Classical Affine Research Articles

IS4-FAM, a fluorescent tool to study CXCR4 affinity and competitive antagonism in native cancer cells.

The ability to accurately measure drug-target interaction is critical for the discovery of new therapeutics. Classical pharmacological bioassays such as radioligand or fluorescent ligand binding assays can define the affinity or Kd of a ligand for a receptor with the lower the Kd, the stronger the binding and the higher the affinity. However, in many drug discovery laboratories today, the target of interest if often artificially upregulated by means of transfection to modify the host cell's genetic makeup. This then potentially invalidates the assumptions of classical pharmacology affinity calculations as the receptor of interest is no longer at normal physiological densities. The CXCR4 receptor is expressed on many different cancer cell types and is associated with metastasis and poor prognosis. Therefore, the CXCR4 receptor is a desirable target for novel therapeutics. In this study, we explore the applicability of the newly developed fluorescently tagged CXCR4 antagonists, IS4-FAM as an investigative tool to study CXCR4 affinity and competitive antagonism in native, non-transfected cancer cells using confocal microscopy and flow cytometry. IS4-FAM directly labels CXCR4 in several cell lines including high CXCR4 expressing SK-MEL-28 (malignant melanoma) and PC3 (metastatic prostate cancer) and lower CXCR4 expressing THP-1 (acute monocytic leukemia) and was competitive with the established CXCR4 antagonist, AMD3100. This highlights the potential of IS4-FAM as a pharmacological tool for drug discovery in native cells lines and tissues.

Classical Whittaker modules for the classical affine Kac-Moody algebras

Inspired by Sugawara operators, we introduce a new basis for the universal non-degenerate Whittaker module of level κ over the classical affine Kac-Moody algebra of type BN(1), CN(1) or DN(1). This basis is different from the one derived from the PBW basis and would help us to understand the structure of Whittaker modules. As a result, we classify simple non-degenerate Whittaker modules for the classical affine Kac-Moody algebras whether at the critical or noncritical level.

Structural basis of nuclear transport for NEIL DNA glycosylases mediated by importin-alpha

NEIL glycosylases, including NEIL1, NEIL2, and NEIL3, play a crucial role in the base excision DNA repair pathway (BER). The classical importin pathway mediated by importin α/β and cargo proteins containing nuclear localization sequences (NLS) is the most common transport mechanism of DNA repair proteins to the nucleus. Previous studies have identified putative NLSs located at the C-terminus of NEIL3 and NEIL1. Crystallographic, bioinformatics, calorimetric (ITC), and fluorescence assays were used to investigate the interaction between NEIL1 and NEIL3 putative NLSs and importin-α (Impα). Our findings showed that NEIL3 contains a typical cNLS, with medium affinity for the major binding site of Impα. In contrast, crystallographic analysis of NEIL1 NLS revealed its binding to Impα, but with high B-factors and a lack of electron density at the linker region. ITC and fluorescence assays indicated no detectable affinity between NEIL1 NLS and Impα. These data suggest that NEIL1 NLS is a non-classical NLS with low affinity to Impα. Additionally, we compared the binding mode of NEIL3 and NEIL1 with Mus musculus Impα to human isoforms HsImpα1 and HsImpα3, which revealed interesting binding differences for HsImpα3 variant. NEIL3 is a classical medium affinity monopartite NLS, while NEIL1 is likely to be an unclassical low-affinity bipartite NLS. The base excision repair pathway is one of the primary systems involved in repairing DNA. Thus, understanding the mechanisms of nuclear transport of NEIL proteins is crucial for comprehending the role of these proteins in DNA repair and disease development.

Recording Binding Information Directly into DNA-Encoded Libraries Using Terminal Deoxynucleotidyl Transferase.

Terminal deoxynucleotidyl transferase (TdT) is an unusual DNA polymerase that adds untemplated dNTPs to 3'-ends of DNA. If a target protein is expressed as a TdT fusion and incubated with a DNA-encoded library (DEL) in the presence of dATP, the binders of the target induce proximity between TdT and the DNA, promoting the synthesis of a poly-adenine (polyA) tail. The polyA tail length is proportional to the binding affinity, effectively serving as a stable molecular record of binding events. The polyA tail is also a convenient handle to enrich binders with magnetic poly(dT)25 beads before sequencing. In a benchmarking system, we show that ligands spanning nanomolar to double-digit micromolar binding can be cleanly identified by TdT extension, whereas only the tightest binding ligands are identified by classical affinity selection. The method is simple to implement and can function on any DEL that bears a free 3'-end.

