Evolutionary tabu search strategies for the simultaneous registration of multiple atomic structures in cryo-EM reconstructions

An Overview on the Latest Nature-Inspired and Metaheuristics-Based Image Registration Algorithms

The development of automated image registration (IR) methods is a well-known issue within the computer vision (CV) field and it has been largely addressed from multiple viewpoints. IR has been applied to a high number of real-world scenarios ranging from remote sensing to medical imaging, artificial vision, and computer-aided design. In the last two decades, there has been an outstanding interest in the application of new optimization approaches for dealing with the main drawbacks present in the early IR methods, e.g., the Iterative Closest Point (ICP) algorithm. In particular, nature-inspired computation, e.g., evolutionary computation (EC), provides computational models that have their origin in evolution theories of nature. Moreover, other general purpose algorithms known as metaheuristics are also considered in this category of methods. Both nature-inspired and metaheuristic algorithms have been extensively adopted for tackling the IR problem, thus becoming a reliable alternative for optimization purposes. In this contribution, we aim to perform a comprehensive overview of the last decade (2009–2019) regarding the successful usage of this family of optimization approaches when facing the IR problem. Specifically, twenty-four methods (around 16 percent) of more than one hundred and fifty different contributions in the state-of-the-art have been selected. Several enhancements have been accordingly provided based on the promising outcomes shown by specific algorithmic designs. Finally, our research has shown that the field of nature-inspired and metaheuristic algorithms has increased its interest in the last decade to address the IR problem, and it has been highlighted that there is still room for improvement.

From Optimization to Mapping: An Evolutionary Algorithm for Protein Energy Landscapes

Stochastic search is often the only viable option to address complex optimization problems. Recently, evolutionary algorithms have been shown to handle challenging continuous optimization problems related to protein structure modeling. Building on recent work in our laboratories, we propose an evolutionary algorithm for efficiently mapping the multi-basin energy landscapes of dynamic proteins that switch between thermodynamically stable or semi-stable structural states to regulate their biological activity in the cell. The proposed algorithm balances computational resources between exploration and exploitation of the nonlinear, multimodal landscapes that characterize multi-state proteins via a novel combination of global and local search to generate a dynamically-updated, information-rich map of a protein's energy landscape. This new mapping-oriented EA is applied to several dynamic proteins and their disease-implicated variants to illustrate its ability to map complex energy landscapes in a computationally feasible manner. We further show that, given the availability of such maps, comparison between the maps of wildtype and variants of a protein allows for the formulation of a structural and thermodynamic basis for the impact of sequence mutations on dysfunction that may prove useful in guiding further wet-laboratory investigations of dysfunction and molecular interventions.

ChromEMT: Visualizing 3D chromatin structure and compaction in interphase and mitotic cells

The chromatin structure of DNA determines genome compaction and activity in the nucleus. On the basis of in vitro structures and electron microscopy (EM) studies, the hierarchical model is that 11-nanometer DNA-nucleosome polymers fold into 30- and subsequently into 120- and 300- to 700-nanometer fibers and mitotic chromosomes. To visualize chromatin in situ, we identified a fluorescent dye that stains DNA with an osmiophilic polymer and selectively enhances its contrast in EM. Using ChromEMT (ChromEM tomography), we reveal the ultrastructure and three-dimensional (3D) organization of individual chromatin polymers, megabase domains, and mitotic chromosomes. We show that chromatin is a disordered 5- to 24-nanometer-diameter curvilinear chain that is packed together at different 3D concentration distributions in interphase and mitosis. Chromatin chains have many different particle arrangements and bend at various lengths to achieve structural compaction and high packing densities.

