Alpha shapes applied to molecular shape characterization exhibit novel properties compared to established shape descriptors

The Importance of Using Realistic 3D Canopy Models to Calculate Light Interception in the Field

Quantifying canopy light interception provides insight into the effects of plant spacing, canopy structure, and leaf orientation on radiation distribution. This is essential for increasing crop yield and improving product quality. Canopy light interception can be quantified using 3-dimensional (3D) plant models and optical simulations. However, virtual 3D canopy models (VCMs) have often been used to quantify canopy light interception because realistic 3D canopy models (RCMs) are difficult to obtain in the field. This study aims to compare the differences in light interception between VCMs and RCM. A realistic 3D maize canopy model (RCM) was reconstructed over a large area of the field using an advanced unmanned aerial vehicle cross-circling oblique (CCO) route and the structure from motion-multi-view stereo method. Three types of VCMs (VCM-1, VCM-4, and VCM-8) were then created by replicating 1, 4, and 8 individual realistic plants constructed by CCO in the center of the corresponding RCM. The daily light interception per unit area (DLI), as computed for the 3 VCMs, exhibited marked deviation from the RCM, as evinced by the relative root mean square error (rRMSE) values of 20.22%, 17.38%, and 15.48%, respectively. Although this difference decreased as the number of plants used to replicate the virtual canopy increased, rRMSE of DLI for VCM-8 and RCM still reached 15.48%. It was also found that the difference in light interception between RCMs and VCMs was substantially smaller in the early stage (48 days after sowing [DAS]) than in the late stage (70 DAS). This study highlights the importance of using RCM when calculating light interception in the field, especially in the later growth stages of plants.

Identifying and profiling structural similarities between Spike of SARS-CoV-2 and other viral or host proteins with Machaon

Using protein structure to predict function, interactions, and evolutionary history is still an open challenge, with existing approaches relying extensively on protein homology and families. Here, we present Machaon, a data-driven method combining orientation invariant metrics on phi-psi angles, inter-residue contacts and surface complexity. It can be readily applied on whole structures or segments-such as domains and binding sites. Machaon was applied on SARS-CoV-2 Spike monomers of native, Delta and Omicron variants and identified correlations with a wide range of viral proteins from close to distant taxonomy ranks, as well as host proteins, such as ACE2 receptor. Machaon's meta-analysis of the results highlights structural, chemical and transcriptional similarities between the Spike monomer and human proteins, indicating a multi-level viral mimicry. This extended analysis also revealed relationships of the Spike protein with biological processes such as ubiquitination and angiogenesis and highlighted different patterns in virus attachment among the studied variants. Available at: https://machaonweb.com .

Machine learning based personalized drug response prediction for lung cancer patients

Lung cancers with a mutated epidermal growth factor receptor (EGFR) are a major contributor to cancer fatalities globally. Targeted tyrosine kinase inhibitors (TKIs) have been developed against EGFR and show encouraging results for survival rate and quality of life. However, drug resistance may affect treatment plans and treatment efficacy may be lost after about a year. Predicting the response to EGFR-TKIs for EGFR-mutated lung cancer patients is a key research area. In this study, we propose a personalized drug response prediction model (PDRP), based on molecular dynamics simulations and machine learning, to predict the response of first generation FDA-approved small molecule EGFR-TKIs, Gefitinib/Erlotinib, in lung cancer patients. The patient's mutation status is taken into consideration in molecular dynamics (MD) simulation. Each patient's unique mutation status was modeled considering MD simulation to extract molecular-level geometric features. Moreover, additional clinical features were incorporated into machine learning model for drug response prediction. The complete feature set includes demographic and clinical information (DCI), geometrical properties of the drug-target binding site, and the binding free energy of the drug-target complex from the MD simulation. PDRP incorporates an XGBoost classifier, which achieves state-of-the-art performance with 97.5% accuracy, 93% recall, 96.5% precision, and 94% F1-score, for a 4-class drug response prediction task. We found that modeling the geometry of the binding pocket combined with binding free energy is a good predictor for drug response. However, we observed that clinical information had a little impact on the performance of the model. The proposed model could be tested on other types of cancers. We believe PDRP will support the planning of effective treatment regimes based on clinical-genomic information. The source code and related files are available on GitHub at:   https://github.com/rizwanqureshi123/PDRP/ .

