Optimizing representations for integrative structural modeling using Bayesian model selection.

MOTIVATION: Integrative structural modeling combines data from experiments, physical principles, statistics of previous structures, and prior models to obtain structures of macromolecular assemblies that are challenging to characterize experimentally. The choice of model representation is a key decision in integrative modeling, as it dictates the accuracy of scoring, efficiency of sampling, and resolution of analysis. But currently, the choice is usually made ad hoc, manually. RESULTS: Here, we report NestOR (Nested Sampling for Optimizing Representation), a fully automated, statistically rigorous method based on Bayesian model selection to identify the optimal coarse-grained representation for a given integrative modeling setup. Given an integrative modeling setup, it determines the optimal representations from given candidate representations based on their model evidence and sampling efficiency. The performance of NestOR was evaluated on a benchmark of four macromolecular assemblies. AVAILABILITY AND IMPLEMENTATION: NestOR is implemented in the Integrative Modeling Platform (https://integrativemodeling.org) and is available at https://github.com/isblab/nestor. Data for the benchmark is at https://www.doi.org/10.5281/zenodo.10360718.

PrISM: precision for integrative structural models.

MOTIVATION: A single-precision value is currently reported for an integrative model. However, precision may vary for different regions of an integrative model owing to varying amounts of input information. RESULTS: We develop PrISM (Precision for Integrative Structural Models) to efficiently identify high- and low-precision regions for integrative models. AVAILABILITY AND IMPLEMENTATION: PrISM is written in Python and available under the GNU General Public License v3.0 at https://github.com/isblab/prism; benchmark data used in this paper are available at doi:10.5281/zenodo.6241200. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Architecture of the Human and Yeast General Transcription and DNA Repair Factor TFIIH.

TFIIH is essential for both RNA polymerase II transcription and DNA repair, and mutations in TFIIH can result in human disease. Here, we determine the molecular architecture of human and yeast TFIIH by an integrative approach using chemical crosslinking/mass spectrometry (CXMS) data, biochemical analyses, and previously published electron microscopy maps. We identified four new conserved "topological regions" that function as hubs for TFIIH assembly and more than 35 conserved topological features within TFIIH, illuminating a network of interactions involved in TFIIH assembly and regulation of its activities. We show that one of these conserved regions, the p62/Tfb1 Anchor region, directly interacts with the DNA helicase subunit XPD/Rad3 in native TFIIH and is required for the integrity and function of TFIIH. We also reveal the structural basis for defects in patients with xeroderma pigmentosum and trichothiodystrophy, with mutations found at the interface between the p62 Anchor region and the XPD subunit.

Optimizing model representation for integrative structure determination of macromolecular assemblies.

Integrative structure determination of macromolecular assemblies requires specifying the representation of the modeled structure, a scoring function for ranking alternative models based on diverse types of data, and a sampling method for generating these models. Structures are often represented at atomic resolution, although ad hoc simplified representations based on generic guidelines and/or trial and error are also used. In contrast, we introduce here the concept of optimizing representation. To illustrate this concept, the optimal representation is selected from a set of candidate representations based on an objective criterion that depends on varying amounts of information available for different parts of the structure. Specifically, an optimal representation is defined as the highest-resolution representation for which sampling is exhaustive at a precision commensurate with the precision of the representation. Thus, the method does not require an input structure and is applicable to any input information. We consider a space of representations in which a representation is a set of nonoverlapping, variable-length segments (i.e., coarse-grained beads) for each component protein sequence. We also implement a method for efficiently finding an optimal representation in our open-source Integrative Modeling Platform (IMP) software (https://integrativemodeling.org/). The approach is illustrated by application to three complexes of two subunits and a large assembly of 10 subunits. The optimized representation facilitates exhaustive sampling and thus can produce a more accurate model and a more accurate estimate of its uncertainty for larger structures than were possible previously.

Assessing Exhaustiveness of Stochastic Sampling for Integrative Modeling of Macromolecular Structures.

