Affinity Of Analogues Research Articles

Weight-Finite Modules Over the Quantum Affine and Double Quantum Affine Algebras of Type $\mathfrak a_{1}$

We define the categories of weight-finite modules over the type \(\mathfrak a_{1}\) quantum affine algebra \(\dot {\mathrm {U}}_{q}(\mathfrak a_{1})\) and over the type \(\mathfrak a_{1}\) double quantum affine algebra \(\ddot {\mathrm {U}}_{q}(\mathfrak a_{1})\) that we introduced in Mounzer and Zegers (2019). In both cases, we classify the simple objects in those categories. In the quantum affine case, we prove that they coincide with the simple finite-dimensional \(\dot {\mathrm {U}}_{q}(\mathfrak a_{1})\)-modules which were classified by Chari and Pressley in terms of their highest (rational and ℓ-dominant) ℓ-weights or, equivalently, by their Drinfel’d polynomials. In the double quantum affine case, we show that simple weight-finite modules are classified by their (t-dominant) highest t-weight spaces, a family of simple modules over the subalgebra \(\ddot {\mathrm {U}}_{q}^{0}(\mathfrak a_{1})\) of \(\ddot {\mathrm {U}}_{q}(\mathfrak a_{1})\) which is conjecturally isomorphic to a split extension of the elliptic Hall algebra \(\mathcal E_{q^{-4}}{q^{2}},{q^{2}}\). The proof of the classification, in the double quantum affine case, relies on the construction of a double quantum affine analogue of the evaluation modules that appear in the quantum affine setting.

Balanced QSAR and Molecular Modeling to Identify Structural Requirements of Imidazopyridine Analogues as Anti-infective Agents Against Trypanosomiases

Human African trypanosomiasis (HAT), a fatal infection caused by Trypanosoma brucei (T. brucei) is considered as a neglected disease in the tropical areas, and newer agents with unique mechanism of action are urgently needed. In this work, 65 Imidazopyridine analogues from known literature were selected for building statistically robust genetic algorithm (GA) based QSAR models. Furthermore, values for the various cross-validation properties supported its statistical robustness (model 1, [Formula: see text], RMSE[Formula: see text], MAE[Formula: see text], CCC[Formula: see text], and [Formula: see text]). Our in silico ADMET analysis revealed that a designed molecule, S10 may act as potent lead (T. brucei, pEC[Formula: see text] ([Formula: see text]M), [Formula: see text]) with better pharmacokinetics, no carcinogenicity, class III acute oral toxicity, minimal OCT1 and OCT2 inhibitions and no eye corrosion profiles. Our molecular docking analysis (on 42 drug targets) for a dataset and designed molecules demonstrated higher binding affinity of Imidazopyridine analogues with T. brucei farnesyl diphosphate synthase (TbFPPS) (PDB id: 2I19). This observation was further supported by 100[Formula: see text]ns molecular dynamics analysis retaining better stability of complex. Thus, imidazopyridine analogues would provide a promising scaffold for the development of anti-HAT agents.

The arc-topology

We study a Grothendieck topology on schemes which we call the arc-topology. This topology is a refinement of the v-topology (the pro-version of Voevodsky’s h-topology), where covers are tested via rank ≤1 valuation rings. Functors which are arc-sheaves are forced to satisfy a variety of gluing conditions such as excision in the sense of algebraic K-theory. We show that etale cohomology is an arc-sheaf, and we deduce various pullback squares in etale cohomology. Using arc-descent, we re-prove the Gabber–Huber affine analogue of proper base change (in a large class of examples), as well as the Fujiwara–Gabber base change theorem on the etale cohomology of the complement of a Henselian pair. As a final application, we prove a rigid analytic version of the Artin–Grothendieck vanishing theorem, extending results of Hansen.

