Normal Mode Analysis Research Articles

Effect of rotation and FLR corrections with radiative heat-loss functions on transverse thermal instability of astrophysical porous plasma in interstellar medium (ISM)

The effect of rotation, finite ion Larmor radius (FLR) corrections and porosity on the thermal instability of infinite homogeneous plasma has been explored taking the effects of radiative heat-loss function and thermal conductivity. The general dispersion relation is derived by means of the normal mode analysis scheme with the help of appropriate linearized perturbation equations of the problem. This dispersion relations is further reduces for rotation axis parallel and perpendicular to the magnetic field for transverse wave propagation. It is found that the presence of rotation, FLR corrections and porosity amend the fundamental thermal criterion of instability. Numerical computations have been executed. Our result demonstrates that the rotation, porosity and FLR corrections affect the dens molecular clouds configuration and star formation.

Two stream instabilities in unmagnetized nonrelativistic quantum plasma

The objective of this study is to analyse instabilities and growth rate in unmagnetized dense non-relativistic collisionless quantum plasma under the impact of dynamics of ions. Model of quantum hydrodynamics is used to observe the streaming instabilities in highly dense inhomogeneous unmagnetized quantum plasma at low temperature. The model includes continuity and momentum equations for degenerate electrons and nondegenerate ions which interact with each other due to electrostatic field. Using normal mode analysis and linearization, perturbed potential is obtained in terms of unperturbed parameters with the help of first order perturbation in densities and velocities of electrons and ions while neglecting higher order perturbations. Variation in growth rates for detected instabilities is observed by using appropriate quantum plasma parameters.

Instabilities in magnetized inhomogeneous dusty plasmas with the effect of recombination

An analytical formalism to understand the impact of various parameters on evolving instabilities in inhomogeneous collisional dusty plasmas is presented here under the effect of recombination. The basic fluid dynamics for electrons and singly charged cold ions is carried out including recombination and collision at constant rate at the surface of dust particles. Dust particles are considered to be static with unperturbed density. Normal mode analysis method has been used along with linear approximation to get perturbed densities (n i1, n e1) which are used along with quasi-neutrality condition to get perturbed potential using Poisson’s equation to obtain dispersion relation. While other authors have detected instabilities in unmagnetized plasmas, here this method has been successfully realized in presence of static magnetic field at various propagation angle and allowed the straightforward calculation of growth rates of observed instability. An extensive study of the unstable modes has been done which are well discriminated and plotted with respect to different plasma parameters like dust charge, dust density, propagation angle, magnetic field, electrostatic potential along with plasma oscillation wavelength to Debye wavelength ratio. We have observed in the said model that the presence of dust particles and propagation angle of applied magnetic field are affecting significantly the growth rate of instability as compared to magnetic field and recombination.

A study of neutral collisions and viscous force on the formation of astronomical objects including with QMHD fluid model

A theoretical study has been undertaken on the influence of neutral collision frequency and viscous force on Jeans instability in radiative magnetized quantum plasma. A study was conducted using linearized quantum magneto-hydrodynamic equations. A general dispersion relation is acquired employing the normal mode analysis technique and the dispersion relation is discussed for longitudinal and transverse propagation. The altered general dispersion relation is derived and discussed to acquire Jean's state of instability by containing the magnetic field and quantum correction. The numerical findings are provided to demonstrate the impact of these changes on the rate of expansion of Jeans instability. The figure captions include too many details in this paper which represent that all considered parameters have a stabilizing or destabilizing effect on the growth rate of instability. The present study is suitable to understand the phenomena of acoustic waves in astronomical space plasma science.

Kinematic Vibrational Entropy Assessment and Analysis of SARS CoV-2 Main Protease.

The three-dimensional conformations of a protein influence its function and select for the ligands it can interact with. The total free energy change during protein-ligand complex formation includes enthalphic and entropic components, which together report on the binding affinity and conformational states of the complex. However, determining the entropic contribution is computationally burdensome. Here, we apply kinematic flexibility analysis (KFA) to efficiently estimate vibrational frequencies from static protein and protein-ligand structures. The vibrational frequencies, in turn, determine the vibrational entropies of the structures and their complexes. Our estimates of the vibrational entropy change caused by ligand binding compare favorably to values obtained from a dynamic Normal Mode Analysis (NMA). Higher correlation factors can be achieved by increasing the distance cutoff in the potential energy model. Furthermore, we apply our new method to analyze the entropy changes of the SARS CoV-2 main protease when binding with different ligand inhibitors, which is relevant for the design of potential drugs.

