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Void distributions reveal structural link between jammed packings and protein cores

Physical Review E 2019年第2期99卷 022416-022416页

作者： John D. Treado Zhe Mei Lynne Regan Corey S. O'Hern Department of Mechanical Engineering & Materials Science Yale University New Haven Connecticut 06520 USA Integrated Graduate Program in Physical & Engineering Biology Yale University New Haven Connecticut 06520 USA Department of Chemistry Yale University New Haven Connecticut 06520 USA Department of Molecular Biophysics & Biochemistry Yale University New Haven Connecticut 06520 USA Department of Physics Yale University New Haven Connecticut 06520 USA Department of Applied Physics Yale University New Haven Connecticut 06520 USA Program in Computational Biology and Bioinformatics Yale University New Haven Connecticut 06520 USA

Dense packing of hydrophobic residues in the cores of globular proteins determines their stability. Recently, we have shown that protein cores possess packing fraction ϕ≈0.56, which is the same as dense, random packing of amino-acid-shaped particles. In this article, we compare the structural properties of protein cores and jammed packings of amino-acid-shaped particles in much greater depth by measuring their local and connected void regions. We find that the distributions of surface Voronoi cell volumes and local porosities obey similar statistics in both systems. We also measure the probability that accessible, connected void regions percolate as a function of the size of a spherical probe particle and show that both systems possess the same critical probe size. We measure the critical exponent τ that characterizes the size distribution of connected void clusters at the onset of percolation. We find that the cluster size statistics are similar for void percolation in packings of amino-acid-shaped particles and randomly placed spheres, but different from that for void percolation in jammed sphere packings. We propose that the connected void regions are a defining structural feature of proteins and can be used to differentiate experimentally observed proteins from decoy structures that are generated using computational protein design software. This work emphasizes that jammed packings of amino-acid-shaped particles can serve as structural and mechanical analogs of protein cores, and could therefore be useful in modeling the response of protein cores to cavity-expanding and -reducing mutations.

关键词： Jamming Protein structure Packing & jamming problems Proteins Crystal structures Finite-size scaling Molecular dynamics Percolation theory

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Characterizing the mechanical response of metallic glasses to uniaxial tension using a spring network model

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Physical Review Materials 2023年第7期7卷 073605-073605页

作者： Aya Nawano Weiwei Jin Jan Schroers Mark D. Shattuck Corey S. O'Hern Department of Mechanical Engineering and Materials Science Yale University New Haven Connecticut 06520 USA Benjamin Levich Institute and Physics Department The City College of New York New York New York 10031 USA Department of Physics Yale University New Haven Connecticut 06520 USA Department of Applied Physics Yale University New Haven Connecticut 06520 USA Graduate Program in Computational Biology and Bioinformatics Yale University New Haven Connecticut 06520 USA

A coarse-grained spring network model is proposed for the prediction of the mechanical response of metallic glasses as a function of the microstructure prior to loading. This model describes the mechanical response of metallic glasses using a network of parallel springs that can break and reform, mimicking atomic rearrangements during deformation. We compare predictions of the spring network model for stress versus strain to results from numerical simulations of athermal quasistatic, uniaxial tensile deformation of Cu50Zr50 metallic glasses using Lennard-Jones (LJ) and embedded atom method (EAM) atomic interactions. We show that both the LJ and EAM models possess qualitatively similar stress σ versus strain γ curves. By specifying five parameters [ultimate strength, strain at ultimate strength, slopes of σ(γ) at γ=0 and at large strain, and strain at fracture where σ=0], we demonstrate that the spring network model can accurately describe the form of the stress-strain curves during uniaxial tension for the computational studies of Cu50Zr50, as well as recent experimental studies of several Zr-based metallic glasses.

