Application of new multi-resolution methods for the comparison of biomolecular electrostatic properties in the absence of global structural similarity

Influential Mutations in the SMAD4 Trimer Complex Can Be Detected from Disruptions of Electrostatic Complementarity

This article examines three techniques for rapidly assessing the electrostatic contribution of individual amino acids to the stability of protein-protein complexes. Whereas the energetic minimization of modeled oligomers may yield more accurate complexes, we examined the possibility that simple modeling may be sufficient to identify amino acids that add to or detract from electrostatic complementarity. The three methods evaluated were (a) the elimination of entire side chains (e.g., glycine scanning), (b) the elimination of the electrostatic contribution from the atoms of a side chain, called nullification, and (c) side chain structure prediction using SCWRL4. These techniques generate models in seconds, enabling large-scale mutational scanning. We evaluated these techniques on the SMAD2/SMAD4 heterotrimer, whose formation plays a crucial role in antitumor pathways. Many studies have documented the clinical and structural effect of specific mutations on trimer formation. Our results describe how glycine scanning yields more specific predictions, although nullification may be more sensitive, and how side chain structure prediction enables the identification of uncharged-to-charge mutations.

Evaluating Shape Alignment via Ensemble Visualization

The visualization of variability in surfaces embedded in 3D, which is a type of ensemble uncertainty visualization, provides a means of understanding the underlying distribution of a collection or ensemble of surfaces. This work extends the contour boxplot technique to 3D and evaluates it against an enumeration-style visualization of the ensemble members and other conventional visualizations used by atlas builders. The authors demonstrate the efficacy of using the 3D contour boxplot ensemble visualization technique to analyze shape alignment and variability in atlas construction and analysis as a real-world application.

VolRoverN: enhancing surface and volumetric reconstruction for realistic dynamical simulation of cellular and subcellular function

Establishing meaningful relationships between cellular structure and function requires accurate morphological reconstructions. In particular, there is an unmet need for high quality surface reconstructions to model subcellular and synaptic interactions among neurons and glia at nanometer resolution. We address this need with VolRoverN, a software package that produces accurate, efficient, and automated 3D surface reconstructions from stacked 2D contour tracings. While many techniques and tools have been developed in the past for 3D visualization of cellular structure, the reconstructions from VolRoverN meet specific quality criteria that are important for dynamical simulations. These criteria include manifoldness, water-tightness, lack of self- and object-object-intersections, and geometric accuracy. These enhanced surface reconstructions are readily extensible to any cell type and are used here on spiny dendrites with complex morphology and axons from mature rat hippocampal area CA1. Both spatially realistic surface reconstructions and reduced skeletonizations are produced and formatted by VolRoverN for easy input into analysis software packages for neurophysiological simulations at multiple spatial and temporal scales ranging from ion electro-diffusion to electrical cable models.

Multiscale Symmetry Detection in Scalar Fields by Clustering Contours

The complexity in visualizing volumetric data often limits the scope of direct exploration of scalar fields. Isocontour extraction is a popular method for exploring scalar fields because of its simplicity in presenting features in the data. In this paper, we present a novel representation of contours with the aim of studying the similarity relationship between the contours. The representation maps contours to points in a high-dimensional transformation-invariant descriptor space. We leverage the power of this representation to design a clustering based algorithm for detecting symmetric regions in a scalar field. Symmetry detection is a challenging problem because it demands both segmentation of the data and identification of transformation invariant segments. While the former task can be addressed using topological analysis of scalar fields, the latter requires geometry based solutions. Our approach combines the two by utilizing the contour tree for segmenting the data and the descriptor space for determining transformation invariance. We discuss two applications, query driven exploration and asymmetry visualization, that demonstrate the effectiveness of the approach.

