Affine Actions Research Articles

Global rigidity of smooth ${\mathbb{Z}}\ltimes _{\unicode{x3bb}}{\mathbb{R}}$ -actions on ${\mathbb{T}}^{2}$

Abstract For $\unicode{x3bb}>1$ , we consider the locally free ${\mathbb Z}\ltimes _\unicode{x3bb} \mathbb R$ actions on $\mathbb T^2$ . We show that if the action is $C^r$ with $r\geq 2$ , then it is $C^{r-\epsilon }$ -conjugate to an affine action generated by a hyperbolic automorphism and a linear translation flow along the expanding eigen-direction of the automorphism. In contrast, there exists a $C^{1+\alpha }$ -action which is semi-conjugate, but not topologically conjugate to an affine action.

Enzymatic biocatalysis processes on the semicrystalline and morphological order of native cassava starches (Manihot esculenta)

Enzymatic biocatalysis has emerged as a green technology in starch modification with divergent results at the morphological level depending on the origin of the starch source. Therefore, various enzymatic biocatalysts were implemented to evaluate their effect on the morphological and semi-crystalline characteristics of native cassava starches. The degree of affinity of the biocatalysts and the conversion rate on native cassava starches were determined by kinetic parameters such as the Michaelis-Menten constant, whose results revealed the following order of affinity from highest to lowest: α-amylase, amyloglucosidase, pullulanase, and β-amylase. In addition, greater biocatalytic activity of α-amylase and β-amylase was evidenced on the amorphous zones of the polymer associated with the decrease in the amylose content and a significant increase in the degree of relative crystallinity. According to morphological analyses and XDR, the action of amyloglucosidase promoted exo-erosion phenomena and the appearance of lacerations on the granular surface of starch with the consequent decrease in the semicrystalline order. The pullulanase caused slightly eroded fragmented granules with greater biocatalytic activity on the crystalline lamellae, associated with a significant increase in the apparent amylose content. FTIR analysis in the 1,200-900 cm-1 region, corresponding to the starch fingerprint, allowed us to detect notable changes in the degree of molecular order after the enzymatic attack; this result was consistent with the degree of relative crystallinity estimated by X-ray diffraction. Likewise, the results allowed us to notice significant changes in the semi-crystalline order and morphological characteristics during the modification with α-amylase (AAM) and amyloglucosidase (AMG) associated with their greater affinity and preferential action on the amorphous structures located on the granular surface of native cassava starch.

Identification of ACHE as the hub gene targeting solasonine associated with non-small cell lung cancer (NSCLC) using integrated bioinformatics analysis.

Solasonine, as a major biological component of Solanum nigrum L., has demonstrated anticancer effects against several malignancies. However, little is understood regarding its biological target and mechanism in non-small cell lung cancer (NSCLC). We conducted an analysis on transcriptomic data to identify differentially expressed genes (DEGs), and employed an artificial intelligence (AI) strategy to predict the target protein for solasonine. Subsequently, genetic dependency analysis and molecular docking were performed, with Acetylcholinesterase (ACHE) selected as a pivotal marker for solasonine. We then employed a range of bioinformatic approaches to explore the relationship between ACHE and solasonine. Furthermore, we investigated the impact of solasonine on A549 cells, a human lung cancer cell line. Cell inhibition of A549 cells following solasonine treatment was analyzed using the CCK8 assay. Additionally, we assessed the protein expression of ACHE, as well as markers associated with apoptosis and inflammation, using western blotting. To investigate their functions, we employed a plasmid-based ACHE overexpression system. Finally, we performed dynamics simulations to simulate the interaction mode between solasonine and ACHE. The results of the genetic dependency analysis revealed that ACHE could be identified as the pivotal target with the highest docking affinity. The cell experiments yielded significant findings, as evidenced by the negative regulatory effect of solasonine treatment on tumor cells, as demonstrated by the CCK8 assay. Western blotting analysis revealed that solasonine treatment resulted in the downregulation of the Bcl-2/Bax ratio and upregulation of cleaved caspase-3 protein expression levels. Moreover, we observed that ACHE overexpression promoted the expression of the Bcl-2/Bax ratio and decreased cleaved caspase-3 expression in the OE-ACHE group. Notably, solasonine treatment rescued the Bcl-2/Bax ratio and cleaved caspase-3 expression in OE-ACHE cells compared to OE-ACHE cells without solasonine treatment, suggesting that solasonine induces apoptosis. Besides, solasonine exhibited its anti-inflammatory effects by inhibiting P38 MAPK. This was supported by the decline in protein levels of IL-1β and TNF-α, as well as the phosphorylated forms of JNK and P38 MAPK. The results from the molecular docking and dynamics simulations further confirmed the potent binding affinity and effective inhibitory action between solasonine and ACHE. The findings of the current investigation show that solasonine exerts its pro-apoptosis and anti-inflammatory effects by suppressing the expression of ACHE.

