scholarly journals Quantum Information in the Protein Codes, 3-Manifolds and the Kummer Surface

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1146
Author(s):  
Michel Planat ◽  
Raymond Aschheim ◽  
Marcelo M. Amaral ◽  
Fang Fang ◽  
Klee Irwin
Keyword(s):  
Quaternary Structure ◽  
Protein Complexes ◽  
Dimensional Space ◽  
Linear Chain ◽  
Secondary Structures ◽  
Kummer Surface ◽  
Linear Sequence ◽  
Multiple Structures ◽  
Quaternary Structures ◽  
Mere Existence

Every protein consists of a linear sequence over an alphabet of 20 letters/amino acids. The sequence unfolds in the 3-dimensional space through secondary (local foldings), tertiary (bonds) and quaternary (disjoint multiple) structures. The mere existence of the genetic code for the 20 letters of the linear chain could be predicted with the (informationally complete) irreducible characters of the finite group Gn:=Zn⋊2O (with n=5 or 7 and 2O the binary octahedral group) in our previous two papers. It turns out that some quaternary structures of protein complexes display n-fold symmetries. We propose an approach of secondary structures based on free group theory. Our results are compared to other approaches of predicting secondary structures of proteins in terms of α helices, β sheets and coils, or more refined techniques. It is shown that the secondary structure of proteins shows similarities to the structure of some hyperbolic 3-manifolds. The hyperbolic 3-manifold of smallest volume—Gieseking manifold—some other 3 manifolds and the oriented hypercartographic group are singled out as tentative models of such secondary structures. For the quaternary structure, there are links to the Kummer surface.

scholarly journals Quantum Information in the Protein Codes, $3$-manifolds and the Kummer Surface

2021 ◽  
Author(s):  
Michel Planat ◽  
Raymond Aschheim ◽  
Marcelo M. Amaral ◽  
Fang Fang ◽  
Klee Irwin
Keyword(s):  
Quaternary Structure ◽  
Protein Complexes ◽  
Dimensional Space ◽  
Linear Chain ◽  
Secondary Structures ◽  
Kummer Surface ◽  
Alpha Helices ◽  
Multiple Structures ◽  
Quaternary Structures ◽  
Mere Existence

Every protein consists of a linear sequence over an alphabet of $20$ letters/amino acids. The sequence unfolds in the $3$-dimensional space through secondary (local foldings), tertiary (bonds) and quaternary (disjoint multiple) structures. The mere existence of the genetic code for the $20$ letters of the linear chain could be predicted with the (informationally complete) irreducible characters of the finite group $G_n:=\mathbb{Z}_n \rtimes 2O$ (with $n=5$ or $7$ and $2O$ the binary octahedral group) in our previous two papers. It turns out that some quaternary structures of protein complexes display $n$-fold symmetries. We propose an approach of secondary structures based on free group theory. Our results are compared to other approaches of predicting secondary structures of proteins in terms of $\alpha$ helices, $\beta$ sheets and coils, or more refined techniques. It is shown that the secondary structure of proteins shows similarities to the structure of some hyperbolic $3$-manifolds. The hyperbolic $3$-manifold of smallest volume --Gieseking manifold--, some other $3$ manifolds and Grothendieck's cartographic group are singled out as tentative models of such secondary structures. For the quaternary structure, there are links to the Kummer surface.

scholarly journals Distance-based Reconstruction of Protein Quaternary Structures from Inter-Chain Contacts

2021 ◽  
Author(s):  
Elham Soltanikazemi ◽  
Farhan Quadir ◽  
Raj Shekhor Roy ◽  
Jianlin Cheng
Keyword(s):  
Quaternary Structure ◽  
Protein Complexes ◽  
Structural Models ◽  
Simulation Method ◽  
Contact Density ◽  
High Quality ◽  
Contact Prediction ◽  
Protein Dimers ◽  
Probability Threshold ◽  
Quaternary Structures