VASP-E: specificity annotation with a volumetric analysis of electrostatic isopotentials

Algorithms for comparing protein structure are frequently used for function annotation. By searching for subtle similarities among very different proteins, these algorithms can identify remote homologs with similar biological functions. In contrast, few comparison algorithms focus on specificity annotation, where the identification of subtle differences among very similar proteins can assist in finding small structural variations that create differences in binding specificity. Few specificity annotation methods consider electrostatic fields, which play a critical role in molecular recognition. To fill this gap, this paper describes VASP-E (Volumetric Analysis of Surface Properties with Electrostatics), a novel volumetric comparison tool based on the electrostatic comparison of protein-ligand and protein-protein binding sites. VASP-E exploits the central observation that three dimensional solids can be used to fully represent and compare both electrostatic isopotentials and molecular surfaces. With this integrated representation, VASP-E is able to dissect the electrostatic environments of protein-ligand and protein-protein binding interfaces, identifying individual amino acids that have an electrostatic influence on binding specificity. VASP-E was used to examine a nonredundant subset of the serine and cysteine proteases as well as the barnase-barstar and Rap1a-raf complexes. Based on amino acids established by various experimental studies to have an electrostatic influence on binding specificity, VASP-E identified electrostatically influential amino acids with 100% precision and 83.3% recall. We also show that VASP-E can accurately classify closely related ligand binding cavities into groups with different binding preferences. These results suggest that VASP-E should prove a useful tool for the characterization of specific binding and the engineering of binding preferences in proteins.

Proteins, the ubiquitous worker molecules of the cell, are a diverse class of molecules that perform very specific tasks. Understanding how proteins achieve specificity is a critical step towards understanding biological systems and a key prerequisite for rationally engineering new proteins. To examine electrostatic influences on specificity in proteins, this paper presents VASP-E, a software tool that generates solid representations of the electrostatic potential fields that surround proteins. VASP-E compares solids with constructive solid geometry, a class of techniques developed first for modeling complex machine parts. We observed that solid representations could quantify the degree of charge complementarity in protein-protein interactions and identify key residues that strengthen or weaken them. VASP-E correctly identified amino acids with established experimental influences on protein-protein binding specificity. We also observed that solid representations of electrostatic fields could identify electrostatic conservations and variations that relate to similarities and differences in binding specificity between proteins and small molecules.

Structural phylogeny by profile extraction and multiple superimposition using electrostatic congruence as a discriminator

Phylogenetic analysis of proteins using multiple sequence alignment (MSA) assumes an underlying evolutionary relationship in these proteins which occasionally remains undetected due to considerable sequence divergence. Structural alignment programs have been developed to unravel such fuzzy relationships. However, none of these structure based methods have used electrostatic properties to discriminate between spatially equivalent residues. We present a methodology for MSA of a set of related proteins with known structures using electrostatic properties as an additional discriminator (STEEP). STEEP first extracts a profile, then generates a multiple structural superimposition providing a consolidated spatial framework for comparing residues and finally emits the MSA. Residues that are aligned differently by including or excluding electrostatic properties can be targeted by directed evolution experiments to transform the enzymatic properties of one protein into another. We have compared STEEP results to those obtained from a MSA program (ClustalW) and a structural alignment method (MUSTANG) for chymotrypsin serine proteases. Subsequently, we used PhyML to generate phylogenetic trees for the serine and metallo-β-lactamase superfamilies from the STEEP generated MSA, and corroborated the accepted relationships in these superfamilies. We have observed that STEEP acts as a functional classifier when electrostatic congruence is used as a discriminator, and thus identifies potential targets for directed evolution experiments. In summary, STEEP is unique among phylogenetic methods for its ability to use electrostatic congruence to specify mutations that might be the source of the functional divergence in a protein family. Based on our results, we also hypothesize that the active site and its close vicinity contains enough information to infer the correct phylogeny for related proteins.