Modeling of macromolecular structures involves structural sampling guided by a scoring function, resulting in an ensemble of good-scoring models. By necessity, the sampling is often stochastic, and must be exhaustive at a precision sufficient for accurate modeling and assessment of model uncertainty. Therefore, the very first step in analyzing the ensemble is an estimation of the highest precision at which the sampling is exhaustive. Here, we present an objective and automated method for this task. As a proxy for sampling exhaustiveness, we evaluate whether two independently and stochastically generated sets of models are sufficiently similar. The protocol includes testing 1) convergence of the model score, 2) whether model scores for the two samples were drawn from the same parent distribution, 3) whether each structural cluster includes models from each sample proportionally to its size, and 4) whether there is sufficient structural similarity between the two model samples in each cluster. The evaluation also provides the sampling precision, defined as the smallest clustering threshold that satisfies the third, most stringent test. We validate the protocol with the aid of enumerated good-scoring models for five illustrative cases of binary protein complexes. Passing the proposed four tests is necessary, but not sufficient for thorough sampling. The protocol is general in nature and can be applied to the stochastic sampling of any set of models, not just structural models. In addition, the tests can be used to stop stochastic sampling as soon as exhaustiveness at desired precision is reached, thereby improving sampling efficiency; they may also help in selecting a model representation that is sufficiently detailed to be informative, yet also sufficiently coarse for sampling to be exhaustive.

Prediction of homoprotein and heteroprotein complexes by protein docking and template-based modeling: A CASP-CAPRI experiment.

We present the results for CAPRI Round 30, the first joint CASP-CAPRI experiment, which brought together experts from the protein structure prediction and protein-protein docking communities. The Round comprised 25 targets from amongst those submitted for the CASP11 prediction experiment of 2014. The targets included mostly homodimers, a few homotetramers, and two heterodimers, and comprised protein chains that could readily be modeled using templates from the Protein Data Bank. On average 24 CAPRI groups and 7 CASP groups submitted docking predictions for each target, and 12 CAPRI groups per target participated in the CAPRI scoring experiment. In total more than 9500 models were assessed against the 3D structures of the corresponding target complexes. Results show that the prediction of homodimer assemblies by homology modeling techniques and docking calculations is quite successful for targets featuring large enough subunit interfaces to represent stable associations. Targets with ambiguous or inaccurate oligomeric state assignments, often featuring crystal contact-sized interfaces, represented a confounding factor. For those, a much poorer prediction performance was achieved, while nonetheless often providing helpful clues on the correct oligomeric state of the protein. The prediction performance was very poor for genuine tetrameric targets, where the inaccuracy of the homology-built subunit models and the smaller pair-wise interfaces severely limited the ability to derive the correct assembly mode. Our analysis also shows that docking procedures tend to perform better than standard homology modeling techniques and that highly accurate models of the protein components are not always required to identify their association modes with acceptable accuracy. Proteins 2016; 84(Suppl 1):323-348. © 2016 Wiley Periodicals, Inc.

Extension of a protein docking algorithm to membranes and applications to amyloid precursor protein dimerization.

Novel adjustments are introduced to the docking algorithm, DOCK/PIERR, for the purpose of predicting structures of transmembrane protein complexes. Incorporating knowledge about the membrane environment is shown to significantly improve docking accuracy. The extended version of DOCK/PIERR is shown to perform comparably to other leading docking packages. This membrane version of DOCK/PIERR is applied to the prediction of coiled-coil homodimer structures of the transmembrane region of the C-terminal peptide of amyloid precursor protein (C99). Results from MD simulation of the C99 homodimer in POPC bilayer and docking are compared. Docking results are found to capture key aspects of the homodimer ensemble, including the existence of three topologically distinct conformers. Furthermore, the extended version of DOCK/PIERR is successful in capturing the effects of solvation in membrane and micelle. Specifically, DOCK/PIERR reproduces essential differences in the homodimer ensembles simulated in POPC bilayer and DPC micelle, where configurational entropy and surface curvature effects bias the handedness and topology of the homodimer ensemble.

The molecular architecture of the desmosomal outer dense plaque by integrative structural modeling.

Desmosomes mediate cell-cell adhesion and are prevalent in tissues under mechanical stress. However, their detailed structural characterization is not available. Here, we characterized the molecular architecture of the desmosomal outer dense plaque (ODP) using Bayesian integrative structural modeling via the Integrative Modeling Platform. Starting principally from the structural interpretation of an electron cryo-tomogram, we integrated information from X-ray crystallography, an immuno-electron microscopy study, biochemical assays, in-silico predictions of transmembrane and disordered regions, homology modeling, and stereochemistry information. The integrative structure was validated by information from imaging, tomography, and biochemical studies that were not used in modeling. The ODP resembles a densely packed cylinder with a PKP layer and a PG layer; the desmosomal cadherins and PKP span these two layers. Our integrative approach allowed us to localize disordered regions, such as N-PKP and PG-C. We refined previous protein-protein interactions between desmosomal proteins and provided possible structural hypotheses for defective cell-cell adhesion in several diseases by mapping disease-related mutations on the structure. Finally, we point to features of the structure that could confer resilience to mechanical stress. Our model provides a basis for generating experimentally verifiable hypotheses on the structure and function of desmosomal proteins in normal and disease states.

