Exploring cavity dynamics in biomolecular systems

Interaction of the new inhibitor paxlovid (PF-07321332) and ivermectin with the monomer of the main protease SARS-CoV-2: A volumetric study based on molecular dynamics, elastic networks, classical thermodynamics and SPT

The COVID-19 pandemic has accelerated the study of drugs, most notably ivermectin and more recently Paxlovid (PF-07321332) which is in phase III clinical trials with experimental data showing covalent binding to the viral protease M^pro. Theoretical developments of catalytic site-directed docking support thermodynamically feasible non-covalent binding to M^pro. Here we show that Paxlovid binds non-covalently at regions other than the catalytic sites with energies stronger than reported and at the same binding site as the ivermectin B1a homologue, all through theoretical methodologies, including blind docking. We volumetrically characterize the non-covalent interaction of the ivermectin homologues (avermectins B1a and B1b) and Paxlovid with the mM^pro monomer, through molecular dynamics and scaled particle theory (SPT). Using the fluctuation-dissipation theorem (FDT), we estimated the electric dipole moment fluctuations at the surface of each of complex involved in this study, with similar trends to that observed in the interaction volume. Using fluctuations of the intrinsic volume and the number of flexible fragments of proteins using anisotropic and Gaussian elastic networks (ANM+GNM) suggests the complexes with ivermectin are more dynamic and flexible than the unbound monomer. In contrast, the binding of Paxlovid to mM^pro shows that the mM^pro-PF complex is the least structurally dynamic of all the species measured in this investigation. The results support a differential molecular mechanism of the ivermectin and PF homologues in the mM^pro monomer. Finally, the results showed that Paxlovid despite beingbound in different sites through covalent or non-covalent forms behaves similarly in terms of its structural flexibility and volumetric behaviour.

A unified framework for packing deformable and non-deformable subcellular structures in crowded cryo-electron tomogram simulation

BACKGROUND

Cryo-electron tomography is an important and powerful technique to explore the structure, abundance, and location of ultrastructure in a near-native state. It contains detailed information of all macromolecular complexes in a sample cell. However, due to the compact and crowded status, the missing edge effect, and low signal to noise ratio (SNR), it is extremely challenging to recover such information with existing image processing methods. Cryo-electron tomogram simulation is an effective solution to test and optimize the performance of the above image processing methods. The simulated images could be regarded as the labeled data which covers a wide range of macromolecular complexes and ultrastructure. To approximate the crowded cellular environment, it is very important to pack these heterogeneous structures as tightly as possible. Besides, simulating non-deformable and deformable components under a unified framework also need to be achieved.

RESULT

In this paper, we proposed a unified framework for simulating crowded cryo-electron tomogram images including non-deformable macromolecular complexes and deformable ultrastructures. A macromolecule was approximated using multiple balls with fixed relative positions to reduce the vacuum volume. A ultrastructure, such as membrane and filament, was approximated using multiple balls with flexible relative positions so that this structure could deform under force field. In the experiment, 400 macromolecules of 20 representative types were packed into simulated cytoplasm by our framework, and numerical verification proved that our method has a smaller volume and higher compression ratio than the baseline single-ball model. We also packed filaments, membranes and macromolecules together, to obtain a simulated cryo-electron tomogram image with deformable structures. The simulated results are closer to the real Cryo-ET, making the analysis more difficult. The DOG particle picking method and the image segmentation method are tested on our simulation data, and the experimental results show that these methods still have much room for improvement.

CONCLUSION

The proposed multi-ball model can achieve more crowded packaging results and contains richer elements with different properties to obtain more realistic cryo-electron tomogram simulation. This enables users to simulate cryo-electron tomogram images with non-deformable macromolecular complexes and deformable ultrastructures under a unified framework. To illustrate the advantages of our framework in improving the compression ratio, we calculated the volume of simulated macromolecular under our multi-ball method and traditional single-ball method. We also performed the packing experiment of filaments and membranes to demonstrate the simulation ability of deformable structures. Our method can be used to do a benchmark by generating large labeled cryo-ET dataset and evaluating existing image processing methods. Since the content of the simulated cryo-ET is more complex and crowded compared with previous ones, it will pose a greater challenge to existing image processing methods.

