Folding Model Research Articles

Challenges and Advantages of Accounting for Backbone Flexibility in Prediction of Protein-Protein Complexes.

Predicting protein binding is a core problem of computational biophysics. That this objective can be partly achieved with some amount of success using docking algorithms based on rigid protein models is remarkable, although going further requires allowing for protein flexibility. However, accurately capturing the conformational changes upon binding remains an enduring challenge for docking algorithms. Here, we adapt our Upside folding model, where side chains are represented as multi-position beads, to explore how flexibility may impact predictions of protein-protein complexes. Specifically, the Upside model is used to investigate where backbone flexibility helps, which types of interactions are important, and what is the impact of coarse graining. These efforts also shed light on the relative challenges posed by folding and docking. After training the Upside energy function for docking, the model is competitive with the established all-atom methods. However, allowing for backbone flexibility during docking is generally detrimental, as the presence of comparatively minor (3-5 Å) deviations relative to the docked structure has a large negative effect on performance. While this issue appears to be inherent to current forcefield-guided flexible docking methods, systems involving the co-folding of flexible loops such as antibody-antigen complexes represent an interesting exception. In this case, binding is improved when backbone flexibility is allowed using the Upside model.

Turning machines: a simple algorithmic model for molecular robotics

Molecular robotics is challenging, so it seems best to keep it simple. We consider an abstract molecular robotics model based on simple folding instructions that execute asynchronously. Turning Machines are a simple 1D to 2D folding model, also easily generalisable to 2D to 3D folding. A Turning Machine starts out as a line of connected monomers in the discrete plane, each with an associated turning number. A monomer turns relative to its neighbours, executing a unit-distance translation that drags other monomers along with it, and through collective motion the initial set of monomers eventually folds into a programmed shape. We provide a suite of tools for reasoning about Turning Machines by fully characterising their ability to execute line rotations: executing an almost-full line rotation of 5π/3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$5\\pi /3$$\\end{document} radians is possible, yet a full 2π\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2\\pi$$\\end{document} rotation is impossible. Furthermore, line rotations up to 5π/3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$5\\pi /3$$\\end{document} are executed efficiently, in O(logn)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(\\log n)$$\\end{document} expected time in our continuous time Markov chain time model. We then show that such line-rotations represent a fundamental primitive in the model, by using them to efficiently and asynchronously fold shapes. In particular, arbitrarily large zig-zag-rastered squares and zig-zag paths are foldable, as are y-monotone shapes albeit with error (bounded by perimeter length). Finally, we give shapes that despite having paths that traverse all their points, are in fact impossible to fold, as well as techniques for folding certain classes of (scaled) shapes without error. Our approach relies on careful geometric-based analyses of the feats possible and impossible by a very simple robotic system, and pushes conceptional hardness towards mathematical analysis and away from molecular implementation.

Establishment of a radiation-induced vocal fold fibrosis mouse model

Post-radiation fibrosis of the vocal folds is thought to cause vocal impairment. However, the mechanism by which this occurs has been poorly documented, probably because of the lack of an appropriate experimental animal model. The purpose of this study was to establish a simple and reproducible mouse model of laryngeal radiation to investigate the development of vocal fold fibrosis over time. C57BL/6 mice individually placed in a lead shield were irradiated with a single dose of 20 Gy. At 1, 2, and 6 months after irradiation, larynges were harvested and subjected to histological examination and gene expression analysis. Irradiated vocal folds showed time-dependent tissue contraction and increased collagen deposition, with no significant difference in the changes in hyaluronic acid levels. Transcriptional analysis revealed upregulated expressions of TGF-β1 and iNOS at 6 months, but downregulated expressions of Acta2, Col1a1, Col3a1, and MMP8. Moreover, elevated TGF-β1 and reduced downstream gene expression levels indicated the existence of an inhibitory factor over the TGF-β/Smad pathway. Discrepancies in histological and transcriptional studies of collagen might suggest that radiation-induced vocal fold fibrosis could be caused by the elongated turnover of collagen. Overall, we established a mouse model of radiation-induced vocal fold fibrosis using a simple protocol. Further investigations are warranted to elucidate the pathogenesis of irradiation-induced fibrosis in vocal folds.

