Integrable Perturbations Research Articles

A hierarchy of heat conduction laws

The purpose of this work is to produce a family of equations describing the evolution of the temperature in a rigid heat conductor. This is obtained by means of successive approximations of the Fourier law, via memory relaxations and integral perturbations.

Free energy reconstruction/decomposition from WHAM, force integration and free energy perturbation for an umbrella sampling simulation

Comparisons between methodologies are usually made by performing separated sampling simulations in conjunction with the corresponding estimator. Here, the accuracy and convergence of three typical approaches (WHAM, force integration, and FEP) for estimating the ion-pairing free energy in water are carefully examined in order to identify which estimator is the most efficient for a particular set of trajectories. The force integration is superior among these methods, whereas the FEP introduces relatively prominent uncertainty arising from the perturbed potential energy. The direct solute-solvent interaction term and the indirect solvent contribution accounting for the reorientation of non-spherically symmetric ions could be straightforwardly extracted using force integration and FEP.

Asymptotic Behavior of Solutions of a Complete Second-Order Integro-Differential Equation

In this paper, we study a complete second-order integro-differential operator equation in a Hilbert space. The difference-type kernel of an integral perturbation is a holomorphic semigroup bordered by unbounded operators. The asymptotic behavior of solutions of this equation is studied. Asymptotic formulas for solutions are proved in the case when the right-hand side is close to an almost periodic function. The obtained formulas are applied to the study of the problem of forced longitudinal vibrations of a viscoelastic rod with Kelvin-Voigt friction.

Comparison of the thermodynamic integration and free energy perturbation in the computing alchemical free energy difference

On an atomistic scale, free energy calculations are important for our understanding of biological processes, which provides an insight to grasp the various mechanisms. Over the years, many computational methods have been developed to calculate free energy differences such as geometrical (e.g. umbrella sampling) and alchemical methods. In this work, we present alchemical-free energy methods, thermodynamic integration (TI) and free energy perturbation (FEP), to investigate polarization effect of paclitaxel drug. Then, we have compared our simulation studies using TI, FEP, and Hamiltonian replica exchange FEP from the perspective of computational cost and accuracy.

A variational framework for the inverse Henderson problem of statistical mechanics

The inverse Henderson problem refers to the determination of the pair potential which specifies the interactions in an ensemble of classical particles in continuous space, given the density and the equilibrium pair correlation function of these particles as data. For a canonical ensemble in a bounded domain, it has been observed that this pair potential minimizes a corresponding convex relative entropy functional, and that the Newton iteration for minimizing this functional coincides with the so-called inverse Monte Carlo (IMC) iterative scheme. In this paper, we show that in the thermodynamic limit analogous connections exist between the specific relative entropy introduced by Georgii and Zessin and a proper formulation of the IMC iteration in the full space. This provides a rigorous variational framework for the inverse Henderson problem, valid within a large class of pair potentials, including, for example, Lennard-Jones-type potentials. It is further shown that the pressure is strictly convex as a function of the pair potential and the chemical potential, and that the specific relative entropy at fixed density is a strictly convex function of the pair potential. At a given reference potential and a corresponding density in the gas phase, we determine the gradient and the Hessian of the specific relative entropy, and we prove that the Hessian extends to a symmetric positive semidefinite quadratic functional in the space of square integrable perturbations of this potential.

Somatostatin interneurons exhibit enhanced functional output and resilience to axotomy after mild traumatic brain injury

Mild traumatic brain injury (mTBI) gives rise to a remarkable breadth of pathobiological consequences, principal among which are traumatic axonal injury and perturbation of the functional integrity of neuronal networks that may arise secondary to the elimination of the presynaptic contribution of axotomized neurons. Because there exists a vast diversity of neocortical neuron subtypes, it is imperative to elucidate the relative vulnerability to axotomy among different subtypes. Toward this end, we exploited SOM-IRES-Cre mice to investigate the consequences of the central fluid percussion model of mTBI on the microanatomical integrity and the functional efficacy of the somatostatin (SOM) interneuron population, one of the principal subtypes of neocortical interneuron. We found that the SOM population is resilient to axotomy, representing only 10% of the global burden of inhibitory interneuron axotomy, a result congruous with past work demonstrating that parvalbumin (PV) interneurons bear most of the burden of interneuron axotomy. However, the intact structure of SOM interneurons after injury did not translate to normal cellular function. One day after mTBI, the SOM population is more intrinsically excitable and demonstrates enhanced synaptic efficacy upon post-synaptic layer 5 pyramidal neurons as measured by optogenetics, yet the global evoked inhibitory tone within layer 5 is stable. Simultaneously, there exists a significant increase in the frequency of miniature inhibitory post-synaptic currents within layer 5 pyramidal neurons. These results are consistent with a scheme in which 1 day after mTBI, SOM interneurons are stimulated to compensate for the release from inhibition of layer 5 pyramidal neurons secondary to the disproportionate axotomy of PV interneurons. The enhancement of SOM interneuron intrinsic excitability and synaptic efficacy may represent the initial phase of a dynamic process of attempted autoregulation of neocortical network homeostasis secondary to mTBI.