A regionalizable statistical model of intersecting regions in protein-ligand binding cavities

Finding elements of proteins that influence ligand binding specificity is an essential aspect of research in many fields. To assist in this effort, this paper presents two statistical models, based on the same theoretical foundation, for evaluating structural similarity among binding cavities. The first model specializes in the "unified" comparison of whole cavities, enabling the selection of cavities that are too dissimilar to have similar binding specificity. The second model enables a "regionalized" comparison of cavities within a user-defined region, enabling the selection of cavities that are too dissimilar to bind the same molecular fragments in the given region. We applied these models to analyze the ligand binding cavities of the serine protease and enolase superfamilies. Next, we observed that our unified model correctly separated sets of cavities with identical binding preferences from other sets with varying binding preferences, and that our regionalized model correctly distinguished cavity regions that are too dissimilar to bind similar molecular fragments in the user-defined region. These observations point to applications of statistical modeling that can be used to examine and, more importantly, identify influential structural similarities within binding site structure in order to better detect influences on protein-ligand binding specificity.

Modeling regionalized volumetric differences in protein-ligand binding cavities

Identifying elements of protein structures that create differences in protein-ligand binding specificity is an essential method for explaining the molecular mechanisms underlying preferential binding. In some cases, influential mechanisms can be visually identified by experts in structural biology, but subtler mechanisms, whose significance may only be apparent from the analysis of many structures, are harder to find. To assist this process, we present a geometric algorithm and two statistical models for identifying significant structural differences in protein-ligand binding cavities. We demonstrate these methods in an analysis of sequentially nonredundant structural representatives of the canonical serine proteases and the enolase superfamily. Here, we observed that statistically significant structural variations identified experimentally established determinants of specificity. We also observed that an analysis of individual regions inside cavities can reveal areas where small differences in shape can correspond to differences in specificity.

Clustering of HIV-1 Subtypes Based on gp120 V3 Loop electrostatic properties

BACKGROUND

The V3 loop of the glycoprotein gp120 of HIV-1 plays an important role in viral entry into cells by utilizing as coreceptor CCR5 or CXCR4, and is implicated in the phenotypic tropisms of HIV viruses. It has been hypothesized that the interaction between the V3 loop and CCR5 or CXCR4 is mediated by electrostatics. We have performed hierarchical clustering analysis of the spatial distributions of electrostatic potentials and charges of V3 loop structures containing consensus sequences of HIV-1 subtypes.

RESULTS

Although the majority of consensus sequences have a net charge of +3, the spatial distribution of their electrostatic potentials and charges may be a discriminating factor for binding and infectivity. This is demonstrated by the formation of several small subclusters, within major clusters, which indicates common origin but distinct spatial details of electrostatic properties. Some of this information may be present, in a coarse manner, in clustering of sequences, but the spatial details are largely lost. We show the effect of ionic strength on clustering of electrostatic potentials, information that is not present in clustering of charges or sequences. We also make correlations between clustering of electrostatic potentials and net charge, coreceptor selectivity, global prevalence, and geographic distribution. Finally, we interpret coreceptor selectivity based on the N6X7T8|S8X9 sequence glycosylation motif, the specific positive charge location according to the 11/24/25 rule, and the overall charge and electrostatic potential distribution.

CONCLUSIONS

We propose that in addition to the sequence and the net charge of the V3 loop of each subtype, the spatial distributions of electrostatic potentials and charges may also be important factors for receptor recognition and binding and subsequent viral entry into cells. This implies that the overall electrostatic potential is responsible for long-range recognition of the V3 loop with coreceptors CCR5/CXCR4, whereas the charge distribution contributes to the specific short-range interactions responsible for the formation of the bound complex. We also propose a scheme for coreceptor selectivity based on the sequence glycosylation motif, the 11/24/25 rule, and net charge.

