Analytical shape computation of macromolecules: I. molecular area and volume through alpha shape

Structure-Based Prediction of lncRNA-Protein Interactions by Deep Learning

The interactions between long noncoding RNA (lncRNA) and protein play crucial roles in various biological processes. Computational methods are essential for predicting lncRNA-protein interactions and deciphering their mechanisms. In this chapter, we aim to introduce the fundamental framework for predicting lncRNA-protein interactions based on three-dimensional structure information. With the increasing availability of lncRNA and protein molecular tertiary structures, the feasibility of using deep learning methods for automatic representation and learning has become evident. This chapter outlines the key steps in predicting lncRNA-protein interactions using deep learning, including three common non-Euclidean data representations for lncRNA and proteins, as well as neural networks tailored to these specific data characteristics. We also highlight the advantages and challenges of structure-based prediction of lncRNA-protein interactions with geometric deep learning methods.

sesA: A Program for the Analytic Computation of Solvent-Excluded Surface Areas

The surface area of a molecule, an inherent geometric property of its structure, plays important roles in its solvation and functioning. Here we present an accurate and robust program, sesA, for the analytic computation of solvent-excluded surface (SES) areas. The accuracy and robustness are achieved through the analytic computations of all the solvent-accessible surface (SAS) regions for a surface atom and probe-probe intersections. The detailed comparisons of the areas for a large set of protein structures by sesA and msms, a de-facto standard for analytic SAS and SES computations, confirm sesA's accuracy to a good extent and in the same time reveal significant differences between them. The unprecedented accuracy and robustness of sesA make it possible to analyze in great detail the surface areas of any molecules in general and biomolecules in particular.

Protein Structure Inspired Discovery of a Novel Inducer of Anoikis in Human Melanoma

Drug discovery historically starts with an established function, either that of compounds or proteins. This can hamper discovery of novel therapeutics. As structure determines function, we hypothesized that unique 3D protein structures constitute primary data that can inform novel discovery. Using a computationally intensive physics-based analytical platform operating at supercomputing speeds, we probed a high-resolution protein X-ray crystallographic library developed by us. For each of the eight identified novel 3D structures, we analyzed binding of sixty million compounds. Top-ranking compounds were acquired and screened for efficacy against breast, prostate, colon, or lung cancer, and for toxicity on normal human bone marrow stem cells, both using eight-day colony formation assays. Effective and non-toxic compounds segregated to two pockets. One compound, Dxr2-017, exhibited selective anti-melanoma activity in the NCI-60 cell line screen. In eight-day assays, Dxr2-017 had an IC50 of 12 nM against melanoma cells, while concentrations over 2100-fold higher had minimal stem cell toxicity. Dxr2-017 induced anoikis, a unique form of programmed cell death in need of targeted therapeutics. Our findings demonstrate proof-of-concept that protein structures represent high-value primary data to support the discovery of novel acting therapeutics. This approach is widely applicable.

Computing the alpha complex using dual active set quadratic programming

The alpha complex is a fundamental data structure from computational geometry, which encodes the topological type of a union of balls B ( x ; r ) ⊂ R m for x ∈ S , including a weighted version that allows for varying radii. It consists of the collection of "simplices" σ = { x 0 , . . . , x k } ⊂ S , which correspond to nonempty ( k + 1 ) -fold intersections of cells in a radius-restricted version of the Voronoi diagramVor ( S , r ) . Existing algorithms for computing the alpha complex require that the points reside in low dimension because they begin by computing the entire Delaunay complex, which rapidly becomes intractable, even when the alpha complex is of a reasonable size. This paper presents a method for computing the alpha complex without computing the full Delaunay triangulation by applying Lagrangian duality, specifically an algorithm based on dual quadratic programming that seeks to rule simplices out rather than ruling them in.

CASTpFold: Computed Atlas of Surface Topography of the universe of protein Folds

Geometric and topological properties of protein structures, including surface pockets, interior cavities and cross channels, are of fundamental importance for proteins to carry out their functions. Computed Atlas of Surface Topography of proteins (CASTp) is a widely used web server for locating, delineating, and measuring these geometric and topological properties of protein structures. Recent developments in AI-based protein structure prediction such as AlphaFold2 (AF2) have significantly expanded our knowledge on protein structures. Here we present CASTpFold, a continuation of CASTp that provides accurate and comprehensive identifications and quantifications of protein topography. It now provides (i) results on an expanded database of proteins, including the Protein Data Bank (PDB) and non-singleton representative structures of AlphaFold2 structures, covering 183 million AF2 structures; (ii) functional pockets prediction with corresponding Gene Ontology (GO) terms or Enzyme Commission (EC) numbers for AF2-predicted structures and (iii) pocket similarity search function for surface and protein-protein interface pockets. The CASTpFold web server is freely accessible at https://cfold.bme.uic.edu/castpfold/.

CASTpFold: Computed Atlas of Surface Topography of the universe of protein Folds

Geometric and topological properties of protein structures, including surface pockets, interior cavities, and cross channels, are of fundamental importance for proteins to carry out their functions. Computed Atlas of Surface Topography of proteins (CASTp) is a widely used web server for locating, delineating, and measuring these geometric and topological properties of protein structures. Recent developments in AI-based protein structure prediction such as AlphaFold2 (AF2) have significantly expanded our knowledge on protein structures. Here we present CASTpFold, a continuation of CASTp that provides accurate and comprehensive identifications and quantifications of protein topography. It now provides (i) results on an expanded database of proteins, including the Protein Data Bank (PDB) and non-singleton representative structures of AlphaFold2 structures, covering 183 million AF2 structures; (ii) functional pockets prediction with corresponding Gene Ontology (GO) terms or Enzyme Commission (EC) numbers for AF2-predicted structures; and (iii) pocket similarity search function for surface and protein-protein interface pockets. The CASTpFold web server is freely accessible at https://cfold.bme.uic.edu/castpfold/.

