Optimizing model representation for integrative structure determination of macromolecular assemblies

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.

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.

Bayesian methods in integrative structure modeling

There is a growing interest in characterizing the structure and dynamics of large biomolecular assemblies and their interactions within the cellular environment. A diverse array of experimental techniques allows us to study biomolecular systems on a variety of length and time scales. These techniques range from imaging with light, X-rays or electrons, to spectroscopic methods, cross-linking mass spectrometry and functional genomics approaches, and are complemented by AI-assisted protein structure prediction methods. A challenge is to integrate all of these data into a model of the system and its functional dynamics. This review focuses on Bayesian approaches to integrative structure modeling. We sketch the principles of Bayesian inference, highlight recent applications to integrative modeling and conclude with a discussion of current challenges and future perspectives.

New opportunities in integrative structural modeling

Integrative structural modeling enables structure determination of macromolecules and their complexes by integrating data from multiple sources. It has been successfully used to characterize macromolecular structures when a single structural biology technique was insufficient. Recent developments in cellular structural biology, including in-cell cryo-electron tomography and artificial intelligence-based structure prediction, have created new opportunities for integrative structural modeling. Here, we will review these opportunities along with the latest developments in integrative modeling methods and their applications. We also highlight open challenges and directions for further development.

Integrative modeling of the cell

A whole-cell model represents certain aspects of the cell structure and/or function. Due to the high complexity of the cell, an integrative modeling approach is often taken to utilize all available information including experimental data, prior knowledge and prior models. In this review, we summarize an emerging workflow of whole-cell modeling into five steps: (i) gather information; (ii) represent the modeled system into modules; (iii) translate input information into scoring function; (iv) sample the whole-cell model; (v) validate and interpret the model. In particular, we propose the integrative modeling of the cell by combining available (whole-cell) models to maximize the accuracy, precision, and completeness. In addition, we list quantitative predictions of various aspects of cell biology from existing whole-cell models. Moreover, we discuss the remaining challenges and future directions, and highlight the opportunity to establish an integrative spatiotemporal multi-scale whole-cell model based on a community approach.

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

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 is available at doi:10.5281/zenodo.6241200.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

From systems to structure - using genetic data to model protein structures

Understanding the effects of genetic variation is a fundamental problem in biology that requires methods to analyse both physical and functional consequences of sequence changes at systems-wide and mechanistic scales. To achieve a systems view, protein interaction networks map which proteins physically interact, while genetic interaction networks inform on the phenotypic consequences of perturbing these protein interactions. Until recently, understanding the molecular mechanisms that underlie these interactions often required biophysical methods to determine the structures of the proteins involved. The past decade has seen the emergence of new approaches based on coevolution, deep mutational scanning and genome-scale genetic or chemical-genetic interaction mapping that enable modelling of the structures of individual proteins or protein complexes. Here, we review the emerging use of large-scale genetic datasets and deep learning approaches to model protein structures and their interactions, and discuss the integration of structural data from different sources.

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.

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.

High resolution ensemble description of metamorphic and intrinsically disordered proteins using an efficient hybrid parallel tempering scheme

Mapping free energy landscapes of complex multi-funneled metamorphic proteins and weakly-funneled intrinsically disordered proteins (IDPs) remains challenging. While rare-event sampling molecular dynamics simulations can be useful, they often need to either impose restraints or reweigh the generated data to match experiments. Here, we present a parallel-tempering method that takes advantage of accelerated water dynamics and allows efficient and accurate conformational sampling across a wide variety of proteins. We demonstrate the improved sampling efficiency by benchmarking against standard model systems such as alanine di-peptide, TRP-cage and β-hairpin. The method successfully scales to large metamorphic proteins such as RFA-H and to highly disordered IDPs such as Histatin-5. Across the diverse proteins, the calculated ensemble averages match well with the NMR, SAXS and other biophysical experiments without the need to reweigh. By allowing accurate sampling across different landscapes, the method opens doors for sampling free energy landscape of complex uncharted proteins.

From integrative structural biology to cell biology

Integrative modeling is an increasingly important tool in structural biology, providing structures by combining data from varied experimental methods and prior information. As a result, molecular architectures of large, heterogeneous, and dynamic systems, such as the ∼52-MDa Nuclear Pore Complex, can be mapped with useful accuracy, precision, and completeness. Key challenges in improving integrative modeling include expanding model representations, increasing the variety of input data and prior information, quantifying a match between input information and a model in a Bayesian fashion, inventing more efficient structural sampling, as well as developing better model validation, analysis, and visualization. In addition, two community-level challenges in integrative modeling are being addressed under the auspices of the Worldwide Protein Data Bank (wwPDB). First, the impact of integrative structures is maximized by PDB-Development, a prototype wwPDB repository for archiving, validating, visualizing, and disseminating integrative structures. Second, the scope of structural biology is expanded by linking the wwPDB resource for integrative structures with archives of data that have not been generally used for structure determination but are increasingly important for computing integrative structures, such as data from various types of mass spectrometry, spectroscopy, optical microscopy, proteomics, and genetics. To address the largest of modeling problems, a type of integrative modeling called metamodeling is being developed; metamodeling combines different types of input models as opposed to different types of data to compute an output model. Collectively, these developments will facilitate the structural biology mindset in cell biology and underpin spatiotemporal mapping of the entire cell.

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).

Principles for Integrative Structural Biology Studies

Integrative structure determination is a powerful approach to modeling the structures of biological systems based on data produced by multiple experimental and theoretical methods, with implications for our understanding of cellular biology and drug discovery. This Primer introduces the theory and methods of integrative approaches, emphasizing the kinds of data that can be effectively included in developing models and using the nuclear pore complex as an example to illustrate the practice and challenges involved. These guidelines are intended to aid the researcher in understanding and applying integrative structural methods to systems of their interest and thus take advantage of this rapidly evolving field.

Role of integrative structural biology in understanding transcriptional initiation

Integrative structural biology combines data from multiple experimental techniques to generate complete structural models for the biological system of interest. Most commonly cross-linking data sets are employed alongside electron microscopy maps, crystallographic structures, and other data by computational methods that integrate all known information and produce structural models at a level of resolution that is appropriate to the input data. The precision of these modelled solutions is limited by the sparseness of cross-links observed, the length of the cross-linking reagent, the ambiguity arisen from the presence of multiple copies of the same protein, and structural and compositional heterogeneity. In recent years integrative structural biology approaches have been successfully applied to a range of RNA polymerase II complexes. Here we will provide a general background to integrative structural biology, a description of how it should be practically implemented and how it has furthered our understanding of the biology of large transcriptional assemblies. Finally, in the context of recent breakthroughs in microscope and direct electron detector technology, where increasingly EM is capable of resolving structural features directly without the aid of other structural techniques, we will discuss the future role of integrative structural techniques.