Determining protein complex structures based on a Bayesian model of in vivo Förster resonance energy transfer (FRET) data.

The use of in vivo Förster resonance energy transfer (FRET) data to determine the molecular architecture of a protein complex in living cells is challenging due to data sparseness, sample heterogeneity, signal contributions from multiple donors and acceptors, unequal fluorophore brightness, photobleaching, flexibility of the linker connecting the fluorophore to the tagged protein, and spectral cross-talk. We addressed these challenges by using a Bayesian approach that produces the posterior probability of a model, given the input data. The posterior probability is defined as a function of the dependence of our FRET metric FRETR on a structure (forward model), a model of noise in the data, as well as prior information about the structure, relative populations of distinct states in the sample, forward model parameters, and data noise. The forward model was validated against kinetic Monte Carlo simulations and in vivo experimental data collected on nine systems of known structure. In addition, our Bayesian approach was validated by a benchmark of 16 protein complexes of known structure. Given the structures of each subunit of the complexes, models were computed from synthetic FRETR data with a distance root-mean-squared deviation error of 14 to 17 Å. The approach is implemented in the open-source Integrative Modeling Platform, allowing us to determine macromolecular structures through a combination of in vivo FRETR data and data from other sources, such as electron microscopy and chemical cross-linking.

Putting the pieces together: integrative modeling platform software for structure determination of macromolecular assemblies.

A set of software tools for building and distributing models of macromolecular assemblies uses an integrative structure modeling approach, which casts the building of models as a computational optimization problem where information is encoded into a scoring function used to evaluate candidate models.

Assembly of macromolecular complexes by satisfaction of spatial restraints from electron microscopy images.

To obtain a structural model of a macromolecular assembly by single-particle EM, a large number of particle images need to be collected, aligned, clustered, averaged, and finally assembled via reconstruction into a 3D density map. This process is limited by the number and quality of the particle images, the accuracy of the initial model, and the compositional and conformational heterogeneity. Here, we describe a structure determination method that avoids the reconstruction procedure. The atomic structures of the individual complex components are assembled by optimizing a match against 2D EM class-average images, an excluded volume criterion, geometric complementarity, and optional restraints from proteomics and chemical cross-linking experiments. The optimization relies on a simulated annealing Monte Carlo search and a divide-and-conquer message-passing algorithm. Using simulated and experimentally determined EM class averages for 12 and 4 protein assemblies, respectively, we show that a few class averages can indeed result in accurate models for complexes of as many as five subunits. Thus, integrative structural biology can now benefit from the relative ease with which the EM class averages are determined.

SAXS Merge: an automated statistical method to merge SAXS profiles using Gaussian processes.

Small-angle X-ray scattering (SAXS) is an experimental technique that allows structural information on biomolecules in solution to be gathered. High-quality SAXS profiles have typically been obtained by manual merging of scattering profiles from different concentrations and exposure times. This procedure is very subjective and results vary from user to user. Up to now, no robust automatic procedure has been published to perform this step, preventing the application of SAXS to high-throughput projects. Here, SAXS Merge, a fully automated statistical method for merging SAXS profiles using Gaussian processes, is presented. This method requires only the buffer-subtracted SAXS profiles in a specific order. At the heart of its formulation is non-linear interpolation using Gaussian processes, which provides a statement of the problem that accounts for correlation in the data.

Integrative spatiotemporal map of nucleocytoplasmic transport.