Matter radii and skins of [formula omitted]He from reaction cross section of proton+[formula omitted]He scattering based on the Love–Franey [formula omitted]-matrix model

Background:For 4,6,8He, Tanihata et al. determined matter radii rm(σI)=1.57(4),2.48(3),2.52(3) fm from interaction cross sections σI for 4,6,8He scattering on Be, C Al targets at 790 MeV/nucleon. Lu et al. measured the atomic isotope shifts (AIS) for 4,6,8He and determined proton radii rp(AIS) for 4,6,8He. As for p+4,6,8He scattering, reaction cross sections σR(exp) are available at 700 MeV with high accuracy. Aim:Our aim is to determine matter radii rm and skins rskin for 6,8He from the σR(exp) and the rp(AIS). Method:Our model is the Love–Franey t-matrix folding model, since the model is better than the optical limit of Glauber model. Results:Our results for 6,8He are rm(exp)=2.48(3),2.53(2) fm and rskin=0.78(3), 0.82(2) fm. Conclusion:For 6,8He, our results rm(σR) agree with those of Tanihata et al.. For 8He, the distance between 4He and the center of mass of valence four neutrons is 2.367 fm.

Reanalysis of 6Li+90Zr angular distributions using different nuclear potentials

The experimental angular distributions for 6Li elastically scattered from a 90Zr target in the energy range 14.89–240 MeV are theoretically reanalyzed using phenomenological and semi-microscopic potentials. The phenomenon of the break-up threshold anomaly (BTA) is well represented in the various used potentials. In analyzing nuclear systems induced by weakly bound projectiles such as 6Li, the well-known reduction in the strength of the real part of potential generated based on double folding (DF) and cluster folding (CF) models is also observed. The Sao Paulo potential (SPP) is used to perform double folding calculations. In order to fit the data fairly, a reduction of ∼ 42% and 45% in the strength of the microscopic real part of potential constructed using SPP and CFM, respectively, is found to be required. By including an additional dynamical polarization potential, the data are also reproduced without renormalizing the real cluster folding potential.

Experimental Study on Inspiratory Phonation Using Physical Model of the Vocal Folds

In inspiratory phonation, the air is inhaled from the mouth. The inhaled air passes through the glottis towards the lungs, thereby inducing the vocal fold vibrations. Such phonation takes place in various situations such as sighs, laughter, and crying. To characterize the inspiratory phonation, an experimental study was carried out using a physical model of the vocal folds. By reversing the direction of the airflow that passed through the vocal fold model, the inspiratory phonation was experimentally realized and compared with the normal expiratory phonation. Our experiments revealed that the phonation threshold pressures as well as the volume flow rates decreased under the inspiratory condition. Accordingly, the vocal efficiency was increased. The fundamental frequency was also increased under the inspiratory condition. The kymograms showed that phase of the upper edge of the vocal fold advanced that of the lower edge under the inspiratory phonation. A mathematical model of the vocal folds was further constructed to elucidate these experiments. Except for few aspects, our experimental findings are in good agreement with the preceding studies on inspiratory phonation (e.g., reversed propagation of the mucosal waves observed in a singer, increased pitches in human subjects, and use of inspiratory phonation in speech therapy).

Fiber-Like Organization as a Basic Principle for Euchromatin Higher-Order Structure.