Affinity Enhancers for Peptide Ligand Binding to the Extracellular Domain of the Amylin Receptor 2

Amylin is a peptide hormone and its activation of amylin receptors controls blood glucose and food intake. Amylin receptor activation is a known drug target for diabetes and has potential for obesity treatment. The amylin receptor consists of the calcitonin receptor (CTR) and the accessary protein called receptor activity-modifying protein (RAMP). CTR is the receptor for peptide hormone calcitonin, whereas the heterodimer of CTR and RAMP gains affinity for peptide hormone amylin. Each of the CTR and RAMP has an extracellular domain (ECD), and CTR ECD is a known binding site for peptide hormones. However, whether RAMP ECD provides a binding site for peptide ligands remains elusive. RAMP has three types in humans and our structural model of the amylin receptor 2 ECD (RAMP2 ECD:CTR ECD complex) suggested the molecular interaction between RAMP2 ECD Glu101 and the C-terminal Tyr residue of an amylin analog AC413. We examined whether this molecular interaction contributes to AC413 binding for amylin receptor 2 ECD and enhances AC413 affinity. In addition, N-glycosylation of the amylin receptor ECD is known to increase the peptide ligand affinity. Despite, which N-glycosite is the most responsible for this effect and the role of the Asn-linked N-acetylglucosamine (GlcNAc) have been unexplored for amylin receptor 2 ECD. Based on our previous reports, we hypothesized that Asn-linked GlcNAc of CTR ECD Asn130 will enhance the peptide ligand affinity for amylin receptor 2 ECD. Here, we established the functional amylin receptor 2 ECD and applied mutagenesis and enzymatic deglycosylation to address the affinity enhancers. We used fluorescence polarization/anisotropy peptide binding assay to measure peptide ligand affinity for purified amylin receptor 2 ECD. Our results showed that the RAMP2 ECD Glu101 to alanine mutation significantly decreased the amylin analog affinity suggesting its potential interaction with the C-terminal Tyr residue of the amylin analog. Using glycan-trimmed CTR ECD, we showed that the Asn-linked GlcNAc residue of CTR ECD Asn130 is the most responsible among N-glycans for enhancing affinity for the amylin receptor 2 ECD. This study provides evidence that both RAMP2 ECD Glu101 and Asn-linked GlcNAc of CTR ECD Asn130 contribute to amylin analog binding as affinity enhancers.

Periodicity and integrability for the cube recurrence

Zamolodchikov periodicity is a property of T- and Y-systems, arising in the thermodynamic Bethe ansatz. Zamolodchikov integrability was recently considered as its affine analog in our joint work with P. Pylyavskyy. Here we prove periodicity and integrability for similar discrete dynamical systems based on the cube recurrence, also known as the discrete BKP equation. The periodicity part was conjectured by Henriques in 2007.

Ligand Strain and Its Conformational Complexity Is a Major Factor in the Binding of Cyclic Dinucleotides to STING Protein.

STING (stimulator of interferon genes) is a key regulator of innate immunity that has recently been recognized as a promising drug target. STING is activated by cyclic dinucleotides (CDNs) which eventually leads to expression of type I interferons and other cytokines. Factors underlying the affinity of various CDN analogues are poorly understood. Herein, we correlate structural biology, isothermal calorimetry (ITC) and computational modeling to elucidate factors contributing to binding of six CDNs—three pairs of natural (ribo) and fluorinated (2′‐fluororibo) 3′,3′‐CDNs. X‐ray structural analyses of six {STING:CDN} complexes did not offer any explanation for the different affinities of the studied ligands. ITC showed entropy/enthalpy compensation up to 25 kcal mol−1 for this set of similar ligands. The higher affinities of fluorinated analogues are explained with help of computational methods by smaller loss of entropy upon binding and by smaller strain (free) energy.

Ligand Strain and Its Conformational Complexity Is a Major Factor in the Binding of Cyclic Dinucleotides to STING Protein

AbstractSTING (stimulator of interferon genes) is a key regulator of innate immunity that has recently been recognized as a promising drug target. STING is activated by cyclic dinucleotides (CDNs) which eventually leads to expression of type I interferons and other cytokines. Factors underlying the affinity of various CDN analogues are poorly understood. Herein, we correlate structural biology, isothermal calorimetry (ITC) and computational modeling to elucidate factors contributing to binding of six CDNs—three pairs of natural (ribo) and fluorinated (2′‐fluororibo) 3′,3′‐CDNs. X‐ray structural analyses of six {STING:CDN} complexes did not offer any explanation for the different affinities of the studied ligands. ITC showed entropy/enthalpy compensation up to 25 kcal mol−1 for this set of similar ligands. The higher affinities of fluorinated analogues are explained with help of computational methods by smaller loss of entropy upon binding and by smaller strain (free) energy.