Symmetry in scalar field topology

Study of symmetric or repeating patterns in scalar fields is important in scientific data analysis because it gives deep insights into the properties of the underlying phenomenon. Though geometric symmetry has been well studied within areas like shape processing, identifying symmetry in scalar fields has remained largely unexplored due to the high computational cost of the associated algorithms. We propose a computationally efficient algorithm for detecting symmetric patterns in a scalar field distribution by analysing the topology of level sets of the scalar field. Our algorithm computes the contour tree of a given scalar field and identifies subtrees that are similar. We define a robust similarity measure for comparing subtrees of the contour tree and use it to group similar subtrees together. Regions of the domain corresponding to subtrees that belong to a common group are extracted and reported to be symmetric. Identifying symmetry in scalar fields finds applications in visualization, data exploration, and feature detection. We describe two applications in detail: symmetry-aware transfer function design and symmetry-aware isosurface extraction.

Electrostatic Similarity Determination Using Multiresolution Analysis

Molecular similarity is an important tool in protein and drug design for analyzing the quantitative relationships between physicochemical properties of two molecules. We present a family of similarity measures which exploits the ability of wavelet transformation to analyze the spectral components of physicochemical properties and suggests a sensitive way for measuring similarities of biological molecules. In order to investigate how effective wavelet-based similarity measures were against conventional measures, we defined several patterns which involve scalar or topological changes in the distribution of electrostatic properties. The wavelet-based measures were more successful in discriminating these patterns in contrast to the current state-of-art similarity measures. We also present the validity of wavelet-based similarity measures through the hierarchical clustering of two protein datasets consisting of families of homologous domains and alanine scan mutants. This type of similarity analysis is useful for protein structure-function studies and protein design.

Simulation of transmission electron microscope images of biological specimens

We present a new approach to simulate electron cryo-microscope images of biological specimens. The framework for simulation consists of two parts; the first is a phantom generator that generates a model of a specimen suitable for simulation, the second is a transmission electron microscope simulator. The phantom generator calculates the scattering potential of an atomic structure in aqueous buffer and allows the user to define the distribution of molecules in the simulated image. The simulator includes a well defined electron-specimen interaction model based on the scalar Schrödinger equation, the contrast transfer function for optics, and a noise model that includes shot noise as well as detector noise including detector blurring. To enable optimal performance, the simulation framework also includes a calibration protocol for setting simulation parameters. To test the accuracy of the new framework for simulation, we compare simulated images to experimental images recorded of the Tobacco Mosaic Virus (TMV) in vitreous ice. The simulated and experimental images show good agreement with respect to contrast variations depending on dose and defocus. Furthermore, random fluctuations present in experimental and simulated images exhibit similar statistical properties. The simulator has been designed to provide a platform for development of new instrumentation and image processing procedures in single particle electron microscopy, two-dimensional crystallography and electron tomography with well documented protocols and an open source code into which new improvements and extensions are easily incorporated.

The effect of electrostatics on factor H function and related pathologies

Factor H (FH) contributes to the regulation of the complement system by binding to polyanionic surfaces and the proteins C3b/C3c/C3d. This implicates charge and electrostatic interactions in recognition and binding of FH. Despite the large amount of experimental and pathology data the exact mechanism at molecular level is not yet known. We have implemented a computational framework for comparative analysis of the charge and electrostatic diversity of FH modules and C3b domains to identify electrostatic hotspots and predict potential binding sites. Our electrostatic potential clustering analysis shows that charge distributions and electrostatic potential distributions are more useful in understanding C3b-FH interactions than net charges alone. We present a model of non-specific electrostatic interactions of FH with polyanion-rich surfaces and specific interactions with C3b, using our computational data and existing experimental data. We discuss the electrostatic contributions to the formation of the C3b-FH complex and the competition between FH and Factor Bb (Bb) for binding to C3b. We also discuss the significance of mutations of charged amino acids in the pathobiology of FH-mediated disease, such as age-related macular degeneration, atypical hemolytic uremic syndrome, and dense deposit disease. Our data can be used to guide future experimental studies.