Structure-based pathogenicity relationship identifier for predicting effects of single missense variants and discovery of higher-order cancer susceptibility clusters of mutations

We report the structure-based pathogenicity relationship identifier (SPRI), a novel computational tool for accurate evaluation of pathological effects of missense single mutations and prediction of higher-order spatially organized units of mutational clusters. SPRI can effectively extract properties determining pathogenicity encoded in protein structures, and can identify deleterious missense mutations of germ line origin associated with Mendelian diseases, as well as mutations of somatic origin associated with cancer drivers. It compares favorably to other methods in predicting deleterious mutations. Furthermore, SPRI can discover spatially organized pathogenic higher-order spatial clusters (patHOS) of deleterious mutations, including those of low recurrence, and can be used for discovery of candidate cancer driver genes and driver mutations. We further demonstrate that SPRI can take advantage of AlphaFold2 predicted structures and can be deployed for saturation mutation analysis of the whole human proteome.

AI in drug discovery and its clinical relevance

The COVID-19 pandemic has emphasized the need for novel drug discovery process. However, the journey from conceptualizing a drug to its eventual implementation in clinical settings is a long, complex, and expensive process, with many potential points of failure. Over the past decade, a vast growth in medical information has coincided with advances in computational hardware (cloud computing, GPUs, and TPUs) and the rise of deep learning. Medical data generated from large molecular screening profiles, personal health or pathology records, and public health organizations could benefit from analysis by Artificial Intelligence (AI) approaches to speed up and prevent failures in the drug discovery pipeline. We present applications of AI at various stages of drug discovery pipelines, including the inherently computational approaches of de novo design and prediction of a drug's likely properties. Open-source databases and AI-based software tools that facilitate drug design are discussed along with their associated problems of molecule representation, data collection, complexity, labeling, and disparities among labels. How contemporary AI methods, such as graph neural networks, reinforcement learning, and generated models, along with structure-based methods, (i.e., molecular dynamics simulations and molecular docking) can contribute to drug discovery applications and analysis of drug responses is also explored. Finally, recent developments and investments in AI-based start-up companies for biotechnology, drug design and their current progress, hopes and promotions are discussed in this article.

Analyzing the Geometry and Dynamics of Viral Structures: A Review of Computational Approaches Based on Alpha Shape Theory, Normal Mode Analysis, and Poisson-Boltzmann Theories

The current SARS-CoV-2 pandemic highlights our fragility when we are exposed to emergent viruses either directly or through zoonotic diseases. Fortunately, our knowledge of the biology of those viruses is improving. In particular, we have more and more structural information on virions, i.e., the infective form of a virus that includes its genomic material and surrounding protective capsid, and on their gene products. It is important to have methods that enable the analyses of structural information on such large macromolecular systems. We review some of those methods in this paper. We focus on understanding the geometry of virions and viral structural proteins, their dynamics, and their energetics, with the ambition that this understanding can help design antiviral agents. We discuss those methods in light of the specificities of those structures, mainly that they are huge. We focus on three of our own methods based on the alpha shape theory for computing geometry, normal mode analyses to study dynamics, and modified Poisson-Boltzmann theories to study the organization of ions and co-solvent and solvent molecules around biomacromolecules. The corresponding software has computing times that are compatible with the use of regular desktop computers. We show examples of their applications on some outer shells and structural proteins of the West Nile Virus.

Investigating the Orientation of an Interfacially Adsorbed Monoclonal Antibody and Its Fragments Using Neutron Reflection

Interfacial adsorption is a molecular process occurring during the production, purification, transport, and storage of antibodies, with a direct impact on their structural stability and subsequent implications on their bioactivities. While the average conformational orientation of an adsorbed protein can be readily determined, its associated structures are more complex to characterize. Neutron reflection has been used in this work to investigate the conformational orientations of the monoclonal antibody COE-3 and its Fab and Fc fragments at the oil/water and air/water interfaces. Rigid body rotation modeling was found to be suitable for globular and relatively rigid proteins such as the Fab and Fc fragments but less so for relatively flexible proteins such as full COE-3. Fab and Fc fragments adopted a 'flat-on' orientation at the air/water interface, minimizing the thickness of the protein layer, but they adopted a substantially tilted orientation at the oil/water interface with increased layer thickness. In contrast, COE-3 was found to adsorb in tilted orientations at both interfaces, with one fragment protruding into the solution. This work demonstrates that rigid-body modeling can provide additional insights into protein layers at various interfaces relevant to bioprocess engineering.

α-SAS: an integrative approach for structural modeling of biological macromolecules in solution

Modern small-angle scattering (SAS) experiments with neutrons (SANS) or X-rays (SAXS) combined with contrast variation provide comprehensive information about the structure of large multicomponent macromolecules in solution and allow the size, shape and relative arrangement of each component to be mapped out. To obtain such information, it is essential to perform well designed experiments, in which all necessary steps, from assessing sample suitability to structure modeling, are properly executed. This paper describes α-SAS, an integrative approach that is useful for effectively planning a biological contrast-variation SAS experiment. The accurate generation of expected experimental intensities using α-SAS allows the substantial acceleratation of research into the structure and function of biomacromolecules by minimizing the time and costs associated with performing a SAS experiment. The method is validated using a few basic structures with known analytical expressions for scattering intensity and using experimental SAXS data from Arabidopsis β-amylase 1 protein and SANS data from the histidine kinase–Sda complex and from human dystrophin without and with a membrane-mimicking nanodisk. Simulation of a SANS contrast-variation experiment is performed for synthetic nanobodies that effectively neutralize SARS-CoV-2.