Non-Stationary Ruijsenaars Functions for κ=t−1/N and Intertwining Operators of Ding-Iohara-Miki Algebra

We construct the non-stationary Ruijsenaars functions (affine analogue of the Macdonald functions) in the special case $\kappa=t^{-1/N}$, using the intertwining operators of the Ding-Iohara-Miki algebra (DIM algebra) associated with $N$-fold Fock tensor spaces. By the $S$-duality of the intertwiners, another expression is obtained for the non-stationary Ruijsenaars functions with $\kappa=t^{-1/N}$, which can be regarded as a natural elliptic lift of the asymptotic Macdonald functions to the multivariate elliptic hypergeometric series. We also investigate some properties of the vertex operator of the DIM algebra appearing in the present algebraic framework; an integral operator which commutes with the elliptic Ruijsenaars operator, and the degeneration of the vertex operators to the Virasoro primary fields in the conformal limit $q \rightarrow 1$.

R matrix for generalized quantum group of type A

The generalized quantum group U(ϵ) of type A is an affine analogue of quantum group associated to a general linear Lie superalgebra glM|N. We prove that there exists a unique R matrix on the tensor product of fundamental type representations of U(ϵ) for arbitrary parameter sequence ϵ corresponding to a non-conjugate Borel subalgebra of glM|N. We give an explicit description of its spectral decomposition, and then as an application, construct a family of finite-dimensional irreducible U(ϵ)-modules which have subspaces isomorphic to the Kirillov-Reshetikhin modules of usual affine type AM−1(1) or AN−1(1).

Abstract 3448: A highly specific 18F-labelled peptide for non-invasive quantification of PD-L1 levels in tumors

Abstract Introduction. Blockade of programmed death ligand-1 (PD-L1) and its receptor (PD-1) has emerged as a foundational treatment strategy for cancer. Immunohistochemical analysis (IHC) of PD-L1 expression is one of the biomarkers used to guide those treatments. However, total PD-L1 levels, dynamics and their relevance to treatment response are poorly understood. To facilitate non-invasive quantification of total PD-L1 levels and dynamics, here we report the synthesis of a highly specific PD-L1 binding radiolabeled peptide, [18F]DK222, and demonstrate its specificity for PD-L1 quantification in vivo in xenograft models of multiple cancer types. Experimental procedures. A 14 amino acid macrocyclic peptide (DK222) was conjugated with a bifunctional chelator (NCS-MP-NODA, Chematech) and the corresponding fluorinated radioactive and non-radioactive analogs, [18/19F]DK222, were synthesized by aluminum fluoride method. In vitro competitive inhibition assays were used to establish peptide analog affinity for PD-L1. We then tested in vitro and in vivo specificity of [18F]DK222 for PD-L1 in cell binding, positron emission (PET) imaging and ex vivo biodistribution studies. Those studies were performed in xenograft models having varying levels of PD-L1 expression and derived from breast, bladder, lung and skin cancers. In vivo PD-L1 specificity was confirmed by co-injecting a blocking dose of 50 mg/kg of parent peptide. PD-L1 expression in cell lines and tumors was validated by flow cytometry and IHC, respectively. Results. We observed half-maximal inhibitory concentrations of < 25 nM for DK222 and its analogs to inhibit PD-L1 interaction with its receptor. We generated [18F]DK222 in 25% radiochemical yield (non-decay corrected) with high purity (>95%) and with a specific activity of 256±18 mCi/micromole. In vitro studies showed that cell uptake of [18F]DK222 is reflective of PD-L1 expression detected by flow cytometry in the PD-L1high (MDAMB231, LOXIMVI, BFTC909) and PD-L1low (SUM149, MeWo, and T24) cells. PET imaging and biodistribution studies showed robust tracer uptake in PD-L1 high but not in PD-L1 low tumors. Blocking studies showed >80% reduction in the uptake of [18F]DK222 in PD-L1high tumors (P<0.0001). Imaging and biodistribution studies collectively demonstrated that [18F]DK222 binds rapidly and specifically to human PD-L1. PET imaging observations were consistent with high immunoreactivity observed in PD-L1 high tumors compared with PD-L1 low tumors. Conclusions. The pharmacokinetics of [18F]DK222 indicate that quantification of PD-L1 levels is feasible within 60 min of radiotracer administration. The developed radiotracer [18F]DK222 could potentially enable non-invasive quantification of PD-L1 levels in vivo by PET imaging. Citation Format: Dhiraj Kumar, Akhilesh Mishra, Ala Lisok, Sagar Shelake, Bryan Wharram, Ravindra Desilva, Ronnie Mease, Sridhar Nimmagadda. A highly specific 18F-labelled peptide for non-invasive quantification of PD-L1 levels in tumors [abstract]. In: Proceedings of the Annual Meeting of the American Association for Cancer Research 2020; 2020 Apr 27-28 and Jun 22-24. Philadelphia (PA): AACR; Cancer Res 2020;80(16 Suppl):Abstract nr 3448.