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.

Alpha Shape Analysis (ASA) Framework for Post- Clustering Property Determination in Atom Probe Tomographic Data

While application of clustering algorithms to atom probe tomography data have enabled quantification of solute clusters in terms of number density, size, and subcomposition there exist other properties (e.g., volume, surface area, and composition) that are better determined by defining an interface between the cluster and the surrounding matrix. The limitation in composition results from an ion selection step where the expected matrix ion types are omitted from the cluster search algorithm to enhance the contrast between the matrix and cluster and to reduce the complexity of the search. Previously, composition determination within solute clusters has utilized a secondary envelopment and erosion step on top of conventional methods such as maximum separation. In this work, we present a novel stochastic method that combines the particle identification fidelity of a conventional clustering algorithm with the analytical flexibility of mesh-based approaches through the generation of alpha shapes for each identified cluster. The corresponding mesh accounts for concave components of the clusters and determines the volume and surface area of the clusters; additionally, the mesh boundary is utilized to update the total composition according to the internal ions.

SAMPL7: Host-guest binding prediction by molecular dynamics and quantum mechanics

Statistical Assessment of Modeling of Proteins and Ligands (SAMPL) challenges provide routes to compare chemical quantities determined using computational chemistry approaches to experimental measurements that are shared after the competition. For this effort, several computational methods have been used to calculate the binding energies of Octa Acid (OA) and exo-Octa Acid (exoOA) host-guest systems for SAMPL7. The initial poses for molecular dynamics (MD) were generated by molecular docking. Binding free energy calculations were performed using molecular mechanics combined with Poisson-Boltzmann or generalized Born surface area solvation (MMPBSA/MMGBSA) approaches. The factors that affect the utility of the MMPBSA/MMGBSA approaches including solvation, partial charge, and solute entropy models were also analyzed. In addition to MD calculations, quantum mechanics (QM) calculations were performed using several different density functional theory (DFT) approaches. From SAMPL6 results, B3PW91-D3 was found to overestimate binding energies though it was effective for geometry optimizations, so it was considered for the DFT geometry optimizations in the current study, with single-point energy calculations carried out with B2PLYP-D3 with double-, triple-, and quadruple-ζ level basis sets. Accounting for dispersion effects, and solvation models was deemed essential for the predictions. MMGBSA and MMPBSA correlated better to experiment when used in conjunction with an empirical/linear correction.

Structural Heterogeneities of the Ribosome: New Frontiers and Opportunities for Cryo-EM

The extent of ribosomal heterogeneity has caught increasing interest over the past few years, as recent studies have highlighted the presence of structural variations of the ribosome. More precisely, the heterogeneity of the ribosome covers multiple scales, including the dynamical aspects of ribosomal motion at the single particle level, specialization at the cellular and subcellular scale, or evolutionary differences across species. Upon solving the ribosome atomic structure at medium to high resolution, cryogenic electron microscopy (cryo-EM) has enabled investigating all these forms of heterogeneity. In this review, we present some recent advances in quantifying ribosome heterogeneity, with a focus on the conformational and evolutionary variations of the ribosome and their functional implications. These efforts highlight the need for new computational methods and comparative tools, to comprehensively model the continuous conformational transition pathways of the ribosome, as well as its evolution. While developing these methods presents some important challenges, it also provides an opportunity to extend our interpretation and usage of cryo-EM data, which would more generally benefit the study of molecular dynamics and evolution of proteins and other complexes.