Structural and functional insights into ABHD5, a ligand-regulated lipase co-activator

Alpha/beta hydrolase domain-containing protein 5 (ABHD5) is a highly conserved protein that regulates various lipid metabolic pathways via interactions with members of the perilipin (PLIN) and Patatin-like phospholipase domain-containing protein (PNPLA) protein families. Loss of function mutations in ABHD5 result in Chanarin-Dorfman Syndrome (CDS), characterized by ectopic lipid accumulation in numerous cell types and severe ichthyosis. Recent data demonstrates that ABHD5 is the target of synthetic and endogenous ligands that might be therapeutic beneficial for treating metabolic diseases and cancers. However, the structural basis of ABHD5 functional activities, such as protein-protein interactions and ligand binding is presently unknown. To address this gap, we constructed theoretical structural models of ABHD5 by comparative modeling and topological shape analysis to assess the spatial patterns of ABHD5 conformations computed in protein dynamics. We identified functionally important residues on ABHD5 surface for lipolysis activation by PNPLA2, lipid droplet targeting and PLIN-binding. We validated the computational model by examining the effects of mutating key residues in ABHD5 on an array of functional assays. Our integrated computational and experimental findings provide new insights into the structural basis of the diverse functions of ABHD5 as well as pathological mutations that result in CDS.

Analysis of changes of cavity volumes in predefined directions of protein motions and cavity flexibility

Dynamics of protein cavities associated with protein fluctuations and conformational plasticity is essential for their biological function. NMR ensembles, molecular dynamics (MD) simulations, and normal mode analysis (NMA) provide appropriate frameworks to explore functionally relevant protein dynamics and cavity changes relationships. Within this context, we have recently developed analysis of null areas (ANA), an efficient method to calculate cavity volumes. ANA is based on a combination of algorithms that guarantees its robustness against numerical differentiations. This is a unique feature with respect to other methods. Herein, we present an updated and improved version that expands it use to quantify changes in cavity features, like volume and flexibility, due to protein structural distortions performed on predefined biologically relevant directions, for example, directions of largest contribution to protein fluctuations (principal component analysis [PCA modes]) obtained by MD simulations or ensembles of NMR structures, collective NMA modes or any other direction of motion associated with specific conformational changes. A web page has been developed where its facilities are explained in detail. First, we show that ANA can be useful to explore gradual changes of cavity volume and flexibility associated with protein ligand binding. Secondly, we perform a comparison study of the extent of variability between protein backbone structural distortions, and changes in cavity volumes and flexibilities evaluated for an ensemble of NMR active and inactive conformers of the epidermal growth factor receptor structures. Finally, we compare changes in size and flexibility between sets of NMR structures for different homologous chains of dynein.

Parameterizing elastic network models to capture the dynamics of proteins

Coarse-grained normal mode analyses of protein dynamics rely on the idea that the geometry of a protein structure contains enough information for computing its fluctuations around its equilibrium conformation. This geometry is captured in the form of an elastic network (EN), namely a network of edges between its residues. The normal modes of a protein are then identified with the normal modes of its EN. Different approaches have been proposed to construct ENs, focusing on the choice of the edges that they are comprised of, and on their parameterizations by the force constants associated with those edges. Here we propose new tools to guide choices on these two facets of EN. We study first different geometric models for ENs. We compare cutoff-based ENs, whose edges have lengths that are smaller than a cutoff distance, with Delaunay-based ENs and find that the latter provide better representations of the geometry of protein structures. We then derive an analytical method for the parameterization of the EN such that its dynamics leads to atomic fluctuations that agree with experimental B-factors. To limit overfitting, we attach a parameter referred to as flexibility constant to each atom instead of to each edge in the EN. The parameterization is expressed as a non-linear optimization problem whose parameters describe both rigid-body and internal motions. We show that this parameterization leads to improved ENs, whose dynamics mimic MD simulations better than ENs with uniform force constants, and reduces the number of normal modes needed to reproduce functional conformational changes.

Voronoia 4-ever

We present an updated version of the Voronoia service that enables fully automated analysis of the atomic packing density of macromolecules. Voronoia combines previous efforts to analyse 3D protein and RNA structures into a single service, combined with state-of-the-art online visualization. Voronoia uses the Voronoi cell method to calculate the free space between neighbouring atoms to estimate van der Waals interactions. Compared to other methods that derive van der Waals interactions by calculating solvent-free surfaces, it explicitly considers volume or packing defects. Large internal voids refer either to water molecules or ions unresolved by X-ray crystallography or cryo-EM, cryptic ligand binding pockets, or parts of a structural model that require further refinement. Voronoia is, therefore mainly used for functional analyses of 3D structures and quality assessments of structural models. Voronoia 4-ever updates the database of precomputed packing densities of PDB entries, allows uploading multiple structures, adds new filter options and facilitates direct access to the results through intuitive display with the NGL viewer. Voronoia is available at: htttp://proteinformatics.org/voronoia.

Identifying Primate ACE2 Variants That Confer Resistance to SARS-CoV-2

SARS-CoV-2 infects humans through the binding of viral S-protein (spike protein) to human angiotensin I converting enzyme 2 (ACE2). The structure of the ACE2-S-protein complex has been deciphered and we focused on the 27 ACE2 residues that bind to S-protein. From human sequence databases, we identified nine ACE2 variants at ACE2-S-protein binding sites. We used both experimental assays and protein structure analysis to evaluate the effect of each variant on the binding affinity of ACE2 to S-protein. We found one variant causing complete binding disruption, two and three variants, respectively, strongly and mildly reducing the binding affinity, and two variants strongly enhancing the binding affinity. We then collected the ACE2 gene sequences from 57 nonhuman primates. Among the 6 apes and 20 Old World monkeys (OWMs) studied, we found no new variants. In contrast, all 11 New World monkeys (NWMs) studied share four variants each causing a strong reduction in binding affinity, the Philippine tarsier also possesses three such variants, and 18 of the 19 prosimian species studied share one variant causing a strong reduction in binding affinity. Moreover, one OWM and three prosimian variants increased binding affinity by >50%. Based on these findings, we proposed that the common ancestor of primates was strongly resistant to and that of NWMs was completely resistant to SARS-CoV-2 and so is the Philippine tarsier, whereas apes and OWMs, like most humans, are susceptible. This study increases our understanding of the differences in susceptibility to SARS-CoV-2 infection among primates.

