On a problem regarding coefficients of cyclotomic polynomials

Let an(k) be the coefficient of tk in the nth cyclotomic polynomial

     

Equilibrium and formation/dissociation kinetics of some Ln(III)PCTA complexes

The protonation constants () of 3,6,9,15-tetraazabicyclo[9.3.1]pentadeca-1(15),11,13-triene-3,6,9-triacetic acid (PCTA) and stability constants of complexes formed between this pyridine-containing macrocycle and several different metal ions have been determined in 1.0 M KCl at 25 degrees C and compared to previous literature values. The first protonation constant was found to be 0.5-0.6 log units higher than the value reported previously, and a total of five protonation steps were detected (log = 11.36, 7.35, 3.83, 2.12, and 1.29). The stability constants of complexes formed between PCTA and Mg2+, Ca2+, Cu2+, and Zn2+ were also somewhat higher than those previously reported, but this difference could be largely attributed to the higher first protonation constant of the ligand. Stability constants of complexes formed between PCTA and the Ln3+ series of ions and Y3+ were determined by using an "out-of-cell" potentiometric method. These values ranged from log K = 18.15 for Ce(PCTA) to log K = 20.63 for Yb(PCTA), increasing along the Ln series in proportion to decreasing Ln3+ cation size. The rates of complex formation for Ce(PCTA), Eu(PCTA), Y(PCTA), and Yb(PCTA) were followed by conventional UV-vis spectroscopy in the pH range 3.5-4.4. First-order rate constants (saturation kinetics) obtained for different ligand-to-metal ion ratios were consistent with the rapid formation of a diprotonated intermediate, Ln(H(2)PCTA)(2+). The stabilities of the intermediates as determined from the kinetic data were 2.81, 3.12, 2.97, and 2.69 log K units for Ce(H(2)PCTA), Eu(H(2)PCTA), Y(H(2)PCTA), and Yb(H(2)PCTA), respectively. Rearrangement of these intermediates to the fully chelated complexes was the rate-determining step, and the rate constant (k(r)) for this process was found to be inversely proportional to the proton concentration. The formation rates (k(OH)) increased with a decrease in the lanthanide ion size [9.68 x 10(7), 1.74 x 10(8), 1.13 x 10(8), and 1.11 x 10(9) M(-1) s(-1) for Ce(PCTA), Eu(PCTA), Y(PCTA), and Yb(PCTA), respectively]. These data indicate that the Ln(PCTA) complexes exhibit the fastest formation rates among all lanthanide macrocyclic ligand complexes studied to date. The acid-catalyzed dissociation rates (k1) varied with the cation from 9.61 x 10(-4), 5.08 x 10(-4), 1.07 x 10(-3), and 2.80 x 10(-4) M(-1) s(-1) for Ce(PCTA), Eu(PCTA), Y(PCTA), and Yb(PCTA), respectively.     

Disposable pipette extraction for the analysis of pesticides in fruit and vegetables using gas chromatography/mass spectrometry

Organochlorine, organophosphate pesticides and fungicides in fruits and vegetables were analyzed using disposable pipette extraction (DPX) followed by gas chromatography–mass spectrometry-selective ion monitoring (GC/MS-SIM). The intrinsic rapid mixing capabilities of DPX result in fast and efficient extractions, and eluates are concentrated by using minimal elution solvent volumes rather than solvent evaporation methods. Matrix-matched calibrations were performed with reversed phase mechanisms (DPX-RP), and the limits of detection (LOD) were determined to be lower than 0.1 μg/mL for all targeted pesticides in carrot and orange sample matrices. Coefficients of determination (r²) were greater than 0.995 for most studied pesticides. DPX-RP exhibited recoveries between 72 and 116% for nonpolar and slightly polar pesticides (log P > 2) with most of the recoveries over 88%. Only very polar pesticides (e.g., acephate, mathamidophos) were not extracted well using DPX-RP.     

Towards the rational design of MRI contrast agents: a practical approach to the synthesis of gadolinium complexes that exhibit optimal water exchange

The gadolinium(iii) complex of S-SSSS-NO(2)BnDOTMA exhibits water exchange kinetics that are optimal for use in high relaxivity or targeted contrast agents. However, the synthesis of this ligand is hampered by the steric encumbrance imparted upon the cyclen ring by the nitrobenzyl substituent. A relatively simple modification has been used to enable the synthesis of larger quantities of a bifunctional ligand that retains similar fast water exchange properties. The gadolinium complex of S-SSS-NO(2)BnDO3MA-1A is shown to retain the rapid water exchange kinetics characteristic of a twisted square antiprismatic (TSAP) coordination geometry (tau(M)= 6 +/- 0.4 ns).     

