Integrative modelling of cellular assemblies

Abstract

A wide variety of experimental techniques can be used for understanding the precise molecular mechanisms underlying the activities of cellular assemblies. The inherent limitations of a single experimental technique often requires integration of data from complementary approaches, to gain sufficient insights into the assembly structure and function. Here, we review popular computational approaches for integrative modelling of cellular assemblies, including protein complexes and genomic assemblies. We provide recent examples of integrative models generated for such assemblies by different experimental techniques, especially including 3D electron microscopy (3D-EM) and HiC data, respectively. We highlight general concepts in integrative modelling and discuss the need for careful formulation and merging of different types of information.

Introduction

Understanding the structure and dynamics of the interacting biomolecules can give great insights into the cell’s function and integrity. These macromolecules are organized at different levels, from small assemblies (involving 2–3 proteins) to very large ones (tens to hundreds of proteins), some of which are organised further, at the supramolecular level: for example, the assembly of ribosomes into polysomes, the assembly of viral particles, and on an even larger scale the organization of chromosome structures and entire organelles such as the nucleome.

Unfortunately, structure determination of assemblies, in particular large ones, at resolutions that enable meaningful function inference is not always viable using a single biophysical technique. This problem can be overcome if the information from several techniques (e.g., assembly subunit composition, topology and overall architecture and dynamics) is combined efficiently using a variety of computational methods. Integrative modelling based on complementary experimental data is increasingly being used as the strategy to compute structural models for large cellular assemblies. Multiple sources of structural information can reduce the ambiguity and noise associated with low-resolution and/or heterogeneous data. In this review, we focus on popular experimental techniques and computational methods used in integrative modelling of cellular assemblies.

Sources of spatial information

High-resolution structures of cellular assemblies have been traditionally characterized in vitro by X-ray crystallography, the success of which is often limited by the ability to form crystals (Fig. 1). Cryo electron microscopy (cryo EM) techniques have been generally used to determine the structures of large assemblies (above ~150–200kD) that could not be crystallised (with the advantage of being carried out at near-native conditions) though at substantially lower resolutions. However, recent developments (including direct electron detectors and advanced image processing methods) have brought a substantial increase in subnanometer and near-atomic resolution structures even of smaller size [1].

Figure 1.

Top: Examples of different types of information from various experimental sources that are integrated for structure determination of protein complexes and genome assemblies. The important steps involved in integrative modeling process are highlighted in the central panel (model generation).

Bottom: Examples of recently-determined integrative models of cellular assemblies across resolution and size scales (from sub-nanometer to ~10 micron range). From left to right: transcription repressive complex CLOCK:BMAL1 (brain and muscle Arnt-like protein 1) bound to CRY1 (cryptochrome-1) (adapted from [78]), atomic model built based on data from SAXS, NMR, Size Exclusion Chromatography and X-ray crystallography; structure of the fungal toxin Pleurotolysin (adapted from [38]), model built based on 11 Å resolution cryo EM map and X-ray crystallography; model of 40S-eIF1-eIF3 complex built using data from, XL-MS and X-ray crystallography (~25 Å negative stain EM map used for validation) (adapted from [9]); model of flagellin-induced NAIP5/NLRC4 inflammasome built based on data from 4nm resolution subtomogram average and X-ray crystallography (adapted from [79]); Ensemble of mouse X chromosome conformations from single cell HiC at 500kb resolution (adapted from [74]); example of a genome model for haploid mouse embryonic stem cells from HiC experiments using chain particles representing 100kb DNA (adapted from [75]).

Although at much lower resolutions, cryo electron tomography (cryo ET) allows in-situ visualization of cellular architectures as well as assembly structures they contain if sub-tomogram averaging is possible [2]. Using fluorescently labelled biomolecules, dynamic interactions of assemblies can also be studied in living cells by super-resolution microscopy, at resolutions in the order of 10nm.

Small-angle X-ray and Neutron scattering (SAXS and SANS) have proven useful in the structural characterization of assemblies under near-native solution conditions, providing information on pairwise electron (or nuclear) distances, which can be used for computing 3D shapes and related features [3]. Nuclear Magnetic Resonance (NMR) is typically limited by sample size, but for large assemblies it can provide information such as direct interactions between monomers and relative orientations [4]. Electron Paramagnetic Resonance (EPR) allows determination of distance distributions (typically 1–10nm) that are generally more precise compared to fluorescence based methods [5].

