Untangling Irregular Actin Cytoskeleton Architectures in Tomograms of the Cell with Struwwel Tracer.

In this work, we established, validated, and optimized a novel computational framework for tracing arbitrarily oriented actin filaments in cryo-electron tomography maps. Our approach was designed for highly complex intracellular architectures in which a long-range cytoskeleton network extends throughout the cell bodies and protrusions. The irregular organization of the actin network, as well as cryo-electron-tomography-specific noise, missing wedge artifacts, and map dimensions call for a specialized implementation that is both robust and efficient. Our proposed solution, Struwwel Tracer, accumulates densities along paths of a specific length in various directions, starting from locally determined seed points. The highest-density paths originating from the seed points form short linear candidate filament segments, which are further scrutinized and classified by users via inspection of a novel pruning map, which visualizes the likelihood of being a part of longer filaments. The pruned linear candidate filament segments are then iteratively fused into continuous, longer, and curved filaments based on their relative orientations, gap spacings, and extendibility. When applied to the simulated phantom tomograms of a Dictyostelium discoideum filopodium under experimental conditions, Struwwel Tracer demonstrated high efficacy, with F1-scores ranging from 0.85 to 0.90, depending on the noise level. Furthermore, when applied to a previously untraced experimental tomogram of mouse fibroblast lamellipodia, the filaments predicted by Struwwel Tracer exhibited a good visual agreement with the experimental map. The Struwwel Tracer framework is highly time efficient and can complete the tracing process in just a few minutes. The source code is publicly available with version 3.2 of the free and open-source Situs software package.

Spaghetti Tracer: A Framework for Tracing Semiregular Filamentous Densities in 3D Tomograms.

Within cells, cytoskeletal filaments are often arranged into loosely aligned bundles. These fibrous bundles are dense enough to exhibit a certain regularity and mean direction, however, their packing is not sufficient to impose a symmetry between-or specific shape on-individual filaments. This intermediate regularity is computationally difficult to handle because individual filaments have a certain directional freedom, however, the filament densities are not well segmented from each other (especially in the presence of noise, such as in cryo-electron tomography). In this paper, we develop a dynamic programming-based framework, Spaghetti Tracer, to characterizing the structural arrangement of filaments in the challenging 3D maps of subcellular components. Assuming that the tomogram can be rotated such that the filaments are oriented in a mean direction, the proposed framework first identifies local seed points for candidate filament segments, which are then grown from the seeds using a dynamic programming algorithm. We validate various algorithmic variations of our framework on simulated tomograms that closely mimic the noise and appearance of experimental maps. As we know the ground truth in the simulated tomograms, the statistical analysis consisting of precision, recall, and F1 scores allows us to optimize the performance of this new approach. We find that a bipyramidal accumulation scheme for path density is superior to straight-line accumulation. In addition, the multiplication of forward and backward path densities provides for an efficient filter that lifts the filament density above the noise level. Resulting from our tests is a robust method that can be expected to perform well (F1 scores 0.86-0.95) under experimental noise conditions.

Refinement of AlphaFold2 models against experimental and hybrid cryo-EM density maps.

Recent breakthroughs in deep learning-based protein structure prediction show that it is possible to obtain highly accurate models for a wide range of difficult protein targets for which only the amino acid sequence is known. The availability of accurately predicted models from sequences can potentially revolutionise many modelling approaches in structural biology, including the interpretation of cryo-EM density maps. Although atomic structures can be readily solved from cryo-EM maps of better than 4 Å resolution, it is still challenging to determine accurate models from lower-resolution density maps. Here, we report on the benefits of models predicted by AlphaFold2 (the best-performing structure prediction method at CASP14) on cryo-EM refinement using the Phenix refinement suite for AlphaFold2 models. To study the robustness of model refinement at a lower resolution of interest, we introduced hybrid maps (i.e. experimental cryo-EM maps) filtered to lower resolutions by real-space convolution. The AlphaFold2 models were refined to attain good accuracies above 0.8 TM scores for 9 of the 13 cryo-EM maps. TM scores improved for AlphaFold2 models refined against all 13 cryo-EM maps of better than 4.5 Å resolution, 8 hybrid maps of 6 Å resolution, and 3 hybrid maps of 8 Å resolution. The results show that it is possible (at least with the Phenix protocol) to extend the refinement success below 4.5 Å resolution. We even found isolated cases in which resolution lowering was slightly beneficial for refinement, suggesting that high-resolution cryo-EM maps might sometimes trap AlphaFold2 models in local optima.

