Folding Model Research Articles

Standard binding free-energy calculation of glycophorin a dimer in non-isotropic media sheds light on the transmembrane alpha-helices association mechanism.

The transmembrane (TM) protein domain recognition and association processes happening in lipid bilayers are pivotal for understanding membrane protein biogenesis. The most straightforward system to study the transmembrane protein binding mechanism is the glycophorin A (GpA) dimeric TM domain. The GpA is a glycoprotein ubiquitous to the human erythrocyte membrane, which forms a non-covalent dimer through the reversible association of its membrane-spanning domain sequences, creating a crossing angle between two alpha-helices. In our study, the membrane protein complex is primarily located in the phosphatidylcholine (POPC) lipid bilayer, surrounded by water. Applying a rigorous theoretical framework of the standard binding free-energy calculation that combines molecular dynamics and potential-of-mean-force calculations, the so-called “geometrical route”, we investigated this complex in non-isotropic media. Our analysis shows that at large separation distances, the helices are pushed together by the lipids, which triggers the interhelical interactions to occur. This observation is in agreement with the “two-stage” model of integral membrane protein folding. Additionally, we observed that the monomers, while reversibly associated, go through a meta-stable state, where the GpA alpha-helices form a different shape compared to the initial one. From the theoretical point of view, we suggest that for the membrane proteins in the non-isotropic environment, the standard binding free-energy estimation via the geometrical route should be analyzed from another perspective compared to those of protein-protein complexes in water media. We revised the separation PMF evaluation, assuming that the lipid bilayer forms a pseudo-cylindrical zone for the reversible separation of the dimer. The methodology employed herein successfully addresses the challenging transmembrane protein-protein binding problem while offering promising perspectives for the binding affinity characterization of different protein complexes in lipid bilayers.

Using HDX-MS to probe the dynamics and denatured state of GlpG, a helical membrane protein.

The denatured state ensemble (DSE) of membrane proteins remains poorly characterized despite its importance in understanding protein folding, thermodynamics, degradation, chaperone action, and other cellular processes. While recent strides have been made in understanding the relationship between the lipid bilayer and the transmembrane domains of helical proteins in the DSE, open questions remain, including whether helices within the membrane can unfold and whether they can leave the membrane entirely or in part. Here, we apply Hydrogen-Deuterium Exchange (HDX) mass spectrometry to probe the dynamics of E. coli helical membrane protein GlpG to complement our previous study that used a combination of proteolysis, DEER and simulations to probe the DSE. Our HDX-MS data provide a much higher resolution picture of the DSE and permit the quantification of the free energies of the structural openings that lead to HDX of helices. Notably, we find that some helices are extremely stable while others are seen to exit the bilayer, if only temporarily, via pistoning motions. Moreover, in order to exchange, these helices are also undergoing at least temporary unfolding as they move in and out of the bilayer. These results expand on the canonical model of membrane protein folding in which helices fold before entering the membrane by characterizing the dynamics of transmembrane helices moving between the native and denatured states.

Comparative Results of Vocal Fold Injury According to the Fiber-Based Laser in a Rabbit Vocal Fold Model

We assessed the safety of flexible fiber-based lasers including the potassium-titanyl-phosphate (KTP), CO2, and Holmium lasers using a rabbit vocal fold model and provided the safety evidence of laser before human clinical trial. In all, 120 male New Zealand white rabbits were used. Each laser was used to induce acute and chronic vocal fold injuries in 40 rabbits. The same laser energy with the same intensity and frequency were used in all cases, and we evaluated outcomes via surface scanning electron microscopy (SEM) and histological examination 1 day after injury. Histological and high-speed vocal fold vibration examinations were evaluated 1 month after injury. Surface injury roughness grading was done via SEM, and the Acute injury ratio and lamina propria (LP) ratio were also calculated. The dynamic glottal gap was measured through functional analyses based on recordings from a high-speed digital camera. The Holmium laser caused significantly more vocal fold damage than did the KTP and CO2 lasers as revealed by SEM and evaluation of acute and chronic injuries. Functional analysis with high-speed digital camera indicated that the holmium laser reduced dynamic glottal gap compared with the normal vocal fold, where the other lasers did not. The histological and functional analyses of rabbit vocal fold experiments indicated that fiber-based laryngeal laser surgery for vocal fold lesions could be performed relatively safely using a KTP or CO2 laser.