A detailed understanding of the principles of the structural organization of genetic material is of great importance for elucidating the mechanisms of differential regulation of genes in development. Modern ideas about the spatial organization of the genome are based on a microscopic analysis of chromatin structure and molecular data on DNA–DNA contact analysis using Chromatin conformation capture (3C) technology, ranging from the “polymer melt” model to a hierarchical folding concept. Heterogeneity of chromatin structure depending on its functional state and cell cycle progression brings another layer of complexity to the interpretation of structural data and requires selective labeling of various transcriptional states under nondestructive conditions. Here, we use a modified approach for replication timing-based metabolic labeling of transcriptionally active chromatin for ultrastructural analysis. The method allows pre-embedding labeling of optimally structurally preserved chromatin, thus making it compatible with various 3D-TEM techniques including electron tomography. By using variable pulse duration, we demonstrate that euchromatic genomic regions adopt a fiber-like higher-order structure of about 200 nm in diameter (chromonema), thus providing support for a hierarchical folding model of chromatin organization as well as the idea of transcription and replication occurring on a highly structured chromatin template.

A Maximum Caliber analysis of the Foldon Hypothesis

Different models of protein folding favor different mechanisms. Some models rely on a defined pathway, while other models rely on a more heterogeneous set of pathways. The Foldon Hypothesis is based on the concept of a defined pathway. According to the Foldon Hypothesis, protein folding is characterized by the stepwise assembly of small, cooperative units called foldons. The Maximum Caliber (Max Cal) method provides an opportunity to test this model. The Max Cal method gives the probabilities for dynamical trajectories, in much the same way that the maximum entropy principle gives the probabilities for equilibrium states. In this study, the Max Cal method was applied to folding data for the protein cytochrome c (cyt c; Hu W, Kan ZY, Mayne L, Englander SW. Proc Natl Acad Sci U S A. 2016;113:3809-3814). The overall picture to emerge from this analysis is that the data do not require a dominant, defined pathway. The folding of cytochrome c is likely a heterogeneous process that includes multiple pathways.

Evolving cellular automata schemes for protein folding modeling using the Rosetta atomic representation

Protein folding is the dynamic process by which a protein folds into its final native structure. This is different to the traditional problem of the prediction of the final protein structure, since it requires a modeling of how protein components interact over time to obtain the final folded structure. In this study we test whether a model of the folding process can be obtained exclusively through machine learning. To this end, protein folding is considered as an emergent process and the cellular automata tool is used to model the folding process. A neural cellular automaton is defined, using a connectionist model that acts as a cellular automaton through the protein chain to define the dynamic folding. Differential evolution is used to automatically obtain the optimized neural cellular automata that provide protein folding. We tested the methods with the Rosetta coarse-grained atomic model of protein representation, using different proteins to analyze the modeling of folding and the structure refinement that the modeling can provide, showing the potential advantages that such methods offer, but also difficulties that arise.

Neutron skin in 48Ca determined from p+48Ca and 48Ca+12C scattering

Background:In our previous paper, we determined rskin208(exp)=0.278±0.035 fm from measured reaction cross sections σR for p+208Pb scattering, using the Kyushu (chiral) g-matrix folding model with the densities calculated with the Gogny-D1S Hartree–Fock–Bogoliubov (D1S-GHFB) with the angular momentum projection (AMP). The value agrees with that of PREX2. Reaction cross sections σR are available for p+48Ca scattering, whereas interaction cross sections σI(≈σR) are available for 48Ca + 12C scattering. As for 48Ca, the high-resolution E1 polarizability experiment (E1pE) yields rskin48(E1pE)=0.14∼0.20fm. Purpose:We determine rskin48(exp) from the data on σR for p+48Ca scattering and from the data on σI for 48Ca+12C scattering. Methods:We use the Kyushu g-matrix folding model with the densities calculated with the D1M-GHFB+AMP densities. The D1M-GHFB+AMP proton and neutron densities are scaled so as to reproduce the data under the condition that the radius rp of the scaled proton density equals the data rp(exp) determined from the electron scattering. We deduce skin values rskin=rn(exp)−rp(exp) from the resulting rn(exp) and the rp(exp) determined from electron scattering. The same procedure is taken for D1S-GHFB+AMP. Results:We regard rskin48(E1pE) as a reference skin value. Using the reference skin value and taking D1M-GHFB+AMP, we determine rskin48(exp)=0.158±0.025 fm for p+48Ca scattering and 0.160±0.058 fm for 48Ca +12C scattering. Conclusion:We take the weighted mean and its error for the two skin values. The result is rskin48(exp)=0.158±(0.023)exp±(0.012)thfm.