Framework for 3D histologic reconstruction and fusion with in vivo MRI: Preliminary results of characterizing pulmonary inflammation in a mouse model

PURPOSE

Pulmonary inflammation is associated with a variety of diseases. Assessing pulmonary inflammation on in vivo imaging may facilitate the early detection and treatment of lung diseases. Although routinely used in thoracic imaging, computed tomography has thus far not been compellingly shown to characterize inflammation in vivo. Alternatively, magnetic resonance imaging (MRI) is a nonionizing radiation technique to better visualize and characterize pulmonary tissue. Prior to routine adoption of MRI for early characterization of inflammation in humans, a rigorous and quantitative characterization of the utility of MRI to identify inflammation is required. Such characterization may be achieved by considering ex vivo histology as the ground truth, since it enables the definitive spatial assessment of inflammation. In this study, the authors introduce a novel framework to integrate 2D histology, ex vivo and in vivo imaging to enable the mapping of the extent of disease from ex vivo histology onto in vivo imaging, with the goal of facilitating computerized feature analysis and interrogation of disease appearance on in vivo imaging. The authors' framework was evaluated in a preclinical preliminary study aimed to identify computer extracted features on in vivo MRI associated with chronic pulmonary inflammation.

METHODS

The authors' image analytics framework first involves reconstructing the histologic volume in 3D from individual histology slices. Second, the authors map the disease ground truth onto in vivo MRI via coregistration with 3D histology using the ex vivo lung MRI as a conduit. Finally, computerized feature analysis of the disease extent is performed to identify candidate in vivo imaging signatures of disease presence and extent.

RESULTS

The authors evaluated the framework by assessing the quality of the 3D histology reconstruction and the histology-MRI fusion, in the context of an initial use case involving characterization of chronic inflammation in a mouse model. The authors' evaluation considered three mice, two with an inflammation phenotype and one control. The authors' iterative 3D histology reconstruction yielded a 70.1% ± 2.7% overlap with the ex vivo MRI volume. Across a total of 17 anatomic landmarks manually delineated at the division of airways, the target registration error between the ex vivo MRI and 3D histology reconstruction was 0.85 ± 0.44 mm, suggesting that a good alignment of the ex vivo 3D histology and ex vivo MRI had been achieved. The 3D histology-in vivo MRI coregistered volumes resulted in an overlap of 73.7% ± 0.9%. Preliminary computerized feature analysis was performed on an additional four control mice, for a total of seven mice considered in this study. Gabor texture filters appeared to best capture differences between the inflamed and noninflamed regions on MRI.

CONCLUSIONS

The authors' 3D histology reconstruction and multimodal registration framework were successfully employed to reconstruct the histology volume of the lung and fuse it with in vivo MRI to create a ground truth map for inflammation on in vivo MRI. The analytic platform presented here lays the framework for a rigorous validation of the identified imaging features for chronic lung inflammation on MRI in a large prospective cohort.

Principles and Overview of Sampling Methods for Modeling Macromolecular Structure and Dynamics

Investigation of macromolecular structure and dynamics is fundamental to understanding how macromolecules carry out their functions in the cell. Significant advances have been made toward this end in silico, with a growing number of computational methods proposed yearly to study and simulate various aspects of macromolecular structure and dynamics. This review aims to provide an overview of recent advances, focusing primarily on methods proposed for exploring the structure space of macromolecules in isolation and in assemblies for the purpose of characterizing equilibrium structure and dynamics. In addition to surveying recent applications that showcase current capabilities of computational methods, this review highlights state-of-the-art algorithmic techniques proposed to overcome challenges posed in silico by the disparate spatial and time scales accessed by dynamic macromolecules. This review is not meant to be exhaustive, as such an endeavor is impossible, but rather aims to balance breadth and depth of strategies for modeling macromolecular structure and dynamics for a broad audience of novices and experts.

γ-TEMPy: Simultaneous Fitting of Components in 3D-EM Maps of Their Assembly Using a Genetic Algorithm

We have developed a genetic algorithm for building macromolecular complexes using only a 3D-electron microscopy density map and the atomic structures of the relevant components. For efficient sampling the method uses map feature points calculated by vector quantization. The fitness function combines a mutual information score that quantifies the goodness of fit with a penalty score that helps to avoid clashes between components. Testing the method on ten assemblies (containing 3–8 protein components) and simulated density maps at 10, 15, and 20 Å resolution resulted in identification of the correct topology in 90%, 70%, and 60% of the cases, respectively. We further tested it on four assemblies with experimental maps at 7.2–23.5 Å resolution, showing the ability of the method to identify the correct topology in all cases. We have also demonstrated the importance of the map feature-point quality on assembly fitting in the lack of additional experimental information.