sensaas: Shape-based Alignment by Registration of Colored Point-based Surfaces

sensaas is a tool developed for aligning and comparing molecular shapes and sub-shapes. Alignment is obtained by registration of 3D point-based representations of the van der Waals surface. The method uses local properties of the shape to identify the correspondence relationships between two point clouds containing up to several thousand colored (labeled) points. Our rigid-body superimposition method follows a two-stage approach. An initial alignment is obtained by matching pose-invariant local 3D descriptors, called FPFH, of the input point clouds. This stage provides a global superimposition of the molecular surfaces, without any knowledge of their initial pose in 3D space. This alignment is then refined by optimizing the matching of colored points. In our study, each point is colored according to its closest atom, which itself belongs to a user defined physico-chemical class. Finally, sensaas provides an alignment and evaluates the molecular similarity by using Tversky coefficients. To assess the efficiency of this approach, we tested its ability to reproduce the superimposition of X-ray structures of the benchmarking AstraZeneca (AZ) data set and, compared its results with those generated by the two shape-alignment approaches shaep and shafts. We also illustrated submatching properties of our method with respect to few substructures and bioisosteric fragments. The code is available upon request from the authors (demo version at https://chemoinfo.ipmc.cnrs.fr/SENSAAS).

Advances in the Development of Shape Similarity Methods and Their Application in Drug Discovery

Molecular similarity is a key concept in drug discovery. It is based on the assumption that structurally similar molecules frequently have similar properties. Assessment of similarity between small molecules has been highly effective in the discovery and development of various drugs. Especially, two-dimensional (2D) similarity approaches have been quite popular due to their simplicity, accuracy and efficiency. Recently, the focus has been shifted toward the development of methods involving the representation and comparison of three-dimensional (3D) conformation of small molecules. Among the 3D similarity methods, evaluation of shape similarity is now gaining attention for its application not only in virtual screening but also in molecular target prediction, drug repurposing and scaffold hopping. A wide range of methods have been developed to describe molecular shape and to determine the shape similarity between small molecules. The most widely used methods include atom distance-based methods, surface-based approaches such as spherical harmonics and 3D Zernike descriptors, atom-centered Gaussian overlay based representations. Several of these methods demonstrated excellent virtual screening performance not only retrospectively but also prospectively. In addition to methods assessing the similarity between small molecules, shape similarity approaches have been developed to compare shapes of protein structures and binding pockets. Additionally, shape comparisons between atomic models and 3D density maps allowed the fitting of atomic models into cryo-electron microscopy maps. This review aims to summarize the methodological advances in shape similarity assessment highlighting advantages, disadvantages and their application in drug discovery.

Following Ramachandran 2: exit vector plot (EVP) analysis of disubstituted saturated rings

EVP analysis of common saturated rings revealed five regions (α–ε); only part of them corresponds to 3D molecular structures.

Facets on the convex hull of d-dimensional Brownian and Lévy motion

For stationary, homogeneous Markov processes (viz., Lévy processes, including Brownian motion) in dimension d≥3, we establish an exact formula for the average number of (d-1)-dimensional facets that can be defined by d points on the process's path. This formula defines a universality class in that it is independent of the increments' distribution, and it admits a closed form when d=3, a case which is of particular interest for applications in biophysics, chemistry, and polymer science. We also show that the asymptotical average number of facets behaves as 〈F_{T}^{(d)}〉∼2[ln(T/Δt)]^{d-1}, where T is the total duration of the motion and Δt is the minimum time lapse separating points that define a facet.

Following Ramachandran: exit vector plots (EVP) as a tool to navigate chemical space covered by 3D bifunctional scaffolds. The case of cycloalkanes

An approach to analysis and visualization of chemical space covered by disubstituted scaffolds, which is based on exit vector plots (EVP), is used for analysis of cycloalkane. Four clearly defined regions (α, β, γ and δ) are found in their EVP.

Three-dimensional compound comparison methods and their application in drug discovery

Virtual screening has been widely used in the drug discovery process. Ligand-based virtual screening (LBVS) methods compare a library of compounds with a known active ligand. Two notable advantages of LBVS methods are that they do not require structural information of a target receptor and that they are faster than structure-based methods. LBVS methods can be classified based on the complexity of ligand structure information utilized: one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D). Unlike 1D and 2D methods, 3D methods can have enhanced performance since they treat the conformational flexibility of compounds. In this paper, a number of 3D methods will be reviewed. In addition, four representative 3D methods were benchmarked to understand their performance in virtual screening. Specifically, we tested overall performance in key aspects including the ability to find dissimilar active compounds, and computational speed.