Cartan actions of higher rank abelian groups and their classification

We study R k × Z ℓ \mathbb {R}^k \times \mathbb {Z}^\ell actions on arbitrary compact manifolds with a projectively dense set of Anosov elements and 1-dimensional coarse Lyapunov foliations. Such actions are called totally Cartan actions. We completely classify such actions as built from low-dimensional Anosov flows and diffeomorphisms and affine actions, verifying the Katok-Spatzier conjecture for this class. This is achieved by introducing a new tool, the action of a dynamically defined topological group describing paths in coarse Lyapunov foliations, and understanding its generators and relations. We obtain applications to the Zimmer program.

Hyperbolicity and uniformly Lipschitz affine actions on subspaces of L1$L^1$

AbstractWe show that every hyperbolic group has a proper uniformly Lipschitz affine action on a subspace of an space. We also prove that every acylindrically hyperbolic group has a uniformly Lipschitz affine action on such a space with unbounded orbits. Our main tools are the ‐bicombings on hyperbolic groups constructed by Mineyev and the characterisation of acylindrical hyperbolicity in terms of actions on quasi‐trees by Balasubramanya.

Affine deformations of quasi‐divisible convex cones

AbstractWe study subgroups of obtained by adding a translation part to the holonomy of a finite‐volume convex projective surface. Under a natural condition on the translations added to the peripheral parabolic elements, we show that the affine action of the group on has convex domains of discontinuity which are regular, generalizing a result of Mess for globally hyperbolic flat spacetimes. We then classify all such domains arising from a fixed group and show that the quotient of each of them is an affine manifold foliated by convex surfaces with constant affine Gaussian curvature (CAGC). The proof is based on the analysis of CAGC surfaces developed in a previous work, along with a correspondence between the geometry of an affine space endowed with a convex cone and the geometry of a convex tube domain. We also show that the moduli space of such groups is a vector bundle over the moduli space of finite‐volume convex projective structures, with rank equal to the dimension of the Teichmüller space.

Structural Prediction of Melanocortin Receptor (MC4R) of Carassius Auratus: An In-silico Approach

Carassius auratus commonly known as goldfish is one of most attractive fish used as ornamental fishes throughout the world. From the ancient times, the melanocortin system is considered to be conserved ranging from teleosts to mammals. Various researches in several fish species presented melanocortin receptors 4 (MC4R) is involved in different functions in fish body. Therefore, in-silico analysis of MC4R of Carassius auratus has been carried out in the study to know the physicochemical properties and 3D structural confirmation of the protein. Sequence containing accession number XM_026207258.1 was taken from National Center for Biotechnology Information (NCBI) and then processed to Expasy’s protparam for the physicochemical characterization, SOPMA for secondary structure prediction. Template search was done by SWISSMODEL/Workspace and Swiss-Pdb-Viewer was used for prediction of 3D structure of the concerned protein. The results suggested MC4R is a stable, hydrophobic and slightly basic nature of protein. The secondary structure of the analysed MC4R protein suggested presence of 50.77% alpha helix, 19.69% extended strands and 3.38% beta turns along with 26.15% random coils. Moreover, it might be resolved from the ramachandran plot that the structural prediction of MC4R is correct in prediction. Further, predicted 3D structure of MC4R protein can also be utilized for docking and simulation studies in future for finding out its relative binding affinity and functional action mechanism aspects. Moreover, the study is an approach for reducing the sequence data and solved structures gap by X-ray crystallography and NMR spectroscopy, which are also tedious and expensive laboratory techniques in application as well. Keywords: Melanocortin receptors 4 (MC4R); In silico analysis; 3D structural prediction; Carassius auratus.

Global rigidity of higher rank lattice actions with dominated splitting

AbstractLet $\alpha $ be a $C^{\infty }$ volume-preserving action on a closed n-manifold M by a lattice $\Gamma $ in $\mathrm {SL}(n,\mathbb {R})$ , $n\ge 3$ . Assume that there is an element $\gamma \in \Gamma $ such that $\alpha (\gamma )$ admits a dominated splitting. We prove that the manifold M is diffeomorphic to the torus ${{\mathbb T}^{n}={\mathbb R}^{n}/{\mathbb Z}^{n}}$ and $\alpha $ is smoothly conjugate to an affine action. Anosov diffeomorphisms and partial hyperbolic diffeomorphisms admit a dominated splitting. We obtained a topological global rigidity when $\alpha $ is $C^{1}$ . We also prove similar theorems for actions on $2n$ -manifolds by lattices in $\textrm {Sp}(2n,{\mathbb R})$ with $n\ge 2$ and $\mathrm {SO}(n,n)$ with $n\ge 5$ .