A novel measure to analyze protein structures: Aspect ratio in protein alpha shapes

Proteins' three-dimensional (3D) structures are analyzed traditionally using geometric descriptors such as torsional angles and inter-atomic distances. In this study a measure that is borrowed from computational geometry, aspect ratio of each tetrahedron in alpha shapes of proteins, is utilized. This geometric descriptor differentiates alpha and beta structural classes of proteins when combined with principal components analysis. The method converts the structures of individual proteins, 3D coordinates of the atoms, to points on a plane. It has a high degree of accuracy in differentiating R and T structures of hemoglobin. Therefore, it is anticipated that the geometric measure can be used successfully in a method that is extended to solve classification problems in machine learning.

Exact Topology of the Dynamic Probability Surface of an Activated Process by Persistent Homology

To gain insight into the reaction mechanism of activated processes, we introduce an exact approach for quantifying the topology of high-dimensional probability surfaces of the underlying dynamic processes. Instead of Morse indexes, we study the homology groups of a sequence of superlevel sets of the probability surface over high-dimensional configuration spaces using persistent homology. For alanine-dipeptide isomerization, a prototype of activated processes, we identify locations of probability peaks and connecting ridges, along with measures of their global prominence. Instead of a saddle point, the transition state ensemble (TSE) of conformations is at the most prominent probability peak after reactants/products, when proper reaction coordinates are included. Intuition-based models, even those exhibiting a double-well, fail to capture the dynamics of the activated process. Peak occurrence, prominence, and locations can be distorted upon subspace projection. While principal component analysis accounts for conformational variance, it inflates the complexity of the surface topology and destroys the dynamic properties of the topological features. In contrast, TSE emerges naturally as the most prominent peak beyond the reactant/product basins, when projected to a subspace of minimum dimension containing the reaction coordinates. Our approach is general and can be applied to investigate the topology of high-dimensional probability surfaces of other activated processes.

Relation-Constrained 3D Reconstruction of Buildings in Metropolitan Areas from Photogrammetric Point Clouds

The complexity and variety of buildings and the defects of point cloud data are the main challenges faced by 3D urban reconstruction from point clouds, especially in metropolitan areas. In this paper, we developed a method that embeds multiple relations into a procedural modelling process for the automatic 3D reconstruction of buildings from photogrammetric point clouds. First, a hybrid tree of constructive solid geometry and boundary representation (CSG-BRep) was built to decompose the building bounding space into multiple polyhedral cells based on geometric-relation constraints. The cells that approximate the shapes of buildings were then selected based on topological-relation constraints and geometric building models were generated using a reconstructing CSG-BRep tree. Finally, different parts of buildings were retrieved from the CSG-BRep trees, and specific surface types were recognized to convert the building models into the City Geography Markup Language (CityGML) format. The point clouds of 105 buildings in a metropolitan area in Hong Kong were used to evaluate the performance of the proposed method. Compared with two existing methods, the proposed method performed the best in terms of robustness, regularity, and topological correctness. The CityGML building models enriched with semantic information were also compared with the manually digitized ground truth, and the high level of consistency between the results suggested that the produced models will be useful in smart city applications.

Simulation of pH-Dependent, Loop-Based Membrane Protein Gating Using Pretzel

Bacterial porins often exhibit ion conductance and gating behavior which can be modulated by pH. However, the underlying control mechanism of gating is often complex, and direct inspection of the protein structure is generally insufficient for full mechanistic understanding. Here we describe Pretzel, a computational framework that can effectively model loop-based gating events in membrane proteins. Our method combines Monte Carlo conformational sampling, structure clustering, ensemble energy evaluation, and a topological gating criterion to model the equilibrium gating state under the pH environment of interest. We discuss details of applying Pretzel to the porin outer membrane protein G (OmpG).

Analytical calculation of the solvent-accessible surface area and its nuclear gradients by stereographic projection: A general approach for molecules, polymers, nanotubes, helices, and surfaces

In this article, we explore an alternative to the analytical Gauss-Bonnet approach for computing the solvent-accessible surface area (SASA) and its nuclear gradients. These two key quantities are required to evaluate the nonelectrostatic contribution to the solvation energy and its nuclear gradients in implicit solvation models. We extend a previously proposed analytical approach for finite systems based on the stereographic projection technique to infinite periodic systems such as polymers, nanotubes, helices, or surfaces and detail its implementation in the Crystal code. We provide the full derivation of the SASA nuclear gradients, and introduce an iterative perturbation scheme of the atomic coordinates to stabilize the gradients calculation for certain difficult symmetric systems. An excellent agreement of computed SASA with reference analytical values is found for finite systems, while the SASA size-extensivity is verified for infinite periodic systems. In addition, correctness of the analytical gradients is confirmed by the excellent agreement obtained with numerical gradients and by the translational invariance achieved, both for finite and infinite periodic systems. Overall therefore, the stereographic projection approach appears as a general, simple, and efficient technique to compute the key quantities required for the calculation of the nonelectrostatic contribution to the solvation energy and its nuclear gradients in implicit solvation models applicable to both finite and infinite periodic systems.

Shape-preserving elastic solid models of macromolecules

Mass-spring models have been a standard approach in molecular modeling for the last few decades, such as elastic network models (ENMs) that are widely used for normal mode analysis. In this work, we present a vastly different elastic solid model (ESM) of macromolecules that shares the same simplicity and efficiency as ENMs in producing the equilibrium dynamics and moreover, offers some significant new features that may greatly benefit the research community. ESM is different from ENM in that it treats macromolecules as elastic solids. Our particular version of ESM presented in this work, named αESM, captures the shape of a given biomolecule most economically using alpha shape, a well-established technique from the computational geometry community. Consequently, it can produce most economical coarse-grained models while faithfully preserving the shape and thus makes normal mode computations and visualization of extremely large complexes more manageable. Secondly, as a solid model, ESM’s close link to finite element analysis renders it ideally suited for studying mechanical responses of macromolecules under external force. Lastly, we show that ESM can be applied also to structures without atomic coordinates such as those from cryo-electron microscopy. The complete MATLAB code of αESM is provided.

