Assessment of scoring functions to rank the quality of 3D subtomogram clusters from cryo-electron tomography.

Cryo-electron tomography provides the opportunity for unsupervised discovery of endogenous complexes in situ. This process usually requires particle picking, clustering and alignment of subtomograms to produce an average structure of the complex. When applied to heterogeneous samples, template-free clustering and alignment of subtomograms can potentially lead to the discovery of structures for unknown endogenous complexes. However, such methods require scoring functions to measure and accurately rank the quality of aligned subtomogram clusters, which can be compromised by contaminations from misclassified complexes and alignment errors. Here, we provide the first study to assess the effectiveness of more than 15 scoring functions for evaluating the quality of subtomogram clusters, which differ in the amount of structural misalignments and contaminations due to misclassified complexes. We assessed both experimental and simulated subtomograms as ground truth data sets. Our analysis showed that the robustness of scoring functions varies largely. Most scores were sensitive to the signal-to-noise ratio of subtomograms and often required Gaussian filtering as preprocessing for improved performance. Two scoring functions, Spectral SNR-based Fourier Shell Correlation and Pearson Correlation in the Fourier domain with missing wedge correction, showed a robust ranking of subtomogram clusters without any preprocessing and irrespective of SNR levels of subtomograms. Of these two scoring functions, Spectral SNR-based Fourier Shell Correlation was fastest to compute and is a better choice for handling large numbers of subtomograms. Our results provide a guidance for choosing an accurate scoring function for template-free approaches to detect complexes from heterogeneous samples.

Self-adaptive multiscaling algorithm for efficient simulations of many-protein systems in crowded conditions.

A method is described for the efficient simulation of multiprotein systems in crowded environments. It is based on an adaptive, reversible structural coarsening algorithm that preserves relevant physical features of the proteins across scales. Water is treated implicitly whereas all the other components of the aqueous solution, such as ions, cosolutes, or osmolytes, are treated in atomic detail. The focus is on the analytical adaptation of the solvent model to different levels of molecular resolutions, which allows continuous, on-the-fly transitions between scales. This permits the analytical calculation of forces during dynamics and preserves detailed balance in Monte Carlo simulations. A major computational speedup can be achieved in systems containing hundreds of proteins without cutting off the long-range interactions. The method can be combined with a self-adaptive configurational-bias sampling technique described previously, designed to detect strong, weak, or ultra-weak protein associations and shown to improve sampling efficiency and convergence. The implementation aims to simulate early stages of multimeric complexation, aggregation, or self-assembly. The method can be adopted as the basis for a more general algorithm to identify vertices, edges, and hubs in protein interaction networks or to predict critical steps in signal transduction pathways.

TomoMiner and TomoMinerCloud: A Software Platform for Large-Scale Subtomogram Structural Analysis.

Cryo-electron tomography (cryo-ET) captures the 3D electron density distribution of macromolecular complexes in close to native state. With the rapid advance of cryo-ET acquisition technologies, it is possible to generate large numbers (>100,000) of subtomograms, each containing a macromolecular complex. Often, these subtomograms represent a heterogeneous sample due to variations in the structure and composition of a complex in situ form or because particles are a mixture of different complexes. In this case subtomograms must be classified. However, classification of large numbers of subtomograms is a time-intensive task and often a limiting bottleneck. This paper introduces an open source software platform, TomoMiner, for large-scale subtomogram classification, template matching, subtomogram averaging, and alignment. Its scalable and robust parallel processing allows efficient classification of tens to hundreds of thousands of subtomograms. In addition, TomoMiner provides a pre-configured TomoMinerCloud computing service permitting users without sufficient computing resources instant access to TomoMiners high-performance features.

Directional Force Originating from ATP Hydrolysis Drives the GroEL Conformational Change.

