Identification of a Novel Delta Opioid Receptor Agonist Chemotype with Potential Negative Allosteric Modulator Capabilities

The δ-opioid receptor (δOR) holds great potential as a therapeutic target. Yet, clinical drug development, which has focused on δOR agonists that mimic the potent and selective tool compound SNC80 have largely failed. It has increasingly become apparent that the SNC80 scaffold carries with it potent and efficacious β-arrestin recruitment. Here, we screened a relatively small (5120 molecules) physical drug library to identify δOR agonists that underrecruit β-arrestin, as it has been suggested that compounds that efficaciously recruit β-arrestin are proconvulsant. The screen identified a hit compound and further characterization using cellular binding and signaling assays revealed that this molecule (R995045, compound 1) exhibited ten-fold selectivity over µ- and κ-opioid receptors. Compound 1 represents a novel chemotype at the δOR. A subsequent characterization of fourteen analogs of compound 1, however did not identify a more potent δOR agonist. Computational modeling and in vitro characterization of compound 1 in the presence of the endogenous agonist leu-enkephalin suggest compound 1 may also bind allosterically and negatively modulate the potency of Leu-enkephalin to inhibit cAMP, acting as a ‘NAM-agonist’ in this assay. The potential physiological utility of such a class of compounds will need to be assessed in future in vivo assays.     

On the approximation of singular source terms in differential equations

We study differential equations with singular source terms. For such equations classical convergence results do not apply, as these rely on the regularity of the solution and the source terms. We study some elliptic and parabolic problems numerically and theoretically, and show that, with the right approximation of the singular source terms, full convergence order can be achieved away from the singularities, whereas the convergence will be poor in a vicinity of these. © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 15: 503–520, 1999     

A stochastic Bass innovation diffusion model for studying the growth of electricity consumption in Greece

In this paper a stochastic innovation diffusion model is proposed derived by introducing stochasticity into the well-known Bass model. The stochastic model is solved analytically by using the theory of reducible stochastic differential equations and the first moment of the resulting stochastic process is presented. The parameter estimators of the model are derived by using a procedure which provides the maximum likelihood estimators (MLE) using time series data. Finally, the model is applied to the data of electricity consumption in Greece. Using a simulation technique, it is possible to predict the performance of the consumption process by defining a subdomain to which all possible trajectories of the process should belong with a predefined probability. © 1997 by John Wiley & Sons, Ltd.     

δ函数SN方法求解含各向异性散射输运方程的本征值问题

将角通量分解成一个δ函数和一个低阶函数,分别采用解析方法和求积组来计算源项.利用δ函数S_N方法,计算了平几何条件下含各向异性散射单速输运方程的临界问题.分析和数值结果表明,采用数量较少的离散方向,能够达到较高计算精度.     

Green's function formulation of multiple nonlinear Dirac δ-function potential in one dimension

In this work, we study the scattering problem of the general nonlinear finitely many Dirac delta potentials with complex coupling constants (or opacities in the context of optics) using the Green's function method and then find the bound state energies and the wave functions for the particular form of the nonlinearity in the case of positive real coupling constants.     

Plant-Derived Antiviral Compounds as Potential Entry Inhibitors against Spike Protein of SARS-CoV-2 Wild-Type and Delta Variant: An Integrative in SilicoApproach

The wild-type SARS-CoV-2 has continuously evolved into several variants with increased transmissibility and virulence. The Delta variant which was initially identified in India created a devastating impact throughout the country during the second wave. While the efficacy of the existing vaccines against the latest SARS-CoV-2 variants remains unclear, extensive research is being carried out to develop potential antiviral drugs through approaches like in silico screening and drug-repurposing. This study aimed to conduct the docking-based virtual screening of 50 potential phytochemical compounds against a Spike glycoprotein of the wild-type and the Delta SARS-CoV-2 variant. Subsequently, molecular docking was performed for the five best compounds, such as Lupeol, Betulin, Hypericin, Corilagin, and Geraniin, along with synthetic controls. From the results obtained, it was evident that Lupeol exhibited a remarkable binding affinity towards the wild-type Spike protein (−8.54 kcal/mol), while Betulin showed significant binding interactions with the mutated Spike protein (−8.83 kcal/mol), respectively. The binding energy values of the selected plant compounds were slightly higher than that of the controls. Key hydrogen bonding and hydrophobic interactions of the resulting complexes were visualized, which explained their greater binding affinity against the target proteins—the Delta S protein of SARS-CoV-2, in particular. The lower RMSD, the RMSF values of the complexes and the ligands, Rg, H-bonds, and the binding free energies of the complexes together revealed the stability of the complexes and significant binding affinities of the ligands towards the target proteins. Our study suggests that Lupeol and Betulin could be considered as potential ligands for SARS-CoV-2 spike antagonists. Further experimental validations might provide new insights for the possible antiviral therapeutic interventions of the identified lead compounds and their analogs against COVID-19 infection.     

α—混合情形非参数密度估计的重对数律

当样本X1，…，Xn,…，是α-混合时，建立了三角数组的重对数律和Rosenblatt-Parzen核估计的重对数律。     

双指数分布位置参数的经验Bayes估计问题

本文在平方损失下导出了双指数分布位置参数的Bayes估计，利用非参数方法构造了位置参数的经验Bayes(EB)估计．在适当的条件下，获得了EB估计的收敛速度．最后，给出了一个例子说明适合定理条件的先验分布是存在的．     

The Taylor series method of order p and Adams–Bashforth method on time scales

A recent study on the Taylor series method of second order and the trapezoidal rule for dynamic equations on time scales has been continued by introducing a derivation of the Taylor series method of arbitrary order $p$ on time scales. The error and convergence analysis of the method is also obtained. The 2-step Adams–Bashforth method for dynamic equations on time scales is concluded and applied to examples of initial value problems for nonlinear dynamic equations. Numerical results are presented and discussed.