Separation functions and mild topologies

Abstract Given M M and N N Hausdorff topological spaces, we study topologies on the space C 0 ( M ; N ) {C}^{0}\left(M;\hspace{0.33em}N) of continuous maps f : M → N f:M\to N . We review two classical topologies, the “strong” and the “weak” topology. We propose a definition of “mild topology” that is coarser than the “strong” and finer than the “weak” topology. We compare properties of these three topologies, in particular with respect to proper continuous maps f : M → N f:M\to N , and affine actions when N = R n N={{\mathbb{R}}}^{n} . To define the “mild topology” we use “separation functions;” these “separation functions” are somewhat similar to the usual “distance function d ( x , y ) d\left(x,y) ” in metric spaces ( M , d ) \left(M,d) , but have weaker requirements. Separation functions are used to define pseudo balls that are a global base for a T2 topology. Under some additional hypotheses, we can define “set separation functions” that prove that the topology is T6. Moreover, under further hypotheses, we will prove that the topology is metrizable. We provide some examples of uses of separation functions: one is the aforementioned case of the mild topology on C 0 ( M ; N ) {C}^{0}\left(M;\hspace{0.33em}N) . Other examples are the Sorgenfrey line and the topology of topological manifolds.

Molecular Recognition Patterns between Vitamin B12 and Proteins Explored through STD-NMR and In Silico Studies.

Ligand-receptor molecular recognition is the basis of biological processes. The Saturation Transfer Difference-NMR (STD-NMR) technique has been recently used to gain qualitative and quantitative information about physiological interactions at an atomic resolution. The molecular recognition patterns between the cyanocobalamin (CNBL)/aqua cobalamin (OHBL) and different plant and animal proteins were investigated via STD-NMR supplemented by molecular docking. This study demonstrates that myoglobin has the highest binding affinity and that gluten has the lowest affinity. Casein also shows a higher binding affinity for cyanocobalamin when compared with that of plant-based proteins. STD-NMR results showed the moderate binding capability of casein with both CNBL and OHBL. Computer simulation confirmed the recognition mode in theory and was compared with the experiments. This work is beneficial for understanding the binding affinity and biological action of cyanocobalamin and will attract researchers to use NMR technology to link the chemical and physiological properties of nutrients.

Entropy and affine actions for surface groups

We give a short and independent proof of a theorem of Danciger and Zhang: surface groups with Hitchin linear part cannot act properly on the affine space. The proof is fundamentally different and relies on ergodic methods.

Bulleyaconitine A is a sensitive substrate and competitive inhibitor of CYP3A4: One of the possible explanations for clinical adverse reactions

Bulleyaconitine A (BLA), a toxic Aconitum alkaloid, is a potent analgesic that is clinically applied to treat rheumatoid arthritis, osteoarthritis and lumbosacral pain. BLA-related adverse reactions occur frequently, but whether the underlying mechanism is related to its metabolic interplay with drug-metabolizing enzymes remains unclear. This study aimed to elucidate the metabolic characteristics of BLA and its affinity action and mechanism to drug-metabolizing enzymes to reveal whether BLA-related adverse reactions are modulated by enzymes. After incubation with human liver microsomes and recombinant human cytochrome P450 enzymes, we found that BLA was predominantly metabolized by CYP3A, in which CYP3A4 had an almost absolute advantage. In vitro, the CYP3A4 inhibitor ketoconazole noticeably suppressed the metabolism of BLA. In vivo, the AUC0-∞ values, cardiotoxicity and neurotoxicity of BLA in Cyp3a-inhibited mice were all obviously enhanced (P < 0.05) compared to those in normal mice. In the enzyme kinetics study, BLA was found to be a sensitive substrate of CYP3A4, and its characteristics were consistent with substrate inhibition (Km = 39.36 ± 10.47 μmol/L, Ks = 83.42 ± 19.65 μmol/L). BLA was further identified to be a competitive inhibitor of CYP3A4 with Ki = 53.64 μmol/L, since the intrinsic clearance (CLint) of midazolam, a selective CYP3A4 substrate, decreased significantly (P < 0.05) when incubated with BLA together in mouse liver microsomes. Overall, BLA is a sensitive substrate and competitive inhibitor of CYP3A4, and clinical adverse reactions of BLA may mechanistically related to the CYP3A4-mediated drug-drug interactions.