Level one Weyl modules for toroidal Lie algebras

We identify level one global Weyl modules for toroidal Lie algebras with certain twists of modules constructed by Moody–Eswara Rao–Yokonuma via vertex operators for type ADE and by Iohara–Saito–Wakimoto and Eswara Rao for general type. The twist is given by an action of \(\mathrm {SL}_{2}(\mathbb {Z})\) on the toroidal Lie algebra. As a by-product, we obtain a formula for the character of the level one local Weyl module over the toroidal Lie algebra and that for the graded character of the level one graded local Weyl module over an affine analog of the current Lie algebra.

Brownian motion in trapping enclosures: steep potential wells, bistable wells and false bistability of induced Feynman–Kac (well) potentials

We investigate signatures of convergence for a sequence of diffusion processes on a line, in conservative force fields stemming from superharmonic potentials U(x) ∼ x m , m = 2n ⩾ 2. This is paralleled by a transformation of each mth diffusion generator L = DΔ + b(x)∇, and likewise the related Fokker–Planck operator L* = DΔ − ∇[b(x) ⋅], into the affiliated Schrödinger one . Upon a proper adjustment of operator domains, the dynamics is set by semigroups exp(tL), exp(tL*) and exp(−tĤ), with t ⩾ 0. The Feynman–Kac integral kernel of exp(−tĤ) is the major building block of the relaxation process transition probability density, from which L and L* actually follow. The spectral ‘closeness’ of the pertinent Ĥ and the Neumann Laplacian in the interval is analyzed for m even and large. As a byproduct of the discussion, we give a detailed description of an analogous affinity, in terms of the m-family of operators Ĥ with a priori chosen , when Ĥ becomes spectrally ‘close’ to the Dirichlet Laplacian for large m. For completness, a somewhat puzzling issue of the absence of negative eigenvalues for Ĥ with a bistable-looking potential has been addressed.

Design, Synthesis, Antitumor Activity and Molecular Docking Study of Novel 5-Deazaalloxazine Analogs.

Protein tyrosine kinases (PTKs) are the most potential therapeutic targets for cancer. Herein, we present a sound rationale for synthesis of a series of novel 2-(methylthio), 2-(substituted alkylamino), 2-(heterocyclic substituted), 2-amino, 2,4-dioxo and 2-deoxo-5-deazaalloxazine derivatives by applying structure-based drug design (SBDD) using AutoDock 4.2. Their antitumor activities against human CCRF-HSB-2, KB, MCF-7 and HeLa have been investigated in vitro. Many 5-deazaalloxazine analogs revealed high selective activities against MCF-7 tumor cell lines (IC50: 0.17–2.17 µM) over HeLa tumor cell lines (IC50 > 100 µM). Protein kinase profiling revealed that compound 3h induced multi- targets kinase inhibition including −43% against (FAK), −40% against (CDKI) and −36% against (SCR). Moreover, the Annexin-V/PI apoptotic assay elucidate that compound 3h showed 33% and potentially 140% increase in early and late apoptosis to MCF-7 cells respectively, compared to the control. The structure-activity relationship (SAR) and molecular docking study using PTK as a target enzyme for the synthesized 7-deazaalloaxazine derivatives were investigated as potential antitumor agents. The AutoDock binding affinities of the 5-deazaalloxazine analogs into c-kit PTK (PDB code: 1t46) revealed reasonable correlations between their AutoDock binding free energy and IC50.