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.

A multi-fingerprint browser for the ZINC database

To confirm the activity of an initial small molecule 'hit compound' from an activity screening, one needs to probe the structure-activity relationships by testing close analogs. The multi-fingerprint browser presented here (http://dcb-reymond23.unibe.ch:8080/MCSS/) enables one to rapidly identify such close analogs among commercially available compounds in the ZINC database (>13 million molecules). The browser retrieves nearest neighbors of any query molecule in multi-dimensional chemical spaces defined by four different fingerprints, each of which represents relevant structural and pharmacophoric features in a different way: sFP (substructure fingerprint), ECFP4 (extended connectivity fingerprint), MQNs (molecular quantum numbers) and SMIfp (SMILES fingerprint). Distances are calculated using the city-block distance, a similarity measure that performs as well as Tanimoto similarity but is much faster to compute. The list of up to 1000 nearest neighbors of any query molecule is retrieved by the browser and can be then clustered using the K-means clustering algorithm to produce a focused list of analogs with likely similar bioactivity to be considered for experimental evaluation.

Measuring the shapes of macromolecules - and why it matters

The molecular basis of life rests on the activity of biological macromolecules, mostly nucleic acids and proteins. A perhaps surprising finding that crystallized over the last handful of decades is that geometric reasoning plays a major role in our attempt to understand these activities. In this paper, we address this connection between geometry and biology, focusing on methods for measuring and characterizing the shapes of macromolecules. We briefly review existing numerical and analytical approaches that solve these problems. We cover in more details our own work in this field, focusing on the alpha shape theory as it provides a unifying mathematical framework that enable the analytical calculations of the surface area and volume of a macromolecule represented as a union of balls, the detection of pockets and cavities in the molecule, and the quantification of contacts between the atomic balls. We have shown that each of these quantities can be related to physical properties of the molecule under study and ultimately provides insight on its activity. We conclude with a brief description of new challenges for the alpha shape theory in modern structural biology.

Skin injury model classification based on shape vector analysis

Background: Skin injuries can be crucial in judicial decision making. Forensic experts base their classification on subjective opinions. This study investigates whether known classes of simulated skin injuries are correctly classified statistically based on 3D surface models and derived numerical shape descriptors.

Methods: Skin injury surface characteristics are simulated with plasticine. Six injury classes – abrasions, incised wounds, gunshot entry wounds, smooth and textured strangulation marks as well as patterned injuries - with 18 instances each are used for a k-fold cross validation with six partitions. Deformed plasticine models are captured with a 3D surface scanner. Mean curvature is estimated for each polygon surface vertex. Subsequently, distance distributions and derived aspect ratios, convex hulls, concentric spheres, hyperbolic points and Fourier transforms are used to generate 1284-dimensional shape vectors. Subsequent descriptor reduction maximizing SNR (signal-to-noise ratio) result in an average of 41 descriptors (varying across k-folds). With non-normal multivariate distribution of heteroskedastic data, requirements for LDA (linear discriminant analysis) are not met. Thus, shrinkage parameters of RDA (regularized discriminant analysis) are optimized yielding a best performance with λ = 0.99 and γ = 0.001.

Results: Receiver Operating Characteristic of a descriptive RDA yields an ideal Area Under the Curve of 1.0for all six categories. Predictive RDA results in an average CRR (correct recognition rate) of 97,22% under a 6 partition k-fold. Adding uniform noise within the range of one standard deviation degrades the average CRR to 71,3%.

Conclusions: Digitized 3D surface shape data can be used to automatically classify idealized shape models of simulated skin injuries. Deriving some well established descriptors such as histograms, saddle shape of hyperbolic points or convex hulls with subsequent reduction of dimensionality while maximizing SNR seem to work well for the data at hand, as predictive RDA results in CRR of 97,22%. Objective basis for discrimination of non-overlapping hypotheses or categories are a major issue in medicolegal skin injury analysis and that is where this method appears to be strong. Technical surface quality is important in that adding noise clearly degrades CRR.