Brain folding increases in sharpness and complexity over third trimester-equivalent development


 
 
 Background and Hypothesis:
 Gyrification, or convolution, of the cerebral cortex is a promising transdiagnostic marker for early neurodevelopment. Previous studies have related differences in sulcogyral shape to schizophrenia, bipolar disorder, and autism spectrum disorder, but the physical mechanisms underlying these differences remain poorly understood. The focus of this study was to explore decomposed curvature metrics, the principal curvatures, as physically meaningful quantitative biomarkers to track brain development. We hypothesize that the average sharpness and complexity of sulci and gyri, reflected by principal curvatures, increase throughout third trimester-equivalent development.
 Methods:
 Cortical surfaces generated from magnetic resonance imaging (MRI) were obtained from the developing Human Connectome Project. Global sharpness was calculated from the principal curvature of maximum magnitude, with average sharpness defined separately for gyral (positive) and sulcal (negative) curvatures. Global complexity of folds (eg., curviness along the length of a fold) was calculated from variance in the principal curvature with minimum magnitude. Trajectory of each summary metric was fit over time using polynomial regression.
 Results:
 Forty-three subjects were removed due to incomplete curvature analysis or missing subject information, such that 541 preterm and term-born infants were evaluated with scan age ranging from 27 to 45 weeks postmenstrual age (PMA). Across this developmental range, sharpness and complexity increased until a plateau around term-equivalent. Average sharpness of gyri was best correlated with age of scan (R2 = 0.877).
 Conclusion and Potential Impact:
 During the pre- and postnatal development period, total cortical surface area continues to increase after birth, but the overall sharpness and complexity of folding plateaus at ~37 weeks post-menstrual age. Exploring these physically meaningful curvature metrics can provide improved parameters for comparison to mechanistic models of brain folding.
 
 

Cluster folding model analysis of the 7Be+28Si elastic scattering in the near-barrier

In the framework of the optical model, the elastic scattering of the radioactive projectile 7Be on the 28Si target at four energies near the Coulomb barrier has been analyzed. The cluster folding model is used to determine the real part of the nuclear optical potential. For comparison, two microscopic optical potentials have been generated using the DDM3Y effective NN interaction based upon two different forms for 7Be density distribution. All the obtained real potentials, in conjunction with phenomenological Woods-Saxon imaginary parts, have successfully reproduced the elastic scattering angular distributions over the measured angular range. The energy dependence of the real and imaginary strengths that are produced by the best-fit of the experimental data was examined. Neither the usual threshold anomaly nor the breakup threshold anomaly can be observed at the considered energy range. The obtained cross sections have been reduced and compared with earlier theoretical and experimental data of 7Li on the same target near the Coulomb barrier.

On a barrier height problem for RNA branching

The branching of an RNA molecule is an important structural characteristic yet difficult to predict correctly, especially for longer sequences. Using plane trees as a combinatorial model for RNA folding, we consider the thermodynamic cost, known as the barrier height, of transitioning between branching configurations. Using branching skew as a coarse energy approximation, we characterize various types of paths in the discrete configuration landscape. In particular, we give sufficient conditions for a path to have both minimal length and minimal branching skew. The proofs offer some biological insights, notably the potential importance of both hairpin stability and domain architecture to higher resolution RNA barrier height analyses.

Effects of stress-dependent growth on evolution of sulcal direction and curvature in models of cortical folding