Correction to: Proper affine actions: a sufficient criterion

Correction to: Proper affine actions: a sufficient criterion

Recognition and Selectivity Analysis Monitoring of Multicomponent Steroid Estrogen Mixtures in Complex Systems Using a Group-Targeting Environmental Sensor.

The same class of steroid estrogen mixtures, coexisting in the environment of 17β-estradiol, estrone (E1), and ethinyl estradiol (EE2), have strong ability to disrupt the human endocrine system and are seriously prejudicial to the health of the organism and environmental safety. Herein, a highly sensitive and group-targeting environmental monitoring sensor was fabricated for a comprehensive analysis of multicomponent steroid estrogens (multi-SEs) in complex systems. This breakthrough was based on the highly sensitive photoelectrochemical response composite material CdSe NPs-TiO2 nanotube and highly group-specific aptamers. The optimized procedure exhibited not only high sensitivity in a wide range of concentrations from 0.1 to 50 nM, indeed, the minimum detection limit was 33 pM, but also strong resistance to interference. The affinity and consistent action pockets of this sensor enable selective detection of multi-SEs in complex systems. It subsequently was applied for the analysis of multi-SEs from three real samples in the environment including medical wastewater, river water, and tap water to provide a means to clarify the fate of multi-SEs in the process of migration and transformation. This monitoring sensor has a brilliant application prospect for the identification and monitoring of the same class of endocrine-disrupting chemical mixtures in environmental complex systems.

Variation of Two S3b Residues in KV4.1-4.3 Channels Underlies Their Different Modulations by Spider Toxin κ-LhTx-1.

The naturally occurred peptide toxins from animal venoms are valuable pharmacological tools in exploring the structure-function relationships of ion channels. Herein we have identified the peptide toxin κ-LhTx-1 from the venom of spider Pandercetes sp (the Lichen huntsman spider) as a novel selective antagonist of the KV4 family potassium channels. κ-LhTx-1 is a gating-modifier toxin impeded KV4 channels’ voltage sensor activation, and mutation analysis has confirmed its binding site on channels’ S3b region. Interestingly, κ-LhTx-1 differently modulated the gating of KV4 channels, as revealed by toxin inhibiting KV4.2/4.3 with much more stronger voltage-dependence than that for KV4.1. We proposed that κ-LhTx-1 trapped the voltage sensor of KV4.1 in a much more stable resting state than that for KV4.2/4.3 and further explored the underlying mechanism. Swapping the non-conserved S3b segments between KV4.1(280FVPK283) and KV4.3(275VMTN278) fully reversed their voltage-dependence phenotypes in inhibition by κ-LhTx-1, and intensive mutation analysis has identified P282 in KV4.1, D281 in KV4.2 and N278 in KV4.3 being the key residues. Furthermore, the last two residues in this segment of each KV4 channel (P282/K283 in KV4.1, T280/D281 in KV4.2 and T277/N278 in KV4.3) likely worked synergistically as revealed by our combinatorial mutations analysis. The present study has clarified the molecular basis in KV4 channels for their different modulations by κ-LhTx-1, which have advanced our understanding on KV4 channels’ structure features. Moreover, κ-LhTx-1 might be useful in developing anti-arrhythmic drugs given its high affinity, high selectivity and unique action mode in interacting with the KV4.2/4.3 channels.

High-efficient nucleic acid separation from animal tissue samples via surface modified magnetic nanoparticles

High efficiency nucleic acid (NA) separation via magnetic nanoparticles (MNPs) is a promising technology for bioengineering, healthcare, etc. Aimed to enhance the selection of MNPs and illustrate the separation mechanism for effective isolation of NAs from complex animal samples, this study fabricated hydroxy-, amino- and carboxyl-functionalized MNPs (MNPs-OH, MNPs-NH2 and MNPs-COOH) with different particle sizes to investigate the hybrid NA separation performance from animal tissue samples. Molecular dynamics (MD) simulation was introduced to predict the affinity action of MNPs with NA and typical impurities. The details of the kinetic separation behavior and the NA separation performance were then illustrated. MD simulation results showed MNPs-NH2 had a stronger affinity with NA, and in most experimental separation systems, NA separation yield via three kinds of MNPs showed a following order of MNPs-NH2 > MNPs-OH > MNPs-COOH. MNPs of different sizes had significantly different sedimentation and dispersion features, leading to diverse separation results. Combining with the proper lysis system, an optimized NA separation method at room temperature with high-throughput and low contamination risk was developed as a promising approach for large-scale samples extracted NA simultaneously. This work could provide a theoretical guidance for the fabrication strategy of advanced MNPs and the enhancement of NA separation from complex samples.