关键词： Alloys Amorphous materials Glasses Packing & jamming problems Molecular dynamics

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Hypostatic jammed packings of frictionless nonspherical particles

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Physical Review E 2018年第1期97卷 012909-012909页

作者： Kyle VanderWerf Weiwei Jin Mark D. Shattuck Corey S. O'Hern Department of Physics Yale University New Haven Connecticut 06520 USA Department of Mechanics and Engineering Science Peking University Beijing 100871 China Department of Mechanical Engineering & Materials Science Yale University New Haven Connecticut 06520 USA Benjamin Levich Institute and Physics Department The City College of New York New York New York 10031 USA Department of Applied Physics Yale University New Haven Connecticut 06520 USA Graduate Program in Computational Biology and Bioinformatics Yale University New Haven Connecticut 06520 USA

We perform computational studies of static packings of a variety of nonspherical particles including circulo-lines, circulo-polygons, ellipses, asymmetric dimers, dumbbells, and others to determine which shapes form packings with fewer contacts than degrees of freedom (hypostatic packings) and which have equal numbers of contacts and degrees of freedom (isostatic packings), and to understand why hypostatic packings of nonspherical particles can be mechanically stable despite having fewer contacts than that predicted from naive constraint counting. To generate highly accurate force- and torque-balanced packings of circulo-lines and cir-polygons, we developed an interparticle potential that gives continuous forces and torques as a function of the particle coordinates. We show that the packing fraction and coordination number at jamming onset obey a masterlike form for all of the nonspherical particle packings we studied when plotted versus the particle asphericity A, which is proportional to the ratio of the squared perimeter to the area of the particle. Further, the eigenvalue spectra of the dynamical matrix for packings of different particle shapes collapse when plotted at the same A. For hypostatic packings of nonspherical particles, we verify that the number of “quartic” modes along which the potential energy increases as the fourth power of the perturbation amplitude matches the number of missing contacts relative to the isostatic value. We show that the fourth derivatives of the total potential energy in the directions of the quartic modes remain nonzero as the pressure of the packings is decreased to zero. In addition, we calculate the principal curvatures of the inequality constraints for each contact in circulo-line packings and identify specific types of contacts with inequality constraints that possess convex curvature. These contacts can constrain multiple degrees of freedom and allow hypostatic packings of nonspherical particles to be mechanically stable.

关键词： Granular materials Granular packing Jamming

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Invasive or More Direct Measurements Can Provide an Objective Early-Stopping Ceiling for Training Deep Neural Networks on Non-invasive or Less-Direct Biomedical Data

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SN computer science 2023年第2期4卷 161页

作者： Bartlett, Christopher W. Bossenbroek, Jamie Ueyama, Yukie McCallinhart, Patricia Peters, Olivia A. Santillan, Donna A. Santillan, Mark K. Trask, Aaron J. Ray, William C. Department of Pediatrics The Ohio State University College of Medicine Columbus OH United States The Steve and Cindy Rasmussen Institute for Genomic Medicine Battelle Center for Computational Biology The Abigail Wexner Research Institute at Nationwide Children’s Hospital Columbus OH United States Department of Computer Science and Engineering The Ohio State University College of Engineering Columbus OH United States Center for Cardiovascular Research The Abigail Wexner Research Institute at Nationwide Children’s Hospital Columbus OH United States Department of Obstetrics & Gynecology University of Iowa Hospitals & Clinics Iowa City IA United States The Interdisciplinary Graduate Program in Biophysics The Ohio State University Graduate School Columbus OH United States

Early stopping is an extremely common tool to minimize overfitting, which would otherwise be a cause of poor generalization of the model to novel data. However, early stopping is a heuristic that, while effective, primarily relies on ad hoc parameters and metrics. Optimizing when to stop remains a challenge. In this paper, we suggest that for some biomedical applications, a natural dichotomy of invasive/non-invasive measurements, or more generally proximal vs distal measurements of a biological system can be exploited to provide objective advice on early stopping. We discuss the conditions where invasive measurements of a biological process should provide better predictions than non-invasive measurements, or at best offer parity. Hence, if data from an invasive measurement are available locally, or from the literature, that information can be leveraged to know with high certainty whether a model of non-invasive data is overfitted. We present paired invasive/non-invasive cardiac and coronary artery measurements from two mouse strains, one of which spontaneously develops type 2 diabetes, posed as a classification problem. Examination of the various stopping rules shows that generalization is reduced with more training epochs and commonly applied stopping rules give widely different generalization error estimates. The use of an empirically derived training ceiling is demonstrated to be helpful as added information to leverage early stopping in order to reduce overfitting. © 2023, The Author(s).