Mechanism for the Unfolding of the TOP7 Protein in Steered Molecular Dynamics Simulations as Revealed by Mutual Information Analysis.

We employed mutual information (MI) analysis to detect motions affecting the mechanical resistance of the human-engineered protein Top7. The results are based on the MI analysis of pair contact correlations measured in steered molecular dynamics (SMD) trajectories and their statistical dependence on global unfolding. This study is the first application of the MI analysis to SMD forced unfolding, and we furnish specific SMD recommendations for the utility of parameters and options in the TimeScapes package. The MI analysis provided a global overview of the effect of perturbation on the stability of the protein. We also employed a more conventional trajectory analysis for a detailed description of the mechanical resistance of Top7. Specifically, we investigated 1) the hydropathy of the interactions of structural segments, 2) the H2O concentration near residues relevant for unfolding, and 3) the changing hydrogen bonding patterns and main chain dihedral angles. The results show that the application of MI in the study of protein mechanical resistance can be useful for the engineering of more resistant mutants when combined with conventional analysis. We propose a novel mutation design based on the hydropathy of residues that would stabilize the unfolding region by mimicking its more stable symmetry mate. The proposed design process does not involve the introduction of covalent crosslinks, so it has the potential to preserve the conformational space and unfolding pathway of the protein.

TomoSim: Simulation of Filamentous Cryo-Electron Tomograms.

As automated filament tracing algorithms in cryo-electron tomography (cryo-ET) continue to improve, the validation of these approaches has become more incumbent. Having a known ground truth on which to base predictions is crucial to reliably test predicted cytoskeletal filaments because the detailed structure of the filaments in experimental tomograms is obscured by a low resolution, as well as by noise and missing Fourier space wedge artifacts. We present a software tool for the realistic simulation of tomographic maps (TomoSim) based on a known filament trace. The parameters of the simulated map are automatically matched to those of a corresponding experimental map. We describe the computational details of the first prototype of our approach, which includes wedge masking in Fourier space, noise color, and signal-to-noise matching. We also discuss current and potential future applications of the approach in the validation of concurrent filament tracing methods in cryo-ET.

Tracing Filaments in Simulated 3D Cryo-Electron Tomography Maps Using a Fast Dynamic Programming Algorithm.

We propose a fast, dynamic programming-based framework for tracing actin filaments in 3D maps of subcellular components in cryo-electron tomography. The approach can identify high-density filament segments in various orientations, but it takes advantage of the arrangement of actin filaments within cells into more or less tightly aligned bundles. Assuming that the tomogram can be rotated such that the filaments can be oriented to be directed in a dominant direction (i.e., the X, Y, or Z axis), the proposed framework first identifies local seed points that form the origin of candidate filament segments (CFSs), which are then grown from the seeds using a fast dynamic programming algorithm. The CFS length l can be tuned to the nominal resolution of the tomogram or the separation of desired features, or it can be used to restrict the curvature of filaments that deviate from the overall bundle direction. In subsequent steps, the CFSs are filtered based on backward tracing and path density analysis. Finally, neighboring CFSs are fused based on a collinearity criterion to bridge any noise artifacts in the 3D map that would otherwise fractionalize the tracing. We validate our proposed framework on simulated tomograms that closely mimic the features and appearance of experimental maps.

Cylindrical Similarity Measurement for Helices in Medium-Resolution Cryo-Electron Microscopy Density Maps.

Cryo-electron microscopy (cryo-EM) density maps at medium resolution (5-10 Å) reveal secondary structural features such as α-helices and ß-sheets, but they lack the side chain details that would enable a direct structure determination. Among the more than 800 entries in the Electron Microscopy Data Bank (EMDB) of medium-resolution density maps that are associated with atomic models, a wide variety of similarities can be observed between maps and models. To validate such atomic models and to classify structural features, a local similarity criterion, the F1 score, is proposed and evaluated in this study. The F1 score is theoretically normalized to a range from zero to one, providing a local measure of cylindrical agreement between the density and atomic model of a helix. A systematic scan of 30,994 helices (among 3,247 protein chains modeled into medium-resolution density maps) reveals an actual range of observed F1 scores from 0.171 to 0.848, suggesting that the cylindrical fit of the current data is well stratified by the proposed measure. The best (highest) F1 scores tend to be associated with regions that exhibit high and spatially homogeneous local resolution (between 5 Å and 7.5 Å) in the helical density. The proposed F1 scores can be used as a discriminative classifier for validation studies and as a ranking criterion for cryo-EM density features in databases.