Mass-spring models have been a standard approach in classical molecular modeling where atoms are modeled as spheres with a mass and their interactions modeled as springs. The models have been extremely successful. Thinking ahead, however, as molecular systems of our interest grow more quickly in size or dimension than what our computation resources can keep up with, some adjustments in methodology are timely. This work presents a vastly different elastic solid model (ESM) of macromolecules that shares the same simplicity and efficiency as mass-spring models in producing the equilibrium dynamics and moreover, offers some unique features that make it suitable for much larger systems. ESM is different from ENMs in that it treats macromolecules as elastic solids. Our particular version of ESM model presented in this work, named αESM, captures the shape of a given biomolecule most economically using alpha shape, a well-established technique from the computational geometry community. Consequently, it can produce most economical coarse-grained models while faithfully preserving the shape. ESM can be applied also to structures without atomic coordinates such as those from cryo-electron microscopy.

Dynamical Detection of Boundaries and Cavities in Biophysical Cell-Based Simulations of Growing Tumor Tissues

Cell-based lattice-free simulations of the growth of tumor tissues require the definition of geometrical and topological relations among cells and the other basic elements of the simulation (most notably the local and the global environments). This is necessary for the correct description of the biochemistry of tumor tissues, and to implement the biomechanical interactions among cells. Weak cell-cell forces and the necrosis of tumor tissues due to poor vascularization can lead to the formation of cavities - i.e., regions without viable cells and filled with cellular debris and fluids. It is important to give an accurate geometrical/topological description of the resulting microenvironment that plays an important role in the pathology of cancer. In this paper, we concentrate on simulations of the growth of avascular solid tumors and we describe the STAR (Shape of Tumors from Algorithmic Reconstruction) algorithm that defines the shape of clusters of cells and searches for the boundary and cavities in a 3D environment. The algorithm is GPU-based and exploits the high degree of parallelism of GPUs. The final implementation achieves a 30-fold speedup with respect to a previous CPU-based version.

Predicting Oncogenic Missense Mutations

With the rapid progress of cancer genome studies, many missense mutations in populations of somatic cells of different cancer types and at different stages have been identified. However, it is challenging to understand the implications of these cancer-related variants. We have developed a computational method that integrates structural, topographical, and evolutionary information for assessments of biochemical effects and the extent of deleteriousness of the cancer-related variants. We have mapped somatic missense mutations from the Catalogue of Somatic Mutations In Cancer (COSMIC) to 3D structures in the Protein Data Bank (PDB). Our results show that a large portion of these missense mutations is located on protein surface pockets, which often serve as a structural and functional unit of cancer variants. We provide detailed analysis of several examples and assessment on the importance of these variants, including prediction of previously unreported cancer-variants, along with independent evidence from the literature. Furthermore, we show our predictions can inform on the functional roles and the mechanism of predicted cancer variants.

LAGUERRE-INTERSECTION METHOD FOR IMPLICIT SOLVATION

Explicit solvent molecular dynamics simulations of a macromolecule are slow as the number of solvent atoms considered typically increases by order of magnitude. Implicit methods introduce surface-dependent corrections to the force field, gaining speed at the expense of accuracy. Properties such as molecular interface surfaces, volumes and cavities are captured by Laguerre tessellations of macromolecules. However, Laguerre cells of exterior atoms tend to be overly large or unbounded. Our method, the inclusion-exclusion based Laguerre-Intersection method, caps cells in a physically accurate manner by considering the intersection of the space-filling diagram with the Laguerre tessellation. We optimize an adjustable parameter, the weight, to ensure the areas and volumes of capped cells exposed to solvent are as close as possible, on average, to those computed from equilibrated explicit solvent simulations. The contact planes are radical planes, meaning that as the solvent weight is varied, interior cells remain constant. We test the consistency of our model using a high-quality trajectory of HIV-protease, a dimer with flexible loops and open-close transitions. We also compare our results with interval-arithmetic Gauss-Bonnet based method. Optimal solvent parameters quickly converge, which we use to illustrate the increased fidelity of the Laguerre-Intersection method over two recently proposed methods as compared to the explicit model.

AZT acts as an anti-influenza nucleotide triphosphate targeting the catalytic site of A/PR/8/34/H1N1 RNA dependent RNA polymerase

To develop potent drugs that inhibit the activity of influenza virus RNA dependent RNA polymerase (RdRp), a set of compounds favipiravir, T-705, T-1105 and T-1106, ribavirin, ribavirin triphosphate viramidine, 2FdGTP (2'-deoxy-2'-fluoroguanosine triphosphate) and AZT-TP (3'-Azido-3'-deoxy-thymidine-5'-triphosphate) were docked with a homology model of IAV RdRp from the A/PR/8/34/H1N1 strain. These compounds bind to four pockets A-D of the IAV RdRp with different mechanism of action. In addition, AZT-TP also binds to the PB1 catalytic site near to the tip of the priming loop with a highest ΔG of - 16.7 Kcal/mol exhibiting an IC₅₀ of 1.12 µM in an in vitro enzyme transcription assay. This shows that AZT-TP mainly prevents the incorporation of incoming nucleotide involved in initiation of vRNA replication. Conversely, 2FdGTP used as a positive control binds to pocket-B at the end of tunnel-II with a highest ΔG of - 16.3 Kcal/mol inhibiting chain termination with a similar IC₅₀ of 1.12 µM. Overall, our computational results in correlation with experimental studies gives information for the first time about the binding modes of the known influenza antiviral compounds in different models of vRNA replication by IAV RdRp. This in turn gives new structural insights for the development of new therapeutics exhibiting high specificity to the PB1 catalytic site of influenza A viruses.