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γ-TEMPy uses a genetic algorithm to fit multiple components into 3D-EM density maps

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The fitness score is a combination of a Mutual Information score and a clash penalty

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Efficient sampling is aided by using map feature points from vector quantization

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Native topologies for assemblies containing up to eight components can be predicted

Numerical geometry of map and model assessment

We are describing best practices and assessment strategies for the atomic interpretation of cryo-electron microscopy (cryo-EM) maps. Multiscale numerical geometry strategies in the Situs package and in secondary structure detection software are currently evolving due to the recent increases in cryo-EM resolution. Criteria that aim to predict the accuracy of fitted atomic models at low (worse than 8Å) and medium (4-8 Å) resolutions remain challenging. However, a high level of confidence in atomic models can be achieved by combining such criteria. The observed errors are due to map-model discrepancies and due to the effect of imperfect global docking strategies. Extending the earlier motion capture approach developed for flexible fitting, we use simulated fiducials (pseudoatoms) at varying levels of coarse-graining to track the local drift of structural features. We compare three tracking approaches: naïve vector quantization, a smoothly deformable model, and a tessellation of the structure into rigid Voronoi cells, which are fitted using a multi-fragment refinement approach. The lowest error is an upper bound for the (small) discrepancy between the crystal structure and the EM map due to different conditions in their structure determination. When internal features such as secondary structures are visible in medium-resolution EM maps, it is possible to extend the idea of point-based fiducials to more complex geometric representations such as helical axes, strands, and skeletons. We propose quantitative strategies to assess map-model pairs when such secondary structure patterns are prominent.

Conformational States of macromolecular assemblies explored by integrative structure calculation

A detailed description of macromolecular assemblies in multiple conformational states can be very valuable for understanding cellular processes. At present, structural determination of most assemblies in different biologically relevant conformations cannot be achieved by a single technique and thus requires an integrative approach that combines information from multiple sources. Different techniques require different computational methods to allow efficient and accurate data processing and analysis. Here, we summarize the latest advances and future challenges in computational methods that help the interpretation of data from two techniques—mass spectrometry and three-dimensional cryo-electron microscopy (with focus on alignment and classification of heterogeneous subtomograms from cryo-electron tomography). We evaluate how new developments in these two broad fields will lead to further integration with atomic structures to broaden our picture of the dynamic behavior of assemblies in their native environment.

Modeling, docking, and fitting of atomic structures to 3D maps from cryo-electron microscopy

Electron microscopy (EM) and image analysis offer an effective approach for determining the three-dimensional structure of macromolecular complexes. The versatility of these methods means that molecular species not normally amenable to other structural methods, e.g., X-ray crystallography and NMR spectroscopy, can be analyzed. However, the resolution of EM structures is often too low to provide an atomic model directly by chain tracing. Instead, a combination of modeling and fitting can be an effective way to analyze the EM structure at an atomic level, thus allowing localization of subunits or evaluation of conformational changes. Here we describe the steps involved in this process: building a homology model, fitting this model to an EM map, and using computational methods for docking of additional domains to the model. As an example, we illustrate the methods using an integral membrane protein, CopA, which functions to pump copper across the membrane in an ATP-dependent manner. In this example, we build a homology model based on the published atomic coordinates for a related calcium pump from sarcoplasmic reticulum (SERCA). After fitting this homology model to a 17 Å resolution EM map, computational software is used to dock a metal-binding domain (MBD) that is unique to the copper pump. Although this software identifies a number of plausible interfaces for docking, the constraints of the EM map steer us to select a unique solution. Thus, the synergy of these two methods allows us to describe both the location of the unknown MBD relative to the other cytoplasmic domains and the atomic details of the domain interface.