Functional Dynamics of Substrate Recognition in TEM Beta-Lactamase

The beta-lactamase enzyme provides effective resistance to beta-lactam antibiotics due to substrate recognition controlled by point mutations. Recently, extended-spectrum and inhibitor-resistant mutants have become a global health problem. Here, the functional dynamics that control substrate recognition in TEM beta-lactamase are investigated using all-atom molecular dynamics simulations. Comparisons are made between wild-type TEM-1 and TEM-2 and the extended-spectrum mutants TEM-10 and TEM-52, both in apo form and in complex with four different antibiotics (ampicillin, amoxicillin, cefotaxime and ceftazidime). Dynamic allostery is predicted based on a quasi-harmonic normal mode analysis using a perturbation scan. An allosteric mechanism known to inhibit enzymatic function in TEM beta-lactamase is identified, along with other allosteric binding targets. Mechanisms for substrate recognition are elucidated using multivariate comparative analysis of molecular dynamics trajectories to identify changes in dynamics resulting from point mutations and ligand binding, and the conserved dynamics, which are functionally important, are extracted as well. The results suggest that the H10-H11 loop (residues 214-221) is a secondary anchor for larger extended spectrum ligands, while the H9-H10 loop (residues 194-202) is distal from the active site and stabilizes the protein against structural changes. These secondary non-catalytically-active loops offer attractive targets for novel noncompetitive inhibitors of TEM beta-lactamase.

Effect of salt fingers on heat transfer for different non‐uniform concentration profiles in a micropolar liquid

AbstractThis paper discusses the theoretical aspects of the effect of salt fingers on heat transfer for different non‐uniform concentration profiles in a micropolar liquid layer kept between two parallel plates of infinite extent separated by a thin layer, heated and soluted from above. The onset of salt finger convection (convection due to the salt finger process) is studied through the linear stability analysis theory. The system of partial differential equations is solved numerically using the normal mode analysis method and the required solution is found by applying the Galerkin method. The effect of heat transfer and concentration of micropolar liquid is obtained for (i) free–free, (ii) rigid–rigid, and (iii) rigid–free isothermal, permeable with no‐spin boundary conditions. The effect of different micropolar parameters (i.e., coupling parameter, micropolar heat conduction parameter, couple stress parameter, and inertia parameter) has been analyzed on the onset of stationary convection, and the results are depicted graphically. It is shown that different non‐uniform concentration gradients, diffusivity ratio, coupling parameter, and solutal Rayleigh number influence the heat transfer in the system. The phase of concentration flow for different boundary conditions is compared and analyzed.

Integrative structure determination reveals functional global flexibility for an ultra-multimodular arabinanase

AbnA is an extracellular GH43 α-L-arabinanase from Geobacillus stearothermophilus, a key bacterial enzyme in the degradation and utilization of arabinan. We present herein its full-length crystal structure, revealing the only ultra-multimodular architecture and the largest structure to be reported so far within the GH43 family. Additionally, the structure of AbnA appears to contain two domains belonging to new uncharacterized carbohydrate-binding module (CBM) families. Three crystallographic conformational states are determined for AbnA, and this conformational flexibility is thoroughly investigated further using the “integrative structure determination” approach, integrating molecular dynamics, metadynamics, normal mode analysis, small angle X-ray scattering, dynamic light scattering, cross-linking, and kinetic experiments to reveal large functional conformational changes for AbnA, involving up to ~100 Å movement in the relative positions of its domains. The integrative structure determination approach demonstrated here may apply also to the conformational study of other ultra-multimodular proteins of diverse functions and structures.

Wave propagation in an elastic coaxial hollow cylinder when exposed to thermal heating and external load

This manuscript examines the propagation of waves in a coaxial hollow infinite isotropic cylinder when exposed to a thermal heating source from the outer cylinder. For the mechanical conditions, the inner and outer cylinders are assumed to be displacement-free, in addition to a perfectly welded interface; while an insulation thermal condition is assumed on the interface to prevent the inner cylinder from being heated by an already-heated outer cylinder. Equally, a situation of an external load on the outer cylinder is also examined. As for the methodology, a mixture of the normal mode analysis method and the numerical Laplace integral transform is employed to study the vibrational displacements in the inner and outer cylinders, as well as the temperature field in the outer cylinder. Lastly, certain graphical illustrations associated with low and higher heating periods are demonstrated after considering some physical data and heating sources of practical application.