Intermolecular Voids in Lipid Bilayers in the Presence of Glycyrrhizic Acid

It is known that glycyrrhizic acid (GA) promotes the enhancement of the activity of several medicines. This is attributed to the fact that GA increases the membrane permeability of small drug molecules. There is an opinion that GA facilitates the formation of additional large voids in the membrane, which enhance the passive diffusion of molecules across the membrane. In this work, we investigate how GA influences the intermolecular voids using the molecular dynamics simulation. We calculate the interstitial spheres (empty spheres inscribed between molecules) in model DPPC and DOPC bilayers, both pure and with the addition of cholesterol. It was observed that the addition of GA does not lead to the formation of new large interstitial spheres; i.e., new large voids do not appear. The distribution of empty volume inside the bilayers is also studied. We calculated the profiles of the empty volume fraction both from the middle plane of the bilayer and from its outer surface (from the lipid-water interface). This analysis has shown that the addition of GA does not cause the increase of the empty volume in the bilayer; moreover, there is a slight decrease in the bilayers with cholesterol. Thus, we have not found a confirmation of the simplest hypothesis that individual GA molecules induce pores in the membrane.

On quantification of geometry and topology of protein pockets and channels for assessing mutation effects

Geometric and topological features of proteins such as voids, pockets and channels are important for protein functions. We discuss a method for visualizing protein pockets and channels based on orthogonal spheres computed from alpha shapes of the protein structures, and how metric properties of channel surfaces can be mapped. In addition, we discuss how structurally prominent sites, such as constriction sties in channels, can be computed, which may help to understand protein functions and mutation effects, with implications in developing novel therapeutic interventions.

Robust Production, Crystallization, Structure Determination, and Analysis of [Fe-S] Proteins: Uncovering Control of Electron Shuttling and Gating in the Respiratory Metabolism of Molybdopterin Guanine Dinucleotide Enzymes

[Fe-S] clusters are essential cofactors in all domains of life. They play many biological roles due to their unique abilities for electron transfer and conformational control. Yet, producing and analyzing Fe-S proteins can be difficult and even misleading if not done anaerobically. Due to unique redox properties of [Fe-S] clusters and their oxygen sensitivity, they pose multiple challenges and can lose enzymatic activity or cause their component proteins to be structurally disordered due to [Fe-S] cluster oxidation and loss in air. Here we highlight tested protocols and strategies enabling efficient and stable [Fe-S] protein production, purification, crystallization, X-ray diffraction data collection, and structure determination. From multiple high-resolution anaerobic crystal structures, we furthermore analyze exemplary data defining [Fe-S] clusters, substrate entry, and product exit for the functional oxidation states of type II molybdo-bis(molybdopterin guanine dinucleotide) (Mo-bisMGD) enzymes. Notably, these enzymes perform electron shuttling between quinone pools and specific substrates to catalyze respiratory metabolism. The identified structure-activity relationships for this enzyme class have broad implications germane to perchlorate environments on Earth and Mars extending to an alternative mechanism underlying metabolic origins for the evolution of the oxygen atmosphere. Integrated structural analyses of type II Mo-bisMGD enzymes unveil novel distinctive shared molecular mechanisms for dynamic control of substrate entry and product release gated by hydrophobic residues. Collective findings support a prototypic model for type II Mo-bisMGD enzymes including insights for a fundamental molecular mechanistic understanding of selectivity and regulation by a conformationally gated channel with general implications for [Fe-S] cluster respiratory enzymes.

A general method for determining molecular interfaces and layers

A general and direct computational scheme to locate the surface separating arbitrarily shaped domains made up of molecules (or any other particles) has been developed and is described and illustrated for several, both artificial and physical examples. The proposed scheme consists of two modules: (i) triangulation and (ii) assignment of simplices to domains. Three different triangulation methods are employed, viz., the Delaunay triangulation, regular triangulation, and quasi-triangulation. In the triangulated system, the assignment step is carried out in two different ways, one based on the characteristic metric of a particular triangulation procedure and the other on the concept of a touching sphere. Some of the combinations of the triangulation and assignment steps lead to methods already used by others to find interfacial or surface molecules, namely the alpha-shape-based method of Usabiaga nad Duque [Phys. Rev. E 79 (2009) 046709] and GITIM of Sega et al. [J. Chem. Phys. 138 (2013) 044110]. The resulting surface is defined not only as a discrete set of particles, but it is build up of facets of the triangulation forming a broken line in two dimensions or a polyhedral surface in three dimensions. Individual molecular layers are identified in a very straightforward manner, starting with the interfacial layer itself and proceeding into the interior of the phase. The proposed scheme is illustrated first by identifying border molecules of pre-sampled domains of several shapes in a plane and then applied to five physically meaningful examples: thin films, near critical water, liquid water slab in an electric field, liquid water at a solid wall, and water at condition of electric-field-induced jetting. Performance of the considered methods is critically assessed. Treatment of domains forming percolating clusters through periodic boundary conditions is also described along with the determination of their periodicity and dimensionality.