Matrix-Ball Construction of affine Robinson-Schensted correspondence

In his study of Kazhdan-Lusztig cells in affine type A, Shi has introduced an affine analog of Robinson- Schensted correspondence. We generalize the Matrix-Ball Construction of Viennot and Fulton to give a more combi- natorial realization of Shi's algorithm. As a biproduct, we also give a way to realize the affine correspondence via the usual Robinson-Schensted bumping algorithm. Next, inspired by Honeywill, we extend the algorithm to a bijection between extended affine symmetric group and triples (P, Q, ρ) where P and Q are tabloids and ρ is a dominant weight. The weights ρ get a natural interpretation in terms of the Affine Matrix-Ball Construction. Finally, we prove that fibers of the inverse map possess a Weyl group symmetry, explaining the dominance condition on weights.

Structure-thermodynamics-relationships of hepatitis C viral NS3 protease inhibitors

Thermodynamic parameters were determined for structurally-related inhibitors of HCV NS3 protease to assess how binding entropies and enthalpies vary with incremental changes at the P2 and P3 inhibitor subsites. Changing the heterocyclic substituent at P2 from a pyridyl to a 7-methoxy-2-phenyl-4-quinolyl group leads to a 710-fold increase in affinity. Annelating a benzene ring onto a pyridine ring leads to quinoline-derived inhibitors having higher affinities, but the individual enthalpy and entropy contributions are markedly different for each ligand pair. Introducing a phenyl group at C2 of the heterocyclic ring at P2 uniformly leads to higher affinity analogs with more favorable binding entropies, while adding a methoxy group at C7 of the quinoline ring at P2 provides derivatives with more favorable binding enthalpies. Significant enthalpy/entropy compensation is observed for structural changes made to inhibitors lacking a 2-phenyl substituent, whereas favorable changes in both binding enthalpies and entropies accompany structural modifications when a 2-phenyl group is present. Overall, binding energetics of inhibitors having a 2-phenyl-4-quinolyl group at P2 are dominated by entropic effects, whereas binding of the corresponding norphenyl analogs are primarily enthalpy driven. Notably, the reversal from an entropy driven association to an enthalpy driven one for this set of inhibitors also correlates with alternate binding modes. When the steric bulk of the side chain at P3 is increased from a hydrogen atom to a tert-butyl group, there is a 770-fold improvement in affinity. The 30-fold increase resulting from the first methyl group is solely the consequence of a more favorable change in entropy, whereas subsequent additions of methyl groups leads to modest increases in affinity that arise primarily from incremental improvements in binding enthalpies accompanied with smaller favorable entropic contributions.

Evaluation of the Influence of Halogenation on the Binding of Bisphenol A to the Estrogen-Related Receptor γ.

Halogenation of organic compounds is one the most important transformations in chemical synthesis and is used for the production of various industrial products. A variety of halogenated bisphenol analogs have recently been developed and are used as alternatives to bisphenol A (BPA), which is a raw material of polycarbonate that has adverse effects in animals. However, limited information is available on the potential toxicity of the halogenated BPA analogs. In the present study, to assess the latent toxicity of halogenated BPA analogs, we evaluated the binding and transcriptional activities of halogenated BPA analogs to the estrogen-related receptor γ (ERRγ), a nuclear receptor that contributes to the growth of nerves and sexual glands. Fluorinated BPA analogs demonstrated strong ERRγ binding potency, and inverse antagonistic activity, similar to BPA. X-ray crystallography and fragment molecular orbital (FMO) calculation revealed that a fluorine-substituted BPA analog could interact with several amino acid residues of ERRγ-LBD, strengthening the binding affinity of the analogs. The ERRγ binding affinity and transcriptional activity of the halogenated BPAs decreased with the increase in the size and number of halogen atom(s). The IC50 values, determined by the competitive binding assay, correlated well with the binding energy obtained from the docking calculation, suggesting that the docking calculation could correctly estimate the ERRγ binding potency of the BPA analogs. These results confirmed that ERRγ has a ligand binding pocket that fits very well to BPA. Furthermore, this study showed that the binding affinity of the BPA analogs can be predicted by the docking calculation, indicating the importance of the calculation method in the risk assessment of halogenated compounds.