Alchemical Free Energy Estimators and Molecular Dynamics Engines: Accuracy, Precision, and Reproducibility.

The binding free energy between a ligand and its target protein is an essential quantity to know at all stages of the drug discovery pipeline. Assessing this value computationally can offer insight into where efforts should be focused in the pursuit of effective therapeutics to treat a myriad of diseases. In this work, we examine the computation of alchemical relative binding free energies with an eye for assessing reproducibility across popular molecular dynamics packages and free energy estimators. The focus of this work is on 54 ligand transformations from a diverse set of protein targets: MCL1, PTP1B, TYK2, CDK2, and thrombin. These targets are studied with three popular molecular dynamics packages: OpenMM, NAMD2, and NAMD3 alpha. Trajectories collected with these packages are used to compare relative binding free energies calculated with thermodynamic integration and free energy perturbation methods. The resulting binding free energies show good agreement between molecular dynamics packages with an average mean unsigned error between them of 0.50 kcal/mol. The correlation between packages is very good, with the lowest Spearman’s, Pearson’s and Kendall’s tau correlation coefficients being 0.92, 0.91, and 0.76, respectively. Agreement between thermodynamic integration and free energy perturbation is shown to be very good when using ensemble averaging.

Thermodynamic and transport properties of amoxicillin

We have carried out MD simulations of amoxicillin, a drug molecule used as antibacterial agent, in water and ethanol to study thermodynamic properties like solvation free energy and transport phenomena like diffusion, viscosity. The free energy of solvation of amoxicillin in water and ethanol have been estimated at 310 K using thermodynamic integration (TI) and free energy perturbation (FEP) based methods. It has been obtained that the free energy of solvation of amoxicillin in water is higher by ≈ 105 kJ/mol in TIP3P model than in ethanol. We have also reported the solvent accessible surface area (SASA) of solute as well as the hydrogen bonds between solute and solvent for different solvents. The analysis of SASA and hydrogen bond provides more insight on effect of solvent environment in solvation process of amoxicillin. We have also estimated the diffusion coefficient and our results show that diffusion coefficients of amoxicillin depends on solvent environment, as expected, and it is higher in water than that of ethanol. Also, applying the idea of system size dependence of diffusion coefficient, the viscosity coefficient of water and solution of amoxicillin in water have also been estimated. Furthermore, the effects of temperature on diffusion has been studied. The estimated values of self-diffusion coefficients of water are in good agreement with previously reported experimental data within ≈13.5%.

Confinement in the tricritical Ising model

We study the leading and sub-leading magnetic perturbations of the thermal E7 integrable deformation of the tricritical Ising model. In the low-temperature phase, these magnetic perturbations lead to the confinement of the kinks of the model. The resulting meson spectrum can be obtained using the semi-classical quantisation, here extended to include also mesonic excitations composed of two different kinks. An interesting feature of the integrable sub-leading magnetic perturbation of the thermal E7 deformation of the model is the possibility to swap the role of the two operators, i.e. the possibility to consider the model as a thermal perturbation of the integrable A3 model associated to the sub-leading magnetic deformation. Due to the occurrence of vacuum degeneracy unrelated to spontaneous symmetry breaking in A3, the confinement pattern shows novel features compared to previously studied models. Interestingly enough, the validity of the semi-classical description in terms of the A3 endpoint extends well beyond small fields, and therefore the full parameter space of the joint thermal and sub-leading magnetic deformation is well described by a combination of semi-classical approaches. All predictions are verified by comparison to finite volume spectrum resulting from truncated conformal space.

Structurally Stable Nondegenerate Singularities of Integrable Systems

In this paper, we study singularities of the Lagrangian fibration given by a completely integrable system. We prove that a non-degenerate singular fibre satisfying the so-called connectedness condition is structurally stable under (small enough) real-analytic integrable perturbations of the system. In other words, the topology of the fibration in a neighbourhood of such a fibre is preserved after any such perturbation. As an illustration, we show that a saddle-saddle singularity of the Kovalevskaya top is structurally stable under real-analytic integrable perturbations, but structurally unstable under $C^\infty$ smooth integrable perturbations.