Molecular Basis of ABHD5 Lipolysis Activation

Alpha-beta hydrolase domain-containing 5 (ABHD5), the defective gene in human Chanarin-Dorfman syndrome, is a highly conserved regulator of adipose triglyceride lipase (ATGL)-mediated lipolysis that plays important roles in metabolism, tumor progression, viral replication, and skin barrier formation. The structural determinants of ABHD5 lipolysis activation, however, are unknown. We performed comparative evolutionary analysis and structural modeling of ABHD5 and ABHD4, a functionally distinct paralog that diverged from ABHD5 ~500 million years ago, to identify determinants of ABHD5 lipolysis activation. Two highly conserved ABHD5 amino acids (R299 and G328) enabled ABHD4 (ABHD4 N303R/S332G) to activate ATGL in Cos7 cells, brown adipocytes, and artificial lipid droplets. The corresponding ABHD5 mutations (ABHD5 R299N and ABHD5 G328S) selectively disrupted lipolysis without affecting ATGL lipid droplet translocation or ABHD5 interactions with perilipin proteins and ABHD5 ligands, demonstrating that ABHD5 lipase activation could be dissociated from its other functions. Structural modeling placed ABHD5 R299/G328 and R303/G332 from gain-of-function ABHD4 in close proximity on the ABHD protein surface, indicating they form part of a novel functional surface required for lipase activation. These data demonstrate distinct ABHD5 functional properties and provide new insights into the functional evolution of ABHD family members and the structural basis of lipase regulation.

Fast and Accurate Accessible Surface Area Prediction Without a Sequence Profile

A fast accessible surface area (ASA) predictor is presented. In this new approach no residue mutation profiles generated by multiple sequence alignments are used as inputs. Instead, we use only single sequence information and global features such as single-residue and two-residue compositions of the chain. The resulting predictor is both highly more efficient than sequence alignment based predictors and of comparable accuracy to them. Introduction of the global inputs significantly helps achieve this comparable accuracy. The predictor, termed ASAquick, is found to perform similarly well for so-called easy and hard cases indicating generalizability and possible usability for de-novo protein structure prediction. The source code and a Linux executables for ASAquick are available from Research and Information Systems at http://mamiris.com and from the Battelle Center for Mathematical Medicine at http://mathmed.org .

Ligand-based virtual screening interface between PyMOL and LiSiCA

Ligand-based virtual screening of large small-molecule databases is an important step in the early stages of drug development. It is based on the similarity principle and is used to reduce the chemical space of large databases to a manageable size where chosen ligands can be experimentally tested. Ligand-based virtual screening can also be used to identify bioactive molecules with different basic scaffolds compared to already known bioactive molecules, thus having the potential to increase the structural variability of compounds. Here, we present an interface between the popular molecular graphics system PyMOL and the ligand-based virtual screening software LiSiCA available at http://insilab.org/lisica-plugin and demonstrate how this interface can be used in the early stages of drug discovery process.Graphical Abstract

The Poisson-Voronoi tessellation: relationships for edges

In a unified approach, this paper presents distributional properties of a Voronoi tessellation generated by a homogeneous Poisson point process in the Euclidean space of arbitrary dimension. Probability density functions and moments are given for characteristics of the ‘typical’ edge in lower-dimensional section hyperplanes (edge lengths, adjacent angles). We investigate relationships between edges and their neighbours, called Poisson points or centres; namely angular distributions, distances, and positions of neighbours relative to the edge. The approach is analytical, and the results are given partly explicitly and partly as integral expressions, which are suitable for the numerical calculations also presented.

Mapping the Accessible Conformational Landscape of an Insect Carboxylesterase Using Conformational Ensemble Analysis and Kinetic Crystallography

The proper function of enzymes often depends upon their efficient interconversion between particular conformational sub-states on a free-energy landscape. Experimentally characterizing these sub-states is challenging, which has limited our understanding of the role of protein dynamics in many enzymes. Here, we have used a combination of kinetic crystallography and detailed analysis of crystallographic protein ensembles to map the accessible conformational landscape of an insect carboxylesterase (LcαE7) as it traverses all steps in its catalytic cycle. LcαE7 is of special interest because of its evolving role in organophosphate insecticide resistance. Our results reveal that a dynamically coupled network of residues extends from the substrate-binding site to a surface loop. Interestingly, the coupling of this network that is apparent in the apoenzyme appears to be reduced in the phosphorylated enzyme intermediate. Altogether, the results of this work highlight the importance of protein dynamics to enzyme function and the evolution of new activity.

Molecular Basis of Ligand-Dependent Regulation of NadR, the Transcriptional Repressor of Meningococcal Virulence Factor NadA

Neisseria adhesin A (NadA) is present on the meningococcal surface and contributes to adhesion to and invasion of human cells. NadA is also one of three recombinant antigens in the recently-approved Bexsero vaccine, which protects against serogroup B meningococcus. The amount of NadA on the bacterial surface is of direct relevance in the constant battle of host-pathogen interactions: it influences the ability of the pathogen to engage human cell surface-exposed receptors and, conversely, the bacterial susceptibility to the antibody-mediated immune response. It is therefore important to understand the mechanisms which regulate nadA expression levels, which are predominantly controlled by the transcriptional regulator NadR (Neisseria adhesin A Regulator) both in vitro and in vivo. NadR binds the nadA promoter and represses gene transcription. In the presence of 4-hydroxyphenylacetate (4-HPA), a catabolite present in human saliva both under physiological conditions and during bacterial infection, the binding of NadR to the nadA promoter is attenuated and nadA expression is induced. NadR also mediates ligand-dependent regulation of many other meningococcal genes, for example the highly-conserved multiple adhesin family (maf) genes, which encode proteins emerging with important roles in host-pathogen interactions, immune evasion and niche adaptation. To gain insights into the regulation of NadR mediated by 4-HPA, we combined structural, biochemical, and mutagenesis studies. In particular, two new crystal structures of ligand-free and ligand-bound NadR revealed (i) the molecular basis of ‘conformational selection’ by which a single molecule of 4-HPA binds and stabilizes dimeric NadR in a conformation unsuitable for DNA-binding, (ii) molecular explanations for the binding specificities of different hydroxyphenylacetate ligands, including 3Cl,4-HPA which is produced during inflammation, (iii) the presence of a leucine residue essential for dimerization and conserved in many MarR family proteins, and (iv) four residues (His7, Ser9, Asn11 and Phe25), which are involved in binding 4-HPA, and were confirmed in vitro to have key roles in the regulatory mechanism in bacteria. Overall, this study deepens our molecular understanding of the sophisticated regulatory mechanisms of the expression of nadA and other genes governed by NadR, dependent on interactions with niche-specific signal molecules that may play important roles during meningococcal pathogenesis.