Proper affine actions for right-angled Coxeter groups

For any right-angled Coxeter group $\Gamma$ on $k$ generators, we construct proper actions of $\Gamma$ on $\mathrm{O}(p,q+1)$ by right and left multiplication, and on the Lie algebra $\mathfrak{o}(p,q+1)$ by affine transformations, for some $p,q\in\mathbb N$ with $p+q+1=k$. As a consequence, any virtually special group admits proper affine actions on some $\mathbb R^n$: this includes e.g. surface groups, hyperbolic 3-manifold groups, examples of word hyperbolic groups of arbitrarily large virtual cohomological dimension, etc. We also study some examples in cohomological dimension two and four, for which the dimension of the affine space may be substantially reduced.

Local rigidity of certain solvable group actions on tori

<p style='text-indent:20px;'>In this paper, we study a local rigidity property of <inline-formula><tex-math id="M1">\begin{document}$ \mathbb Z \ltimes_\lambda \mathbb R $\end{document}</tex-math></inline-formula> affine action on tori generated by an irreducible toral automorphism and a linear flow along an eigenspace. Such an action exhibits a weak version of local rigidity, i.e., any smooth perturbations close enough to an affine action is smoothly conjugate to the affine action up to constant time change.

Design of first in class bitopic ligands targeting the sodium binding pocket in opioid receptors

Opioid agonists have been used in the field of pain management for centuries, but are considered a major public health concern, especially in the US. One of the biggest challenges consists in understanding the ability to target specifically the different subtypes of opioid receptors and to trigger a specific functional response correlating with an in vivo analgesic response devoid of side‐effects.These opioid receptors are part of the GPCRs family, which is known to have common features across different subfamilies. One important feature of these receptors is the presence of allosteric binding pockets, which is progressively gaining momentum as a novel target for current therapeutic strategies. We hypothesized that targeting an allosteric site could potentially allow for receptor functional selectivity, helping to reduce the overall side effects profile. One site, in particular, known as the Na+ binding pocket, is known to play a key role in GPCR function and is thought to be the center of the functional mechanism, with several bias switches characterized in the pocket residues (Katritch et al., Trends Biochem Sci. 2014).Here we report structure‐based rational drug design of bitopic ligands targeting the Na+ pocket of mu (MOR) and kappa opioid receptors (KOR). Our designed bitopics show high affinity, subtype selectivity, G‐protein bias and analgesic actions in mice. Mutations in Na+ binding pocket diminished functional potency validating allosteric site targeting. Together, results suggest the possibility of achieving subtype selectivity and identification of an additional subpocket in both MOR and KOR to reduce βarrestin‐2 recruitment by targeting an allosteric pocket in the opioid receptors. The highly conserved constitution of the Na+ binding pocket opens the opportunity for rational discovery of new GPCR modulators with desired functional, and potentially therapeutic profile for opioids as well as other class A GPCRs.Support or Funding InformationWe gratefully acknowledge the financial support from Faculty Research Incentive Fund, NIDA, NIAAA and US department of defense. We also would like to thank the Philippe Foundation for their financial support.

Dehn filling Dehn twists

AbstractLet$\Sigma _{g,p}$be the genus–goriented surface withppunctures, with eitherg&gt; 0 orp&gt; 3. We show that$MCG(\Sigma _{g,p})/DT$is acylindrically hyperbolic whereDTis the normal subgroup of the mapping class group$MCG(\Sigma _{g,p})$generated by$K^{th}$powers of Dehn twists about curves in$\Sigma _{g,p}$for suitableK.Moreover, we show that in low complexity$MCG(\Sigma _{g,p})/DT$is in fact hyperbolic. In particular, for 3g− 3 +p⩽ 2, we show that the mapping class group$MCG(\Sigma _{g,p})$is fully residually non-elementary hyperbolic and admits an affine isometric action with unbounded orbits on some$L^q$space. Moreover, if every hyperbolic group is residually finite, then every convex-cocompact subgroup of$MCG(\Sigma _{g,p})$is separable.The aforementioned results follow from general theorems about composite rotating families, in the sense of [13], that come from a collection of subgroups of vertex stabilizers for the action of a groupGon a hyperbolic graphX. We give conditions ensuring that the graphX/Nis again hyperbolic and various properties of the action ofGonXpersist for the action ofG/NonX/N.