showedthat, among the set with the top ranking docked hits, several designsshowed a Tanimoto score significantly above 0.500 with experimentalligands 6c have been tested, success has been somewhat limited. In thiscontext, the recent use of physics-based models that take the dynamicsof the target protein explicitly into account combined with fragment-bindingsimulations has proven successful for the simultaneous discovery ofcryptic sites and of suitable binding moieties. In this context, fragment-basedapproaches are interesting and attractive because they allow ad hocconstruction of new ligands using the target as a template, directingthe selection of functional groups based on the interactions thatare presented by the protein to potential partners.66PPI targeting has blossomed into a very broadand attractive fieldfor drug discovery, as many pathologic processes depend on the PPImalfunction.67Our goal in this work was to make the constructionof new HITsas direct and simple as possible using an unbiased prediction of potentialprotein interaction surfaces. We demonstrated that it is possibleto find “raw” starting molecules that, with classicalmedicinal chemistry modifications, could lead to novel leads. A possiblecaveat to mention here is that the hits, at this stage, are not evaluatedor screened for their synthesizability: integrating this feature wouldaptly improve the quality of the selection and the prioritizationof compounds. An important point worth noting here is that the designedmolecules emerging from our work already show a high degree of similarityto known active ligands, a result that is particularly significantconsidering that no prior information on binding regions or ligandidentities was used.This clearlysupports the possibility of applying FOES to yet undruggableproteins or orphan targets. Thanks to the simple and straightforwardnature of the method, the simple knowledge of the 3D structure ofthe protein is the only requirement to start the molecular designprocess. In this context, the limitation of possible fragment-dockingareas helps make the selection of optimal fragments and the constructionof new ligands effective. We suggest that our approach can find applicativevenues in a wide range of problems.In summary, we have presented a novel,simple, and general designstrategy that integrates the characterization of the dynamics andenergetics signature of specific protein regions involved in interactionswith other proteins with the docking, selection, and combination ofdrug-like fragments. This approach naturally permits us to identifythe binding determinants of new PPI inhibitor candidates. This protocolwas applied to study difficult and important pharmacologic targetswhose cell mechanisms are indeed linked to the formation of PPIs,namely, Bcl, VHL, and HIV1 integrase. FOES allowed us to explore themolecular diversity space of potential ligands, with no requirementof prior information on the location and properties of potential interactionsurface inhibitors or on the structures of potential lead compounds.Importantly, the ensembles of best designed candidates as PPI antagonistscontain a significant number of HITs with a high chemical similarityto known active PPI inhibitors that had previously been experimentallytested. The ability to generate novel actionable compounds ab initioprovides viable opportunities for the further lead development andrefinement.Finally, our results may have larger ramificationsin the understandingof the mechanisms of chemical biology via the possibility to designligands that modify functional interactions and demonstrate an unappreciateddelicate interplay between the dynamics and energetics of specificprotein regions and the possibility to exploit these traits for moleculardesign.