Folding-model approach to reaction cross section of [formula omitted]He+12C scattering at 790 MeV

Tanihata et al. (1988) determined matter radii rm(σI) for 4,6,8He from interaction cross sections σI of 4,6,8He+12C scattering at 790 MeV per nucleon, using the optical limit of the Glauber model. Lu et al. (2013) determined proton radii rp(AIS) for 4,6,8He with the atomic isotope shifts (AIS). We investigate whether the Love-Franey t-matrix folding model is good for 4,6,8He+12C scattering at 790 MeV per nucleon.

Constraining the α-nucleus potential for α-decay calculation with nuclear rainbow scattering

Introduction: The emission of a particles is a powerful probe for the α-cluster structure of heavy nuclei. The α-nucleus potential is a crucial ingredient in the a-decay calculation within the preformed cluster model. One of the most reliable ways to construct this potential is the double folding model, where an effective nucleon-nucleon interaction is folded with the nuclear densities. In the folding model calculation, there are many ambiguities in the choice of the nuclear densities of the daughter nucleus for α-decay. We propose to directly constrain the α-nucleus potential for α- decay and choose the daughter nuclear density using the nuclear rainbow scattering phenomenon. Methods: The refractive rainbow pattern in the elastic scattering cross section within the optical model can probe deep into the interior region of the α-nucleus potential. We apply this method to investigate the reliability of the nuclear potential used in the α-decay of the 212Po nucleus leading to the 208Pb daughter nucleus by examining the elastic a scattering on 208Pb. In such an approach, we perform the double-folding calculation to construct the α-nucleus potential using several common parametrizations of the daughter nuclear densities. These parametrizations include the mean-field Hartree-Fock-Bogoliubov calculations with the BSk14 and D1S interactions, the independent particle model, and the 2-parameter Fermi distributions. The obtained nuclear potentials are applied to the optical model to calculate the elastic α-208Pb scattering cross sections that are compared with the experimental data. These nuclear potentials are further used in the preformed cluster model to study thea-decay half-life of 212Po. Results: The nuclear densities from the Hartree-Fock-Bogoliubov calculations are shown to provide the best description for both the nuclear rainbow scattering anda-decay half-life. The results indicate a strong correspondence between the capabilities of the nuclear potential to reproduce the cross section ofa scattering and the α-decay half-life. The extracteda preformation factors from the semiclassical preformed cluster model with folding potentials are in good agreement with those from other studies. Conclusion: The nuclear rainbow scattering phenomenon can be used to provide reliable a-nucleus potential for α-decay studies within the preformed cluster model. The nuclear densities from the mean-field Hartree-Fock-Bogoliubov method with the BSk14 and D1S interactions are the appropriate choices for the DFM calculation used in the α-decay study.

Multi-scale phase separation by explosive percolation with single-chromatin loop resolution

The 2 m-long human DNA is tightly intertwined into the cell nucleus of the size of 10 μm. The DNA packing is explained by folding of chromatin fiber. This folding leads to the formation of such hierarchical structures as: chromosomal territories, compartments; densely-packed genomic regions known as Topologically Associating Domains (TADs), or Chromatin Contact Domains (CCDs), and loops. We propose models of dynamical human genome folding into hierarchical components in human lymphoblastoid, stem cell, and fibroblast cell lines. Our models are based on explosive percolation theory. The chromosomes are modeled as graphs where CTCF chromatin loops are represented as edges. The folding trajectory is simulated by gradually introducing loops to the graph following various edge addition strategies that are based on topological network properties, chromatin loop frequencies, compartmentalization, or epigenomic features. Finally, we propose the genome folding model - a biophysical pseudo-time process guided by a single scalar order parameter. The parameter is calculated by Linear Discriminant Analysis of chromatin features. We also include dynamics of loop formation by using Loop Extrusion Model (LEM) while adding them to the system. The chromatin phase separation, where fiber folds in 3D space into topological domains and compartments, is observed when the critical number of contacts is reached. We also observe that at least 80% of the loops are needed for chromatin fiber to condense in 3D space, and this is constant through various cell lines. Overall, our in-silico model integrates the high-throughput 3D genome interaction experimental data with the novel theoretical concept of phase separation, which allows us to model event-based time dynamics of chromatin loop formation and folding trajectories.

