Physiological and chaos effect on dynamics of neurological disorder with memory effect of fractional operator: A mathematical study.

BACKGROUND AND OBJECTIVE: To study the dynamical system, it is necessary to formulate the mathematical model to understand the dynamics of various diseases that are spread worldwide. The main objective of our work is to examine neurological disorders by early detection and treatment by taking asymptomatic. The central nervous system (CNS) is impacted by the prevalent neurological condition known as multiple sclerosis (MS), which can result in lesions that spread across time and place. It is widely acknowledged that multiple sclerosis (MS) is an unpredictable disease that can cause lifelong damage to the brain, spinal cord, and optic nerves. The use of integral operators and fractional order (FO) derivatives in mathematical models has become popular in the field of epidemiology. METHOD: The model consists of segments of healthy or barian brain cells, infected brain cells, and damaged brain cells as a result of immunological or viral effectors with novel fractal fractional operator in sight Mittag Leffler function. The stability analysis, positivity, boundedness, existence, and uniqueness are treated for a proposed model with novel fractional operators. RESULTS: Model is verified the local and global with the Lyapunov function. Chaos Control will use the regulate for linear responses approach to bring the system to stabilize according to its points of equilibrium so that solutions are bounded in the feasible domain. To ensure the existence and uniqueness of the solutions to the suggested model, it makes use of Banach's fixed point and the Leray Schauder nonlinear alternative theorem. For numerical simulation and results the steps Lagrange interpolation method at different fractional order values and the outcomes are compared with those obtained using the well-known FFM method. CONCLUSION: Overall, by offering a mathematical model that can be used to replicate and examine the behavior of disease models, this research advances our understanding of the course and recurrence of disease. Such type of investigation will be useful to investigate the spread of disease as well as helpful in developing control strategies from our justified outcomes.

Ultrasound-Assisted Synthesis of Piperidinyl-Quinoline Acylhydrazones as New Anti-Alzheimer's Agents: Assessment of Cholinesterase Inhibitory Profile, Molecular Docking Analysis, and Drug-like Properties.

Alzheimer's disease (AD) is one of the progressive neurological disorders and the main cause of dementia all over the world. The multifactorial nature of Alzheimer's disease is a reason for the lack of effective drugs as well as a basis for the development of new structural leads. In addition, the appalling side effects such as nausea, vomiting, loss of appetite, muscle cramps, and headaches associated with the marketed treatment modalities and many failed clinical trials significantly limit the use of drugs and alarm for a detailed understanding of disease heterogeneity and the development of preventive and multifaceted remedial approach desperately. With this motivation, we herein report a diverse series of piperidinyl-quinoline acylhydrazone therapeutics as selective as well as potent inhibitors of cholinesterase enzymes. Ultrasound-assisted conjugation of 6/8-methyl-2-(piperidin-1-yl)quinoline-3-carbaldehydes (4a,b) and (un)substituted aromatic acid hydrazides (7a-m) provided facile access to target compounds (8a-m and 9a-j) in 4-6 min in excellent yields. The structures were fully established using spectroscopic techniques such as FTIR, 1H- and 13C NMR, and purity was estimated using elemental analysis. The synthesized compounds were investigated for their cholinesterase inhibitory potential. In vitro enzymatic studies revealed potent and selective inhibitors of AChE and BuChE. Compound 8c showed remarkable results and emerged as a lead candidate for the inhibition of AChE with an IC50 value of 5.3 ± 0.51 µM. The inhibitory strength of the optimal compound was 3-fold higher compared to neostigmine (IC50 = 16.3 ± 1.12 µM). Compound 8g exhibited the highest potency and inhibited the BuChE selectively with an IC50 value of 1.31 ± 0.05 µM. Several compounds, such as 8a-c, also displayed dual inhibitory strength, and acquired data were superior to the standard drugs. In vitro results were further supported by molecular docking analysis, where potent compounds revealed various important interactions with the key amino acid residues in the active site of both enzymes. Molecular dynamics simulation data, as well as physicochemical properties of the lead compounds, supported the identified class of hybrid compounds as a promising avenue for the discovery and development of new molecules for multifactorial diseases, such as Alzheimer's disease (AD).

Synthesis of imidazole-pyrazole conjugates bearing aryl spacer and exploring their enzyme inhibition potentials.