Serogroup B meningococcus (MenB) causes fatal sepsis and invasive meningococcal disease, particularly in young children and adolescents, as highlighted by recent MenB outbreaks in universities of the United States and Canada. The Bexsero vaccine protects against MenB and has recently been approved in > 35 countries worldwide. Neisseria adhesin A (NadA) present on the meningococcal surface can mediate binding to human cells and is one of the three MenB vaccine protein antigens. The amount of NadA exposed on the meningococcal surface also influences the antibody-mediated serum bactericidal response measured in vitro. A deep understanding of nadA expression is therefore important, otherwise the contribution of NadA to vaccine-induced protection against meningococcal meningitis may be underestimated. The abundance of surface-exposed NadA is regulated by the ligand-responsive transcriptional repressor NadR. Here, we present functional, biochemical and high-resolution structural data on NadR. Our studies provide detailed insights into how small molecule ligands, such as hydroxyphenylacetate derivatives, found in relevant host niches, modulate the structure and activity of NadR, by ‘conformational selection’ of inactive forms. These findings shed light on the regulation of NadR, a key MarR-family virulence factor of this important human pathogen.

Cavities and Excited States in Proteins

Protein cavities or voids are observed as defects in atomic packing. Cavities have long been suggested to play important roles in protein dynamics and function, but the underlying origin and mechanism remains elusive. Here, recent studies about the cavities characterized by high-pressure NMR spectroscopy have been reviewed. Analysis of the pressure-dependent chemical shifts showed both linear and nonlinear response of proteins to pressure. The linear response corresponded to compression within the native ensemble, while the nonlinear response indicated the involvement of low-lying excited states that were different from the native state. The finding of non-linear pressure shifts in various proteins suggested that the existence of the low-lying excited states was common for globular proteins. However, the absolute nonlinear coefficient values varied significantly from protein to protein, and showed a good correlation with the density of cavities. Extensive studies on hen lysozyme as a model system showed that the cavity hydration and water penetration into the interior of proteins was an origin of the conformational transition to the excited states. The importance of cavities for protein function and evolution has also been explained. In addition to these "equilibrium" cavities, there are also "transient" cavities formed in the interior of the protein structure, as manifested by the ring flip motions of aromatic rings. The significance of transient cavities, reflecting an intrinsic dynamic nature within the native state, has also been discussed.

Insights into stabilizing interactions in the distorted domain-swapped dimer ofSalmonella typhimuriumsurvival protein

The survival protein SurE fromSalmonella typhimurium(StSurE) is a dimeric protein that functions as a phosphatase. SurE dimers are formed by the swapping of a loop with a pair of β-strands and a C-terminal helix between two protomers. In a previous study, the Asp230 and His234 residues were mutated to Ala to abolish a hydrogen bond that was thought to be crucial for C-terminal helix swapping. These mutations led to functionally inactive and distorted dimers in which the two protomers were related by a rotation of 167°. New salt bridges involving Glu112 were observed in the dimeric interface of the H234A and D230A/H234A mutants. To explore the role of these salt bridges in the stability of the distorted structure, E112A, E112A/D230A, E112A/H234A, E112A/D230A/H234A, R179L/H180A/H234A and E112A/R179L/H180A/H234A mutants were constructed. X-ray crystal structures of the E112A, E112A/H234A and E112A/D230A mutants could be determined. The dimeric structures of the E112A and E112A/H234A mutants were similar to that of native SurE, while the E112A/D230A mutant had a residual rotation of 11° between theBchains upon superposition of theAchains of the mutant and native dimers. The native dimeric structure was nearly restored in the E112A/H234A mutant, suggesting that the new salt bridge observed in the H234A and D230A/H234A mutants was indeed responsible for the stability of their distorted structures. Catalytic activity was also restored in these mutants, implying that appropriate dimeric organization is necessary for the activity of SurE.

The effect of myoglobin crowding on the dynamics of water: an infrared study

Solutions containing 8 and 32 wt% myoglobin are studied by means of infrared spectroscopy, as a function of temperature (290 K and lower temperatures), in the mid- and far-infrared spectral range. Moreover, ultrafast time-resolved infrared measurements are performed at ambient temperature in the O-D stretching region. The results evidence that the vibrational properties of water remain the same in these myoglobin solutions (anharmonicity, vibrational relaxation lifetime…) and in neat water. However, the collective properties of the water molecules are significantly affected by the presence of the protein: the orientational time increases, the solid-liquid transition is affected in the most concentrated solution and the dynamical transition of the protein is observed, from the point of view of water, even in the least concentrated solution, proving that the water and myoglobin dynamics are coupled.

Alpha shape theory for 3D visualization and volumetric measurement of brain tumor progression using magnetic resonance images

Resection of brain tumors is a tricky task in surgery due to its direct influence on the patients' survival rate. Determining the tumor resection extent for its complete information via-à-vis volume and dimensions in pre- and post-operative Magnetic Resonance Images (MRI) requires accurate estimation and comparison. The active contour segmentation technique is used to segment brain tumors on pre-operative MR images using self-developed software. Tumor volume is acquired from its contours via alpha shape theory. The graphical user interface is developed for rendering, visualizing and estimating the volume of a brain tumor. Internet Brain Segmentation Repository dataset (IBSR) is employed to analyze and determine the repeatability and reproducibility of tumor volume. Accuracy of the method is validated by comparing the estimated volume using the proposed method with that of gold-standard. Segmentation by active contour technique is found to be capable of detecting the brain tumor boundaries. Furthermore, the volume description and visualization enable an interactive examination of tumor tissue and its surrounding. Admirable features of our results demonstrate that alpha shape theory in comparison to other existing standard methods is superior for precise volumetric measurement of tumor.