Integrable Perturbations Research Articles

BAX/BAK-Induced Apoptosis Results in Caspase-8-Dependent IL-1β Maturation in Macrophages

IL-1β is a cytokine of pivotal importance to the orchestration of inflammatory responses. Synthesized as an inactive pro-cytokine, IL-1β requires proteolytic maturation to gain biological activity. Here, we identify intrinsic apoptosis as a non-canonical trigger of IL-1β maturation. Guided by the discovery of the immunomodulatory activity of vioprolides, cyclic peptides isolated from myxobacteria, we observe IL-1β maturation independent of canonical inflammasome pathways, yet dependent on intrinsic apoptosis. Mechanistically, vioprolides inhibit MCL-1 and BCL2, which in turn triggers BAX/BAK-dependent mitochondrial outer membrane permeabilization (MOMP). Induction of MOMP results in the release of pro-apoptotic factors initiating intrinsic apoptosis, as well as the depletion of IAPs (inhibitors of apoptosis proteins). IAP depletion, in turn, operates upstream of ripoptosome complex formation, subsequently resulting in caspase-8-dependent IL-1β maturation. These results establish the ripoptosome/caspase-8 complex as a pro-inflammatory checkpoint that senses the perturbation of mitochondrial integrity.

Estimates for Solutions to Fokker–Planck–Kolmogorov Equations with Integrable Drifts

The result of this paper states that every probability measure satisfying the stationary Fokker–Planck–Kolmogorov equation obtained by a -integrable perturbation of the drift term–x of the Ornstein–Uhlenbeck operator is absolutely continuous with respect to the corresponding Gaussian measure γ and $$f = \frac{{d\mu }}{{d\gamma }}$$ for the density the integral of $$f\left| {\log } \right|{\left( {f + 1} \right)^\alpha }$$ with respect to γ is estimated via $${\left\| v \right\|_{{L^1}\left( \mu \right)}}$$ for all α < $$\frac{1}{4}$$ . This shows that stationary measures of infinite-dimensional diffusions whose drifts are integrable perturbations of–are absolutely continuous with respect to Gaussian measures. A generalization is obtained for equations on Riemannian manifolds.

Integrable perturbations of saddle singularities of rank 0 of integrable Hamiltonian systems

We study the stability property of singularities of integrable Hamiltonian systems under integrable perturbations. It is known that among singularities of corank , only singularities of complexity are stable. As it turns out, in the case of two degrees of freedom, there are both stable and unstable singularities of rank and complexity . A complete list of singularities of saddle-saddle type of complexity is known and it consists of 39 pairwise non-equivalent singularities. In this paper we prove a criterion for the stability of multi-dimensional saddle singularities of rank under component-wise perturbations. Using this criterion, in the case of two degrees of freedom, for each of the 39 singularities of complexity we obtain an answer to the question of whether this singularity is component-wise stable. For a singularity of saddle-saddle type we analyse the connection between the stability property and the characteristics of its loop molecule. Bibliography: 27 titles.

Targeted Perturbation of Nuclear Envelope Integrity with Vapor Nanobubble-Mediated Photoporation.

The nuclear envelope (NE) has long been considered to dismantle only during mitosis. However, recent observations in cancer cells and laminopathy patient cells have revealed that the NE can also transiently rupture during interphase, thereby perturbing cellular homeostasis. Although NE ruptures are promoted by mechanical force and the loss of lamins, their stochastic nature and variable frequency preclude the study of their direct downstream consequences. We have developed a method based on vapor nanobubble-mediated photoporation that allows for deliberately inducing NE ruptures in a spatiotemporally controlled manner. Our method relies on wide-field laser illumination of perinuclear gold nanoparticles, resulting in the formation of short-lived vapor nanobubbles that inflict minute mechanical damage to the NE, thus creating small pores. We demonstrate that perinuclear localization of gold nanoparticles can be achieved after endocytic uptake or electroporation-facilitated delivery and that both strategies result in NE rupture upon laser irradiation. Furthermore, we prove that photoporation-induced nuclear ruptures are transient and recapitulate hallmarks of spontaneous NE ruptures that occur in A-type lamin-depleted cells. Finally, we show that the same approach can be used to promote influx of macromolecules that are too large to passively migrate through the NE. Thus, by providing unprecedented control over nuclear compartmentalization, nuclear photoporation offers a powerful tool for both fundamental cell biology research and drug delivery applications.

On the local Birkhoff conjecture for convex billiards

The classical Birkhoff conjecture claims that the boundary of a strictly convex integrable billiard table is necessarily an ellipse (or a circle as a special case). In this article we prove a complete local version of this conjecture: a small integrable perturbation of an ellipse must be an ellipse. This extends and completes the result in Avila-De Simoi-Kaloshin, where nearly circular domains were considered. One of the crucial ideas in the proof is to extend action-angle coordinates for elliptic billiards into complex domains (with respect to the angle), and to thoroughly analyze the nature of their complex singularities. As an application, we are able to prove some spectral rigidity results for elliptic domains.