Conventions and workflows for using Situs

Situs is a modular program package for the multi-scale modeling of atomic resolution structures and low-resolution biophysical data from electron microscopy, tomography or small-angle X-ray scattering. This article provides an overview of recent developments in the Situs package, with an emphasis on workflows and conventions that are important for practical applications. The modular design of the programs facilitates scripting in the bash shell that allows specific programs to be combined in creative ways that go beyond the original intent of the developers. Several scripting-enabled functionalities, such as flexible transformations of data type, the use of symmetry constraints or the creation of two-dimensional projection images, are described. The processing of low-resolution biophysical maps in such workflows follows not only first principles but often relies on implicit conventions. Situs conventions related to map formats, resolution, correlation functions and feature detection are reviewed and summarized. The compatibility of the Situs workflow with CCP4 conventions and programs is discussed.

Automated tracing of filaments in 3D electron tomography reconstructions using Sculptor and Situs

The molecular graphics program Sculptor and the command-line suite Situs are software packages for the integration of biophysical data across spatial resolution scales. Herein, we provide an overview of recently developed tools relevant to cryo-electron tomography (cryo-ET), with an emphasis on functionality supported by Situs 2.7.1 and Sculptor 2.1.1. We describe a work flow for automatically segmenting filaments in cryo-ET maps including denoising, local normalization, feature detection, and tracing. Tomograms of cellular actin networks exhibit both cross-linked and bundled filament densities. Such filamentous regions in cryo-ET data sets can then be segmented using a stochastic template-based search, VolTrac. The approach combines a genetic algorithm and a bidirectional expansion with a tabu search strategy to localize and characterize filamentous regions. The automated filament segmentation by VolTrac compares well to a manual one performed by expert users, and it allows an efficient and reproducible analysis of large data sets. The software is free, open source, and can be used on Linux, Macintosh or Windows computers.

Evolutionary bidirectional expansion for the tracing of alpha helices in cryo-electron microscopy reconstructions

Cryo-electron microscopy (cryo-EM) enables the imaging of macromolecular complexes in near-native environments at resolutions that often permit the visualization of secondary structure elements. For example, alpha helices frequently show consistent patterns in volumetric maps, exhibiting rod-like structures of high density. Here, we introduce VolTrac (Volume Tracer) - a novel technique for the annotation of alpha-helical density in cryo-EM data sets. VolTrac combines a genetic algorithm and a bidirectional expansion with a tabu search strategy to trace helical regions. Our method takes advantage of the stochastic search by using a genetic algorithm to identify optimal placements for a short cylindrical template, avoiding exploration of already characterized tabu regions. These placements are then utilized as starting positions for the adaptive bidirectional expansion that characterizes the curvature and length of the helical region. The method reliably predicted helices with seven or more residues in experimental and simulated maps at intermediate (4-10Å) resolution. The observed success rates, ranging from 70.6% to 100%, depended on the map resolution and validation parameters. For successful predictions, the helical axes were located within 2Å from known helical axes of atomic structures.

Using Sculptor and Situs for simultaneous assembly of atomic components into low-resolution shapes

We describe an integrated software system called Sculptor that combines visualization capabilities with molecular modeling algorithms for the analysis of multi-scale data sets. Sculptor features extensive special purpose visualization techniques that are based on modern GPU programming and are capable of representing complex molecular assemblies in real-time. The integration of graphics and modeling offers several advantages. The user interface not only eases the usually steep learning curve of pure algorithmic techniques, but it also permits instant analysis and post-processing of results, as well as the integration of results from external software. Here, we implemented an interactive peak-selection strategy that enables the user to explore a preliminary score landscape generated by the colors tool of Situs. The interactive placement of components, one at a time, is advantageous for low-resolution or ambiguously shaped maps, which are sometimes difficult to interpret by the fully automatic peak selection of colors. For the subsequent refinement of the preliminary models resulting from both interactive and automatic peak selection, we have implemented a novel simultaneous multi-body docking in Sculptor and Situs that softly enforces shape complementarities between components using the normalization of the cross-correlation coefficient. The proposed techniques are freely available in Situs version 2.6 and Sculptor version 2.0.