WKB analysis of the linear problem for modified affine Toda field equations

We study the WKB analysis of the solutions to the linear problem for a modified affine Toda field equation, which is equivalent to the higher-order ordinary differential equation (ODE) studied in the ODE/IM correspondence. After gauge transformation, we diagonalize the flat connection of the linear problem to reduce the latter to a set of independent first-order linear differential equations. We explicitly perform this procedure for classical affine Lie algebras with lower ranks. In particular, we study the WKB solutions of the {D}_r^{(1)} - and {D}_{r+1}^{(2)} -type linear problems, which correspond to the higher-order ODEs with the pseudo-differential operator. The diagonalized connection is obtained from the Riccati equations of the adjoint linear problem and related to the conserved currents of the integrable hierarchy constructed by Drinfeld and Sokolov up to total derivatives.

Cameron–Liebler sets for maximal totally isotropic flats in classical affine spaces

AbstractLet be the ‐dimensional classical affine space with parameter over a ‐element finite field , and be the set of all maximal totally isotropic flats in . In this paper, we discuss Cameron–Liebler sets in , obtain several equivalent definitions and present some classification results.

Finite-dimensional representations of map superalgebras

We describe the block decomposition of the categories of finite-dimensional modules for classical map superalgebras and affine superalgebras in terms of spectral characters. En route to showing these block decompositions, we obtain a new description of finite-dimensional irreducible modules for classical map and affine superalgebras, provide formulas for their (super)characters and describe their extension groups. As an application, we establish a relation between the highest weights of a given finite-dimensional irreducible module for a classical map superalgebra with respect to non-conjugate Borel subalgebras.

Helmholtz-equation solution in nonsmooth media by a physics-informed neural network incorporating quadratic terms and a perfectly matching layer condition

Frequency-domain simulation of seismic waves plays an important role in seismic inversion, but it remains challenging in large models. The recently proposed physics-informed neural network (PINN), as an effective deep-learning method, has achieved successful applications in solving a wide range of partial differential equations (PDEs), and there is still room for improvement on this front. For example, PINN can lead to inaccurate solutions when PDE coefficients are nonsmooth and describe structurally complex media. Thus, we solve the acoustic and visco-acoustic scattered-field (Lippmann-Schwinger) wave equation in the frequency domain with PINN instead of the wave equation to remove the source singularity. We first illustrate that nonsmooth velocity models lead to inaccurate wavefields when no boundary conditions are implemented in the loss function. Then, we add the perfectly matched layer (PML) conditions in the loss function to better couple the real and imaginary parts of the wavefield. Moreover, we design new neurons by replacing the classical affine function with a quadratic function in the argument of the activation function to better capture the nonsmooth features of the wavefields. We find that the PML condition and the quadratic functions improve the results including handling attenuation and discuss the reason for this improvement. We also illustrate that a network trained to predict a wavefield for a specific medium can be used as an initial model of the neural network for predicting other wavefields corresponding to PDE-coefficient alterations and improving the convergence speed accordingly. This pretraining strategy should find applications in iterative full-waveform inversion and time-lag target-oriented imaging when the model perturbation between two consecutive iterations or two consecutive experiments is small.

Polyhedral realizations for crystal bases of integrable highest weight modules and combinatorial objects of type $$\textrm{A}^{(1)}_{n-1}$$, $$\textrm{C}^{(1)}_{n-1}$$, $$\textrm{A}^{(2)}_{2n-2}$$, $$\textrm{D}^{(2)}_{n}$$

In this paper, we consider polyhedral realizations for crystal bases $B(\lambda)$ of irreducible integrable highest weight modules of a quantized enveloping algebra $U_q(\mathfrak{g})$, where $\mathfrak{g}$ is a classical affine Lie algebra of type ${\rm A}^{(1)}_{n-1}$, ${\rm C}^{(1)}_{n-1}$, ${\rm A}^{(2)}_{2n-2}$ or ${\rm D}^{(2)}_{n}$. We will give explicit forms of polyhedral realizations in terms of extended Young diagrams or Young walls that appear in the representation theory of quantized enveloping algebras of classical affine type. As an application, a combinatorial description of $\varepsilon_k^*$ functions on $B(\infty)$ will be given.