Conformational Dynamics Linking Kinase and Endonuclease Domains Explain the Divergent Function of IRE1 Paralogues

The ER stress sensors IRE1α and IRE1β have dual kinase and endonuclease activities that mediate cellular proteostasis by splicing Xbp1 mRNA and degrading other ER‐targeted transcripts. Although the two paralogues share a high degree of sequence homology, the epithelial cell‐specific paralogue IRE1β, which is expressed at mucosal surfaces, has impaired kinase activity and phosphorylation that restrict stress‐induced activation of the endonuclease domain. To uncover structural features that explain these differences, we used normal mode analysis to build dynamic correlation networks describing active and inactive conformations of IRE1 kinase‐endonuclease domains. For human IRE1α, we identified a fingerprint of intra‐ and interdomain dynamic couplings that distinguish between the two conformations. Mutations that disrupted IRE1α endonuclease activity perturbed the dynamic networks of the active conformation and enhanced features of an inactive conformation, thus validating our approach. Strikingly, the dynamic networks of human IRE1β when modeled in an active conformation resembled the inactive IRE1α network. A set of non‐conserved amino acids were found to distinguish between the dynamic networks linking kinase‐endonuclease domains for the two IRE1 paralogues. In most cases, however, these divergent network‐determining amino acids were found only in IRE1β sequences from mammals. In lower vertebrates, the key amino acids and the dynamic couplings of IRE1α active state were conserved in IRE1β. Thus, IRE1β evolved distinct conformational dynamics and enzymatic activity for a role in mucus barrier function that is unique to higher vertebrates.

A thermoelastic model with higher order time derivatives for a crack in a rotating solid

This article represents a refined one-temperature thermoelastic model with higher order time derivatives and phase-lags for a Mode-I crack in a rotating fiber-reinforced solid. The crack is subjected to a stipulated temperature and normal stress. The exact expressions of displacement, temperature and stress components are obtained by normal mode analysis. Some generalized thermoelasticity theories are obtained as special cases. The convergency of the present refined model is tabulated and is compared with other theories. The variations of the temperature, displacements and stresses are presented graphically with the crack length to show the effect of phase-lags and thermal relaxation time through Refined-phase-lag (RPL), simple-phase-lag (SPL), Green-Naghdi (G-N) theory, Lord-Shulman (L-S) theory and the Coupled thermoelasticity (CTE) theory in the presence and absence of rotation.

The chirality of isotopomers of glycine compared using next‐generationQTAIM

AbstractThe effect of a deuterium (D) or tritium (T) isotope bonded to the alpha carbon of glycine is determined without the need to apply external forces, for example, electric fields or using normal mode analysis. Isotopic effects were accounted for using the mass‐dependent diagonal Born‐Oppenheimer energy correction (DBOC) at the CCSD level of theory. We calculated the stress tensor trajectories of the dominant C‐N bond within next generation quantum theory of atoms in molecules (NG‐QTAIM). S‐character chirality was discovered using the stress tensor trajectories, instead of the Cahn–Ingold–Prelog (CIP) rules, for ordinary glycine. The S‐character chirality was preserved after the substitution of the H on the alpha carbon for a D isotope but transformed to R‐character chirality after replacement with the T isotope. This reversal of the chirality depending on the presence of a single D or T isotope bound to the alpha carbon adds to the debate on the nature of the extraterrestrial origins of chirality in simple amino acids. We demonstrate that NG‐QTAIM is a promising tool for understanding isotopic induced electronic charge density changes, useful in analysis of infrared (IR) or circular dichroism (CD) spectra explaining changes in mode couplings and bands intensities or sign.

An Energy-Based Summation-by-Parts Finite Difference Method For the Wave Equation in Second Order Form

We develop a new finite difference method for the wave equation in second order form. The finite difference operators satisfy a summation-by-parts (SBP) property. With boundary conditions and material interface conditions imposed weakly by the simultaneous-approximation-term (SAT) method, we derive energy estimates for the semi-discretization. In addition, error estimates are derived by the normal mode analysis. The proposed method is termed as energy-based because of its similarity with the energy-based discontinuous Galerkin method. When imposing the Dirichlet boundary condition and material interface conditions, the traditional SBP-SAT discretization uses a penalty term with a mesh-dependent parameter, which is not needed in our method. Furthermore, numerical dissipation can be added to the discretization through the boundary and interface conditions. We present numerical experiments that verify convergence and robustness of the proposed method.