Automated computational framework for the analysis of electrostatic similarities of proteins

Charge plays an important role in protein-protein interactions. In the case of excessively charged proteins, their electrostatic potentials contribute to the processes of recognition and binding with other proteins or ligands. We present an automated computational framework for determining the contribution of each charged amino acid to the electrostatic properties of proteins, at atomic resolution level. This framework involves computational alanine scans, calculation of Poisson-Boltzmann electrostatic potentials, calculation of electrostatic similarity distances (ESDs), hierarchical clustering analysis of ESDs, calculation of solvation free energies of association, and visualization of the spatial distributions of electrostatic potentials. The framework is useful to classify families of mutants with similar electrostatic properties and to compare them with the parent proteins in the complex. The alanine scan mutants introduce perturbations in the local electrostatic properties of the proteins and aim in delineating the contribution of each mutated amino acid in the spatial distribution of electrostatic potential, and in biological function when electrostatics is a dominant contributing factor in protein-protein interactions. The framework can be used to design new proteins with tailored electrostatic properties, such as immune system regulators, inhibitors, and vaccines, and in guiding experimental studies. We present an example for the interaction of the immune system protein C3d (the d-fragment of complement protein C3) with its receptor CR2, and we discuss our data in view of a binding site controversy.

Electrostatic clustering and free energy calculations provide a foundation for protein design and optimization

Electrostatic interactions are ubiquitous in proteins and dictate stability and function. In this review, we discuss several methods for the analysis of electrostatics in protein–protein interactions. We discuss alanine-scanning mutagenesis, Poisson–Boltzmann electrostatics, free energy calculations, electrostatic similarity distances, and hierarchical clustering of electrostatic potentials. Our recently developed computational framework, known as Analysis of Electrostatic Similarities Of Proteins (AESOP), incorporates these tools to efficiently elucidate the role of electrostatic potentials in protein interactions. We present the application of AESOP to several proteins and protein complexes, for which charge is purported to facilitate protein association. Specifically, we illustrate how recent work has shaped the formulation of electrostatic calculations, the correlation of electrostatic free energies and electrostatic potential clustering results with experimental binding and activity data, the pH dependence of protein stability and association, the design of mutant proteins with enhanced immunological activity, and how AESOP can expose deficiencies in structural models and experimental data. This integrative approach can be utilized to develop mechanistic models and to guide experimental studies by predicting mutations with desired physicochemical properties and function. Alteration of the electrostatic properties of proteins offers a basis for the design of proteins with optimized binding and activity.

New evidence for the role of calcium in the glycosidase reaction of GH43 arabinanases

Endo-1,5-α-L-arabinanases are glycosyl hydrolases that are able to cleave the glycosidic bonds of α-1,5-L-arabinan, releasing arabino-oligosaccharides and L-arabinose. Two extracellular endo-1,5-α-L-arabinanases have been isolated from Bacillus subtilis, BsArb43A and BsArb43B (formally named AbnA and Abn2, respectively). BsArb43B shows low sequence identity with previously characterized 1,5-α-L-arabinanases and is a much larger enzyme. Here we describe the 3D structure of native BsArb43B, biochemical and structure characterization of two BsArb43B mutant proteins (H318A and D171A), and the 3D structure of the BsArb43B D171A mutant enzyme in complex with arabinohexose. The 3D structure of BsArb43B is different from that of other structurally characterized endo-1,5-α-L-arabinanases, as it comprises two domains, an N-terminal catalytic domain, with a 3D fold similar to that observed for other endo-1,5-α-L-arabinanases, and an additional C-terminal domain. Moreover, this work also provides experimental evidence for the presence of a cluster containing a calcium ion in the catalytic domain, and the importance of this calcium ion in the enzymatic mechanism of BsArb43B.