Synthesis of theories on cellular powering, coherence, homeostasis and electro-mechanics: Murburn concept and evolutionary perspectives.

If evolution was/is a fact, a simplified/unifying approach to explain cellular physiology is warranted. Such a perspective should agree with the thermodynamic, kinetic, structural, and operational-probabilistic considerations; without invoking overt intelligence or determinism, and must enable a synthesis from chaos. In this regard, we first list salient theories in cellular physiology for (i) powering (generation of chemical/heat energy), (ii) coherence (interconnectivity and workability as a unit), (iii) homeostasis (metabolizing and expelling of unfamiliar/unwanted materials, maintaining concentration/volume), and (iv) cellular electrical-mechanical activities. While doing so, we discuss the scopes and limitations of (a) the classical active-site affinity and recognition-based modality of lock-key and induced-fit enzyme-catalytic mechanisms established by Fischer/Koshland, (b) membrane-pump hypothesis acclaimed by biologists-physicians and historically championed by the British Nobel-laureates like Hodgkin-Huxley-Katz-Mitchell, and (c) association-induction hypothesis advocated by physicists-physiologists from various parts of the world, for example, Gilbert Ling (China-USA), Gerald Pollack (USA), Ludwig Edelmann (Germany), Vladimir Matveev (Russia), and so on. We apply murburn concept (from "mured burning," capturing the thesis that one-electron redox equilibriums involving diffusible reactive species play vital roles in maintaining life order) to amalgamate several core cellular functions and further discuss the prospects for establishing the continuum of the principles of physics in biology.

Geometric structure of affine Deligne-Lusztig varieties for GL3

In this paper we study the geometric structure of affine Deligne-Lusztig varieties Xλ(b) for GL3 and b basic. We completely determine the irreducible components of the affine Deligne-Lusztig variety. In particular, we classify the cases where all of the irreducible components are classical Deligne-Lusztig varieties times finite-dimensional affine spaces. If this is the case, then the irreducible components are pairwise disjoint.

Combining the classic vulnerability index and affinity propagation clustering algorithm to assess the intrinsic aquifer vulnerability of coastal aquifers on an integrated scale

In the northern plains of Laizhou City, groundwater quality suffers dual threats from anthropogenic activities: seawater intrusion caused by overextraction of fresh groundwater, and vertical infiltration of agricultural pollutants. Groundwater management requires a comprehensive analysis of both horizontal and vertical pollution in coastal aquifers. In this paper, Intrinsic Aquifer Vulnerability (IAV) was assessed on an integrated scale using two classic IAV models (DRASTIC and GALDIT) separately based on a GIS database. Hydrogeological parameters from two classic IAV models were clustered using affinity propagation (AP) clustering algorithm, and silhouette coefficients were used to determine the optimal classification result.In our application, the objects of the AP algorithm are 3320 units divided from the whole study area with 500 m*500 m precision. A comparison of all four outputs in AP-DRASTIC shows that the clustering results of the 4-classification yielded the best silhouette coefficient of 0.406 out of all four. Cluster 4, which comprises 21% of the area, had relatively low level of groundwater contamination, despite its high level of vulnerability as indicated by the classic DRASTIC index. In the second level of vulnerability Cluster 3, 53.8% of all water samples were found to be contaminated, indicating a greater level of nitrate contamination. With respect to AP-GALDIT, the silhouette coefficient for result 7-classification reaches the highest value of 0.343. There was a high level of vulnerability identified in Clusters 2, 4 and 5 (34.7% of the study area) relating to the classic GALDIT index. The concentration of chloride in all water samples obtained in these areas was extremely high. Groundwater management should be addressed by AP-DRASTIC results on anthropogenic activity/contamination control, and by AP-GALDIT results on groundwater extraction limitation. Overall, this method allows for the evaluation of IAV in other coastal areas on an integrated scale, facilitating the development of groundwater management strategies based on a better understanding of the aquifer's essential characteristics.