Regularization of the Abel Integral Equation with Perturbation

For some modification of the classical Abel equation—the Abel equation with integral perturbation—the form of the inverse operator is found and a regularization method in the problem of finding uniform approximations of the exact solution of the equation with an approximately specified right-hand side is developed.

Analytical integrability problem for perturbations of cubic Kolmogorov systems

We solve, by using normal forms, the analytical integrability problem for differential systems in the plane whose first homogeneous component is a cubic Kolmogorov system whose origin is an isolated singularity. As an application, we give the analytically integrable systems of a class of systems x˙=x(P2+P3),y˙=y(Q2+Q3), with Pi, Qi homogeneous polynomials of degree i. We also prove that for any n ≥ 3, there are analytically integrable perturbations of x˙=xPn,y˙=yQn which are not orbital equivalent to its first homogeneous component.

Asymptotic Integration of Certain Volterra Integro-Differential Equations with Oscillatory Decreasing Kernels

We construct the asymptotics for solutions of two second-order integro-differential equations of Volterra type as independent variable tends to infinity. These equations are considered as integral perturbations of the harmonic oscillator. The specific feature of the considered integral perturbations is an oscillatory decreasing character of their kernels. To obtain the asymptotic formulas we use the special method proposed for the asymptotic integration of the linear dynamical systems with oscillatory decreasing coefficients. The method uses the ideas of the averaging theory and some known asymptotic theorems.

Generation of bright-dark soliton trains with a central wide dip in optical fibers

The nonlinear propagation dynamics of the dark soliton pulse with hyperbolic tangent profile in the anomalous dispersion regime of an optical fiber is investigated numerically. The corresponding temporal evolutions are provided for different integral or non-integral soliton order and loss perturbations. The results show that, irrespective of the integral or non-integral soliton order, with increase of distance, the width of the dark soliton broadens and more and more bright and dark pulses appear symmetrically on the two sides of the central black soliton. Correspondingly, bright-dark soliton trains with a central wide black soliton can gradually form. The higher the soliton order, the more the bright-dark pulses at the same distance. With increase of distance, the peak values of the bright pulses exhibit oscillation behavior. The loss perturbation only influences the evolutions slightly, which means that the generated soliton trains can resist loss perturbations to some extent. Moreover, this work provides us an alternative approach to generate bright-dark soliton trains by using the dark soliton pulse propagating in the anomalous dispersion regime of the passive optical fiber besides directly using the fiber laser.

Asymptotics for Solutions of Harmonic Oscillator with Integral Perturbation

We construct the asymptotics for solutions of a harmonic oscillator with integral perturbation when the independent variable tends to infinity. The distinctive feature of the considered integral perturbation is the oscillatory decreasing character of its kernel. We assume that the integral kernel is degenerate. This makes it possible to reduce the initial integro-differential equation to an ordinary differential system. To get the asymptotic formulas for the fundamental solutions of the obtained ordinary differential system, we use a special method proposed for the asymptotic integration of linear dynamical systems with oscillatory decreasing coefficients. By the use of special transformations, we reduce the ordinary differential system to the so-called L-diagonal form. We then apply the classical Levinson’s theorem to construct the asymptotics for the fundamental matrix of the L-diagonal system. The obtained asymptotic formulas allow us to reveal the resonant frequencies, i.e., the frequencies of the oscillatory component of the kernel that give rise to unbounded oscillations in the initial integro-differential equation. It appears that these frequencies differ slightly from the resonant frequencies that occur in the adiabatic oscillator with the sinusoidal component of the time-decreasing perturbation.

An efficient method for computing excess free energy of liquid

We present a new theoretical method for efficient calculation of free energy of liquid. This interaction entropy method allows one to compute entropy and free energy of liquid from standard single step MD (molecular dynamics) simulation directly in liquid state without the need to perform MD simulations at many intermediate states as required in thermodynamic integration or free energy perturbation methods. In this new approach, one only needs to evaluate the interaction energy of a single (fixed) liquid molecule with the rest of liquid molecules as a function of time from a standard MD simulation of liquid and the fluctuation of distribution of this interaction energy is then used to calculate the interaction entropy of the liquid. Explicit theoretical derivation of this interaction entropy approach is provided and numerical calculations for the benchmark liquid water system were carried out using three different water models. Numerical analysis of the result was performed and comparison of the computational result with experimental data and other theoretical results were provided. Excellent agreement of calculated free energies with the experimental data using TIP4P model is obtained for liquid water.