TN strain proteome mediated therapeutic target mapping and multi-epitopic peptide-based vaccine development for Mycobacterium leprae.

Leprosy is a significant universal health problem that is remarkably still a concern in developing countries due to infection frequency. New therapeutic molecules and next-generation vaccines are urgently needed to accelerate the leprosy-free world. In this direction, the present study was performed using two routes: proteome-mediated therapeutic target identification and mapping as well as multi-epitopic peptide-based novel vaccine development using state of the art of computational biology for the TN strain of M. leprae. The TN strain was selected from 65 Mycobacterium strains, and TN strain proteome mediated 83 therapeutic protein targets were mapped and characterized according to subcellular localization. Also, drug molecules were mapped with respect to protein targets localization. The Druggability potential of proteins was also evaluated. For multi-epitope peptide-based vaccine development, the four common types of B and T cell epitopes were identified (SLFQSHNRK, VVGIGQHAA, MMHRSPRTR, LGVDQTQPV) and combined with the suitable peptide linker. The vaccine component had an acceptable protective antigenic score (0.9751). The molecular docking of vaccine components with TLR4/MD2 complex exhibited a low ACE value (-244.12) which signifies the proper binding between the two molecules. The estimated free Gibbs binding energy ensured accurate protein-protein interactions (-112.46kcal/mol). The vaccine was evaluated through adaptive immunity stimulation as well as immune interactions. The molecular dynamic simulation was carried out by using CHARMM topology-based parameters to minimize the docked complex. Subsequently, the Normal Mode Analysis in the internal coordinates showed a low eigen-value (1.3982892e-05), which also signifies the stability of molecular docking. Finally, the vaccine components were adopted for reverse transcription and codon optimization in E. coli strain K12 for the pGEX-4T1 vector, which supports in silico cloning of the vaccine components against the pathogen. The study directs the experimental study for therapeutics molecules discovery and vaccine candidate development with higher reliability.

Neutrino Flavor Pendulum Reloaded: The Case of Fast Pairwise Conversion.

In core-collapse supernovae or compact binary merger remnants, neutrino-neutrino refraction can spawn fast pair conversion of the type ν_{e}ν[over ¯]_{e}↔ν_{x}ν[over ¯]_{x} (with x=μ, τ), governed by the angle-dependent density matrices of flavor lepton number. In a homogeneous and axially symmetric two-flavor system, all angle modes evolve coherently, and we show that the nonlinear equations of motion are formally equivalent to those of a gyroscopic pendulum. Within this analogy, our main innovation is to identify the elusive characteristic of the lepton-number angle distribution that determines the depth of conversion with the "pendulum spin." The latter is given by the real part of the eigenfrequency resulting from the linear normal-mode analysis of the neutrino system. This simple analogy allows one to predict the depth of flavor conversion without solving the nonlinear evolution equations. Our approach provides a novel diagnostic tool to explore the physics of nonlinear systems.

Reversible motions and disordered structure of soft particles in amorphous solids

In amorphous solids, soft vibrational modes derived from normal mode analysis can be utilized to identify the soft particles that are prone to irreversible rearrangements. However, the normal mode analysis approach cannot explain why the spatial distributions of clustered soft particles do not change over time. We define a softness parameter based on the vibrational density of states calculated directly from molecular dynamics simulations with both the harmonic vibrations and anharmonic relaxations being properly captured at finite temperatures. This parameter spontaneously correlates with the real space atomic motions and the dynamics heterogeneity. Using the softness parameter, we show that the softest particles are confined within rigid cages. These particles keep rearranging reversibly without long-range diffusion. The moderately soft particles rearrange irreversibly, and the hard particles mainly participate in vibrations without rearrangement. We also show that the soft particles form locally disordered structures, while the hard particles present strong ordering. These findings confirm the defective nature of soft particles, and provide insights on the nature of softness as the ability to rearrange, but not necessarily irreversibly.

Response of Terahertz Protein Vibrations to Ligand Binding: Calmodulin-Peptide Complexes as a Case Study.