ODE/IM correspondence and supersymmetric affine Toda field equations

We study the linear differential system associated with the supersymmetric affine Toda field equations for affine Lie superalgebras, which has a purely odd simple root system. For an affine Lie algebra, the linear problem modified by conformal transformation leads to an ordinary differential equation (ODE) that provides the functional relations in the integrable models. This is known as the ODE/IM correspondence. For the affine Lie superalgebras, the linear equations modified by a superconformal transformation are shown to reduce to a couple of ODEs for each bosonic subalgebra. In particular, for osp(2,2)(2), the corresponding ODE becomes the second-order ODE with squared potential, which is related to the N=1 supersymmetric minimal model via the ODE/IM correspondence. We also find ODEs for classical affine Lie superalgebras with purely odd simple root systems.

Representations of affine Lie superalgebras and their quantization in type A

We construct a new family of irreducible modules over any basic classical affine Kac-Moody Lie superalgebra which are induced from modules over the Heisenberg subalgebra. We also obtain irreducible deformations of these modules for the quantum affine superalgebra Uqslˆ(m|n).

On two conjectures about the intersection distribution

Recently, Li and Pott proposed a new concept of intersection distribution concerning the interaction between the graph \(\{(x,f(x))~|~x\in {\mathbb {F}}_{q}\}\) of f and the lines in the classical affine plane AG(2, q). Later, Kyureghyan et al. proceeded to consider the next simplest case, and derived the intersection distribution for all degree three polynomials over \({\mathbb {F}}_{q}\) with q both odd and even. They also proposed several conjectures therein. In this paper, we completely solve two conjectures of Kyureghyan et al. Namely, we prove two classes of power functions having intersection distribution: \(v_{0}(f)=\frac{q(q-1)}{3},~v_{1}(f)=\frac{q(q+1)}{2},~v_{2}(f)=0,~v_{3}(f)=\frac{q(q-1)}{6}\). We mainly make use of the multivariate method and a certain type of equivalence on 2-to-1 mappings. The key point of our proof is to consider the number of the solutions of some low-degree equations.

Mechanistic Insights into a CDK9 Inhibitor Via Orthogonal Proteomics Methods.

Cyclin-dependent-kinases (CDKs) are members of the serine/threonine kinase family and are highly regulated by cyclins, a family of regulatory subunits that bind to CDKs. CDK9 represents one of the most studied examples of these transcriptional CDKs. CDK9 forms a heterodimeric complex with its regulatory subunit cyclins T1, T2 and K to form the positive transcription elongation factor b (P-TEFb). This complex regulates transcription via the phosphorylation of RNA polymerase II (RNAPolII) on Ser-2, facilitating promoter clearance and transcription elongation and thus remains an attractive therapeutic target. Herein, we have utilized classical affinity purification chemical proteomics, kinobeads assay, compressed CEllular Thermal Shift Assay (CETSA)-MS and Limited Proteolysis (LiP) to study the selectivity, target engagement and downstream mechanistic insights of a CDK9 tool compound. The above experiments highlight the value of quantitative mass spectrometry approaches to drug discovery, specifically proteome wide target identification and selectivity profiling. The approaches utilized in this study unanimously indicated that the CDK family of kinases are the main target of the compound of interest, with CDK9, showing the highest target affinity with remarkable consistency across approaches. We aim to provide guidance to the scientific community on the available chemical biology/proteomic tools to study advanced lead molecules and to highlight pros and cons of each technology while describing our findings in the context of the CDKs biology.

Limiting Directions for Random Walks in Classical Affine Weyl Groups

Abstract Let $W$ be a finite Weyl group and $\widetilde W$ the corresponding affine Weyl group. A random element of $\widetilde W$ can be obtained as a reduced random walk on the alcoves of $\widetilde W$. By a theorem of Lam (Ann. Prob. 2015), such a walk almost surely approaches one of $|W|$ many directions. We compute these directions when $W$ is $B_n$, $C_n$, and $D_n$ and the random walk is weighted by Kac and dual Kac labels. This settles Lam’s questions for types $B$ and $C$ in the affirmative and for type $D$ in the negative. The main tool is a combinatorial two row model for a totally asymmetric simple exclusion process (TASEP) called the $D^*$-TASEP, with four parameters. By specializing the parameters in different ways, we obtain TASEPs for each of the Weyl groups mentioned above. Computing certain correlations in these TASEPs gives the desired limiting directions.