Improving ranking of models for protein complexes with side chain modeling and atomic potentials.

An atomically detailed potential for docking pairs of proteins is derived using mathematical programming. A refinement algorithm that builds atomically detailed models of the complex and combines coarse grained and atomic scoring is introduced. The refinement step consists of remodeling the interface side chains of the top scoring decoys from rigid docking followed by a short energy minimization. The refined models are then re-ranked using a combination of coarse grained and atomic potentials. The docking algorithm including the refinement and re-ranking, is compared favorably to other leading docking packages like ZDOCK, Cluspro, and PATCHDOCK, on the ZLAB 3.0 Benchmark and a test set of 30 novel complexes. A detailed analysis shows that coarse grained potentials perform better than atomic potentials for realistic unbound docking (where the exact structures of the individual bound proteins are unknown), probably because atomic potentials are more sensitive to local errors. Nevertheless, the atomic potential captures a different signal from the residue potential and as a result a combination of the two scores provides a significantly better prediction than each of the approaches alone.

Analyzing milestoning networks for molecular kinetics: definitions, algorithms, and examples.

Network representations are becoming increasingly popular for analyzing kinetic data from techniques like Milestoning, Markov State Models, and Transition Path Theory. Mapping continuous phase space trajectories into a relatively small number of discrete states helps in visualization of the data and in dissecting complex dynamics to concrete mechanisms. However, not only are molecular networks derived from molecular dynamics simulations growing in number, they are also getting increasingly complex, owing partly to the growth in computer power that allows us to generate longer and better converged trajectories. The increased complexity of the networks makes simple interpretation and qualitative insight of the molecular systems more difficult to achieve. In this paper, we focus on various network representations of kinetic data and algorithms to identify important edges and pathways in these networks. The kinetic data can be local and partial (such as the value of rate coefficients between states) or an exact solution to kinetic equations for the entire system (such as the stationary flux between vertices). In particular, we focus on the Milestoning method that provides fluxes as the main output. We proposed Global Maximum Weight Pathways as a useful tool for analyzing molecular mechanism in Milestoning networks. A closely related definition was made in the context of Transition Path Theory. We consider three algorithms to find Global Maximum Weight Pathways: Recursive Dijkstra's, Edge-Elimination, and Edge-List Bisection. The asymptotic efficiency of the algorithms is analyzed and numerical tests on finite networks show that Edge-List Bisection and Recursive Dijkstra's algorithms are most efficient for sparse and dense networks, respectively. Pathways are illustrated for two examples: helix unfolding and membrane permeation. Finally, we illustrate that networks based on local kinetic information can lead to incorrect interpretation of molecular mechanisms.

Optimizing representations for integrative structural modeling using Bayesian model selection.

Motivation: Integrative structural modeling combines data from experiments, physical principles, statistics of previous structures, and prior models to obtain structures of macromolecular assemblies that are challenging to characterize experimentally. The choice of model representation is a key decision in integrative modeling, as it dictates the accuracy of scoring, efficiency of sampling, and resolution of analysis. But currently, the choice is usually made ad hoc, manually. Results: Here, we report NestOR (Nested Sampling for Optimizing Representation), a fully automated, statistically rigorous method based on Bayesian model selection to identify the optimal coarse-grained representation for a given integrative modeling setup. Given an integrative modeling setup, it determines the optimal representations from given candidate representations based on their model evidence and sampling efficiency. The performance of NestOR was evaluated on a benchmark of four macromolecular assemblies. Availability: NestOR is implemented in the Integrative Modeling Platform (https://integrativemodeling.org) and is available at https://github.com/isblab/nestor.

Identification of potential modulators of IFITM3 by in-silico modeling and virtual screening.

IFITM3 is a transmembrane protein that confers innate immunity. It has been established to restrict entry of multiple viruses. Overexpression of IFITM3 has been shown to be associated with multiple cancers, implying IFITM3 to be good therapeutic target. The regulation of IFITM3 activity is mediated by multiple post-translational modifications (PTM). In this study, we have modelled the structure of IFITM3, consistent with experimental predictions on its membrane topology. MD simulation in membrane-aqueous environment revealed the stability of the model. Ligand binding sites on the IFITM3 surface were predicted and it was observed that the best site includes important residues involved in PTM and has good druggable score. Molecular docking was performed using FDA approved ligands and natural ligands from Super Natural II database. The ligands were re-ranked by calculating binding free energy. Select docking complexes were simulated again to substantiate the binding between ligand and IFITM3. We observed that known drugs like Eluxadoline and natural products like SN00224572 and Parishin A have good binding affinity against IFITM3. These ligands form persistent interactions with key lysine residues (Lys83, Lys104) and hence can potentially alter the activity of IFITM3. The results of this computational study can provide a starting point for experimental investigations on IFITM3 modulators.