Protein functional mechanisms usually require conformational changes, and often there are known structures for the different conformational states. However, usually neither the origin of the driving force nor the underlying pathways for these conformational transitions is known. Exothermic chemical reactions may be an important source of forces that drive conformational changes. Here we investigate this type of force originating from ATP hydrolysis in the chaperonin GroEL, by applying forces originating from the chemical reaction. Specifically, we apply directed forces to drive the GroEL conformational changes and learn that there is a highly specific direction for applied forces to drive the closed form to the open form. For this purpose, we utilize coarse-grained elastic network models. Principal component analysis on 38 GroEL experimental structures yields the most important motions, and these are used in structural interpolation for the construction of a coarse-grained free energy landscape. In addition, we investigate a more random application of forces with a Monte Carlo method and demonstrate pathways for the closed-open conformational transition in both directions by computing trajectories that are shown upon the free energy landscape. Initial root mean square deviation (RMSD) between the open and closed forms of the subunit is 14.7 Å and final forms from our simulations reach an average RMSD of 3.6 Å from the target forms, closely matching the level of resolution of the coarse-grained model.

Refinement of atomic models in high resolution EM reconstructions using Flex-EM and local assessment.

As the resolutions of Three Dimensional Electron Microscopic reconstructions of biological macromolecules are being improved, there is a need for better fitting and refinement methods at high resolutions and robust approaches for model assessment. Flex-EM/MODELLER has been used for flexible fitting of atomic models in intermediate-to-low resolution density maps of different biological systems. Here, we demonstrate the suitability of the method to successfully refine structures at higher resolutions (2.5-4.5Å) using both simulated and experimental data, including a newly processed map of Apo-GroEL. A hierarchical refinement protocol was adopted where the rigid body definitions are relaxed and atom displacement steps are reduced progressively at successive stages of refinement. For the assessment of local fit, we used the SMOC (segment-based Manders' overlap coefficient) score, while the model quality was checked using the Qmean score. Comparison of SMOC profiles at different stages of refinement helped in detecting regions that are poorly fitted. We also show how initial model errors can have significant impact on the goodness-of-fit. Finally, we discuss the implementation of Flex-EM in the CCP-EM software suite.

Features of large hinge-bending conformational transitions. Prediction of closed structure from open state.

We performed a detailed analysis of conformational transition pathways for a set of 10 proteins, which undergo large hinge-bending-type motions with 4-12 Å RMSD (root mean-square distance) between open and closed crystal structures. Anisotropic network model-Monte Carlo (ANM-MC) algorithm generates a targeted pathway between two conformations, where the collective modes from the ANM are used for deformation at each iteration and the conformational energy of the deformed structure is minimized via an MC algorithm. The target structure was approached successfully with an RMSD of 0.9-4.1 Å when a relatively low cutoff radius of 10 Å was used in ANM. Even though one predominant mode (first or second) directed the open-to-closed conformational transition, changes in the dominant mode character were observed for most cases along the transition. By imposing radius of gyration constraint during mode selection, it was possible to predict the closed structure for eight out of 10 proteins (with initial 4.1-7.1 Å and final 1.7-2.9 Å RMSD to target). Deforming along a single mode leads to most successful predictions. Based on the previously reported free energy surface of adenylate kinase, deformations along the first mode produced an energetically favorable path, which was interestingly facilitated by a change in mode shape (resembling second and third modes) at key points. Pathway intermediates are provided in our database of conformational transitions (http://safir.prc.boun.edu.tr/anmmc/method/1).

Perturbation-based Markovian transmission model for probing allosteric dynamics of large macromolecular assembling: a study of GroEL-GroES.

Large macromolecular assemblies are often important for biological processes in cells. Allosteric communications between different parts of these molecular machines play critical roles in cellular signaling. Although studies of the topology and fluctuation dynamics of coarse-grained residue networks can yield important insights, they do not provide characterization of the time-dependent dynamic behavior of these macromolecular assemblies. Here we develop a novel approach called Perturbation-based Markovian Transmission (PMT) model to study globally the dynamic responses of the macromolecular assemblies. By monitoring simultaneous responses of all residues (>8,000) across many (>6) decades of time spanning from the initial perturbation until reaching equilibrium using a Krylov subspace projection method, we show that this approach can yield rich information. With criteria based on quantitative measurements of relaxation half-time, flow amplitude change, and oscillation dynamics, this approach can identify pivot residues that are important for macromolecular movement, messenger residues that are key to signal mediating, and anchor residues important for binding interactions. Based on a detailed analysis of the GroEL-GroES chaperone system, we found that our predictions have an accuracy of 71-84% judged by independent experimental studies reported in the literature. This approach is general and can be applied to other large macromolecular machineries such as the virus capsid and ribosomal complex.

Protein structure fitting and refinement guided by cryo-EM density.