Correction of Missing-Wedge Artifacts in Filamentous Tomograms by Template-Based Constrained Deconvolution.

Cryo-electron tomography maps often exhibit considerable noise and anisotropic resolution, due to the low-dose requirements and the missing wedge in Fourier space. These spurious features are visually unappealing and, more importantly, prevent an automated segmentation of geometric shapes, requiring a subjective and labor-intensive manual tracing. We developed a novel computational strategy for objectively denoising and correcting missing-wedge artifacts in homogeneous specimen areas of tomograms, where it is assumed that a template repeats itself across the volume under consideration, as happens in the case of filaments. In our deconvolution approach, we use a template and a map of corresponding template locations, allowing us to compensate for the information lost in the missing wedge. We applied the method to tomograms of actin-filament bundles of inner-ear stereocilia, which are critical for the senses of hearing and balance. In addition, we demonstrate that our method can be used for cell membrane detection.

A cryo-tomography-based volumetric model of the actin core of mouse vestibular hair cell stereocilia lacking plastin 1.

Electron cryo-tomography allows for high-resolution imaging of stereocilia in their native state. Because their actin filaments have a higher degree of order, we imaged stereocilia from mice lacking the actin crosslinker plastin 1 (PLS1). We found that while stereocilia actin filaments run 13 nm apart in parallel for long distances, there were gaps of significant size that were stochastically distributed throughout the actin core. Actin crosslinkers were distributed through the stereocilium, but did not occupy all possible binding sites. At stereocilia tips, protein density extended beyond actin filaments, especially on the side of the tip where a tip link is expected to anchor. Along the shaft, repeating density was observed that corresponds to actin-to-membrane connectors. In the taper region, most actin filaments terminated near the plasma membrane. The remaining filaments twisted together to make a tighter bundle than was present in the shaft region; the spacing between them decreased from 13 nm to 9 nm, and the apparent filament diameter decreased from 6.4 to 4.8 nm. Our models illustrate detailed features of distinct structural domains that are present within the stereocilium.

Accurate flexible refinement of atomic models against medium-resolution cryo-EM maps using damped dynamics.

BACKGROUND: Dramatic progress has recently been made in cryo-electron microscopy technologies, which now make possible the reconstruction of a growing number of biomolecular structures to near-atomic resolution. However, the need persists for fitting and refinement approaches that address those cases that require modeling assistance. METHODS: In this paper, we describe algorithms to optimize the performance of such medium-resolution refinement methods. These algorithms aim to automatically optimize the parameters that define the density shape of the flexibly fitted model, as well as the time-dependent damper cutoff distance. Atomic distance constraints can be prescribed for cases where extra containment of parts of the structure is helpful, such as in regions where the density map is poorly defined. Also, we propose a simple stopping criterion that estimates the probable onset of overfitting during the simulation. RESULTS: The new set of algorithms produce more accurate fitting and refinement results, and yield a faster rate of convergence of the trajectory toward the fitted conformation. The latter is also more reliable due to the overfitting warning provided to the user. CONCLUSIONS: The algorithms described here were implemented in the new Damped-Dynamics Flexible Fitting simulation tool "DDforge" in the Situs package.

Tracing Actin Filament Bundles in Three-Dimensional Electron Tomography Density Maps of Hair Cell Stereocilia.

Cryo-electron tomography (cryo-ET) is a powerful method of visualizing the three-dimensional organization of supramolecular complexes, such as the cytoskeleton, in their native cell and tissue contexts. Due to its minimal electron dose and reconstruction artifacts arising from the missing wedge during data collection, cryo-ET typically results in noisy density maps that display anisotropic XY versus Z resolution. Molecular crowding further exacerbates the challenge of automatically detecting supramolecular complexes, such as the actin bundle in hair cell stereocilia. Stereocilia are pivotal to the mechanoelectrical transduction process in inner ear sensory epithelial hair cells. Given the complexity and dense arrangement of actin bundles, traditional approaches to filament detection and tracing have failed in these cases. In this study, we introduce BundleTrac, an effective method to trace hundreds of filaments in a bundle. A comparison between BundleTrac and manually tracing the actin filaments in a stereocilium showed that BundleTrac accurately built 326 of 330 filaments (98.8%), with an overall cross-distance of 1.3 voxels for the 330 filaments. BundleTrac is an effective semi-automatic modeling approach in which a seed point is provided for each filament and the rest of the filament is computationally identified. We also demonstrate the potential of a denoising method that uses a polynomial regression to address the resolution and high-noise anisotropic environment of the density map.