Predicting the quaternary structure of a protein complex is an important and challenging problem. Inter-chain residue-residue contact prediction can provide useful information to guide the ab initio reconstruction of quaternary structures of protein complexes. However, few methods have been developed to build quaternary structures from predicted inter-chain contacts. Here, we introduce a new gradient descent optimization algorithm (GD) to build quaternary structures of protein dimers utilizing inter-chain contacts as distance restraints. We evaluate GD on several datasets of homodimers and heterodimers using true or predicted contacts. GD consistently performs better than a simulated annealing method and a Markov Chain Monte Carlo simulation method. Using true inter-chain contacts as input, GD can reconstruct high-quality structural models for homodimers and heterodimers with average TM-score ranging from 0.92 to 0.99 and average interface root mean square distance (I-RMSD) from 0.72 Å to 1.64 Å. On a dataset of 115 homodimers, using predicted inter-chain contacts as input, the average TM-score of the structural models built by GD is 0.76. For 46% of the homodimers, high-quality structural models with TM-score >= 0.9 are reconstructed from predicted contacts. There is a strong correlation between the quality of the reconstructed models and the precision and recall of predicted contacts. If the precision or recall of predicted contacts is >20%, GD can reconstruct good models for most homodimers, indicating only a moderate precision or recall of inter-chain contact prediction is needed to build good structural models for most homodimers. Moreover, the accuracy of reconstructed models positively correlates with the contact density in dimers and depends on the initial model and the probability threshold of selecting predicted contacts for the distance-based structure optimization.

scholarly journals Evolution of interface binding strengths in simplified model of protein quaternary structure

2019 ◽  
Author(s):  
Alexander S. Leonard ◽  
Sebastian E. Ahnert
Keyword(s):  
Self Assembly ◽  
Quaternary Structure ◽  
Protein Complexes ◽  
Lattice Models ◽  
Evolutionary Selection ◽  
Wide Range ◽  
Simple Change ◽  
Quaternary Structures ◽  
Assembly Pathways ◽  
New Framework

AbstractThe self-assembly of proteins into protein quaternary structures is of fundamental importance to many biological processes, and protein misassembly is responsible for a wide range of proteopathic diseases. In recent years, abstract lattice models of protein self-assembly have been used to simulate the evolution and assembly of protein quaternary structure, and to provide a tractable way to study the genotype-phenotype map of such systems. Here we generalize these models by representing the interfaces as mutable binary strings. This simple change enables us to model the evolution of interface strengths, interface symmetry, and deterministic assembly pathways. Using the generalized model we are able to reproduce two important results established for real protein complexes: The first is that protein assembly pathways are under evolutionary selection to minimize misassembly. The second is that the assembly pathway of a complex mirrors its evolutionary history, and that both can be derived from the relative strengths of interfaces. These results demonstrate that the generalized lattice model offers a powerful new framework for the study of protein self-assembly processes and their evolution.

scholarly journals The Formation of a Cavity in a 3D Flux Rope

2013 ◽  
Vol 8 (S300) ◽  
pp. 147-150 ◽  
Author(s):  
Donald Schmit ◽  
Sarah Gibson
Keyword(s):  
Ad Hoc ◽  
Numerical Models ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Flux Rope ◽  
Multiple Structures ◽  
Field Lines ◽  
Hydrostatic Balance ◽  
Distinct Field ◽  
Three Dimensional Space

AbstractThere are currently no three dimensional numerical models which describe the magnetic and energetic formation of prominences self-consistently. Consequently, there has not been significant progress made in understanding the connection between the dense prominence plasma and the coronal cavity. We have taken an ad-hoc approach to understanding the energetic implications of the magnetic models of prominence structure. We extract one dimensional magnetic field lines from a 3D MHD model of a flux rope and solve for hydrostatic balance along these field lines incorporating field-aligned thermal conduction, uniform heating, and radiative losses. The 1D hydrostatic solutions for density and temperature are then mapped back into three dimensional space, which allows us to consider the projection of multiple structures. We find that the 3D flux rope is composed of several distinct field line types. A majority of the flux rope interior field lines are twisted but not dipped. These field lines are density-reduced relative to unsheared arcade field lines. We suggest the cavity may form along these short interior field lines which are surrounded by a sheath of dipped field lines. This geometric arrangement would create a cavity on top of a prominence, but the two structures would not share field lines or plasma.

scholarly journals Three-Dimensional Graph Matching to Identify Secondary Structure Correspondence of Medium-Resolution Cryo-EM Density Maps

