Conic projection as manifold enable calculation dihedral θHnHn+1[deg] angles from differences between two atoms of carbon ΔδCnCn+1[ppm] in three steps or from only one atom of carbon δCn[ppm] in close relationships with tetrahedral φCn[deg] angles under 3-Sphere approach. Hopf fibration and Lie algebra ensuring calculation dihedral θHnHn+1[deg] angles from vicinal ϕ[deg] angle, angle results from vicinal coupling constant 3JHH[Hz]. Real Hopf fibration for calculation dihedral θHnHn+1[deg] angle in real space, and R16 octonionic Hopf fibration, double of quaternionic R7, for all cis, trans-ee, trans-aa stereochemistry, unreal space relative to calculated dihedral θHnHn+1[deg] angle. Continue “deformation”, homotopic behaviour h ⇆ h-1 characteristic for wave NMR data, probably a point of swich on Möbius band, in case of radius r of the cone inscribes on sphere at tangent point, calculated from height of cone h or inverse of height h-1, the tan function of h is equal with sin function of h-1. Dihedral θHnHn+1[deg] and tetrahedral φCn[deg] angles are from the trigonometric point of view under sin and tan function, or viceversa, homotopic behavior of NMR data under conic projection demonstrating that. Because the dihedral θHnHn+1[deg] angles are not found in first unit, for few vicinal coupling constants 3JHH[Hz], the rule accepted until now are explored taking in consideration other sets for building unit along the set C, respectively D, E and F, G, or vicinal angle ϕ[deg] with its three possible dihedral θHnHn+1[deg] angles in close relationships with tetrahedral φCn[deg] angles under seven sets unit. Building units through sets U or S calculated from sin or tan functions until calculated angles are almost equals with angles of unit U1 or S1, required long time for calculation.

Carprofen, a nonsteroidal anti-inflammatory drug (NSAID) derived from propanoic acid, is known for its analgesic and antipyretic properties. Although it has long been employed in veterinary medicine as an anti-inflammatory agent, its use in humans was discontinued shortly after its market launch due to costly raw materials, complex synthesis, and labor-intensive production processes-factors that made it less competitive compared with other NSAIDs. Despite this, the carprofen molecule remains a subject of significant scientific interest. Recent advancements in its synthesis have introduced simplified and more cost-effective methods, reigniting its potential for both novel applications and drug repurposing. Exciting new research is exploring carprofen's broader therapeutic possibilities, extending beyond its original anti-inflammatory role. Studies are investigating its efficacy in antimicrobial therapy-including antibiofilm, anticancer, antiviral, and anti-Alzheimer's applications-opening doors to a wealth of untapped possibilities. This review delves into these emerging areas, highlighting how carprofen's molecular structure and derivatives can be leveraged to expand its therapeutic reach. The literature review was conducted using four databases: Web of Science, ScienceDirect, Scopus, Embase, and Reaxys. The review focused on English-language original research and review articles, examining carprofen and its derivatives in terms of their synthesis methods as well as their use as small molecules in various therapeutic applications, both human and veterinary. With ongoing research pushing the boundaries of its potential, carprofen remains a promising candidate for innovation in drug development and treatment strategies.

Dihedral angles are predicted from vicinal coupling constant 3JHH[Hz] with 3-sphere approach, sphere or torus trigonometric equations of circle 1, 2 and circle inversion 3-5 for all cis-, trans-ee, trans-aa stereochemistry. The existence of circle inversion was demonstrated with conformational analysis on five and six membered rings. The sign and the stereochemistry result from vicinal coupling constant under trigonometric equations confirmed by algebraic equations, Hopf and Lie algebra theory. 3-Sphere, a hypersphere in 4D enable for all stereochemistry calculation dihedral angles under magnetic wave (NMR data -3JHH[Hz]), and all isomers from only one vicinal coupling constant.