Disruption of adherens junction and alterations in YAP-related proliferation behavior as part of the underlying cell transformation process of alcohol-induced oral carcinogenesis

Accumulating evidences indicate that alcohol might play a causative in oral cancer. Unfortunately, in vitro cell systems, uncovering the molecular background of the underlying cell transformation process, are rare. Therefore, this study was conducted, to identify molecular changes and characterize their putative cell behavioral consequences in epitheloid (EPI) and fibroblastoid (FIB) oral keratinocyte phenotypes, arising from chronical alcohol treatment. Concerning adherens junctions (AJs), both EPI and FIB showed membrane-bound β-catenin, but exhibited differences for E-cadherin and zyxin. While EPI revealed E-cadherin/β-catenin membrane co-localization, which in parts also applied for zyxin, FIB membranes were devoid of E-cadherin and exhibited marginal zyxin expression. Fetal calf serum (FCS) administration in starved cells promoted proliferation in both keratinocyte phenotypes, whereat EPI and FIB yielded a strikingly modified FCS sensitivity on the temporal scale. Impedance measurement-based cell index detection yielded proliferation stimulation occurring much earlier in FIB (<20h) compared to EPI (>45h). Nuclear preference of the proliferation-associated YAP co-transcription factor in FIB was FCS independent, while it required FCS in EPI. Taken together, the lack of membrane-inherent E-cadherin/β-catenin co-localization together with low zyxin - reveals perturbation of AJ integrity in FIB. Regarding cell behavior, perturbed AJs in FIB correlate with temporal proliferation sensitivity towards FCS. CYF of 5.6 strongly suggests involvement of chromatin-bound YAP in FIB's proliferation temperosensitivity. These molecular differences detected for EPI and FIB are part of the underlying cell transformation process of alcohol-induced oral carcinogenesis, and indicate FIB being in a more advanced transformation stage.

Integrable Deformations of Sine-Liouville Conformal Field Theory and Duality

We study integrable deformations of sine-Liouville conformal field theory. Every integrable perturbation of this model is related to the series of quantum integrals of motion (hierarchy). We construct the factorized scattering matrices for different integrable perturbed conformal field theories. The perturbation theory, Bethe ansatz technique, renormalization group and methods of perturbed conformal field theory are applied to show that all integrable deformations of sine-Liouville model possess non-trivial duality properties.

DLR transonic inverse design code, extensions and modifications to increase versatility and robustness

ABSTRACTThe DLR inverse design code computes the wing geometry for a prescribed target pressure distribution. It is based on the numerical solution of the integral inverse transonic small perturbation (TSP) equations. In this work, several extensions and modifications of the inverse design code are described. Results are validated with corresponding redesign test cases. The first modification concerns applications for high transonic Mach numbers or cases with strong shocks. The introduced modifications enable converged design solutions for cases where the original method failed. The second modification is the extension of the code to general non-planar wings. Previously, the design code was restricted to non-planar wing designs with small dihedral or to nacelle design. A third modification concerns aerofoil/wings designed for wind-tunnel design. In order to design a swept wing between two wind-tunnel walls, the solution method was extended to two symmetry planes. The introduced extensions and modifications have increased the robustness and range of applicability of the inverse design code.

A quartet of fermionic expressions for M(k,2k ± 1) Virasoro characters via half-lattice paths

We derive new fermionic expressions for the characters of the Virasoro minimal models M(k,2k±1) by analysing the recently introduced half-lattice paths. These fermionic expressions display a quasiparticle formulation characteristic of the ϕ2,1 and ϕ1,5 integrable perturbations. We find that they arise by imposing a simple restriction on the RSOS quasiparticle states of the unitary models M(p,p+1). In fact, four fermionic expressions are obtained for each generating function of half-lattice paths of finite length L, and these lead to four distinct expressions for most characters χr,sk,2k±1. These are direct analogues of Melzer's expressions for M(p,p+1), and their proof entails revisiting, reworking and refining a proof of Melzer's identities which used combinatorial transforms on lattice paths.We also derive a bosonic version of the generating functions of length L half-lattice paths, this expression being notable in that it involves q-trinomial coefficients. Taking the L→∞ limit shows that the generating functions for infinite length half-lattice paths are indeed the Virasoro characters χr,sk,2k±1.

Computational methodology for solubility prediction: Application to the sparingly soluble solutes.