An Algorithm for Computing Side Chain Conformational Variations of a Protein Tunnel/Channel

In this paper, a novel method to compute side chain conformational variations for a protein molecule tunnel (or channel) is proposed. From the conformational variations, we compute the flexibly deformed shapes of the initial tunnel, and present a way to compute the maximum size of the ligand that can pass through the deformed tunnel. By using the two types of graphs corresponding to amino acids and their side chain rotamers, the suggested algorithm classifies amino acids and rotamers which possibly have collisions. Based on the divide and conquer technique, local side chain conformations are computed first, and then a global conformation is generated by combining them. With the exception of certain cases, experimental results show that the algorithm finds up to 327,680 valid side chain conformations from 12⁸~12³³ conformation candidates within three seconds.

Analyzing protein topology based on Laguerre tessellation of a pore-traversing water network

Given the tight relation between protein structure and function, we present a set of methods to analyze protein topology, implemented in the VLDP program, relying on Laguerre space partitions built from series of molecular dynamics snapshots. The Laguerre partition specifies inter-atomic contacts, formalized in graphs. The deduced properties are the existence and count of water aggregates, possible passage ways and constrictions, the structure, connectivity, stability and depth of the water network. As a test-case, the membrane protein FepA is investigated in its full environment, yielding a more precise description of the protein surface. Inside FepA, the solvent splits into isolated clusters and an intricate network connecting both sides of the lipid bilayer. The network is dynamic, connections set on and off, occasionally substantially relocating traversing paths. Subtle differences are detected between two forms of FepA, ligand-free and complexed with its natural iron carrier, the enterobactin. The complexed form has more constricted and more centered openings in the upper part whereas, in the lower part, constriction is released: two main channels between the plug and barrel lead directly to the periplasm. Reliability, precision and the variety of topological features are the main interest of the method.

Geometric Detection Algorithms for Cavities on Protein Surfaces in Molecular Graphics: A Survey

Detecting and analyzing protein cavities provides significant information about active sites for biological processes (e.g., protein-protein or protein-ligand binding) in molecular graphics and modeling. Using the three-dimensional structure of a given protein (i.e., atom types and their locations in 3D) as retrieved from a PDB (Protein Data Bank) file, it is now computationally viable to determine a description of these cavities. Such cavities correspond to pockets, clefts, invaginations, voids, tunnels, channels, and grooves on the surface of a given protein. In this work, we survey the literature on protein cavity computation and classify algorithmic approaches into three categories: evolution-based, energy-based, and geometry-based. Our survey focuses on geometric algorithms, whose taxonomy is extended to include not only sphere-, grid-, and tessellation-based methods, but also surface-based, hybrid geometric, consensus, and time-varying methods. Finally, we detail those techniques that have been customized for GPU (Graphics Processing Unit) computing.

Hybrid Voronoi diagrams, their computation and reduction for applications in computational biochemistry

Geometric models of molecular structures are often described as a set of balls, where balls represent individual atoms. The ability to describe and explore the empty space among these balls is important, e.g., in the analysis of the interaction of enzymes with substrates, ligands and solvent molecules. Voronoi diagrams from the field of computational geometry are often used here, because they provide a mathematical description of how the whole space can be divided into regions assigned to individual atoms. This paper introduces a combination of two different types of Voronoi diagrams into a new hybrid Voronoi diagram - one part of this diagram belongs to the additively weighted (aw-Voronoi) diagram and the other to the power diagram. The boundary between them is controlled by a user-defined constant (the probe radius). Both parts are computed by different algorithms, which are already known. The reduced aw-Voronoi diagram is then obtained by removing the power diagram part from the hybrid diagram. Reduced aw-Voronoi diagrams are perfectly tailored for the analysis of dynamic molecular structures, their computation is faster and storage requirements are lower than in the case of complete aw-Voronoi diagrams. Here, we showed their application to key proteins in cancer research such as p53 and ARID proteins as case study. We identified a biologically relevant cavity in p53 structural ensembles generated by molecular dynamics simulations and analyzed its accessibility, attesting the potential of our approach. This method is relevant for cancer research since it permits to depict a dynamical view of cavities and pockets in proteins that could be affected by mutations in the disease. Our approach opens novel prospects for the study of cancer-related proteins by molecular simulations and the identification of novel targets for drug design.