Triangular body-cover model of the vocal folds with coordinated activation of the five intrinsic laryngeal muscles.

Poor laryngeal muscle coordination that results in abnormal glottal posturing is believed to be a primary etiologic factor in common voice disorders such as non-phonotraumatic vocal hyperfunction. Abnormal activity of antagonistic laryngeal muscles is hypothesized to play a key role in the alteration of normal vocal fold biomechanics that results in the dysphonia associated with such disorders. Current low-order models of the vocal folds are unsatisfactory to test this hypothesis since they do not capture the co-contraction of antagonist laryngeal muscle pairs. To address this limitation, a self-sustained triangular body-cover model with full intrinsic muscle control is introduced. The proposed scheme shows good agreement with prior studies using finite element models, excised larynges, and clinical studies in sustained and time-varying vocal gestures. Simulations of vocal fold posturing obtained with distinct antagonistic muscle activation yield clear differences in kinematic, aerodynamic, and acoustic measures. The proposed tool is deemed sufficiently accurate and flexible for future comprehensive investigations of non-phonotraumatic vocal hyperfunction and other laryngeal motor control disorders.

Experimental model for controlled endoscopic subepithelial vocal fold injury in rats.

ABSTRACTPurpose:To present a detailed, reproducible, cost-efficient surgical model for controlled subepithelial endoscopic vocal fold injury in the rat model.Methods:Six male Sprague Dawley rats were enrolled in the experiment. The left vocal folds were used to carry out the injury model, and the right vocal fold served as control. After deep sedation, the rats were placed on a custom operating platform. The vocal fold injury by subepithelial stripping was carried out using custom-made microsurgical instruments under endoscopic guidance. Data were analyzed for procedural time and post-procedural pain. Microcomputed tomography (micro-CT) scan and histologic images were obtained to assess the length, area, and depth of injury to the vocal fold.Results:The mean procedural time was 112 s. The mean control vocal fold length was 0.96 ± 0.04 mm. The mean vocal fold injury length was 0.53 ± 0.04 mm. The mean vocal fold surface was 0.18 ± 0.01 mm2 with a mean lesion area of 0.05 ± 0.00 mm2. Mean vocal fold injury depth was 375.4 ± 42.8 μm. The lesion length to vocal fold length ratio was 0.55 ± 0.03, as well as lesion area to vocal fold surface area was 0.29 ± 0.02.Conclusions:Our described experimental vocal fold injury model in rats is found to be fast, safe, cost-efficient, and reproducible with a rapid learning curve.

The α-decay half-lives of heavy nuclei via the double folding model with the use of relativistic NN interactions

In this study, the half-lives of [Formula: see text]-decay from some heavy nuclei in the range [Formula: see text] have been studied using the WKB semi-classical approximation. The nuclear interaction potential between the [Formula: see text]-particle and the daughter nuclei is obtained within the double folding model. The [Formula: see text] interactions employed are those derived from relativistic mean field (RMF) theory, called as R3Y [Formula: see text] interactions. Six different R3Y [Formula: see text] interactions are considered in the study to determine the most appropriate R3Y parametrization for heavy nuclei. Some of the R3Y interactions (such as R3Y-HS, R3Y-L1, R3Y-Z, R3Y-W) contain only linear [Formula: see text], [Formula: see text], and [Formula: see text] mesons, while the others (such as R3Y-NL2, R3Y-NLSH) contain nonlinear terms, in addition to the linear terms. All the R3Y [Formula: see text] interactions used are found to be efficient in describing the [Formula: see text]-decay half-lives data. However, R3Y [Formula: see text] interactions containing nonlinear terms are found to perform better than those containing only linear terms of the mesons.