Biomolecules ◽  
2021 ◽  
Vol 11 (12) ◽  
pp. 1773
Author(s):  
Bahareh Behkamal ◽  
Mahmoud Naghibzadeh ◽  
Mohammad Reza Saberi ◽  
Zeinab Amiri Tehranizadeh ◽  
Andrea Pagnani ◽  
...  
Keyword(s):  
Secondary Structure ◽  
Graph Matching ◽  
Protein Complexes ◽  
Three Dimensional ◽  
Protein Structure Determination ◽  
Secondary Structures ◽  
Computational Method ◽  
Target Sequence ◽  
Matching Problem ◽  
Medium Resolution

Cryo-electron microscopy (cryo-EM) is a structural technique that has played a significant role in protein structure determination in recent years. Compared to the traditional methods of X-ray crystallography and NMR spectroscopy, cryo-EM is capable of producing images of much larger protein complexes. However, cryo-EM reconstructions are limited to medium-resolution (~4–10 Å) for some cases. At this resolution range, a cryo-EM density map can hardly be used to directly determine the structure of proteins at atomic level resolutions, or even at their amino acid residue backbones. At such a resolution, only the position and orientation of secondary structure elements (SSEs) such as α-helices and β-sheets are observable. Consequently, finding the mapping of the secondary structures of the modeled structure (SSEs-A) to the cryo-EM map (SSEs-C) is one of the primary concerns in cryo-EM modeling. To address this issue, this study proposes a novel automatic computational method to identify SSEs correspondence in three-dimensional (3D) space. Initially, through a modeling of the target sequence with the aid of extracting highly reliable features from a generated 3D model and map, the SSEs matching problem is formulated as a 3D vector matching problem. Afterward, the 3D vector matching problem is transformed into a 3D graph matching problem. Finally, a similarity-based voting algorithm combined with the principle of least conflict (PLC) concept is developed to obtain the SSEs correspondence. To evaluate the accuracy of the method, a testing set of 25 experimental and simulated maps with a maximum of 65 SSEs is selected. Comparative studies are also conducted to demonstrate the superiority of the proposed method over some state-of-the-art techniques. The results demonstrate that the method is efficient, robust, and works well in the presence of errors in the predicted secondary structures of the cryo-EM images.

scholarly journals Can We Still Trust Docking Results? An Extension of the Applicability of DockBench on PDBbind Database

2019 ◽  
Vol 20 (14) ◽  
pp. 3558 ◽  
Author(s):  
Giovanni Bolcato ◽  
Alberto Cuzzolin ◽  
Maicol Bissaro ◽  
Stefano Moro ◽  
Mattia Sturlese
Keyword(s):  
Protein Complexes ◽  
Scoring Function ◽  
Data Bank ◽  
The Self ◽  
Protein Families ◽  
Docking Protocol ◽  
Multiple Structures ◽  
Huge Impact ◽  
Ligand Conformation

The number of entries in the Protein Data Bank (PDB) has doubled in the last decade, and it has increased tenfold in the last twenty years. The availability of an ever-growing number of structures is having a huge impact on the Structure-Based Drug Discovery (SBDD), allowing investigation of new targets and giving the possibility to have multiple structures of the same macromolecule in a complex with different ligands. Such a large resource often implies the choice of the most suitable complex for molecular docking calculation, and this task is complicated by the plethora of possible posing and scoring function algorithms available, which may influence the quality of the outcomes. Here, we report a large benchmark performed on the PDBbind database containing more than four thousand entries and seventeen popular docking protocols. We found that, even in protein families wherein docking protocols generally showed acceptable results, certain ligand-protein complexes are poorly reproduced in the self-docking procedure. Such a trend in certain protein families is more pronounced, and this underlines the importance in identification of a suitable protein–ligand conformation coupled to a well-performing docking protocol.

scholarly journals Aβ(M1–40) and Wild-Type Aβ40 Self-Assemble into Oligomers with Distinct Quaternary Structures

Molecules ◽  
2019 ◽  
Vol 24 (12) ◽  
pp. 2242 ◽  
Author(s):  
Jacob L. Bouchard ◽  
Taylor C. Davey ◽  
Todd M. Doran
Keyword(s):  
Self Assembly ◽  
Quaternary Structure ◽  
Biological Activities ◽  
Amyloid Β ◽  
Long Term Potentiation ◽  
Wild Type ◽  
Molecular Weights ◽  
Term Potentiation ◽  
Quaternary Structures