Mass Spectrometry (MS) approaches have been used to obtain spatial information, stoichiometry and connectivity on entire assemblies in the gas phase (assuming they maintain their interactions) with the advantage of dealing with limited sample amounts. Advancements in protein and peptide separation techniques in MS make the method tolerant to a high degree of sample heterogeneity [6] and samples involving small protein mixtures and even large viral assemblies can be characterized. Ion mobility MS (IM-MS) allows separation of coexisting forms of the same complex. The time taken by an ion to traverse the ion mobility cell is related to its mass, charge, and their rotationally averaged collision cross-section (which gives a measure of the overall shape) [7]. Chemical cross-linking coupled to MS (XL-MS) is very popular as it can reveal interactions within or between biomolecules by providing an upper-limit distance between specific residues [8]. A number of methods have been used to calculate the optimal cross-link distances on a given atomistic model and score these against XL-MS data [9–12]. Hydrogen-Deuterium Exchange (HDX) experiments combined with either NMR or MS provide information on biomolecular interaction surfaces and conformational changes [4,13].

Protein interaction data can also be inferred using evolutionary approaches. Recent advances in the detection of correlated mutations in sequences across species enable prediction of residue pairs that interact not only within but also between proteins [14]. Experimental interaction data can be combined with evolutionary information, by mapping known interactions [15–17] and the 3D structure of the related complex if available [18,19].

Information about the nucleome organisation comes from recent technologies. For example, Chromosome Conformation Capture (3C) and related technologies (4C, 5C, HiC, in situ HiC, TCC) detect the genome-wide frequencies of spatial co-location between non-consecutive genomic regions in a population of cells [20]. Mapping of chromatin interactions is also possible in single cells, although at relatively lower coverage in comparison to ensemble HiC [21]. Lamina-DamID (DNA adenine methyltransferase identification) experiments provide probabilities with which chromatin regions are exposed to the lamina at the nuclear envelope.

Multi-color fluorescence in situ hybridization (FISH) uses fluorescent probes to detect the positions of targeted genomic loci in single cells; this decades old technique has lately witnessed impressive improvements in the number of simultaneous target loci, making it possible to trace entire chromosomes [22]. Finally, imaging technologies such as soft X-ray cryo tomography (cryo SXT) provide insights into spatial distributions of chromatin in different functional states [23], while cryo ET can reveal folding patterns of individual nucleosomal chromatin fibers.

Approaches to integrative modelling

It remains a major challenge to develop computational methods that can generate reliable models of cellular assemblies, ranging from small protein complexes to structural maps of entire organelles such as the nucleome. Below we describe modelling approaches driven by integration of different types of experimental data (Figure 1).

Protein complexes

Proteins and their assemblies are usually characterised by one or a few stable observable conformations under specific experimental conditions (except loops and disordered regions). A typical strategy for integrative modelling of protein assemblies (including domain-domain, protein-protein, protein-RNA or protein-DNA interactions) relies on minimizing a scoring function, which measures the agreement between the model and the experimental data (as well as penalizing violations from known standard geometries). The model can be represented as full-atomic, coarse-grained (e.g. secondary structure elements, domains, whole protein), or partial (ie. some parts of the model are missing). Experimental information is typically represented in the form of restraints that help in reducing the sampling space. The reliability of individual experimental restraints can be considered, for example, by adding weights in the scoring function or by selectively using subsets of them at different stages of the optimisation [24,25]. Alternatively, several initial models may be generated by using only a fraction of restraints (random subset) each time, the size of the fraction being a crude indicator of the reliability of restraints [26]. Integrative approaches yield a model or an ensemble of models that will have minimal restraints violations. The generated models can be clustered and ranked based on a score or a consensus among multiple scores and/or size of the clusters [27]. For cross validation, part of the experimental data can be excluded during the modelling process.

A classical example of integrative modeling is to obtain an atomic model from cryo EM data by fitting individual assembly components into the 3D map. This usually involves a global search to get the best fit between the model/s and the map, for which many programs have been developed [7,28], such as the Situs package (which can also fit models to SAXS data) [29]. Geometric features from the 3D-EM map can also be used as restraints, instead of directly fitting the subunit models into the EM density [30,31]. Interactive fitting of atomic models is popular, and is enabled by visualization tools like Coot [32] and Chimera [33]. Chimera provides methods for fitting atomic models in 3D shapes from cryo EM/ET through both global and local searches in a user-friendly and interactive manner.

TEMPy is a python package for integrative modeling primarily based on EM density [27] (but also crosslinking data). Simultaneous fitting of multiple components is carried out by a genetic algorithm, which uses the mutual information to account for the goodness-of-fit and penalises for steric clashes [34]. This is followed by a real-space refinement in the density using MODELLER/Flex-EM [35,36]. TEMPy integrates various scoring functions, including correlation-based scores, surface based-scores and statistical scores. In a recent application, low-resolution density from sub-tomogram averaging was combined with chemical cross-linking to identify the oligomerization state of the HSV-1 glycoprotein B assembly in vesicle membranes. Multiple methods of hierarchical constrained density-fitting were employed for building atomic models for the pre- and post-fusion conformations [37]. Models were generated and scored by TEMPy using an ensemble of alternate conformations and validated using insertion mutational data, revealing a surprising pre-fusion conformation. Integrative modelling using a combination of density fitting with other experimental data has also been useful in the intermediate resolution range [38,39].