Java Script programs for calculation dihedral angles from NMR data with manifold equations of 3-Sphere approach: rectangle, Villarceau circles of cyclide (Torus – Dupin Cyclide), polar equations, Euler-Conic. Manifolds are curves or surface in higher dimension used for calculation of dihedral angles under wave character of NMR data, carbon and/or proton chemical shift δXn[ppm] and vicinal coupling constant 3JHnHn+1[Hz]. 3-Sphere approach for calculation of the dihedral angles from NMR data in four steps: 1. Prediction, or more exactly calculation of the dihedral angles from vicinal coupling constant with trigonometric equations, 2. Calculation of the dihedral angles from manifold equations; 3. Building units from angle calculated with one of the manifold equations; 4. Calculation the vicinal coupling constant of the manifold dihedral angle. In this paper are presented Java Script programs of step 2 and from step 3 only the Java Script program for calculation of seven sets angles. The bond distances lCnCn+1[A0] between two atoms of carbon are under different polar equations (i.e. limaçons or cardioid, rose or lemniscale), our expectation was to find different manifold equations for calculation the best angle, differences are smaller but can be find sometimes a preferred one for a vicinal coupling constant. 3-Sphere approach has the advantages of calculation from vicinal angle or/and chemical shift the dihedral angle, tetrahedral angle and the bond distance lCnCn+1[A0], with application on conformational and configurational analysis.

The present study aimed to synthesize, characterize, and validate a separation and quantification method of new N-acyl thiourea derivatives (1a–1o), incorporating thiazole or pyridine nucleus in the same molecule and showing antimicrobial potential previously predicted in silico. The compounds have been physiochemically characterized by their melting points, IR, NMR and MS spectra. Among the tested compounds, 1a, 1g, 1h, and 1o were the most active against planktonic Staphylococcus aureus and Pseudomonas aeruginosa, as revealed by the minimal inhibitory concentration values, while 1e exhibited the best anti-biofilm activity against Escherichia coli (showing the lowest value of minimal inhibitory concentration of biofilm development). The total antioxidant activity (TAC) assessed by the DPPH method, evidenced the highest values for the compound 1i, followed by 1a. A routine quality control method for the separation of highly related compounds bearing a chlorine atom on the molecular backbone (1g, 1h, 1i, 1j, 1m, 1n) has been developed and validated by reversed-phase high-performance liquid chromatography (RP—HPLC), the results being satisfactory for all validation parameters recommended by the ICH guidelines (i.e., system suitability, specificity, the limits of detection and quantification, linearity, precision, accuracy and robustness) and recommending it for routine separation of these highly similar compounds.

Configurational and conformational analysis with 3-Sphere approach on selective iodination of α, β-methyl D-ribofuranose (2-α:2-β) with iodotriphenilphosphonium iodide complex [Ph3P+I]I- generated in situ, under RT, reflux, microwave and sonochemistry. Introduction of the unit and hypersphere trigonometric equations, under Hopf fibration and Lie algebra theories, on Lambert-Wu methods enable calculation of the dihedral angles from NMR data (13C chemical shift, vicinal coupling constant 3JHH[Hz]) and the ratio of anomers. The conformation/configuration at anomeric position is cis: trans with axial:axial 3-α:3-β (3JH1H2 3 or 4.5:0[Hz]) or equatorial:axial 3-α:3-β (3JH1H2 6 or 4.5:0[Hz]) as state based on dihedral angles θH1H2[deg], recorded carbon chemical shift δCn[deg] and VISION molecular models. The conformation of 3-β anomer is 3E, and in case of 3-α anomer 3E on Altona's map, the last having the succession of sign (+, -, -) with θH3H4α trans-ee, or alternatively 32T conformation having the succession of sign (-, +, -) with θH3H4α trans-aa. An equilibrium between 3E α and 32T α was confirmed by 3JH1H2 of 4.5[Hz], i.e. negative θH1H2α with 32T and equatorial OCH3, or positive θH1H2α with 3E and axial OCH3. The APT experiment (attached proton test) demonstrated the formation of tetrahydro 2H-pyran-2-ol as side product after selective iodination of methyl 5-deoxy-β-D-ribofuranoside 2-β.