The majority of human brain folding occurs during the third trimester of gestation. Although many studies have investigated the physical mechanisms of brain folding, a comprehensive understanding of this complex process has not yet been achieved. In mechanical terms, the “differential growth hypothesis” suggests that the formation of folds results from a difference in expansion rates between cortical and subcortical layers, which eventually leads to mechanical instability akin to buckling. It has also been observed that axons, a substantial component of subcortical tissue, can elongate or shrink under tensile or compressive stress, respectively. Previous work has proposed that this cell-scale behavior in aggregate can produce stress-dependent growth in the subcortical layers. The current study investigates the potential role of stress-dependent growth on cortical surface morphology, in particular the variations in folding direction and curvature over the course of development. Evolution of sulcal direction and mid-cortical surface curvature were calculated from finite element simulations of three-dimensional folding in four different initial geometries: (i) sphere; (ii) axisymmetric oblate spheroid; (iii) axisymmetric prolate spheroid; and (iv) triaxial spheroid. The results were compared to mid-cortical surface reconstructions from four preterm human infants, imaged and analyzed at four time points during the period of brain folding. Results indicate that models incorporating subcortical stress-dependent growth predict folding patterns that more closely resemble those in the developing human brain. Statement of SignificanceCortical folding is a critical process in human brain development. Aberrant folding is associated with disorders such as autism and schizophrenia, yet our understanding of the physical mechanism of folding remains limited. Ultimately mechanical forces must shape the brain. An important question is whether mechanical forces simply deform tissue elastically, or whether stresses in the tissue modulate growth. Evidence from this paper, consisting of quantitative comparisons between patterns of folding in the developing human brain and corresponding patterns in simulations, supports a key role for stress-dependent growth in cortical folding.

Sequence-dependent folding of monolayered DNA origami domains.

Current models of DNA origami folding can explain the yield of the assembly process and the isomerization of the structure upon the application of mechanical forces. Nevertheless, the role of the sequence in this conformational transformation is still unclear. In this work, we address this question by performing a systematic thermodynamic study of three origami domains that have an identical design but different sequence contents. By comparing the thermal stability of the domains in various settings and measuring the extent of isomerization at equilibrium (both at the global and single-molecule levels), we extract the contribution to folding given by the sequence and propose thermal criton maps of the isomers to rationalize our findings. Our data contribute to a deeper understanding of DNA origami assembly by considering both the topological- and thermal-dependent properties of the sites of initial folding. While the former are responsible for the mechanical aspects of the process, the latter justify the observed sequence-dependent conformational preferences, which appear evident in simple origami structures but remain typically undisclosed in large and more intricate architectures.

DrTransformer: Heuristic cotranscriptional RNA folding using the nearest neighbor energy model.

Folding during transcription can have an important influence on the structure and function of RNA molecules, as regions closer to the 5' end can fold into metastable structures before potentially stronger interactions with the 3' end become available. Thermodynamic RNA folding models are not suitable to predict structures that result from cotranscriptional folding, as they can only calculate properties of the equilibrium distribution. Other software packages that simulate the kinetic process of RNA folding during transcription exist, but they are mostly applicable for short sequences. We present a new algorithm that tracks changes to the RNA secondary structure ensemble during transcription. At every transcription step, new representative local minima are identified, a neighborhood relation is defined and transition rates are estimated for kinetic simulations. After every simulation, a part of the ensemble is removed and the remainder is used to search for new representative structures. The presented algorithm is deterministic (up to numeric instabilities of simulations), fast (in comparison with existing methods), and it is capable of folding RNAs much longer than 200 nucleotides. This software is open-source and available at https://github.com/ViennaRNA/drtransformer. Supplementary data are available at Bioinformatics online.

Effect of nodule size and stiffness on phonation threshold and collision pressures in a synthetic hemilaryngeal vocal fold model.

Synthetic vocal fold (VF) replicas were used to explore the role of nodule size and stiffness on kinematic, aerodynamic, and acoustic measures of voiced speech production. Emphasis was placed on determining how changes in collision pressure may contribute to the development of phonotrauma. This was performed by adding spherical beads with different sizes and moduli of elasticity at the middle of the medial surface of synthetic silicone VF models, representing nodules of varying size and stiffness. The VF models were incorporated into a hemilaryngeal flow facility. For each case, self-sustained oscillations were investigated at the phonation threshold pressure. It was found that increasing the nodule diameter increased the open quotient, phonation threshold pressure, and phonation threshold flow rate. However, these values did not change considerably as a function of the modulus of elasticity of the nodule. Nevertheless, the ratio of collision pressure to subglottal pressure increased significantly for both increasing nodule size and stiffness. This suggests that over time, both growth in size and fibrosis of nodules will lead to an increasing cycle of compensatory vocal hyperfunction that accelerates phonotrauma.

Striving to be the fittest: quantitative P2/N95 respirator fit test results among hospital staff during the COVID-19 pandemic.