Trial registration: This study does not cover the results of a controlled health care intervention as only plasticine was used. Thus, there was no trial registration.

Chemical informatics: using molecular shape descriptors in structure-based drug design

The concept of molecular shape has been considered in various forms in the context of drug design. The following chapter details the application of molecular shape to the design of compound libraries for assessment of potential biological activity. Whilst the utility of shape descriptors is well documented in the area of ligand similarity, the use of shape descriptors is equally applicable to protein structures. Indeed, work has been published using various descriptors to compare proteins but little published where protein shape descriptors have been used to investigate ligand selectivity.

Bioactive Molecules: Perfectly Shaped for Their Target?

In this study, we examined target subsets extracted from the MDL Drug Data Report (MDDR)1 to identify specific molecular shape profiles that are representative for compounds active on those targets. Normalized Principal Moments of Inertia Ratios (NPRs)2 have been used to describe molecular shape of small molecules in a finite triangular descriptor space. The clustering behavior of the MDDR target subsets in a cell-based triangular system shows a significant difference compared to randomly sampled datasets and proves the capability of the NPR descriptor to provide information. For some of the target subsets, certain parts of the descriptor space are unlikely to be occupied by bioactive compounds. All analyzed datasets show a generally biased distribution of molecular shapes: the majority of their compounds exhibit a rod-like character. The influence of the employed 3D conformer generators on this distribution has been assessed as well as the capability of multiple conformations of compounds to increase the shape space covered.

Discovery of new antimalarial chemotypes through chemical methodology and library development

In an effort to expand the stereochemical and structural complexity of chemical libraries used in drug discovery, the Center for Chemical Methodology and Library Development at Boston University has established an infrastructure to translate methodologies accessing diverse chemotypes into arrayed libraries for biological evaluation. In a collaborative effort, the NIH Chemical Genomics Center determined IC(50)'s for Plasmodium falciparum viability for each of 2,070 members of the CMLD-BU compound collection using quantitative high-throughput screening across five parasite lines of distinct geographic origin. Three compound classes displaying either differential or comprehensive antimalarial activity across the lines were identified, and the nascent structure activity relationships (SAR) from this experiment used to initiate optimization of these chemotypes for further development.

Quantifying structure and performance diversity for sets of small molecules comprising small-molecule screening collections

Using a diverse collection of small molecules we recently found that compound sets from different sources (commercial; academic; natural) have different protein-binding behaviors, and these behaviors correlate with trends in stereochemical complexity for these compound sets. These results lend insight into structural features that synthetic chemists might target when synthesizing screening collections for biological discovery. We report extensive characterization of structural properties and diversity of biological performance for these compounds and expand comparative analyses to include physicochemical properties and three-dimensional shapes of predicted conformers. The results highlight additional similarities and differences between the sets, but also the dependence of such comparisons on the choice of molecular descriptors. Using a protein-binding dataset, we introduce an information-theoretic measure to assess diversity of performance with a constraint on specificity. Rather than relying on finding individual active compounds, this measure allows rational judgment of compound subsets as groups. We also apply this measure to publicly available data from ChemBank for the same compound sets across a diverse group of functional assays. We find that performance diversity of compound sets is relatively stable across a range of property values as judged by this measure, both in protein-binding studies and functional assays. Because building screening collections with improved performance depends on efficient use of synthetic organic chemistry resources, these studies illustrate an important quantitative framework to help prioritize choices made in building such collections.

Expanding stereochemical and skeletal diversity using petasis reactions and 1,3-dipolar cycloadditions

A short and modular synthetic pathway using intramolecular 1,3-dipolar cycloaddition reactions and yielding functionalized isoxazoles, isoxazolines, and isoxazolidines is described. The change in shape of previous compounds and those in this study is quantified and compared using principal moment-of-inertia shape analysis.