关键词： Health Invasive Machine learning Model Non-invasive Overfitting

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Comprehensive analysis of the pseudogenes of glycolytic enzymes in vertebrates: The anomalously high number of GAPDH pseudogenes highlights a recent burst of retrotrans-positional activity

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BMC Genomics 2009年第1期10卷 480-480页

作者： Liu, Yuen-Jong Zheng, Deyou Balasubramanian, Suganthi Carriero, Nicholas Khurana, Ekta Robilotto, Rebecca Gerstein, Mark B. Department of Surgery Beth Israel Deaconess Medical Center Harvard Medical School Boston MA 110 Francis Street United States Department of Molecular Biophysics and Biochemistry Yale University New Haven CT 06520 P.O. Box 208114 United States Albert Einstein College of Medicine of Yeshiva University Department of Neurology Rose F. Kennedy Center Bronx NY 10461 1410 Pelham Parkway South United States Program in Computational Biology and Bioinformatics Yale University New Haven CT 06520 United States Department of Computer Science Yale University New Haven CT 06520 Bass 432 266 Whitney Avenue United States

Background: Pseudogenes provide a record of the molecular evolution of genes. As glycolysis is such a highly conserved and fundamental metabolic pathway, the pseudogenes of glycolytic enzymes comprise a standardized genomic measuring stick and an ideal platform for studying molecular evolution. One of the glycolytic enzymes, glyceraldehyde-3-phosphate dehydrogenase (GAPDH), has already been noted to have one of the largest numbers of associated pseudogenes, among all proteins. Results: We assembled the first comprehensive catalog of the processed and duplicated pseudogenes of glycolytic enzymes in many vertebrate model-organism genomes, including human, chimpanzee, mouse, rat, chicken, zebrafish, pufferfish, fruitfly, and worm (available at http://***/glycolysis/). We found that glycolytic pseudogenes are predominantly processed, i.e. retrotransposed from the mRNA of their parent genes. Although each glycolytic enzyme plays a unique role, GAPDH has by far the most pseudogenes, perhaps reflecting its large number of non-glycolytic functions or its possession of a particularly retrotranspositionally active sub-sequence. Furthermore, the number of GAPDH pseudogenes varies significantly among the genomes we studied: none in zebrafish, pufferfish, fruitfly, and worm, 1 in chicken, 50 in chimpanzee, 62 in human, 331 in mouse, and 364 in rat. Next, we developed a simple method of identifying conserved syntenic blocks (consistently applicable to the wide range of organisms in the study) by using orthologous genes as anchors delimiting a conserved block between a pair of genomes. This approach showed that few glycolytic pseudogenes are shared between primate and rodent lineages. Finally, by estimating pseudogene ages using Kimura's two-parameter model of nucleotide substitution, we found evidence for bursts of retrotranspositional activity approximately 42, 36, and 26 million years ago in the human, mouse, and rat lineages, respectively. Conclusion: Overall, we pe

关键词： Glycolytic Enzyme Segmental Duplication Chimpanzee Genome Assembly Version ENSEMBL Release

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DOMMINO 2.0: Integrating structurally resolved protein-, RNA-, and DNA-mediated Macromolecular interactions

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Database 2016年第2016期2016卷 bav114页

作者： Kuang, Xingyan Dhroso, Andi Han, Jing Ginger Shyu, Chi-Ren Korkin, Dmitry Informatics Institute University of Missouri Columbia MO United States Department of Computer Science Bioinformatics and Computational Biology Program Worcester Polytechnic Institute Worcester MA United States Department of Electrical and Computer Engineering United States Department of Computer Science University of Missouri Columbia MO United States Ohio State University Comprehensive Cancer Center Columbus OH United States