Protecting the cell mebrane against pore-forming agents via a brain-permeable aminosterol

Cells are vulnerable to both chemical and biological threat agents that can induce cytotoxicity. These toxins act by disrupting the ion and lipid homeostasis of the cell through perturbation of cellular membrane integrity. Previous work has demonstrated the ability of aminosterols to protect cell membranes from protein misfolded oligomers implicit in neurodegenerative disease. Herein, we investigated the utility of aminosterols to protect cells from additional biological, protein-based threat agents.

Theoretical analysis of Ledinegg instability and density wave oscillation using dimensionless numbers

• Dimensionless number criteria determining two phase flow stability is established. • Flow direction on stability is non-monotonic, the turning point expression is given. • Increasing flow rate and power proportionally can be good or bad for stability. • Contrary conclusions of flow direction and power level on stability are clarified. • The influences of tube length and diameter on stability are discussed and presented. Two-phase flow instability is influenced by many factors. The reported parameter effects on instability boundary are incomplete and sometimes conflict. Dimensionless numbers are more effective to reveal the mechanisms and describe the instability boundary. In this paper, dimensionless numbers are used to systematically analyze various parameters’ effects. One-dimensional governing equations describing the convective boiling process in a tube are simplified to a set of linear ordinary differential equations through integration and small perturbation methods. The judging inequalities expressed by six dimensionless numbers are obtained by the Routh stability criterion. The relationship between the judging inequalities and the instability types are identified theoretically for the first time. The boundary of density wave oscillation obtained from the fourth dimensionless number inequality agrees well with experimental data. The effects of Froude number, friction number, inlet temperature, inlet and outlet flow resistances, tube length and tube diameter are discussed in detail. Some contrary conclusions presented by previous investigators are clarified. The effect of varying Froude number (or flow orientation) on system stability is non-monotonic, and the turning point expression is given. The effects of geometric parameters are complex. The effects of tube length and tube diameter on the instability boundary are discussed systematically based on Froude number and friction number when operation parameters keep unchanged. Though many of the parameters’ influences are non-monotonic, some new universal laws or findings are extracted. For example, according to the conclusions of friction number effect, increasing the steam generator working power levels (heating power and mass flow rate increase proportionally) can be good or bad for stability according to different inlet flow resistances.

Deuterium Isotope Effects on Acid-Base Equilibrium of Organic Compounds.

Deuterium isotope effects on acid–base equilibrium have been investigated using a combined path integral and free-energy perturbation simulation method. To understand the origin of the linear free-energy relationship of versus , we examined two theoretical models for computing the deuterium isotope effects. In Model 1, only the intrinsic isotope exchange effect of the acid itself in water was included by replacing the titratable protons with deuterons. Here, the dominant contribution is due to the difference in zero-point energy between the two isotopologues. In Model 2, the medium isotope effects are considered, in which the free energy change as a result of replacing H2O by D2O in solute–solvent hydrogen-bonding complexes is determined. Although the average change from Model 1 was found to be in reasonable agreement with the experimental average result, the dependence of the solvent isotope effects is absent. A linear free-energy relationship is obtained by including the medium effect in Model 2, and the main factor is due to solvent isotope effects in the anion–water complexes. The present study highlights the significant roles of both the intrinsic isotope exchange effect and the medium solvent isotope effect.

Control of Vibrations of a Beam with Nonlocal Boundary Conditions

The control problem the first eigenvalues of the Euler-Bernoulli beam vibration with hinged and clamped fixings at both ends is considered. The control is based on Kanguzhin’s algorithm through integral perturbations of the boundary conditions of the original problem. Conditions for the boundary parameters for controlling the first eigenvalues are found.

Hidden toric symmetry and structural stability of singularities in integrable systems

The goal of the paper is to develop a systematic approach to the study of (perhaps degenerate) singularities of integrable systems and their structural stability. As the main tool, we use "hidden" system-preserving torus actions near singular orbits. We give sufficient conditions for the existence of such actions and show that they are persistent under integrable perturbations. We find toric symmetries for several infinite series of singularities and prove, as an application, structural stability of Kalashnikov's parabolic orbits with resonances in the real-analytic case. We also classify all Hamiltonian $k$-torus actions near a singular orbit on a symplectic manifold $M^{2n}$ (or on its complexification) and prove that the normal forms of these actions are persistent under small perturbations. As a by-product, we prove an equivariant version of the Vey theorem (1978) about local symplectic normal form of nondegenerate singularities.