The Nuclear Pore Complex (NPC) facilitates rapid and selective nucleocytoplasmic transport of molecules as large as ribosomal subunits and viral capsids. It is not clear how key emergent properties of this transport arise from the system components and their interactions. To address this question, we constructed an integrative coarse-grained Brownian dynamics model of transport through a single NPC, followed by coupling it with a kinetic model of Ran-dependent transport in an entire cell. The microscopic model parameters were fitted to reflect experimental data and theoretical information regarding the transport, without making any assumptions about its emergent properties. The resulting reductionist model is validated by reproducing several features of transport not used for its construction, such as the morphology of the central transporter, rates of passive and facilitated diffusion as a function of size and valency, in situ radial distributions of pre-ribosomal subunits, and active transport rates for viral capsids. The model suggests that the NPC functions essentially as a virtual gate whose flexible phenylalanine-glycine (FG) repeat proteins raise an entropy barrier to diffusion through the pore. Importantly, this core functionality is greatly enhanced by several key design features, including 'fuzzy' and transient interactions, multivalency, redundancy in the copy number of FG nucleoporins, exponential coupling of transport kinetics and thermodynamics in accordance with the transition state theory, and coupling to the energy-reliant RanGTP concentration gradient. These design features result in the robust and resilient rate and selectivity of transport for a wide array of cargo ranging from a few kilodaltons to megadaltons in size. By dissecting these features, our model provides a quantitative starting point for rationally modulating the transport system and its artificial mimics.

Integrative structure modeling of macromolecular assemblies from proteomics data.

Proteomics techniques have been used to generate comprehensive lists of protein interactions in a number of species. However, relatively little is known about how these interactions result in functional multiprotein complexes. This gap can be bridged by combining data from proteomics experiments with data from established structure determination techniques. Correspondingly, integrative computational methods are being developed to provide descriptions of protein complexes at varying levels of accuracy and resolution, ranging from complex compositions to detailed atomic structures.

Prediction of enzymatic pathways by integrative pathway mapping.

The functions of most proteins are yet to be determined. The function of an enzyme is often defined by its interacting partners, including its substrate and product, and its role in larger metabolic networks. Here, we describe a computational method that predicts the functions of orphan enzymes by organizing them into a linear metabolic pathway. Given candidate enzyme and metabolite pathway members, this aim is achieved by finding those pathways that satisfy structural and network restraints implied by varied input information, including that from virtual screening, chemoinformatics, genomic context analysis, and ligand -binding experiments. We demonstrate this integrative pathway mapping method by predicting the L-gulonate catabolic pathway in Haemophilus influenzae Rd KW20. The prediction was subsequently validated experimentally by enzymology, crystallography, and metabolomics. Integrative pathway mapping by satisfaction of structural and network restraints is extensible to molecular networks in general and thus formally bridges the gap between structural biology and systems biology.

A package for exact kinetic data structures and sweepline algorithms.

In this paper we present a package for implementing exact kinetic data structures built on objects which move along polynomial trajectories. We discuss how the package design was influenced by various considerations, including extensibility, support for multiple kinetic data structures, access to existing data structures and algorithms in CGAL, as well as debugging. Due to the similarity between the operations involved, the software can also be used to compute arrangements of polynomial objects using a sweepline approach. The package consists of three main parts, the kinetic data structure framework support code, an algebraic kernel which implements the set of algebraic operations required for kinetic data structure processing, and kinetic data structures for Delaunay triangulations in one and two dimensions, and Delaunay and regular triangulations in three dimensions. The models provided for the algebraic kernel support both exact operations and inexact approximations with heuristics to improve numerical stability.

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.

Simple rules for passive diffusion through the nuclear pore complex.

Passive macromolecular diffusion through nuclear pore complexes (NPCs) is thought to decrease dramatically beyond a 30-60-kD size threshold. Using thousands of independent time-resolved fluorescence microscopy measurements in vivo, we show that the NPC lacks such a firm size threshold; instead, it forms a soft barrier to passive diffusion that intensifies gradually with increasing molecular mass in both the wild-type and mutant strains with various subsets of phenylalanine-glycine (FG) domains and different levels of baseline passive permeability. Brownian dynamics simulations replicate these findings and indicate that the soft barrier results from the highly dynamic FG repeat domains and the diffusing macromolecules mutually constraining and competing for available volume in the interior of the NPC, setting up entropic repulsion forces. We found that FG domains with exceptionally high net charge and low hydropathy near the cytoplasmic end of the central channel contribute more strongly to obstruction of passive diffusion than to facilitated transport, revealing a compartmentalized functional arrangement within the NPC.