Molecular architecture of nucleosome remodeling and deacetylase sub-complexes by integrative structure determination.

The nucleosome remodeling and deacetylase (NuRD) complex is a chromatin-modifying assembly that regulates gene expression and DNA damage repair. Despite its importance, limited structural information describing the complete NuRD complex is available and a detailed understanding of its mechanism is therefore lacking. Drawing on information from SEC-MALLS, DIA-MS, XLMS, negative-stain EM, X-ray crystallography, NMR spectroscopy, secondary structure predictions, and homology models, we applied Bayesian integrative structure determination to investigate the molecular architecture of three NuRD sub-complexes: MTA1-HDAC1-RBBP4, MTA1N -HDAC1-MBD3GATAD2CC , and MTA1-HDAC1-RBBP4-MBD3-GATAD2A [nucleosome deacetylase (NuDe)]. The integrative structures were corroborated by examining independent crosslinks, cryo-EM maps, biochemical assays, known cancer-associated mutations, and structure predictions from AlphaFold. The robustness of the models was assessed by jack-knifing. Localization of the full-length MBD3, which connects the deacetylase and chromatin remodeling modules in NuRD, has not previously been possible; our models indicate two different locations for MBD3, suggesting a mechanism by which MBD3 in the presence of GATAD2A asymmetrically bridges the two modules in NuRD. Further, our models uncovered three previously unrecognized subunit interfaces in NuDe: HDAC1C -MTA1BAH , MTA1BAH -MBD3MBD , and HDAC160-100 -MBD3MBD . Our approach also allowed us to localize regions of unknown structure, such as HDAC1C and MBD3IDR , thereby resulting in the most complete and robustly cross-validated structural characterization of these NuRD sub-complexes so far.

A Framework for Stochastic Optimization of Parameters for Integrative Modeling of Macromolecular Assemblies.

Integrative modeling of macromolecular assemblies requires stochastic sampling, for example, via MCMC (Markov Chain Monte Carlo), since exhaustively enumerating all structural degrees of freedom is infeasible. MCMC-based methods usually require tuning several parameters, such as the move sizes for coarse-grained beads and rigid bodies, for sampling to be efficient and accurate. Currently, these parameters are tuned manually. To automate this process, we developed a general heuristic for derivative-free, global, stochastic, parallel, multiobjective optimization, termed StOP (Stochastic Optimization of Parameters) and applied it to optimize sampling-related parameters for the Integrative Modeling Platform (IMP). Given an integrative modeling setup, list of parameters to optimize, their domains, metrics that they influence, and the target ranges of these metrics, StOP produces the optimal values of these parameters. StOP is adaptable to the available computing capacity and converges quickly, allowing for the simultaneous optimization of a large number of parameters. However, it is not efficient at high dimensions and not guaranteed to find optima in complex landscapes. We demonstrate its performance on several examples of random functions, as well as on two integrative modeling examples, showing that StOP enhances the efficiency of sampling the posterior distribution, resulting in more good-scoring models and better sampling precision.

Using Integrative Modeling Platform to compute, validate, and archive a model of a protein complex structure.

Biology is advanced by producing structural models of biological systems, such as protein complexes. Some systems are recalcitrant to traditional structure determination methods. In such cases, it may still be possible to produce useful models by integrative structure determination that depends on simultaneous use of multiple types of data. An ensemble of models that are sufficiently consistent with the data is produced by a structural sampling method guided by a data-dependent scoring function. The variation in the ensemble of models quantified the uncertainty of the structure, generally resulting from the uncertainty in the input information and actual structural heterogeneity in the samples used to produce the data. Here, we describe how to generate, assess, and interpret ensembles of integrative structural models using our open source Integrative Modeling Platform program (https://integrativemodeling.org).

CM1-driven assembly and activation of yeast γ-tubulin small complex underlies microtubule nucleation.