GC-MS/FID analysis, antibacterial activity and modes of action of essential oils from three Aframomum species found in Cameroon against foodborne pathogenic bacteria

Background: The current study examined the chemical profile and in vitro antibacterial activity of essential oils (EOs) extracted from Aframomum danielli (leaves and seeds), Aframomum chlamydentum (leaves), and Aframomum melegueta (leaves) against foodborne pathogenic bacteria.
 Methods: The hydro-distillation technique using a Clevenger-type apparatus was used to extract EOs, whereas the Gas Chromatography-Mass Spectrometry (GC-MS) and GC coupled to Flame Ionization Detector (GC-FID) allowed the chemical characterization of oil constituents. The broth micro-dilution method was applied for the determination of the minimum inhibitory concentration (MIC) and minimum bactericidal concentration (MBC). Besides, some modes of action were studied on the cell membrane integrity and biofilm formation of Salmonella typhi.
 Results: The major compounds identified from EOs of A. danielli seeds were eucalyptol (48.707%), limonene (11.368%), beta pinene (10.342-10.335%), and alpha terpineol (8.785-9.049%), whereas EOs from A. danielli leaves were dominated by sabinene (42.87%), beta pinene, (11.22%), caryophyllene (7.84%), terpinen-4-ol (5.68%), linalool (3.48%) and gamma terpinene (2.02%). Major volatile markers from EOs of A. chlamydentum leaves comprised beta pinene (49.72%), caryophyllene (10.62%), alpha pinene (6.21%) and linalool (2.96%), while those of EOs from A. melegueta included beta pinene (37.15%), caryophyllene (17.64%), caryophyllene oxide (8.72%) and alpha pinene (8.26%). This study is the first to report on the chemical constituents of EOs from A. chlamydentum. Test oils displayed significant antibacterial activity with the MIC ranging from 0.0625 to 0.5% (v/v). EOs from A. melegueta (leaves) appeared to be the most active, acting against all tested bacteria. All EOs identified displayed bactericidal effects against Citrobacter freundii, a bacterium known to cause a broad range of infections associated with a higher rate of in-hospital mortality. The EOs from A. melegueta may act through perturbation of cell membrane integrity and permeability as well as the inhibition of bacterial biofilm formation.
 Conclusion: Our findings suggest the possible application of essential oils in agricultural food products for the control of bacterial diseases.

Tracking and vibration control of a free-floating space manipulator system with flexible links and joints

The problem of modeling and controlling of a free-floating space manipulator with flexures in both links and joints is addressed in this study. A mathematical model of the system is developed by combining Lagrange’s equations and momentum conservation. The finite element method is introduced to discretize multi-links with complex cross-sections. In order to reduce the dimensions and maintain the precision of a rigid-flexible coupled system, an iterated improved reduction system method is adopted. Then, a novel composite control scheme for the reduced system is presented that uses the concept of integral manifolds and singular perturbation theory. Finally, an augmented computed torque controller is applied to the under-actuated slow subsystem to realize trajectory tracking in joint space, while a linear-quadratic controller is designed to damp out the vibration of joints and links. Numerical simulation results verified that the proposed hybrid controller can successfully suppress vibration and track trajectory at the same time.

On a three step two‐grid finite element method for the Oldroyd model of order one

AbstractIn this work, an optimal error analysis of a three step two‐grid method for the equations of motion arising in the 2DOldroyd model of order one is discussed. The model, which can be thought of as an integral perturbation of Navier‐Stokes equations (NSE), represents linear viscoelastic fluid flows. This non‐linear model is analyzed here using a three step numerical scheme. In the first step the problem is solved on a coarse grid, and we use this course grid solution to linearize the problem and solve it in second step, on a finer grid. Third step is a correcting step done on the finer grid. Optimal error estimates for the velocity in and ‐norms and for the pressure in ‐norm in the semidiscrete case are established. Estimates are shown to be uniform under the uniqueness assumption. Then, based on backward Euler method, a completely discrete scheme is analyzed and optimal a priori error estimates are derived. All the analysis are carried out for the non‐smooth initial data. Finally we present some numerical results to validate our theoretical results. These examples show that the three step two‐grid method is efficient than solving a nonlinear problem directly, as is expected.

ZAR1 resistosome and helper NLRs: Bringing in calcium and inducing cell death

ZAR1 resistosome and helper NLRs: Bringing in calcium and inducing cell death

Perturbation of cellular integrity by nicotine: A major component of e-cigarette smoke

Perturbation of cellular integrity by nicotine: A major component of e-cigarette smoke