Terahertz vibrations are sensitive reporters of the structure and interactions of proteins. Ligand binding alters the nature and distribution of these collective vibrations. The ligand-induced changes in the terahertz protein vibrations contribute to the binding entropy and to the overall thermodynamic stability of the resultant protein-ligand complexes. Here, we have examined the response of the low-frequency (below 6 terahertz) collective vibrations of the calcium-loaded calmodulin (CaM) to binding to five different ligands, both in the presence and absence of water, using normal-mode analysis and molecular dynamics simulations. A comparison of the vibrational spectra of hydrated and dry systems reveals that protein-solvent interactions stiffen the terahertz protein vibrations and that these solvent-coupled collective vibrations contribute significantly to the hydration-sensitive variation in the vibrational entropy of CaM. In the absence of water, the low-frequency vibrations of CaM are stiffened by ligand binding. On the contrary, the number and the cumulative vibrational entropy of low-frequency vibrational modes (ω < 200 cm-1) of the hydrated CaM are increased noticeably after binding to the peptides, indicating binding-induced softening of collective vibrations of the protein. Although the calculated and experimental binding affinities of the chosen complexes correlated reasonably well, no systematic correlation was observed between the protein vibrational entropy and the binding affinity. The results underscored the importance of the interplay of protein-ligand and solvent interactions in modulating the low-frequency vibrations of proteins.

Probing terahertz dynamics of multidomain protein in cell-like confinement

The development of meaningful descriptions of multidomain proteins exhibiting complex inter-domain dynamics modes is a key challenge for understanding their roles in molecular recognition and signalling processes. Here we developed a generally applicable approach for probing the low frequency collective hydration dynamics of multidomain proteins that uses terahertz spectroscopy of a protein molecule confined in a phospholipid reverse micelles environment (named Droplet THz). With the combination of normal mode analysis, we demonstrated the binding of calcium ions modulates the local inter-domain motion of the human coagulant factor VIII protein in a concentration-dependent manner. These findings highlight the Droplet THz as a valuable tool for dissecting the ultrafast dynamics of domain motion in the multidomain proteins and suggest a modulating mechanism of calcium ions on the structural flexibility and function of human coagulant proteins.

Computational studies on the design of NCI natural products as inhibitors to SARS-CoV-2 main protease

The pandemic coronavirus disease (COVID-19) caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has resulted in more than 5 million deaths globally. Currently there are no effective drugs available to treat COVID-19. The viral protease replication can be blocked by the inhibition of main protease that is encoded in polyprotein 1a and is therefore a potential protein target for drug discovery. We have carried out virtual screening of NCI natural compounds followed by molecular docking in order to identify hit molecules as probable SARS-CoV-2 main protease inhibitors. The molecular dynamics (MD) simulations of apo form in complex with N3, α-ketoamide and NCI natural products was used to validate the screened compounds. The MD simulations trajectories were analyzed using normal mode analysis and principal component analysis revealing dynamical nature of the protein. These findings aid in understanding the binding of natural products and molecular mechanisms of SARS-CoV-2 main protease inhibition. Communicated by Ramaswamy H. Sarma

Protein dynamics developments for the large scale and cryoEM: case study of ProDy 2.0.

Cryo-electron microscopy (cryoEM) has become a well established technique with the potential to produce structures of large and dynamic supramolecular complexes that are not amenable to traditional approaches for studying structure and dynamics. The size and low resolution of such molecular systems often make structural modelling and molecular dynamics simulations challenging and computationally expensive. This, together with the growing wealth ofstructural data arising from cryoEM and other structural biology methods, hasdriven a trend in the computational biophysics community towards the development of new pipelines for analysing global dynamics using coarse-grained models and methods. At the centre of this trend has been a return to elastic network models, normal mode analysis (NMA) and ensemble analyses such as principal component analysis, and the growth of hybrid simulation methodologies that make use of them. Here, this field is reviewed with a focus on ProDy, the Python application programming interface for protein dynamics, which has been developed over the last decade. Two key developments in this area are highlighted: (i) ensemble NMA towards extracting and comparing the signature dynamics of homologous structures, aided by the recent SignDy pipeline, and (ii) pseudoatom fitting for more efficient global dynamics analyses of large and low-resolution supramolecular assemblies from cryoEM, revisited in the CryoDy pipeline. It is believed that such a renewal and extension of old models and methods in new pipelines will be critical for driving the field forward into the next cryoEM revolution.