Another related Monte-Carlo based method – PyRy3D [40] – uses a scoring function based on a combination of restraints, fitness to the shape data (EM, SAXS) and penalties for steric clashes. This method was recently used to model the structure of CCR4-NOT complex, based on EM data and component interaction restraints from X-ray and biochemical experiments [41]. POW^ER employs particle swarm optimization to predict the component arrangement in a symmetric assembly, based on a few geometric or distance restraints [42]. The program uses ensembles of subunits from molecular dynamics simulations or experiments to explore conformational changes of subunits during assembly optimization. Using this method, intrinsic flexibility derived from X-ray structures of subunits was integrated with cryo EM data of the assembly, to build near-atomistic models of aerolysin at different stages of pore formation [43].

A few integrative methods are also developed to work primarily on SAXS data [44]. For example, the ATSAS suite provides a collection of methods for processing and analysis of both SAXS and SANS data, including tools for integrative modelling and flexible optimization [45]. SAXS, like EM, is often used in combination with other techniques for integrative modelling. Recently, SAXS, HDX and RNA SHAPE (selective 2’-hydroxyl acylation analysed by primer extension) data based restraints were used to provide a dynamic model of a machinery involved in HIV-1 pro-viral transcription [46]. The SHAPE data highlights RNA segments that are potentially involved in interaction based on changes in reactivity of nucleotides upon assembly.

The Rosetta software suite also uses a Monte-Carlo approach for conformational sampling, which recombines frequently occurring protein backbone structural features with different types of restraints, such as sparse NMR data based on NOE, chemical shifts, and Residual dipolar coupling (RDCs, as orientation restraint) as well as XL-MS and cryo EM [25]. The reliability of NMR restraints is considered by their relative contributions in the scoring function. Distance constraints can be enforced (e.g., [47]) as part of the scoring function involving statistical interaction potentials and evaluation of standard geometry (atoms and secondary structures) and clashes. In a recent structure of S. flexneri type III secretion system (T3SS) needle several solid-state NMR (ssNMR) distance restraints were used to build models with a 7.7 Å cryo EM density map [48]. Intra and inter-subunit distance constraints from ssNMR experiment were integrated in iterative modeling and the final models were identified using a weighted sum of the Rosetta scoring function, number of constraint violations and correlation with EM density.

In Haddock, sparse experimental data can be added as ambiguous interaction restraints and random sets of these are used to generate initial configurations. Rigid-body protein-protein docking and energy minimization is followed by the Haddock flexible refinement, with an additional density cross-correlation score added to non-bonded interaction terms, for integrating EM data [49]. For example, chemical shift perturbations were used as restraints to map the potential active site and model the interaction between bacterial outer membrane receptor FusA and host cell ferredoxin using a comparative model of FusA and crystal structures of ferredoxin [50].

In IMP, assembly components can be represented as sets of particles of different types, depending on the available information and structural resolution. Such representations can be useful when some high-resolution information is missing (e.g., there are no atomic models for some of the proteins/domains in the complex). These components can be assembled using different optimization schemes (such as Monte Carlo, Conjugate Gradients, Molecular dynamics) and many different types of spatial restraints [24], such as connectivity and interaction restraints from various MS techniques [51]. A notable example of an IMP application is a model of the Yeast Mediator complex (YMC), which performs an essential regulatory role in eukaryotic transcription initiation [52]. Regions of known atomic structure or comparative models were modelled as rigid bodies, whereas unknown regions were represented as a flexible string of beads. Positions and orientations of rigid and polymer beads were iteratively sampled to minimize a scoring function which accounted for excluded volume, sequence connectivity, cryo EM, and crosslinking restraints. A Bayesian framework was used to assign confidence to subsets of cross-linking data based on relative consistency [9]. Finally, a single cluster with the best average score was chosen. The model was successfully validated with independent experimental data on protein–protein interactions. XL-MOD [53] also uses a Bayesian framework to reweight conflicting or ambiguous distance restraints from XL-MS, represented as log-harmonic potentials. An elastic network model based on a low-resolution representation of the subunit structures is used to sample conformational changes upon assembly and the component positions and orientations are sampled by a Monte-Carlo optimization scheme followed by relaxation using molecular dynamics.