To provide fit rates for specific P2/N95 respirators and compare these results by age, sex, clean-shaven status, and fit tester experience. Exploratory audit involving secondary analysis of existing quantitative fit testing data. In response to the COVID-19 pandemic, healthcare services across Australia implemented respiratory protection protocols. This study details healthcare workers' (HCWs) fit testing results from a large Victorian public health service. Fit-tested employees of a large tertiary public health network. Fit rates for ten individual P2/N95 respirators were calculated, and the effect of age, sex, clean-shaven status, and fit tester experience was examined via logistic regression. 4593 employees were included, with 97.98% successfully fitting at least one respirator. Males were found to have significantly increased odds of achieving fit success compared to females (OR 11.61 95%CI 1.60-84.10). Fit rates dropped by 4% with each 1-year age increase (OR 0.96 95%CI 0.94-0.98). Clean-shaven individuals were also more likely to achieve a fit compared to non-clean-shaved individuals (OR 79.23 95%CI 10.21-614.62). More experienced fit testers also yielded significantly higher fit rates (OR 3.95, 95%CI 2.34-6.67). 98% of staff achieved a successful fitting of at least one respirator, with three-panel flat fold models (Industree Trident, 3M Aura 9320A+, and 3M Aura 1870+) performing the most consistently. An individual's ability to achieve a successful fit was associated with; male sex, younger age, clean-shaven status, and fit tester experience.

GB1 hairpin kinetics: capturing the folding pathway with molecular dynamics, replica exchange and optimal dimensionality reduction

We have performed molecular dynamics (MD) and replica-exchange (REMD) simulations of folding of the GB1 hairpin peptide in aqueous solution. REMD results were consistent with a cooperative zipper folding model. 120 MD trajectories at 320 K yielded relaxation times of 1.8 and 100 ns, with the slower assigned to global folding. The MD folding/unfolding transitions also followed the cooperative zipper model, specifying nucleation at the central turn followed by consecutive hydrogen bond formation. Formation of hydrogen bonds and hydrophobic contacts were highly correlated. Coarse-grained kinetic models constructed with the Optimal Dimensionality Reduction (ODR) approach found a folding time of 3.3 and unfolding time of 4.0 Additionally, relaxation times in the 130–170 ns range could be assigned to formation of the transition state and off-path intermediates. The unfolded state was the most highly populated and, significantly, most heterogenous, assembling the largest number of microstates, primarily composed of extended and turn structures. The folded state was also heterogenous, but a to a lesser degree, involving the fully folded and partially folded in-register hairpins at early stages of the zipper pathway. The transition state corresponded to the nucleated hairpin, with central turn and first beta-sheet hydrogen bond, while the off-path intermediates were off-register partial hairpins. Our simulation results were in excellent agreement with experimental data on folded fraction, relaxation time and folding mechanism. The new findings from this work suggest a highly cooperative zipper folding mechanism, nascent hairpin transition state and ∼100 ns relaxation related to intermediate formation. Communicated by Ramaswamy H. Sarma

Phase-averaged, frequency dependence of jet dynamics in a scaled up vocal fold model with full and incomplete closure

This article explores the fluid dynamics underlying voice production. The key parameters explored in this paper are frequency (from adult male to children and adult females) and the degree of closure of the vocal folds during phonation. The latter can be a pathological condition, but is common in children and females without being problematic. The findings of this study indicate that changes in jet dynamics across the human frequency range may explain the fundamental differences between male and female voices.

Examining the influence of epithelium layer modeling approaches on vocal fold kinematics and kinetics.

Grouping the thin epithelium and thicker superficial lamina propria layers into a single cover layer has been widely adopted in finite element vocal fold models. Recent silicone vocal fold studies have suggested, however, that inclusion of a distinct epithelial layer leads to more physiologically representative motion. This study systematically explores the ramifications of incorporating an epithelial layer into a cover grouping for finite element vocal fold modeling. A membrane model for the epithelium is introduced to facilitate parametric investigation by reducing the mesh density requirement of the epithelium into a single infinitesimally thin layer. Excluding the epithelium entirely leads to increased energy in higher order modes and larger inferior-superior excursion of the folds. Integrating the epithelium into a cover layer with volume-weighted average stiffness results in similar kinematics to that of a model treating the epithelium as a distinct layer. However, the internal stress/strain and contact pressure during collision are higher, and viscous dissipation is lower, when the epithelium is integrated into the cover. Thus, careful treatment of the epithelium is recommended for finite element studies, particularly when employing the models for estimating measures dependent upon internal stress/strain and/or collision pressure, such as vocal dose.