New N-acyl thiourea derivatives with heterocyclic rings have been synthesized by first obtaining isothiocyanate, which further reacted with a heterocyclic amine, characterized by (FT-IR, NMR spectroscopy and FT-ICR) and tested for their in vitro antimicrobial, anti-biofilm and antioxidant activities to obtain a drug candidate in a lead-optimization process. From the tested compounds, those bearing benzothiazole (1b) and 6-methylpyridine (1d) moieties revealed anti-biofilm activity against E. coli ATCC 25922 at MBIC values of 625 µg/mL. Compound 1d exhibited the highest antioxidant capacity (~43%) in the in vitro assay using 1,1-diphenyl-2-picrylhydrazyl (DPPH). Considering the in vitro results, the highest anti-biofilm and antioxidant activities were obtained for compound 1d. Therefore, a reversed-phase high-performance liquid chromatography (RP-HPLC) method has been optimized and validated for the quantitative determination of compound 1d. The detection and quantitation limits were 0.0174 μg/mL and 0.0521 μg/mL, respectively. The R2 correlation coefficient of the LOQ and linearity curves were greater than 0.99, over the concentration range of 0.05 μg/mL–40 μg/mL. The precision and accuracy of the analytical method were within 98–102%, confirming that the method is suitable for the quantitative determination of compound 1d in routine quality control analyses. Evaluating the results, the promising potential of the new N-acyl thiourea derivatives bearing 6-methylpyridine moiety will be further investigated for developing agents with anti-biofilm and antioxidant activities.

A different synthesis was performed for obtaining nucleoside analogs with an oxabicyclo[3.3.0]octane frag-ment containing the omega-side chain of PG analog Clo-prostenol. The key intermedi-ate 1 was acetylated to the lactol group for activation in Vorbuggen glycosylation, concomitant with the acetylation of 5,11-hydroxyls. The route gave the acetylated nucleoside analogs together with their anomers in near 2 :1 ratio. All acetylated nucleosides and anomers were separated and the pure compounds were hydrolyzed in high yields. Uracil nucleoside was also hydrogeneted to the 13,14-double bond and we obtained a new nucleoside analog 7.

Dihedral angles with right sign and stereochemistry are calculated with 3-sphere method in four steps having as main manifold equations the rectangle geometries, skew or middle lines transformed in circles. Non-coplanar Villarceau circles (eq. 4) gives better result for all stereochemistry of iminocyclitols 1-5, since middle (eq. 6) and antirectangle circles (eq. 7) are the best solution for vicinal coupling constants 3JHH[Hz] of 3.1 (2-cis-D-H1H2), 4.8 (3-cis-L-H1H2) and 5.4 (1-cis-D-H2H3), 5.2 (4-cis-L-H2H3). Results pointing out the influence of carbon and proton chemical shift delta[ppm] on calculation of the dihedral angle 0HnHn+1[deg] in close relationships with vicinal coupling constant 3JHH[Hz], through the vicinal angle [deg]. 0An = 2x[(delta delta HnHn+1x delta delta CnCn+1)/2)x90]1/2: n=2, cis-ea, ae, trans-ee 0An = [(delta delta HnHn+1 x delta delta CnCn+1)/2)x90]1/2: n=1, trans-aa6,1 0An = 2x[90x(& UDelta;delta HnHn+1 + delta delta CnCn+1)/2]1/2, n=2, cis-ea,-ae, trans-ee 0An = [90x(delta delta HnHn+1 -& U delta delta CnCn+1)/2]1/2, n = 1, trans-aa6,1 [deg].

Hydrogenation of the 5,6-double bond of the 11-THP protected 13- dimethylacetal, without careful neutralization of the acidity of the Pd/C catalyst, conducted to the removal of the THP group with the consequence of no possibility to use selectively the 9- or 11-hydroxyl groups in the next step of prostaglandin synthesis. The selective protection of the 11-hydroxyl group of the hydrogenated compound 2 and good LPC was realized in 50% as pivalate and 52.4% as benzoate; the compound is key intermediate for synthesis of PGE1 analogs. The other pure separated compounds are also key intermediates for PGF1 analogs (9,11bis-esters, 6 and 9) or PGD1 (9-esters, 5 and 8).