Developing improved enzyme inhibitors is an effective therapy to counter various diseases. Aiming to build up biologically active templates, a new series of bis-diazoles conjugated with an aryl linker was designed and prepared through a convenient synthetic approach. Synthesized derivatives 6(a-m), having different substitutions at the 2nd position of the imidazole nucleus, depict the scope of present study. These compounds were characterized through spectroscopic methods and further examined for their in vitro enzyme inhibitory potentials against two selected enzymes: α-glucosidase and lipoxygenase (LOX). Overall, this series was found to be effective against α-glucosidase and moderately active against LOX enzyme. Compound 6k was the most potent α-glucosidase inhibitor with IC50 = 54.25 ± 0.67 µM as compared to reference drug acarbose (IC50 = 375.82 ± 1.76 µM). The docked conformation revealed the involvement of substituent's heteroatoms with amino acid residue Gly280 through hydrogen bonding. The most active LOX inhibitor was 6a with IC50 = 41.75 ± 0.04 µM as compared to standard baicalein (IC50 = 22.4 ± 1.3 µM). Docking model of 6a suggested the strong interaction of imidazole's nitrogen with iron atom of the active pocket of enzyme. Other features like lipophilicity, bulkiness of compounds, pi-pi interactions and/or pi-alkyl interactions also affected the inhibiting potentials of all prepared scaffolds.

Exploiting oxadiazole-sulfonamide hybrids as new structural leads to combat diabetic complications via aldose reductase inhibition.

A series of oxadiazole-sulfonamide hybrids was synthesized through multistep reaction and for the formation of targeted thioethers 6(a-l), a much facile route was adopted through which S-alkylation was successfully carried out at room temperature. These novel thioethers 6(a-l) were later screened against aldehyde reductase (ALR1) and aldose reductase (ALR2). Beside the enzyme inhibition studies, the compounds were also tested against cervical cancer cell lines (HeLa). The results suggested the significant inhibition pattern towards ALR2, while few compounds were active against ALR1. The synthesized derivatives have shown weak to moderate cytotoxicity. The most potent inhibitors (6b, 6e, 6f and 6l) were selected for molecular docking studies and the binding interactions were reported.

Imidazole-pyrazole hybrids: Synthesis, characterization and in-vitro bioevaluation against α-glucosidase enzyme with molecular docking studies.

Herein, substituted imidazole-pyrazole hybrids (2a-2n) were prepared via a multi component reaction employing pyrazole-4-carbaldehydes (1a-1d), ammonium acetate, benzil and arylamines as reactants. All the new compounds were characterized through their spectral and elemental analyses. Further these compounds were tested against α-glucosidase enzyme. The compounds 2k, 2l and 2n possessed good inhibition potencies, however, compounds 2f (IC50 value: 25.19 ±â€¯0.004 µM) and 2m (IC50 value: 33.62 ±â€¯0.03 µM) were the most effective compounds of the series. Furthermore, molecular docking helped to understand the binding interactions of 2f and 2m with the understudy yeast's α-glucosidase enzyme.

Evaluation of α-glucosidase inhibiting potentials with docking calculations of synthesized arylidene-pyrazolones.

Herein, condensation of aryl(hetaryl)pyrazole-4-carbaldehydes 1(a-c) with substituted pyrazolones 2(a-d) lead to the corresponding arylidene-pyrazolones 3(a-l) which were tested against α-glucosidase enzyme. The synthesized compounds displayed moderate to good activity. Among these, a coumarin derivative 3k exhibited excellent results (IC50 2.10 ±â€¯0.004 µM) in comparison to clinical drug acarbose (IC50 37.38 ±â€¯0.12 µM). The ligand-protein interactions were identified through docking and stabilizing energy calculations.

Biological evaluation of new imidazole derivatives tethered with indole moiety as potent α-glucosidase inhibitors.

A series of triarylimidazoles substituted with 2-arylindoles (4a-4j) were prepared and evaluated for their in vitro α-Glucosidase inhibition. α-Glucosidase inhibition assay displayed a new class of highly potent agents The new compounds showed significant α-glucosidase inhibitory activity as compared to the standard inhibitor acrabose. Structures of synthesized compounds were determined by using Mass spectrometry FT-IR, 1H NMR and 13C NMR.

Hetarylcoumarins: Synthesis and biological evaluation as potent α-glucosidase inhibitors.