Macromolecular interactions are formed between proteins, DNA and RNA molecules. Being a principle building block in macromolecular assemblies and pathways, the interactions underlie most of cellular functions. Malfunctioning of macromolecular interactions is also linked to a number of diseases. Structural knowledge of the macromolecular interaction allows one to understand the interaction's mechanism, determine its functional implications and characterize the effects of genetic variations, such as single nucleotide polymorphisms, on the interaction. Unfortunately, until now the interactions mediated by different types of macromolecules, e.g. protein-protein interactions or protein-DNA interactions, are collected into individual and unrelated structural databases. This presents a significant obstacle in the analysis of macromolecular interactions. For instance, the homogeneous structural interaction databases prevent scientists from studying structural interactions of different types but occurring in the same macromolecular complex. Here, we introduce DOMMINO 2.0, a structural Database Of Macro-Molecular INteractiOns. Compared to DOMMINO 1.0, a comprehensive database on protein-protein interactions, DOMMINO 2.0 includes the interactions between all three basic types of macromolecules extracted from PDB files. DOMMINO 2.0 is automatically updated on a weekly basis. It currently includes ∼1 040 000 interactions between two polypeptide subunits (e.g. domains, peptides, termini and interdomain linkers), ∼43 000 RNA-mediated interactions, and ∼12 000 DNA-mediated interactions. All protein structures in the database are annotated using SCOP and SUPERFAMILY family annotation. As a result, protein-mediated interactions involving protein domains, interdomain linkers, C- and N-termini, and peptides are identified. Our database provides an intuitive web interface, allowing one to investigate interactions at three different resolution levels: whole subunit network, binary intera

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Random close packing in protein cores

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Physical Review E 2016年第3期93卷 032415-032415页

作者： Jennifer C. Gaines W. Wendell Smith Lynne Regan Corey S. O'Hern Program in Computational Biology and Bioinformatics Yale University New Haven Connecticut 06520 USA Integrated Graduate Program in Physical and Engineering Biology (IGPPEB) Yale University New Haven Connecticut 06520 USA Department of Physics Yale University New Haven Connecticut 06520 USA Department of Molecular Biophysics & Biochemistry Yale University New Haven Connecticut 06520 USA Department of Chemistry Yale University New Haven Connecticut 06520 USA Department of Mechanical Engineering & Materials Science Yale University New Haven Connecticut 06520 USA Department of Applied Physics Yale University New Haven Connecticut 06520 USA

Shortly after the determination of the first protein x-ray crystal structures, researchers analyzed their cores and reported packing fractions ϕ≈0.75, a value that is similar to close packing of equal-sized spheres. A limitation of these analyses was the use of extended atom models, rather than the more physically accurate explicit hydrogen model. The validity of the explicit hydrogen model was proved in our previous studies by its ability to predict the side chain dihedral angle distributions observed in proteins. In contrast, the extended atom model is not able to recapitulate the side chain dihedral angle distributions, and gives rise to large atomic clashes at side chain dihedral angle combinations that are highly probable in protein crystal structures. Here, we employ the explicit hydrogen model to calculate the packing fraction of the cores of over 200 high-resolution protein structures. We find that these protein cores have ϕ≈0.56, which is similar to results obtained from simulations of random packings of individual amino acids. This result provides a deeper understanding of the physical basis of protein structure that will enable predictions of the effects of amino acid mutations to protein cores and interfaces of known structure.

关键词： Protein structure Proteins

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Spectral Top-Down Recovery of Latent Tree Models

arXiv

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arXiv 2021年

作者： Aizenbud, Yariv Jaffe, Ariel Wang, Meng Hu, Amber Amsel, Noah Nadler, Boaz Chang, Joseph T. Kluger, Yuval Program in Applied Mathematics Yale University New HavenCT06511 United States Department of Computer Science Weizmann Institute of Science Rehovot76100 Israel Department of Statistics Yale University New HavenCT06520 United States Interdepartmental Program in Computational Biology and Bioinformatics Yale University New HavenCT06511 United States Department of Pathology Yale University New HavenCT06511 United States