Approximation of restrictions of $q$-valued logic functions to linear manifolds by affine analogues

Для конечного поля $\mathbf{F}_q$ из $q$ элементов установлена связь между параметрами, задающими меру приближения функции $q$-значной логики аффинными отображениями, и аналогичными параметрами для ее ограничений на линейные многообразия. При $q>2$ доказан аналог равенства Парсеваля относительно данных параметров, из которого следуют содержательные верхние оценки нелинейности функции $q$-значной логики от $n$ переменных и ее ограничений на многообразия размерности $r$, равные $q^{n-1}(q - 1) - q^{n/2-1}$ и $q^{r-1}(q - 1) - q^{r/2-1}$ соответственно. Получены оценки, характеризующие распределение нелинейности на многообразиях фиксированной размерности.

Affinity, binding kinetics and functional characterization of draflazine analogues for human equilibrative nucleoside transporter 1 (SLC29A1)

In the last decade it has been recapitulated that receptor-ligand binding kinetics is a relevant additional parameter in drug discovery to improve in vivo drug efficacy and safety. The equilibrative nucleoside transporter-1 (ENT1, SLC29A1) is an important drug target, as transporter inhibition is a potential treatment of ischemic heart disease, stroke, and cancer. Currently, two non-selective ENT1 inhibitors (dilazep and dipyridamole) are on the market as vasodilators. However, their binding kinetics are unknown; moreover, novel, more effective and selective inhibitors are still needed. Hence, this study focused on the incorporation of binding kinetics for finding new and improved ENT1 inhibitors.We developed a radioligand competition association assay to determine the binding kinetics of ENT1 inhibitors with four chemical scaffolds (including dilazep and dipyridamole). The kinetic parameters were compared to the affinities obtained from a radioligand displacement assay. Three of the scaffolds presented high affinities with relatively fast dissociation kinetics, yielding short to moderate residence times (RTs) at the protein (1–44 min). While compounds from the fourth scaffold, i.e. draflazine analogues, also had high affinity, they displayed significantly longer RTs, with one analogue (4) having a RT of over 10 h. Finally, a label-free assay was used to evaluate the impact of divergent ENT1 inhibitor binding kinetics in a functional assay. It was shown that the potency of compound 4 increased with longer incubation times, which was not observed for draflazine, supporting the importance of long RT for increased target-occupancy and effect.In conclusion, our research shows that high affinity ENT1 inhibitors show a large variation in residence times at this transport protein. As a consequence, incorporation of binding kinetic parameters adds to the design criteria and may thus result in a different lead compound selection. Taken together, this kinetic approach could inspire future drug discovery in the field of ENT1 and membrane transport proteins in general.

Moving Frames and Differential Invariants on Fully Affine Planar Curves

In this paper, by the affine analogue of the fundamental theorem for Euclidean planar curves, we classify the affine curves with constant affine curvatures. Note that we use the fully affine group and not the equi-affine subgroup consisting of area-preserving affine transformations. (Caution: much of the literature omits the “equi-” in their treatment.) According to the equivariant method of moving frames, explicit formulas for the generating affine differential invariants and invariant differential operators are constructed. At the same time, by using the fact that the affine transformation group GA$$(2,\mathbb {R})$$ can factor as a product of two subgroup $$B\cdot \mathrm{SE}(2,\mathbb {R})$$ and the moving frame of the subgroup SE$$(2,\mathbb {R})$$, we build the moving frame of GA$$(2,\mathbb {R})$$ and obtain the relations among invariants of group GA$$(2,\mathbb {R})$$ and its subgroup SE$$(2,\mathbb {R})$$. Applying the affine curvature to recognize affine equivalent objects is considered in the last part of this paper.

Conformational Stability Effect of Polymeric Iron Chelators.

SummaryThe design and synthesis of metal chelators with extraordinary metal affinities is a basic and challenging scientific problem of both fundamental and practical importance. Here, we demonstrate a “conformational stability effect” that can significantly enhance the metal affinity of ligands after conjugation to polymer chains with the ability to spontaneously adopt a specific conformation as an optimal “soft” scaffold to ensure maximum thermodynamic stability of the metal complexes. Using iron chelators as models, we show that simple conjugation of small molecule catechol ligands to a polyallylamine chain resulted in more than 8–9 orders of magnitude enhancement of the iron-binding affinity, which is comparable to that of enterobactin, the strongest iron chelator ever known. This study demonstrates that flexible polymer chelators may realize the highest possible metal affinities of the conjugated ligands owing to their ability to achieve an optimal conformation, which could advance the identification of strong metal chelators.