The solubility of a crystalline substance in the solution can be estimated from its absolute solid free energy and excess solvation free energy. Here, we present a numerical method, which enables convenient solubility estimation of general molecular crystals at arbitrary thermodynamic conditions where solid and solution can coexist. The methodology is based on standard alchemical free energy methods, such as thermodynamic integration and free energy perturbation, and consists of two parts: (1) systematic extension of the Einstein crystal method to calculate the absolute solid free energies of molecular crystals at arbitrary temperatures and pressures and (2) a flexible cavity method that can yield accurate estimates of the excess solvation free energies. As an illustration, via classical Molecular Dynamic simulations, we show that our approach can predict the solubility of OPLS-AA-based (Optimized Potentials for Liquid Simulations All Atomic) naphthalene in SPC (Simple Point Charge) water in good agreement with experimental data at various temperatures and pressures. Because the procedure is simple and general and only makes use of readily available open-source software, the methodology should provide a powerful tool for universal solubility prediction.

Primary human polarized small intestinal epithelial barriers respond differently to a hazardous and an innocuous protein

An experimental platform employing human derived intestinal epithelial cell (IEC) line monolayers grown on permeable Transwell® filters was previously investigated to differentiate between hazardous and innocuous proteins. This approach was effective at distinguishing these types of proteins and perturbation of monolayer integrity, particularly transepithelial electrical resistance (TEER), was the most sensitive indicator. In the current report, in vitro indicators of monolayer integrity, cytotoxicity, and inflammation were evaluated using primary (non-transformed) human polarized small intestinal epithelial barriers cultured on Transwell® filters to compare effects of a hazardous protein (Clostridium difficile Toxin A [ToxA]) and an innocuous protein (bovine serum albumin [BSA]). ToxA exerted a reproducible decrease on barrier integrity at doses comparable to those producing effects observed from cell line-derived IEC monolayers, with TEER being the most sensitive indicator. In contrast, BSA, tested at concentrations substantially higher than ToxA, did not cause changes in any of the tested variables. These results demonstrate a similarity in response to certain proteins between cell line-derived polarized IEC models and a primary human polarized small intestinal epithelial barrier model, thereby reinforcing the potential usefulness of cell line-derived polarized IECs as a valid experimental platform to differentiate between hazardous and non-hazardous proteins.

Elaboration of antibacterial plastic surfaces by a combination of antiadhesive and biocidal coatings of natural products

Antibacterial polyolefins surfaces, combining biocidal and antiadhesive properties, were elaborated by a covalent grafting of antimicrobial peptides (AMPs), able to kill adherent bacteria, on a pre-immobilized hyaluronic acid (HA) layer, able to repel the micro-organisms. Different HA activation rate for its immobilization, were used to change HA layer morphology and number of residual free carboxylic acid functions for AMPs grafting. Based on adhesion tests on Staphylococcus epidermidis and microscopy fluorescent observations, the presence of the two combined properties was shown to be depended on the HA activation rate. Thus, the best addition effect was observed for an AMP grafting on a surface based on a high HA activation, data pointing out a decrease of the bacterial adhesion up to 99.8% and a perturbation of the bacterial membrane integrity of adhered bacteria. On the contrary, a decrease of the antibacterial activity was observed for an AMP grafting on a surface based on a low HA activation.

A regular differential operator with perturbed boundary condition

The operator ℒ0 generated by a linear ordinary differential expression of nth order and regular boundary conditions of general form is considered on a closed interval. The characteristic determinant of the spectral problem for the operator ℒ1, where ℒ1 is an operator with the integral perturbation of one of its boundary conditions, is constructed, assuming that the unperturbed operator ℒ0 possesses a system of eigenfunctions and associated functions generating an unconditional basis in L 2(0, 1). Using the obtained formula, we derive conclusions about the stability or instability of the unconditional basis properties of the system of eigenfunctions and associated functions of the problem under an integral perturbation of the boundary condition. The Samarskii–Ionkin problem with integral perturbation of its boundary condition is used as an example of the application of the formula.

Efficient solvation free energy simulations: impact of soft-core potential and a new adaptive λ-spacing method

ABSTRACTThe calculation of Gibbs free energy of solvation ΔG is commonly applied to predict the solubility of solutes in different solvents. The transition path between the thermodynamic end states of full and non-existent solute–solvent interactions is described by the spacing of intermediate states and the soft-core potential employed to scale the interactions. The choice of both, the soft-core potential and the distribution of intermediate states, has a large impact on the simulated ΔG. In this work, we determine the free energy of hydration for 10 neutral amino acid side chain analogues to analyse the impact of different soft-core potentials on the consistency of results from two different free energy methods, i.e. thermodynamic integration and free energy perturbation. Additionally, we propose a new method to improve the alchemical pathway by adaptive spacing of intermediate states. Our technique is easy to implement and not limited to any simulation package or free energy technique in particular, making it easily adaptable to a variety of workflows. Exploiting the ability to systematically optimise alchemical pathways, we introduce a scheme to define a suitable number of windows based on prescribed configurational space overlap. With this, excessive sampling is avoided and computational costs can be reduced.