ManyFold: an efficient and flexible library for training and validating protein folding models.

ManyFold is a flexible library for protein structure prediction with deep learning that (i) supports models that use both multiple sequence alignments (MSAs) and protein language model (pLM) embedding as inputs, (ii) allows inference of existing models (AlphaFold and OpenFold), (iii) is fully trainable, allowing for both fine-tuning and the training of new models from scratch and (iv) is written in Jax to support efficient batched operation in distributed settings. A proof-of-concept pLM-based model, pLMFold, is trained from scratch to obtain reasonable results with reduced computational overheads in comparison to AlphaFold. The source code for ManyFold, the validation dataset and a small sample of training data are available at https://github.com/instadeepai/manyfold. Supplementary data are available at Bioinformatics online.

Applying deep reinforcement learning to the HP model for protein structure prediction

A central problem in computational biophysics is protein structure prediction, i.e., finding the optimal folding of a given amino acid sequence. This problem has been studied in a classical abstract model, the HP model, where the protein is modeled as a sequence of H (hydrophobic) and P (polar) amino acids on a lattice. The objective is to find conformations maximizing H–H contacts. It is known that even in this reduced setting, the problem is intractable (NP-hard). In this work, we apply deep reinforcement learning (DRL) to the two-dimensional HP model. We can obtain the conformations of best known energies for benchmark HP sequences with lengths from 20 to 50. Our DRL is based on a deep Q-network (DQN). We find that a DQN based on long short-term memory (LSTM) architecture greatly enhances the RL learning ability and significantly improves the search process. DRL can sample the state space efficiently, without the need of manual heuristics. Experimentally we show that it can find multiple distinct best-known solutions per trial. This study demonstrates the effectiveness of deep reinforcement learning in the HP model for protein folding.

Aerodynamic-induced Effects of Artificial Subglottic Stenosis on Vocal Fold Model Phonatory Response

ObjectiveSubglottic stenosis (SGS) is characterized by a narrowing of the trachea near the cricotracheal junction and impairs breathing. SGS may also adversely affect voice quality, but for reasons that are not fully understood. The purpose of this study is to provide experiment-based data concerning the effects on phonation of airway obstruction due to SGS. Study DesignBasic science MethodsA device simulating a SGS of adjustable severity ranging from 36% to 99.8% obstruction was created. Self-oscillating synthetic VF models were mounted downstream of the device and data were acquired to evaluate the effects of the obstruction on phonatory response. ResultsOnset pressures were relatively insensitive to obstructions of up to approximately 80% to 90% reductions in subglottic airway area and sharply increased thereafter. Flow rate (under conditions of constant pressure), flow resistance, and fundamental frequency all exhibited similar degrees of sensitivity to SGS obstruction as onset pressure. High-frequency noise became significant by 80% obstruction. Glottal area appeared to be less sensitive, not being affected until approximately 90% obstruction. ConclusionsConsistent with previous computational studies, this study found that aerodynamic, acoustic, and vibratory responses of self-oscillating VF models were largely unaffected by SGS until approximately 80% to 90% obstruction, and significantly affected at higher obstructions. This suggests that Grades I and II stenoses are unlikely to introduce subglottic airway aerodynamic disturbances that are sufficient in and of themselves to significantly alter phonatory output. The SGS model introduces a framework for future benchtop studies involving subglottic and supraglottic airway constrictions.