The inactivation of prostaglandin (PG) and prostaglandin analogs (PGs) is realized with enzyme oxidation of the 15α-OH to the 15-keto group via the 15-PGDH pathway [...]

3-Sphere theory, a hypersphere in four dimensions, is applied for calculation dihedral angles with the right stereochemistry and sign in D, -L ribitol series from proton and carbon chemical shift (∆δ XnXn+1 [ppm], X = H, C) and vicinal coupling constant ( 3 J HnHn+1 [Hz]) with Java Script.A method in three steps, easy to calculate by hand or with Java Script program: 1. prediction of the dihedral angle only from 3 J HnHn+1 [Hz], 2. calculation the angle of set A with manifold equation (conic section, Villarceau circles) from chemical shift, 3. building of the seven sets unit or six sets units, from which is chose an angle almost equal with the predicted one having its stereochemistry and sign.Angles of set A and set B, relationships between vicinal angle and dihedral angle (X 0 -X 15 ) are introduced instead of polar angle and azimuthal angle in spherical coordinates (eq. 1 versus eq.3).Hopf coordinates, trigonometric equations, confirmed by algebraic equations are disclosed for all cis-ae/ea, trans-ee, trans-aa stereochemistry.Octonionic fibration S 7 →S 15 →S 8 in R 16 , with real fibration S 0 →S 1 →S 1 as unit, reassembles all possible stereochemistry gives by the HCCH fragment on two congruent disks, each centered on the perimeter of the other with equilateral triangles as vertices.Complex Hopf fibration in R 4 ensuring the calculation of the dihedral angle from vicinal angle and vice versa, demonstrating the relationships between sets A, B, C.

Relationships between vicinal angles, angles result from vicinal coupling constant (3)J(HH)[Hz], and tetrahedral angles of five membered ring iminocyclitols with ribitol stereochemistry are demonstrate with polyhedron and 3-sphere methods. Tetrahedral angles phi[deg] and internal angles gamma[deg] are calculated from C-13-NMR, or H-1-NMR chemical shift delta[ppm] in case of heteroatom, with energy-graph theory approach. The vicinal coupling constant can be calculated from one atom of carbon chemical shift delta(Cn)[ppm], and also the corresponding dihedral angle under 3-sphere approach.

3-Sphere approach is applied on prediction dihedral angle θHnHn+1[deg] only from vicinal coupling constant 3JHnHn+1[Hz] with Java script, in comparation with angles calculated from the differences between two atoms of carbon chemical shift (ΔδCnCn+1[ppm]) and Karplus equations. The trigonometric equations 1, 2 ensuring the right sign along the D-, L series rule.

Cancer is a rapidly growing disease of current era. Continuous research is going on in the direction to develop effective molecules for the treatment of the cancer. The new compounds such as 2,5-diaryl/heteroaryl-1,3,4-oxadiazoles were synthesized and evaluated for anticancer activity. The new 1,3,4-oxadiazole derivatives were obtained by the treatment of aromatic carboxylic acids, with different hydrazide derivatives in the presence of phosphorus oxychloride. Elemental analysis, IR and NMR spectral data confirmed the structures of the compounds. To analyze the antitumor effect of these new compounds, in vitro treatments were performed on two standardized human tumor cell lines, HT-29 (colon adenocarcinoma) and MDA-MB-231 (breast adenocarcinoma), treated with different concentrations of the compounds for different periods of time. The cytotoxic activity of the new compounds was assessed by the colorimetric MTS test. Flow cytometry assay was used to evaluate how compounds influence some processes such as the cell cycle or apoptosis in tumor cells. The analysis of the results shows that the compound with pyridine ring presented the best antitumor profile of the series, probably due to the presence of the pyridine ring next to the oxadiazole structure, acting differently on the two tumor cell lines. The obtained results support the antitumor effect of the analyzed compounds and encourage the extension of the study on other tumor cells in order to improve the anticancer activity and reduce the toxicological risks of the obtained compounds.