Interactive exploration of ligand transportation through protein tunnels

BACKGROUND

Protein structures and their interaction with ligands have been in the focus of biochemistry and structural biology research for decades. The transportation of ligand into the protein active site is often complex process, driven by geometric and physico-chemical properties, which renders the ligand path full of jitter and impasses. This prevents understanding of the ligand transportation and reasoning behind its behavior along the path.

RESULTS

To address the needs of the domain experts we design an explorative visualization solution based on a multi-scale simplification model. It helps to navigate the user to the most interesting parts of the ligand trajectory by exploring different attributes of the ligand and its movement, such as its distance to the active site, changes of amino acids lining the ligand, or ligand "stuckness". The process is supported by three linked views - 3D representation of the simplified trajectory, scatterplot matrix, and bar charts with line representation of ligand-lining amino acids.

CONCLUSIONS

The usage of our tool is demonstrated on molecular dynamics simulations provided by the domain experts. The tool was tested by the domain experts from protein engineering and the results confirm that it helps to navigate the user to the most interesting parts of the ligand trajectory and to understand the ligand behavior.

Simulating cryo electron tomograms of crowded cell cytoplasm for assessment of automated particle picking

BACKGROUND

Cryo-electron tomography is an important tool to study structures of macromolecular complexes in close to native states. A whole cell cryo electron tomogram contains structural information of all its macromolecular complexes. However, extracting this information remains challenging, and relies on sophisticated image processing, in particular for template-free particle extraction, classification and averaging. To develop these methods it is crucial to realistically simulate tomograms of crowded cellular environments, which can then serve as ground truth models for assessing and optimizing methods for detection of complexes in cell tomograms.

RESULTS

We present a framework to generate crowded mixtures of macromolecular complexes for realistically simulating cryo electron tomograms including noise and image distortions due to the missing-wedge effects. Simulated tomograms are then used for assessing the template-free Difference-of-Gaussian (DoG) particle-picking method to detect complexes of different shapes and sizes under various crowding and noise levels. We identified DoG parameter settings that maximize precision and recall for detecting particles over a wide range of sizes and shapes. We observed that medium sized DoG scaling factors showed the overall best performance. To further improve performance, we propose a combination strategy for integrating results from multiple parameter settings. With increasing macromolecular crowding levels, the precision of particle picking remained relatively high, while the recall was dramatically reduced, which limits the detection of sufficient copy numbers of complexes in a crowded environment. Over a wide range of increasing noise levels, the DoG particle picking performance remained stable, but dramatically reduced beyond a specific noise threshold.

CONCLUSIONS

Automatic and reference-free particle picking is an important first step in a visual proteomics analysis of cell tomograms. However, cell cytoplasm is highly crowded, which makes particle detection challenging. It is therefore important to test particle-picking methods in a realistic crowded setting. Here, we present a framework for simulating tomograms of cellular environments at high crowding levels and assess the DoG particle picking method. We determined optimal parameter settings to maximize the performance of the DoG particle-picking method.

CAVER: Algorithms for Analyzing Dynamics of Tunnels in Macromolecules

The biological function of a macromolecule often requires that a small molecule or ion is transported through its structure. The transport pathway often leads through void spaces in the structure. The properties of transport pathways change significantly in time; therefore, the analysis of a trajectory from molecular dynamics rather than of a single static structure is needed for understanding the function of pathways. The identification and analysis of transport pathways are challenging because of the high complexity and diversity of macromolecular shapes, the thermal motion of their atoms, and the large amount of conformations needed to properly describe conformational space of protein structure. In this paper, we describe the principles of the CAVER 3.0 algorithms for the identification and analysis of properties of transport pathways both in static and dynamic structures. Moreover, we introduce the improved clustering solution for finding tunnels in macromolecules, which is included in the latest CAVER 3.02 version. Voronoi diagrams are used to identify potential pathways in each snapshot of a molecular dynamics trajectory and clustering is then used to find the correspondence between tunnels from different snapshots. Furthermore, the geometrical properties of pathways and their evolution in time are computed and visualized.