Genome assemblies

A common challenge in resolving structures of genomes is the wide range of spatial and time scales involved compared to protein assemblies: the human genome counts ~6 billion basepairs in a diploid cell and its structure arguably never reaches thermodynamic equilibrium [54]. These complexities demand a level of coarse graining, ranging from models of the 10nm chromatin fiber to chromatin domains. Chromatin can be segmented into self-interacting chromatin domains (e.g. topologically associated domains (TAD) [55] or contact domains [56]), often bordered by chromatin loops. Chromatin domains with similar functional properties form sub-compartments and chromosomes organize in territories with stochastic preferences in their nuclear locations.

Recent physics-based polymer simulations of chromosomal regions revealed potential mechanisms into chromatin loop and TAD domain formation [57–60]. However, our focus will be based on data-driven (or restrained-based) approaches. Those methods use experimental data (mostly from HiC experiments) as input information for generating genome assembly structures. The interpretation of the data and its use differs widely depending on the chosen approach.

Some schemes generate a single representative structure (a consensus model) from ensemble HiC data. Contact frequencies are usually mapped to spatial distances, used to generate a 3D structure by optimizing a scoring function [61], Bayesian inference (BACH) [62] or multidimensional scaling (ShRec3D) [63]. These consensus models represent data averaged over millions of cells and cannot describe the actual physical nature of individual genomes, including the considerable structural variability between cells observed in 3D FISH and single-cell HiC experiments [21].

In contrast, resampling approaches perform many independent optimizations of a single scoring function from random starting configurations to resample an ensemble of structures. In TADBit, models are calculated by IMP, followed by a cluster analysis of the ensemble [64]. It has been used to investigate structures of TADs and bacterial genomes [65]. Resampling is also applied in several other examples (reviewed in [66]). Chrom3D relies on contact restraints for the most significant HiC contacts and lamina DamID data [67].

Population-based modelling (PM) techniques differ conceptually from resampling ones, in that they attempt to de-convolve ensemble HiC data into a population of individual structures. These methods explicitly address the variability of genome structures by creating a large population of models so that the cumulated chromatin contacts of all the structures reconstitute the ensemble HiC data rather than each structure individually. Such approaches avoid unphysical structures from simultaneous enforcement of conflicting restraints. One of the first HiC-based PM methods for modelling complete diploid genomes was introduced by Kalhor et al [68] and refined in a recent publication [69] (PGS software: https://www.github.com/alberlab/PGS). PGS has been applied to complete diploid genomes of human, mouse and Drosophila melanogastor cells [69,70].

Other PM approaches use a maximum entropy method combined with molecular dynamics sampling to construct effective energy landscapes that reproduced experimental HiC maps of individual chromosomes [71]. In another example, chromatin was represented by a few functional states and chromosome models were generated using chromatin state binding affinities as parameters [72]. In an earlier method a polymer model combined with Monte Carlo sampling was used to study chromatin conformations within TADs from ensemble 5C data [73].

Recently, the development of single cell HiC assays enabled the modelling of genomes of individual cells [21,74,75]. In Stevens et al. 10 individual genome structures of haploid mouse embryonic stem cells were modelled from single cell HiC data at 100kb resolution and validated by fluorescence imaging [75].

A challenge remains in the analysis of structure populations, either generated from deconvolution or single cell modeling. Dai et al. addressed this challenge by identifying frequently occurring chromatin clusters [76], which are often enriched in binding of specific regulatory factors.

Concluding paragraph

With the developments in biophysical techniques for structure determination of cellular assemblies, the need to integrate these data for solving a biological problem is becoming increasingly evident. Many of the approaches discussed in this review reflect recent advancements in this fields of integrative modelling of protein and genome assemblies. Although providing models of the two types of assemblies often requires different representations and different experimental information overall, the methodology used for data integration has many overlaps. The data used in integrative modelling is often sparse, noisy and ambiguous. Therefore, it is important to choose an adequate representation and formulation of the restraints (and their relative weights) to represent the data as accurately as possible. Thorough sampling is another important requirement to ascertain that optimal or near-optimal models are generated. The final model(s) should also reflect uncertainty and completeness of input information, apart from providing relevant structural details of the assembly. Cross-validation against an independent set of data is recommended for model assessment and the detection of over-fitting. Finally, large conformational variability in cellular assemblies often affect the consistency between different experimental data and this requires generation of an ensemble of models to more accurately represent the data. New community effort aims at addressing issues related to standardization of representation, validation and archiving of integrative models [77].

Highlights.

• Approaches to integrative modeling of protein complexes and genomic assemblies.

• Advances in experimental and computational methods help integrative structure determination of cellular assemblies

• Multiple models provide insights into dynamics and structural variations of cellular assemblies.

• Recent examples of integrative modelling.