Design,synthesis and biological evaluation of 2,4‐diamino‐6‐methyl‐5‐substitutedpyrrolo[2,3‐d]pyrimidines as dihydrofolate reductase inhibitors

Nine novel nonclassical 2,4‐diamino‐6‐methyl‐5‐mioarylsubstituted‐ 7H ‐pyrrolo[2,3‐d]pyrimidines 2‐10 were synthesized as potential inhibitors of dihydrofolate reductase and as antitumor agents. The analogues contain various electron donating and electron withdrawing substituents on the phenylsulfanyl ring of the side chains and were synthesized from the key intermediate 2,6‐diamino‐6‐methyl‐7H‐pyrrolo[2,3‐d]‐pyrimidine, 14 . Compound 14 , was in turn obtained by chlorination of 4‐position of 2‐amino‐6‐methylpyrrolo[2,3‐d]pyrimidin‐4(3H)‐one, 16 followed by displacement with ammonia. Appropriately substituted phenyl thiols were appended to the 5‐position of 14 via an oxidative addition reaction using iodine, ethanol and water. The compounds were evaluated against rat liver, rat‐derived Pneumocystis, Mycobacterium avium and Toxoplasma gondii dihydrofolate reductase. The most potent and selective inhibitor, (2) has a 1‐naphthyl side chain. In this series of compounds electron‐withdrawing and bulky substituents in the side chain afford marginally active dihydrofolate reductase inhibitors. The single atom sulfur bridge in the side chain of these compounds is not conducive to potent dihydrofolate reductase inhibition.     

Stereochemistry of the allylation and crotylation reactions of alpha-methyl-beta-hydroxy aldehydes with allyl- and crotyltrifluorosilanes. Synthesis of anti,anti-dipropionate stereotriads and stereodivergent pathways for the reactions with 2,3-anti- and 2,3-syn-alpha-methyl-beta-hydroxy aldehydes

A new method for the stereoselective synthesis of the anti,anti-dipropionate stereotriad via the reaction of alpha-methyl-beta-hydroxy aldehydes with (Z)-crotyltrifluorosilane (24) is described. These reactions were designed to occur through bicyclic transition states (e.g., 31) in which the silane reagent is covalently bound to the beta-hydroxyl group of the aldehyde and the crotyl group is transferred intramolecularly. This methodology was used to synthesize the C(7)-C(16) segment (58) of zincophorin, which contains a synthetically challenging all-anti stereopentad unit. Surprisingly, 2,3-anti- and 2,3-syn-alpha-methyl-beta-hydroxy aldehydes react in a stereodivergent manner with 24: 2,3-anti-beta-hydroxy aldehydes give the targeted anti,anti-dipropionate adducts with high selectivity, but the reactions of 2,3-syn-beta-hydroxy aldehydes are poorly selective. The stereodivergent behavior of 2,3-syn- vs 2,3-anti-alpha-methyl-beta-hydroxy aldehydes is also exhibited in their reactions with the allyl- (68) and (E)-crotyltrifluorosilanes (27). Competition experiments performed with beta-hydroxy aldehydes 37a (anti) and the corresponding p-methoxybenzyl (PMB) ether 48, and between aldehyde 39 (syn) and the PMB ether 90, established that the 2,3-anti-beta-hydroxy aldehydes react predominantly through bicyclic transition states while the 2,3-syn aldehydes react predominantly through conventional Zimmerman-Traxler transition states. NMR studies established that both the 2,3-syn and the 2,3-anti aldehydes form stable, pentavalent silicate intermediates (98 and 100) with PhSiF(3), but chelated structures 99 and 101 could not be detected. The activation energies for the competing bicyclic and conventional Zimmerman-Traxler transition states were calculated by using semiemperical methods (MNDO/d). These calculations indicate that the stereodivergent behavior of the 2,3-syn-beta-hydroxy aldehydes and the 2,3-anti-beta-hydroxy aldehydes is due to differences in nonbonded interactions in the bicyclic transition states. Specifically, nonbonded interactions in the bicyclic transition states for the allylation/crotylation reactions of the 2,3-syn-beta-hydroxy aldehydes permits the traditional Zimmerman-Traxler transition states to be preferentially utilized.     

Synthesis of three carbon atom bridged 2,4‐diaminopyrrolo[2,3‐d]‐pyrimidines as nonclassical dihydrofolate reductase inhibitors

A series of seven nonclassical three carbon atom bridged 2,4‐diamino‐5‐substituted‐pyrrolo[2,3‐d]‐pyrirnidines 1a‐g were synthesized as potential inhibitors of dihydrofolate reductase. Selective oxidation of diols 7a‐g affords α‐hydroxy ketones 8a‐g. Subsequent condensation with malononitrile gave the requisite 2‐amino‐3‐cyano‐4‐substituted furan precursors 9a‐g. Cyclocondensation with guanidine in refluxing ethanol in one step affords the three carbon atom bridged 2,4‐diamino‐5‐substituted‐pyrrolo[2,3‐d]‐pyrimidines 1a‐g. Preliminary biological results indicated that these compounds showed moderate inhibitory activities against dihydrofolate reductases from Pneumocystis carinii, Toxoplasma gondii, Mycobacterium avium and rat liver with IC₅₀ values in the 0.66 μM ‐ 70.1 μM range and some compounds had marginal selectivity for T. gondii dihydrofolate reductase.