Amyloid-β oligomers (AβOs) self-assemble into polymorphic species with diverse biological activities that are implicated causally to Alzheimer’s disease (AD). Synaptotoxicity of AβO species is dependent on their quaternary structure, however, low-abundance and environmental sensitivity of AβOs in vivo have impeded a thorough assessment of structure–function relationships. We developed a simple biochemical assay to quantify the relative abundance and morphology of cross-linked AβOs. We compared oligomers derived from synthetic Aβ40 (wild-type (WT) Aβ40) and a recombinant source, called Aβ(M1–40). Both peptides assemble into oligomers with common sizes and morphology, however, the predominant quaternary structures of Aβ(M1–40) oligomeric states were more diverse in terms of dispersity and morphology. We identified self-assembly conditions that stabilize high-molecular weight oligomers of Aβ(M1–40) with apparent molecular weights greater than 36 kDa. Given that mixtures of AβOs derived from both peptides have been shown to be potent neurotoxins that disrupt long-term potentiation, we anticipate that the diverse quaternary structures reported for Aβ(M1–40) oligomers using the assays reported here will facilitate research efforts aimed at isolating and identifying common toxic species that contribute to synaptic dysfunction.

A new crosslinker for mass spectrometric analysis of the quaternary structure of protein complexes

2001 ◽  
Vol 12 (2) ◽  
pp. 222-227 ◽  
Author(s):  
J. W. Back ◽  
A. F. Hartog ◽  
H. L. Dekker ◽  
Anton O. Muijsers ◽  
L. J. Koning ◽  
...  
Keyword(s):  
Quaternary Structure ◽  
Protein Complexes ◽  
Mass Spectrometric ◽  
Mass Spectrometric Analysis ◽  
Spectrometric Analysis

Three-Body Correlation in the Diluted Generalized Hubbard Model

1997 ◽  
Vol 491 ◽  
Author(s):  
O. Navarro ◽  
M. Avignon
Keyword(s):  
Nearest Neighbor ◽  
Dimensional Space ◽  
Linear Chain ◽  
Tight Binding ◽  
Real Space ◽  
Many Body ◽  
Higher Dimensional ◽  
Generalized Hubbard Model ◽  
Three Body ◽  
Body Correlation

ABSTRACTA real-space method has been used to solve the generalized Hubbard Hamiltonian for a system with few electrons. The method is based on mapping the correlated many-body problem onto an equivalent tight-binding one in a higher dimensional space. For a linear chain, we have obtained an exact solution of the problem of three non-parallel electrons. The three-body correlation are studied by examining the binding energy in the ground state, for different values of the hopping parameters and of the on-site (U) and nearest-neighbor (V) interactions.

scholarly journals The process for the activation of frog epidermis pro-tyrosinase

1982 ◽  
Vol 205 (2) ◽  
pp. 397-404 ◽  
Author(s):  
R Peñafiel ◽  
J D Galindo ◽  
E Pedreño ◽  
J A Lozano
Keyword(s):  
Quaternary Structure ◽  
Polypeptide Chain ◽  
Rana Esculenta ◽  
Single Type ◽  
Low Molecular Weight ◽  
Activation Process ◽  
Proteolytic Activation ◽  
Molecular Weights ◽  
Quaternary Structures

1. Purified pro-tyrosinase from epidermis of the frog Rana esculenta ridibunda can be activated in vitro by several proteinases (trypsin, alpha-chymotrypsin, Pronase) and by light. 2. Both pro-tyrosinase and tyrosinase are composed of a single type of subunit having pI 7.2 and approximate molecular weights 68000 and 62000 respectively. A peptide of low molecular weight is released as a consequence of the proteolytic activation. Pro-tyrosinase and tyrosinase have different quaternary structures, the proenzyme being a dimer of Mr approx. 115000 and the enzyme a tetramer of Mr approx. 210 000. 3. The activation process was affected by several agents (L-3,4-dihydroxyphenylalanine, urea, formamide) that prevented, partially or totally, the activation of pro-tyrosinase. 4. The activation of pro-tyrosinase seems to be the result of a cleavage of the polypeptide chain that determines changes in tertiary or quaternary structure.

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