Microtubule (MT) nucleation is regulated by the γ-tubulin ring complex (γTuRC), conserved from yeast to humans. In Saccharomyces cerevisiae, γTuRC is composed of seven identical γ-tubulin small complex (γTuSC) sub-assemblies, which associate helically to template MT growth. γTuRC assembly provides a key point of regulation for the MT cytoskeleton. Here, we combine crosslinking mass spectrometry, X-ray crystallography, and cryo-EM structures of both monomeric and dimeric γTuSCs, and open and closed helical γTuRC assemblies in complex with Spc110p to elucidate the mechanisms of γTuRC assembly. γTuRC assembly is substantially aided by the evolutionarily conserved CM1 motif in Spc110p spanning a pair of adjacent γTuSCs. By providing the highest resolution and most complete views of any γTuSC assembly, our structures allow phosphorylation sites to be mapped, surprisingly suggesting that they are mostly inhibitory. A comparison of our structures with the CM1 binding site in the human γTuRC structure at the interface between GCP2 and GCP6 allows for the interpretation of significant structural changes arising from CM1 helix binding to metazoan γTuRC.

Modeling Biological Complexes Using Integrative Modeling Platform.

Integrative structure modeling provides 3D models of macromolecular systems that are based on information from multiple types of experiments, physical principles, statistical inferences, and prior structural models. Here, we provide a hands-on realistic example of integrative structure modeling of the quaternary structure of the actin, tropomyosin, and gelsolin protein assembly based on electron microscopy, solution X-ray scattering, and chemical crosslinking data for the complex as well as excluded volume, sequence connectivity, and rigid atomic X-ray structures of the individual subunits. We follow the general four-stage process for integrative modeling, including gathering the input information, converting the input information into a representation of the system and a scoring function, sampling alternative model configurations guided by the scoring function, and analyzing the results. The computational aspects of this approach are implemented in our open-source Integrative Modeling Platform (IMP), a comprehensive and extensible software package for integrative modeling ( https://integrativemodeling.org ). In particular, we rely on the Python Modeling Interface (PMI) module of IMP that provides facile mixing and matching of macromolecular representations, restraints based on different types of information, sampling algorithms, and analysis including validations of the input data and output models. Finally, we also outline how to deposit an integrative structure and corresponding experimental data into PDB-Dev, the nascent worldwide Protein Data Bank (wwPDB) resource for archiving and disseminating integrative structures ( https://pdb-dev.wwpdb.org ). The example application provides a starting point for a user interested in using IMP for integrative modeling of other biomolecular systems.

Integrative structure modeling with the Integrative Modeling Platform.

Building models of a biological system that are consistent with the myriad data available is one of the key challenges in biology. Modeling the structure and dynamics of macromolecular assemblies, for example, can give insights into how biological systems work, evolved, might be controlled, and even designed. Integrative structure modeling casts the building of structural models as a computational optimization problem, for which information about the assembly is encoded into a scoring function that evaluates candidate models. Here, we describe our open source software suite for integrative structure modeling, Integrative Modeling Platform (https://integrativemodeling.org), and demonstrate its use.

The molecular architecture of the yeast spindle pole body core determined by Bayesian integrative modeling.

Microtubule-organizing centers (MTOCs) form, anchor, and stabilize the polarized network of microtubules in a cell. The central MTOC is the centrosome that duplicates during the cell cycle and assembles a bipolar spindle during mitosis to capture and segregate sister chromatids. Yet, despite their importance in cell biology, the physical structure of MTOCs is poorly understood. Here we determine the molecular architecture of the core of the yeast spindle pole body (SPB) by Bayesian integrative structure modeling based on in vivo fluorescence resonance energy transfer (FRET), small-angle x-ray scattering (SAXS), x-ray crystallography, electron microscopy, and two-hybrid analysis. The model is validated by several methods that include a genetic analysis of the conserved PACT domain that recruits Spc110, a protein related to pericentrin, to the SPB. The model suggests that calmodulin can act as a protein cross-linker and Spc29 is an extended, flexible protein. The model led to the identification of a single, essential heptad in the coiled-coil of Spc110 and a minimal PACT domain. It also led to a proposed pathway for the integration of Spc110 into the SPB.

DOCK/PIERR: web server for structure prediction of protein-protein complexes.

In protein docking we aim to find the structure of the complex formed when two proteins interact. Protein-protein interactions are crucial for cell function. Here we discuss the usage of DOCK/PIERR. In DOCK/PIERR, a uniformly discrete sampling of orientations of one protein with respect to the other, are scored, followed by clustering, refinement, and reranking of structures. The novelty of this method lies in the scoring functions used. These are obtained by examining hundreds of millions of correctly and incorrectly docked structures, using an algorithm based on mathematical programming, with provable convergence properties.