Modeling the distribution of high dimensional data by a latent tree graphical model is a prevalent approach in multiple scientific domains. A common task is to infer the underlying tree structure, given only observations of its terminal nodes. Many algorithms for tree recovery are computationally intensive, which limits their applicability to trees of moderate size. For large trees, a common approach, termed divide-and-conquer, is to recover the tree structure in two steps. First, recover the structure separately of multiple, possibly random subsets of the terminal nodes. Second, merge the resulting subtrees to form a full tree. Here, we develop Spectral Top-Down Recovery (STDR), a deterministic divide-and-conquer approach to infer large latent tree models. Unlike previous methods, STDR partitions the terminal nodes in a non random way, based on the Fiedler vector of a suitable Laplacian matrix related to the observed nodes. We prove that under certain conditions, this partitioning is consistent with the tree structure. This, in turn, leads to a significantly simpler merging procedure of the small subtrees. We prove that STDR is statistically consistent and bound the number of samples required to accurately recover the tree with high probability. Using simulated data from several common tree models in phylogenetics, we demonstrate that STDR has a significant advantage in terms of runtime, with improved or similar accuracy. Copyright © 2021, The Authors. All rights reserved.

关键词： Recovery

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Bayesian Formulations for Graph Spectral Denoising

arXiv

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arXiv 2023年

作者： Leone, Sam Sun, Xingzhi Perlmutter, Michael Krishnaswamy, Smita Program for Applied Mathematics Yale University United States Department of Computer Science Yale University United States Department of Mathematics Boise State University United States Department of Genetics Yale School of Medicine United States Wu Tsai Institute Yale University United States FAIR Meta AI United States Computational Biology and Bioinformatics Program Yale University United States

Here we consider the problem of denoising features associated to complex data, modeled as signals on a graph, via a smoothness prior. This is motivated in part by settings such as single-cell RNA where the data is very high-dimensional, but its structure can be captured via an affinity graph. This allows us to utilize ideas from graph signal processing. In particular, we present algorithms for the cases where the signal is perturbed by Gaussian noise, dropout, and uniformly distributed noise. The signals are assumed to follow a prior distribution defined in the frequency domain which favors signals which are smooth across the edges of the graph. By pairing this prior distribution with our three models of noise generation, we propose Maximum A Posteriori (M.A.P.) estimates of the true signal in the presence of noisy data and provide algorithms for computing the M.A.P. Finally, we demonstrate the algorithms' ability to effectively restore signals from white noise on image data and from severe dropout in single-cell RNA sequence data. © 2023, CC BY.

关键词： Frequency domain analysis

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ReLSO: A Transformer-based Model for Latent Space Optimization and Generation of Proteins

arXiv

引用

arXiv 2022年

作者： Castro, Egbert Godavarthi, Abhinav Rubinfien, Julian Givechian, Kevin Bhaskar, Dhananjay Krishnaswamy, Smita Computational Biology and Bioinformatics Program Yale University New HavenCT06511 United States Department of Applied Mathematics Yale University New HavenCT06511 United States Department of Genetics Yale University New HavenCT06511 United States Department of Computer Science Yale University New HavenCT06511 United States

The development of powerful natural language models have increased the ability to learn meaningful representations of protein sequences. In addition, advances in high-throughput mutagenesis, directed evolution, and next-generation sequencing have allowed for the accumulation of large amounts of labeled fitness data. Leveraging these two trends, we introduce Regularized Latent Space Optimization (ReLSO), a deep transformer-based autoencoder which features a highly structured latent space that is trained to jointly generate sequences as well as predict fitness. Through regularized prediction heads, ReLSO introduces a powerful protein sequence encoder and novel approach for efficient fitness landscape traversal. Using ReLSO, we explicitly model the sequence-function landscape of large labeled datasets and generate new molecules by optimizing within the latent space using gradient-based methods. We evaluate this approach on several publicly-available protein datasets, including variant sets of anti-ranibizumab and GFP. We observe a greater sequence optimization efficiency (increase in fitness per optimization step) by ReLSO compared to other approaches, where ReLSO more robustly generates high-fitness sequences. Furthermore, the attention-based relationships learned by the jointly-trained ReLSO models provides a potential avenue towards sequence-level fitness attribution information. © 2022, CC BY-NC-ND.

关键词： Proteins

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