Topological models of heteromeric protein assemblies from mass spectrometry: application to the yeast eIF3:eIF5 complex.

Describing, understanding, and modulating the function of the cell require elucidation of the structures of macromolecular assemblies. Here, we describe an integrative method for modeling heteromeric complexes using as a starting point disassembly pathways determined by native mass spectrometry (MS). In this method, the pathway data and other available information are encoded as a scoring function on the positions of the subunits of the complex. The method was assessed on its ability to reproduce the native contacts in five benchmark cases with simulated MS data and two cases with real MS data. To illustrate the power of our method, we purified the yeast initiation factor 3 (eIF3) complex and characterized it by native MS and chemical crosslinking MS. We established substoichiometric binding of eIF5 and derived a model for the five-subunit eIF3 complex, at domain level, consistent with its role as a scaffold for other initiation factors.

Modeling of proteins and their assemblies with the Integrative Modeling Platform.

To understand the workings of the living cell, we need to characterize protein assemblies that constitute the cell (for example, the ribosome, 26S proteasome, and the nuclear pore complex). A reliable high-resolution structural characterization of these assemblies is frequently beyond the reach of current experimental methods, such as X-ray crystallography, NMR spectroscopy, electron microscopy, footprinting, chemical cross-linking, FRET spectroscopy, small angle X-ray scattering, and proteomics. However, the information garnered from different methods can be combined and used to build models of the assembly structures that are consistent with all of the available datasets, and therefore more accurate, precise, and complete. Here, we describe a protocol for this integration, whereby the information is converted to a set of spatial restraints and a variety of optimization procedures can be used to generate models that satisfy the restraints as well as possible. These generated models can then potentially inform about the precision and accuracy of structure determination, the accuracy of the input datasets, and further data generation. We also demonstrate the Integrative Modeling Platform (IMP) software, which provides the necessary computational framework to implement this protocol, and several applications for specific use cases.

Modeling of proteins and their assemblies with the integrative modeling platform.

To understand the workings of the living cell, we need to characterize protein assemblies that constitute the cell (for example, the ribosome, 26S proteasome, and the nuclear pore complex). A reliable high-resolution structural characterization of these assemblies is frequently beyond the reach of current experimental methods, such as X-ray crystallography, NMR spectroscopy, electron microscopy, footprinting, chemical cross-linking, FRET spectroscopy, small-angle X-ray scattering, and proteomics. However, the information garnered from different methods can be combined and used to build computational models of the assembly structures that are consistent with all of the available datasets. Here, we describe a protocol for this integration, whereby the information is converted to a set of spatial restraints and a variety of optimization procedures can be used to generate models that satisfy the restraints as much as possible. These generated models can then potentially inform about the precision and accuracy of structure determination, the accuracy of the input datasets, and further data generation. We also demonstrate the Integrative Modeling Platform (IMP) software, which provides the necessary computational framework to implement this protocol, and several applications for specific-use cases.

The structural dynamics of macromolecular processes.

Dynamic processes involving macromolecular complexes are essential to cell function. These processes take place over a wide variety of length scales from nanometers to micrometers, and over time scales from nanoseconds to minutes. As a result, information from a variety of different experimental and computational approaches is required. We review the relevant sources of information and introduce a framework for integrating the data to produce representations of dynamic processes.

Automated crystallographic ligand building using the medial axis transform of an electron-density isosurface.

Automatic fitting methods that build molecules into electron-density maps usually fail below 3.5 A resolution. As a first step towards addressing this problem, an algorithm has been developed using an approximation of the medial axis to simplify an electron-density isosurface. This approximation captures the central axis of the isosurface with a graph which is then matched against a graph of the molecular model. One of the first applications of the medial axis to X-ray crystallography is presented here. When applied to ligand fitting, the method performs at least as well as methods based on selecting peaks in electron-density maps. Generalization of the method to recognition of common features across multiple contour levels could lead to powerful automatic fitting methods that perform well even at low resolution.