A Pattern Recognition Tool for Medium-resolution Cryo-EM Density Maps and Low-resolution Cryo-ET Density maps.

Cryo-electron microscopy (Cryo-EM) and cryo-electron tomography (cryo-ET) produce 3-D density maps of biological molecules at a range of resolution levels. Pattern recognition tools are important in distinguishing biological components from volumetric maps with the available resolutions. One of the most distinct characters in density maps at medium (5-10 Å) resolution is the visibility of protein secondary structures. Although computational methods have been developed, the accurate detection of helices and ß-strands from cryo-EM density maps is still an active research area. We have developed a tool for protein secondary structure detection and evaluation of medium resolution 3-D cryo-EM density maps which combines three computational methods (SSETracer, StrandTwister, and AxisComparison). The program was integrated in UCSF Chimera, a popular visualization software in the cryo-EM community. In related work, we have developed BundleTrac, a computational method to trace filaments in a bundle from lower resolution cryo-ET density maps. It has been applied to actin filament tracing in stereocilia with good accuracy and can be potentially added as a tool in Chimera.

Computing Spatiotemporal Heat Maps of Lipid Electropore Formation: A Statistical Approach.

We extend the multiscale spatiotemporal heat map strategies originally developed for interpreting molecular dynamics simulations of well-structured proteins to liquids such as lipid bilayers and solvents. Our analysis informs the experimental and theoretical investigation of electroporation, that is, the externally imposed breaching of the cell membrane under the influence of an electric field of sufficient magnitude. To understand the nanoscale architecture of electroporation, we transform time domain data of the coarse-grained interaction networks of lipids and solvents into spatial heat maps of the most relevant constituent molecules. The application takes advantage of our earlier graph-based activity functions by accounting for the contact-forming and -breaking activity of the lipids in the bilayer. Our novel analysis of lipid interaction networks under periodic boundary conditions shows that the disruption of the bilayer, as measured by the breaking activity, is associated with the externally imposed pore formation. Moreover, the breaking activity can be used for statistically ranking the importance of individual lipids and solvent molecules through a bridging between fast and slow degrees of freedom. The heat map approach highlighted a small number of important lipids and solvent molecules, which allowed us to efficiently search the trajectories for any functionally relevant mechanisms. Our algorithms are freely disseminated with the open-source package TimeScapes.

A Balanced Approach to Adaptive Probability Density Estimation.

Our development of a Fast (Mutual) Information Matching (FIM) of molecular dynamics time series data led us to the general problem of how to accurately estimate the probability density function of a random variable, especially in cases of very uneven samples. Here, we propose a novel Balanced Adaptive Density Estimation (BADE) method that effectively optimizes the amount of smoothing at each point. To do this, BADE relies on an efficient nearest-neighbor search which results in good scaling for large data sizes. Our tests on simulated data show that BADE exhibits equal or better accuracy than existing methods, and visual tests on univariate and bivariate experimental data show that the results are also aesthetically pleasing. This is due in part to the use of a visual criterion for setting the smoothing level of the density estimate. Our results suggest that BADE offers an attractive new take on the fundamental density estimation problem in statistics. We have applied it on molecular dynamics simulations of membrane pore formation. We also expect BADE to be generally useful for low-dimensional applications in other statistical application domains such as bioinformatics, signal processing and econometrics.

Comparing an Atomic Model or Structure to a Corresponding Cryo-electron Microscopy Image at the Central Axis of a Helix.

Three-dimensional density maps of biological specimens from cryo-electron microscopy (cryo-EM) can be interpreted in the form of atomic models that are modeled into the density, or they can be compared to known atomic structures. When the central axis of a helix is detectable in a cryo-EM density map, it is possible to quantify the agreement between this central axis and a central axis calculated from the atomic model or structure. We propose a novel arc-length association method to compare the two axes reliably. This method was applied to 79 helices in simulated density maps and six case studies using cryo-EM maps at 6.4-7.7 Å resolution. The arc-length association method is then compared to three existing measures that evaluate the separation of two helical axes: a two-way distance between point sets, the length difference between two axes, and the individual amino acid detection accuracy. The results show that our proposed method sensitively distinguishes lateral and longitudinal discrepancies between the two axes, which makes the method particularly suitable for the systematic investigation of cryo-EM map-model pairs.