BiInNet: Bilateral Inversion Network for Real-Time Velocity Analysis

Most previous studies focus on using complex deep neural networks to learn diverse features of massive synthetic data. In more realistic situations with a limited number of data pairs, complex networks not only have higher computational complexity, increasing training time and reducing inference speed, but also tend to over-fit a small amount of training data, thus having weak generalization capability. To address the aforementioned problem, we propose a lightweight architecture for real-time velocity inversion in realistic situations, the bilateral inversion network (BiInNet). BiInNet uses lightweight ResNet18, ShuffleNetV2, and modified MobileNetV2 as backbones, taking into account the inversion accuracy and inference speed. To reduce the redundant information in common shot gathers and focus on graphical property features which are strongly correlated with velocity, the intermediate results of velocity analysis, semblances, and interval velocity models are prepared as data pairs. Numerical experiments show that BiInNet can infer interval velocity models in real-time, with frames per second (FPS) up to 76.90 when ResNet18 is used as the backbone. Moreover, BiInNet achieves the best inversion accuracy on more realistic fold models, fault models, salt models, and noisy dataset (NFOMD) when adopting ShuffleNetV2 as the backbone, which illustrates that BiInNet can be applied to velocity inversion tasks of different geological structures and is robust to noise. Adopting transfer learning to fine-tune pretrained model, BiInNet is effectively applicable to velocity reversal models and field data, which further demonstrates the reliability of the proposed method and provides a practical velocity inversion scheme when the field data pairs are insufficient.

A New Modeling of Classical Folds in Computational Origami

This paper shows a cut along a crease on an origami sheet makes simple modeling of popular traditional basic folds such as a squash fold in computational origami. The cut operation can be applied to other classical folds and significantly simplify their modeling and subsequent implementation in the context of computational origami.

Active Remodeling of Chromatin and Implications for In Vivo Folding.

Building on the observation that chromatin compaction can be locally modulated by activity, we propose a model of in vivo chromatin as an active polymer and study its large scale conformations. In particular, we study an active mechanochemical model of chromosomal folding based on the interplay among polymer elasticity, confinement, topological constraints, and fluctuating active stresses arising from the ATP-dependent action of a variety of chromatin-associated protein machines and chromatin-remodeling proteins and their stochastic turnover. We find that activity drives the chromatin to a nonequilibrium steady state; the statistics of conformations in this nonequilibrium steady state are consistent with recent measurements on intrachromosomal contact probabilities and chromosomal compaction. The contact exponents at steady state show a systematic variation with changes in the nature of activity and the rates of turnover. The steady state configuration of the active chromatin in two dimensions resembles a space-filling Peano curve, which might have implications for the optimization of genome information storage.

Pauli blocking potential applied to heavy-ion fusion reactions * *Supported by the National Natural Science Foundation of China (12105080, 11822503, 11975091) and the Program for Innovative Research Team (in Science and Technology) in University of Henan Province (21IRTSTHN011), China

In this study, the Pauli blocking potential between two colliding nuclei in the density overlapping region is applied to describe the heavy nuclei fusion process. Inspired by the Pauli blocking effect in the -decay of heavy nuclei, the Pauli blocking potential of single nucleon from the surrounding matter is obtained. In fusion reactions with strong density overlap, the Pauli blocking potential between the projectile and target can be constructed using a single folding model. By considering this potential, the double folding model with a new parameter set is employed to analyze the fusion processes of 95 systems. A wider Coulomb barrier and shallower potential pocket are formed in the inner part of the potential between the two colliding nuclei, compared to that calculated using the Akyüz-Winther potential. The fusion hindrance phenomena at deep sub-barrier energies are described well for fusion systems O + Pb and Ni + Ni.