In search of better α-glucosidase inhibitors, a series of novel hetarylcoumarins (3a-3j) were designed and synthesized through a facile multicomponent route where p-toluenesulfonic acid (PTSA) was explored as an efficient catalyst. These new scaffolds were further evaluated for their α-glucosidase inhibition potentials. All the derivatives exhibited good to excellent results which were comparable or even better than of standard drug acarbose. Of these compounds, a dihalogenated compound 3f was found to be the most effective one with IC50: 2.53±0.002µM. Molecular docking has predicted the plausible binding interactions of compounds 3f, 3g and 3j with α-glucosidase.

Green synthesis, inhibition studies of yeast α-glucosidase and molecular docking of pyrazolylpyridazine amines.

An efficient and environmentally benign simple fusion reaction of 3-chloro-6-(3,5-dimethyl-1H-pyrazol-1-yl)pyridazine (1a) or 3-chloro-6-(3,5-dimethyl-4-nitro-1H-pyrazol-1-yl)pyridazine (2a) with different aliphatic/aromatic amines have produced a series of novel pyrazolylpyridazine amines (4a-4c &5a-5m). All compounds exhibited moderate in vitro yeast α-glucosidase inhibition except m-chloro derivative 5g, which was found potent inhibitor of this enzyme with IC50 value of 19.27±0.005µM. The molecular docking further helped in understanding the structure activity relationship of these compounds including 5g.

In search of new α-glucosidase inhibitors: Imidazolylpyrazole derivatives.

Under three different reaction conditions (conventional heating, microwave irradiations and amino acid catalysis), a series of imidazolylpyrazoles (2a-2k) were synthesized in good to excellent yields from a mixture of three precursors: aryl(hetaryl)pyrazole-4-carbaldehydes (1a-1k), benzil and ammonium acetate. α-Glucosidase inhibition assay revealed a new class of highly potent agents wherein each compound displayed significant inhibitory potentials (in terms of percentage inhibition and relative IC50 values) as compared to that of the reference drug (Acarbose). Moreover, molecular modelling of most potent compounds 2h, 2j and 2k also helped in understanding the structure and activity relationship.

Discovery of indole-based tetraarylimidazoles as potent inhibitors of urease with low antilipoxygenase activity.

A series of tetraarylimidazoles (5A-5O) were prepared by one pot four component condensation reactions of 2-arylindole-3-carbaldehydes, substituted anilines, benzil and ammonium acetate in acetic acid. The synthesized compounds exhibited potent antiurease activity with IC50 values ranging from 0.12 ± 0.06 µM to 29.12 ± 0.18 µM as compared with thiourea. However, low inhibition profiles were observed for lipoxygenase. The data show that tetraarylimidazoles containing a substituted 2-penylindole have emerged as a new class of potent inhibitors of urease enzyme.

(4Z)-4-[(2E)-1-Hy-droxy-3-(3-nitro-phen-yl)prop-2-en-1-yl-idene]-3-methyl-1-(4-methyl-phen-yl)-1H-pyrazol-5(4H)-one.

In the title compound, C(20)H(17)N(3)O(4), the dihedral angles between the heterocyclic ring and the toluene and nitro-benzene rings are 4.21 (15) and 11.43 (14)°, respectively. The whole mol-ecule is close to planar (r.m.s. deviation for the 27 non-H atoms = 0.171 Å). Two S(6) rings are formed due to intra-molecular C-H⋯O and O-H⋯O hydrogen bonds. In the crystal, inversion dimers linked by pairs of C-H⋯O bonds generate R(2) (2)(10) loops and further C-H⋯O bonds link the dimers along the b-axis direction. There exist π-π inter-actions between the heterocyclic rings at a centroid-centroid distance of 3.7126 (10) Šand between the centroids of the benzene rings at a distance of 3.8710 (16) Å.

1,3-Diphenyl-1H-pyrazole-4-carbaldehyde.

There are four mol-ecules in the asymmetric unit of the title compound, C(16)H(12)N(2)O. The dihedral angle between the phenyl rings in the mol-ecules are 22.2 (2), 22.4 (2), 25.1 (3) and 41.9 (2)°. In the crystal, mol-ecules form dimers due to inter-molecular C-H⋯O hydrogen bonds, which result in one R(2) (2)(10) and two R(2) (1)(7) ring motifs. Weak aromatic π-π stacking [centroid-centroid separation = 3.788 (3) Å] and C-H⋯π inter-actions may also consolidate the packing.