Affine opers and conformal affine Toda

For $\mathfrak g$ a Kac-Moody algebra of affine type, we show that there is an $\text{Aut}\, \mathcal O$-equivariant identification between $\text{Fun}\,\text{Op}_{\mathfrak g}(D)$, the algebra of functions on the space of ${\mathfrak g}$-opers on the disc, and $W\subset \pi_0$, the intersection of kernels of screenings inside a vacuum Fock module $\pi_0$. This kernel $W$ is generated by two states: a conformal vector, and a state $\delta_{-1}\left|0\right>$. We show that the latter endows $\pi_0$ with a canonical notion of translation $T^{\text{(aff)}}$, and use it to define the densities in $\pi_0$ of integrals of motion of classical Conformal Affine Toda field theory. The $\text{Aut}\,\mathcal O$-action defines a bundle $\Pi$ over $\mathbb P^1$ with fibre $\pi_0$. We show that the product bundles $\Pi \otimes \Omega^j$, where $\Omega^j$ are tensor powers of the canonical bundle, come endowed with a one-parameter family of holomorphic connections, $\nabla^{\text{(aff)}} - \alpha T^{\text{(aff)}}$, $\alpha\in \mathbb C$. The integrals of motion of Conformal Affine Toda define global sections $[\mathbf v_j dt^{j+1} ] \in H^1(\mathbb P^1, \Pi\otimes \Omega^j,\nabla^{\text{(aff)}})$ of the de Rham cohomology of $\nabla^{\mathrm{(aff)}}$. Any choice of ${\mathfrak g}$-Miura oper $\chi$ gives a connection $\nabla^{\mathrm{(aff)}}_\chi$ on $\Omega^j$. Using coinvariants, we define a map $\mathsf F_\chi$ from sections of $\Pi \otimes \Omega^j$ to sections of $\Omega^j$. We show that $\mathsf F_\chi \nabla^{\text{(aff)}} = \nabla^{\text{(aff)}}_\chi \mathsf F_\chi$, so that $\mathsf F_\chi$ descends to a well-defined map of cohomologies. Under this map, the classes $[\mathbf v_j dt^{j+1} ]$ are sent to the classes in $H^1(\mathbb P^1, \Omega^j,\nabla^{\text{(aff)}}_\chi)$ defined by the ${\mathfrak g}$-oper underlying $\chi$.

High contrast cleavage detection.

Photonic biosensors that use optical resonances to amplify signals from refractive index changes offer high sensitivity, real-time readout, and scalable, low-cost fabrication. However, when used with classic affinity assays, they struggle with noise from nonspecific binding and are limited by the low refractive index and small size of target biological molecules. In this Letter, we evaluate the performance of an integrated microring photonic biosensor using the high contrast cleavage detection (HCCD) mechanism, which we recently introduced. The HCCD sensors make use of dramatic optical signal amplification caused by the cleavage of large numbers of high-contrast nanoparticle reporters instead of the adsorption of labeled or unlabeled low-index biological molecules. We evaluate the advantages of the HCCD detection mechanism over conventional target-capture detection techniques with the same label and the same sensor platform, using an example of a silicon ring resonator as an optical transducer decorated with silicon nanoparticles as high-contrast reporters. In the practical realization of this detection scheme, detection specificity and signal amplification can be achieved via collateral nucleic acid cleavage caused by enzymes such as CRISPR Cas12a and Cas13 after binding to a target DNA/RNA sequence in solution.

INTEGRABILITY OF CLASSICAL AFFINE W-ALGEBRAS

We prove that all classical affine W-algebras \U0001d4b2(\U0001d524; f), where g is a simple Lie algebra and f is its non-zero nilpotent element, admit an integrable hierarchy of bi-Hamiltonian PDEs, except possibly for one nilpotent conjugacy class in G2, one in F4, and five in E8.