For many macromolecular assemblies, both a cryo-electron microscopy map and atomic structures of its component proteins are available. Here we describe a method for fitting and refining a component structure within its map at intermediate resolution (<15 A). The atomic positions are optimized with respect to a scoring function that includes the crosscorrelation coefficient between the structure and the map as well as stereochemical and nonbonded interaction terms. A heuristic optimization that relies on a Monte Carlo search, a conjugate-gradients minimization, and simulated annealing molecular dynamics is applied to a series of subdivisions of the structure into progressively smaller rigid bodies. The method was tested on 15 proteins of known structure with 13 simulated maps and 3 experimentally determined maps. At approximately 10 A resolution, Calpha rmsd between the initial and final structures was reduced on average by approximately 53%. The method is automated and can refine both experimental and predicted atomic structures.

Markov methods for hierarchical coarse-graining of large protein dynamics.

Elastic network models (ENMs) and, in particular, the Gaussian Network Model (GNM) have been widely used in recent years to gain insights into the machinery of proteins. The extension of ENMs to supramolecular assemblies presents computational challenges, because of the difficulty in retaining atomic details in mode decomposition of large protein dynamics. Here, we present a novel approach to address this problem. We rely on the premise that, all the residues of the protein machinery (network) must communicate with each other and operate in a coordinated manner to perform their function successfully. To gain insight into the mechanism of information transfer between residues, we study a Markov model of network communication. Using the Markov chain perspective, we map the full-atom network representation into a hierarchy of ENMs of decreasing resolution, perform analysis of dominant communication (or dynamic) patterns in reduced space(s) and reconstruct the detailed models with minimal loss of information. The communication properties at different levels of the hierarchy are intrinsically defined by the network topology. This new representation has several features, including: soft clustering of the protein structure into stochastically coherent regions thus providing a useful assessment of elements serving as hubs and/or transmitters in propagating information/interaction; automatic computation of the contact matrices for ENMs at each level of the hierarchy to facilitate computation of both Gaussian and anisotropic fluctuation dynamics. We illustrate the utility of the hierarchical decomposition in providing an insightful description of the supramolecular machinery by applying the methodology to the chaperonin GroEL-GroES.

Markov propagation of allosteric effects in biomolecular systems: application to GroEL-GroES.

We introduce a novel approach for elucidating the potential pathways of allosteric communication in biomolecular systems. The methodology, based on Markov propagation of 'information' across the structure, permits us to partition the network of interactions into soft clusters distinguished by their coherent stochastics. Probabilistic participation of residues in these clusters defines the communication patterns inherent to the network architecture. Application to bacterial chaperonin complex GroEL-GroES, an allostery-driven structure, identifies residues engaged in intra- and inter-subunit communication, including those acting as hubs and messengers. A number of residues are distinguished by their high potentials to transmit allosteric signals, including Pro33 and Thr90 at the nucleotide-binding site and Glu461 and Arg197 mediating inter- and intra-ring communication, respectively. We propose two most likely pathways of signal transmission, between nucleotide- and GroES-binding sites across the cis and trans rings, which involve several conserved residues. A striking observation is the opposite direction of information flow within cis and trans rings, consistent with negative inter-ring cooperativity. Comparison with collective modes deduced from normal mode analysis reveals the propensity of global hinge regions to act as messengers in the transmission of allosteric signals.

Normal mode analysis of proteins: a comparison of rigid cluster modes with C(alpha) coarse graining.

The ability to infer dynamic motions from an equilibrium (static) conformation of a protein can be essential in establishing structure-function relationships. In particular, the low-frequency motions are of functional interest because statistical mechanics predicts these motions will have the largest amplitudes. In this paper, we address the computational cost of normal mode analysis (NMA) applied to a C(alpha)-based elastic network model (C(alpha)-NMA) and present a new coarse-grained rigid-body-based analysis (cluster-NMA). This new method represents a protein as a collection of rigid bodies interconnected with harmonic potentials. This representation produces reduced degree-of-freedom (DOF) equations of motion (EOMs) which, even in the case of large structures (10(3+) residues), enables the computation of normal modes to be done on a desktop PC. We present the complete theory and analysis of cluster-NMA and also include its application to a variety of structures. The results of the new method are compared with C(alpha)-NMA and it is shown that cluster-NMA produces very good approximations to the lowest modes at a fraction of the computational cost.