AnimoAminoMiner: Exploration of Protein Tunnels and their Properties in Molecular Dynamics

In this paper we propose a novel method for the interactive exploration of protein tunnels. The basic principle of our approach is that we entirely abstract from the 3D/4D space the simulated phenomenon is embedded in. A complex 3D structure and its curvature information is represented only by a straightened tunnel centerline and its width profile. This representation focuses on a key aspect of the studied geometry and frees up graphical estate to key chemical and physical properties represented by surrounding amino acids. The method shows the detailed tunnel profile and its temporal aggregation. The profile is interactively linked with a visual overview of all amino acids which are lining the tunnel over time. In this overview, each amino acid is represented by a set of colored lines depicting the spatial and temporal impact of the amino acid on the corresponding tunnel. This representation clearly shows the importance of amino acids with respect to selected criteria. It helps the biochemists to select the candidate amino acids for mutation which changes the protein function in a desired way. The AnimoAminoMiner was designed in close cooperation with domain experts. Its usefulness is documented by their feedback and a case study, which are included.

Membrane Protein Structure, Function, and Dynamics: a Perspective from Experiments and Theory

Membrane proteins mediate processes that are fundamental for the flourishing of biological cells. Membrane-embedded transporters move ions and larger solutes across membranes; receptors mediate communication between the cell and its environment and membrane-embedded enzymes catalyze chemical reactions. Understanding these mechanisms of action requires knowledge of how the proteins couple to their fluid, hydrated lipid membrane environment. We present here current studies in computational and experimental membrane protein biophysics, and show how they address outstanding challenges in understanding the complex environmental effects on the structure, function, and dynamics of membrane proteins.

CHEXVIS: a tool for molecular channel extraction and visualization

Background

Understanding channel structures that lead to active sites or traverse the molecule is important in the study of molecular functions such as ion, ligand, and small molecule transport. Efficient methods for extracting, storing, and analyzing protein channels are required to support such studies. Further, there is a need for an integrated framework that supports computation of the channels, interactive exploration of their structure, and detailed visual analysis of their properties.

Results

We describe a method for molecular channel extraction based on the alpha complex representation. The method computes geometrically feasible channels, stores both the volume occupied by the channel and its centerline in a unified representation, and reports significant channels. The representation also supports efficient computation of channel profiles that help understand channel properties. We describe methods for effective visualization of the channels and their profiles. These methods and the visual analysis framework are implemented in a software tool, ChExVis. We apply the method on a number of known channel containing proteins to extract pore features. Results from these experiments on several proteins show that ChExVis performance is comparable to, and in some cases, better than existing channel extraction techniques. Using several case studies, we demonstrate how ChExVis can be used to study channels, extract their properties and gain insights into molecular function.

Conclusion

ChExVis supports the visual exploration of multiple channels together with their geometric and physico-chemical properties thereby enabling the understanding of the basic biology of transport through protein channels. The ChExVis web-server is freely available at http://vgl.serc.iisc.ernet.in/chexvis/. The web-server is supported on all modern browsers with latest Java plug-in.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-015-0545-9) contains supplementary material, which is available to authorized users.

Ligand Excluded Surface: A New Type of Molecular Surface

The most popular molecular surface in molecular visualization is the solvent excluded surface (SES). It provides information about the accessibility of a biomolecule for a solvent molecule that is geometrically approximated by a sphere. During a period of almost four decades, the SES has served for many purposes - including visualization, analysis of molecular interactions and the study of cavities in molecular structures. However, if one is interested in the surface that is accessible to a molecule whose shape differs significantly from a sphere, a different concept is necessary. To address this problem, we generalize the definition of the SES by replacing the probe sphere with the full geometry of the ligand defined by the arrangement of its van der Waals spheres. We call the new surface ligand excluded surface (LES) and present an efficient, grid-based algorithm for its computation. Furthermore, we show that this algorithm can also be used to compute molecular cavities that could host the ligand molecule. We provide a detailed description of its implementation on CPU and GPU. Furthermore, we present a performance and convergence analysis and compare the LES for several molecules, using as ligands either water or small organic molecules.