VASP: a volumetric analysis of surface properties yields insights into protein-ligand binding specificity

Many algorithms that compare protein structures can reveal similarities that suggest related biological functions, even at great evolutionary distances. Proteins with related function often exhibit differences in binding specificity, but few algorithms identify structural variations that effect specificity. To address this problem, we describe the Volumetric Analysis of Surface Properties (VASP), a novel volumetric analysis tool for the comparison of binding sites in aligned protein structures. VASP uses solid volumes to represent protein shape and the shape of surface cavities, clefts and tunnels that are defined with other methods. Our approach, inspired by techniques from constructive solid geometry, enables the isolation of volumetrically conserved and variable regions within three dimensionally superposed volumes. We applied VASP to compute a comparative volumetric analysis of the ligand binding sites formed by members of the steroidogenic acute regulatory protein (StAR)-related lipid transfer (START) domains and the serine proteases. Within both families, VASP isolated individual amino acids that create structural differences between ligand binding cavities that are known to influence differences in binding specificity. Also, VASP isolated cavity subregions that differ between ligand binding cavities which are essential for differences in binding specificity. As such, VASP should prove a valuable tool in the study of protein-ligand binding specificity.

Proteins carry out vital and specific functions by physically binding other molecules. Understanding specificity, the preferential binding of certain molecules to one another, is essential for numerous medical and industrial applications. Given the structure of a protein with unknown function, algorithms are available that suggest hypothetical functions based on structural similarities to better-studied proteins, even at vast evolutionary distances. In contrast, few algorithms identify structural differences that relate to differences in specificity among closely-related proteins. To address this problem, we present a Volumetric Analysis of Surface Properties (VASP). VASP differs from existing methods because it compares solid representations of protein structures and cavities based on principles from computer graphics and computer aided design. In our results, solid representations enabled VASP to isolate elements of protein structure that create differences in binding sites and thereby lead to differences in binding preferences. These observations point to applications for the annotation and engineering of protein specificity.

Rapid comparison of properties on protein surface

The mapping of physicochemical characteristics onto the surface of a protein provides crucial insights into its function and evolution. This information can be further used in the characterization and identification of similarities within protein surface regions. We propose a novel method which quantitatively compares global and local properties on the protein surface. We have tested the method on comparison of electrostatic potentials and hydrophobicity. The method is based on 3D Zernike descriptors, which provides a compact representation of a given property defined on a protein surface. Compactness and rotational invariance of this descriptor enable fast comparison suitable for database searches. The usefulness of this method is exemplified by studying several protein families including globins, thermophilic and mesophilic proteins, and active sites of TIM beta/alpha barrel proteins. In all the cases studied, the descriptor is able to cluster proteins into functionally relevant groups. The proposed approach can also be easily extended to other surface properties. This protein surface-based approach will add a new way of viewing and comparing proteins to conventional methods, which compare proteins in terms of their primary sequence or tertiary structure.

Topology Based Selection and Curation of Level Sets

The selection of appropriate level sets for the quantitative visualization of three dimensional imaging or simulation data is a problem that is both fundamental and essential. The selected level set needs to satisfy several topological and geometric constraints to be useful for subsequent quantitative processing and visualization. For an initial selection of an isosurface, guided by contour tree data structures, we detect the topological features by computing stable and unstable manifolds of the critical points of the distance function induced by the isosurface. We further enhance the description of these features by associating geometric attributes with them. We then rank the attributed features and provide a handle to them for curation of the topological anomalies.

Electrostatic similarity of proteins: application of three dimensional spherical harmonic decomposition

We present a method for describing and comparing global electrostatic properties of biomolecules based on the spherical harmonic decomposition of electrostatic potential data. Unlike other approaches our method does not require any prior three dimensional structural alignment. The electrostatic potential, given as a volumetric data set from a numerical solution of the Poisson or Poisson-Boltzmann equation, is represented with descriptors that are rotation invariant. The method can be applied to large and structurally diverse sets of biomolecules enabling to cluster them according to their electrostatic features.