BiFold: A Python code for the calculation of double-folded (bifold) potentials with density-in/dependent nucleon-nucleon interactions

BiFold calculates the density-dependent (DDM3Yn, BDM3Yn, CDM3Yn) or independent double-folded potentials between two colliding spherical nuclei. It is written in a Python package form to give the ability to use the potentials directly in a nuclear reaction/structure code. In addition to using Woods-Saxon/Fermi or Gaussian functions, the code also allows the definition of nuclear matter densities using pre-calculated densities in a data file. The manuscript provides an overview of the double folding model and the use of the code. Program summaryProgram Title: BiFoldCPC Library link to program files:https://doi.org/10.17632/rmdx86p9dg.1Developer's repository link:https://github.com/mkarakoc/BiFoldCode Ocean capsule:https://codeocean.com/capsule/5286231Licensing provisions: GPLv3Programming language: Python 3.xNature of problem: BiFold calculates the real part of the nuclear potential between two colliding spherical nuclei by integrating a density-independent/dependent nucleon-nucleon (NN) interaction [1,2,3] over the nuclear matter densities of the two nuclei. The code is based on M3Y Reid/Paris NN interactions [1,2,3] by default, but it is possible to define custom NN interactions when necessary.Solution method: The code uses the Fourier transform method in spherical coordinates to calculate the potential. The method simplifies the sixfold integration [1] and makes the calculation significantly faster. The integration is done by default using Simpson's integration method, but Filon's integration method is also available.

Reaction channel contributions to the proton +Pb208 optical potential at 40 MeV

Background: Reaction channel coupling substantially modifies the real and imaginary nucleon-nucleus interactions for nuclei of $Z=20$ or less in ways that cannot be represented as uniform renormalizations of folding model potentials. For such nuclei coupling to inelastic channels also contributes. This raises the question of the effect of these couplings for heavier target nuclei.Purpose: To establish and characterize the contribution to the proton-nucleus interaction generated by coupling to neutron pickup (outgoing deuteron) channels for 40 MeV protons on the heavy closed shell nucleus $^{208}\mathrm{Pb}$. To identify and evaluate the consequent dynamical non-locality.Methods: Coupled reaction channel (CRC) calculations provide the elastic channel $S$-matrix ${S}_{lj}$ due to the included processes. Inversion of ${S}_{lj}$ will produce the local potential that would yield, in a single channel calculation, the elastic scattering observables from the CRC calculation. Subtracting the bare potential of the CRC calculations gives a local and $l$-independent representation of the dynamical polarization potential (DPP). From the DPPs due to various combinations of channel couplings, the influence of dynamically generated nonlocality can be identified.Results: Coupling to deuteron channels generates a repulsive component for the real potential and an absorptive component for the imaginary term. The radial shapes of both terms were modified in ways that could not be represented by uniform renormalization; the rms radius of the real part was substantially altered. Evidence of the dynamical nonlocality of the DPP due to pickup is provided by the nonadditivity of contributions of different couplings and other effects. For the doubly closed shell $^{208}\mathrm{Pb}$ coupling to low-lying (nongiant) collective states has a very small effect on elastic scattering, making a negligible contribution compared with pickup, and was not included.Conclusions: The DPPs established here strongly challenge the notion that folding models, in particular local density models, provide a satisfactory description of elastic scattering of protons from heavy nuclei. Coupling to neutron pickup channels induces dynamical nonlocality in the proton optical model potential with implications for direct reactions.

Three-Dimensional Printing of Ultrasoft Silicone with a Functional Stiffness Gradient.

A methodology for three-dimensionally printing ultrasoft silicone with a functional stiffness gradient is presented. Ultraviolet-cure silicone was deposited via two independently controlled extruders into a thixotropic, gel-like, silicone oil-based support matrix. Each extruder contained a different liquid silicone formulation. The extrusion rates were independently varied during printing such that the combined selectively deposited material contained different ratios of the two silicones, resulting in localized control of material stiffness. Tests to validate the process are reported, including tensile testing of homogeneous cubic specimens to quantify the range of material stiffness that could be printed, indentation testing of cuboid specimens to characterize printed stiffness gradients, and vibratory testing of synthetic multilayer vocal fold (VF) models to demonstrate that the method may be applied to the fabrication of biomechanical models for voice production research. The cubic specimens exhibited linear stress-strain data with tensile elasticity modulus values between 1.11 and 27.1 kPa, more than a factor of 20 in stiffness variation. The cuboid specimens exhibited material variations that were visually recognizable and quantifiable via indentation testing. The VF models withstood rigorous phonatory flow-induced vibration and exhibited vibratory characteristics comparable to those of previous models. Overall, while process refinements are needed, the results of these tests demonstrate the ability to print ultrasoft silicone with stiffness gradients.