Inverse problems for Sturm-Liouville equations with boundary conditions linearly dependent on the spectral parameter from partial information

[[abstract]]Abstract.In this paper, we study the inverse spectral problems for Sturm–Liouville equations with boundary conditions linearly dependent on the spectral parameter and show that the potential of such problem can be uniquely determined from partial information on the potential and parts of two spectra, or alternatively, from partial information on the potential and a subset of pairs of eigenvalues and the normalization constants of the corresponding eigenvalues.[[notice]]補正完畢[[journaltype]]國外[[incitationindex]]SCI[[ispeerreviewed]]Y[[booktype]]紙本[[booktype]]電子版[[countrycodes]]DE

The enhancement of enantioselectivities for lipase-catalyzed reactions by using carbamates

The enantioselectivity of porcine pancreatic lipase-catalyzed resolution of 1-indanol was enhanced up to 3 fold in the presence of carbamates. The optimum incubation time for 4-nitrophenyl-N-hexyl carbamate and the enzyme was 18 h before this biocatalytic resolution. The optimum concentration of the inhibitor 4-nitrophenyl-N-hexyl carbamate in this resolution was 1 % mole equivalent of the substrate 1-indanol. (C) 1998 Elsevier Science Ltd. All rights reserved

Structure-reactivity probes for active site shapes of cholesterol esterase by carbamate inhibitors

4.4'-Biphenyl-di-N-butylcarbamate (1), (S)-1,1'-bi-2-naphthyl-2,2'-di-N-butylcarbama (S-2), (S)-1,1'-bi-2-naphthyl-2-N-butylcarbamate-2'-butyrate (S-3), 2,2'-biphenyl-di-N-butylcarbamate (4), 2,2'-biphenyl-2-N-octadecylcarbamate-2'-N-octylcarbamate (5), 2,2'-biphenyl-2-N-octadecylcarbamate-2'-N-phenylcarbamate (6), 2,2'-biphenyl-2-N-butylcarbamate-2'-butyrate (7), 2,2'-biphenyl-2-N-butylcarbamate-2'-ol (8), 2,2'-biphnyl-2-N-octylcarbamate-2'-ol (9), (R)-1,1'-bi-2-N-naphthyl-2-butylcarbamate-2'-ol (R-10), and glyceryl-1,2,3-tri-N-butylcarbarnate (11) are prepared and evaluated for their inhibition effects on porcine pancreatic cholesterol esterase. All inhibitors are irreversible inhibitors of the enzyme. Carbamates 1-3 and 7-10 are the first alkyl chain and esteratic binding site-directed irreversible inhibitors due to the fact that the reactivity of the enzyme is protected by the irreversible inhibitor, trifluoroacetophenone in the presence of these carbamates. Carbamate 1 is the least potent inhibitor for the enzyme probably due to the fact that the inhibitor molecule adopts a linear conformation and one of the carbamyl groups of the inhibitor molecule covalently interacts with the first alkyl chain binding site of the enzyme while the other carbamyl group of the inhibitor molecule exposes outside the active site. With near orthogonal conformations at the pivot bond of biaryl groups, one carbamyl group of carbamates S-2, S-3, and R-10 covalently binds to the first alkyl chain binding site of the enzyme while the other carbamyl, butyryl, or hydroxy group can not bind covalently to the second alkyl chain binding site probably due to the orthogonal conformations. Carbamates 4-9 and 11 are very potent inhibitors for the enzyme probably due to the fact that all these molecules freely rotate at the pivot bond of the biphenyl or glyceryl group and therefore can fit well into the bent-shaped first and second alkyl chains binding sites of the enzyme. Although, carbamates 4-6 and 11 are irreversible inhibitors of cholesterol esterase, the enzyme is not protected but further inhibited by trifluoroacetophenone in the presence of these carbamates. Therefore, carbamates 4-6 and 11 covalently bind to the first alkyl chain binding site of the enzyme by one of the carbamyl groups and may also bind to the second alkyl chain binding site of the enzyme by the second carbamyl group. Besides the bent-shaped conformation, the inhibition by carbamate 6 is probably assisted by a favorable pi-pi interaction between Phe 324 at the second alkyl chain binding site of the enzyme and the phenyl group of the inhibitor molecule. For cholesterol esterase, carbamates 8-10 are more potent than carbamates S-2, 4, and 5 probably due to the fact that the inhibitor molecules interact with the second alkyl chain binding site of the enzyme through a hydrogen bond between the phenol hydroxy group of the inhibitor molecules and the His 435 residue in that site. (C) 1999 Published by Elsevier Science B.V. All rights reserved

Structure-reactivity relationships for the inhibition mechanism at the second alkyl-chain-binding site of cholesterol esterase and lipase

Alkyl-N-phenyl carbamates (2-8) (see Figure 1), alkyl-N-phenyl thiocarbamates (9-15), 2,2'-biphenyl-2-ol-2'-N-substituted carbamates (16-23), and 2, 2'-biphenyl-2-N-octadecylcarbamate-2'-N-substituted carbamates (24-31) are prepared and evaluated for their inhibition effects on porcine pancreatic cholesterol esterase and Pseudomona species lipase. All inhibitors are characterized as transient or pseudo substrate inhibitors for both enzymes. Both enzymes are not protected from inhibition and further inactivated by carbamates 2-8 and thiocarbamates 9-15 in the presence of trifluoroacetophenone. Therefore, carbamates 2-8 and thiocarbamates 9-15 are exceptions for active site binding inhibitors and are probably the second alkyl-chain binding-site-directed inhibitors for both enzymes. The inhibition data for carbamates 2-8 and thiocarbamates 9-15 are correlated with the steric constant, E-s, and the hydrophobicity constant, pi; however, the inhibition data are not correlated with the Taft substituent constant, sigma*. A comparison of the inhibition data for carbamates 2-8 and thiocarbamates 9-15 toward both enzymes indicates that thiocarbamates 9-15 are more potent inhibitors than carbamates 2-8. A comparison of the inhibition data for cholesterol esterase and Pseudomona species lipase by carbamates 2-8 or thiocarbamates 9-15 indicates that cholesterol esterase is more sensitive to the E-s and pi values than Pseudomona species lipase. The negative slope values for the logarithms of inhibition data for Pseudomona species lipase by carbamates 2-8 and thiocarbamates 9-15 versus E-s and pi indicate that the second alkyl-chain-binding site of Pseudomona species lipase is huge, hydrophilic, compared to that of cholesterol esterase, and prefers to interact with a bulky, hydrophilic inhibitor rather than a small, hydrophobic one. On the contrary, the second alkyl-chain-binding site of cholesterol esterase prefers to bind to a small, hydrophobic inhibitor. Both enzymes are protected from inhibition by carbamates 16-23 in the presence of trifluoroacetophenone. Therefore, carbamates 16-23 are characterized as the alkyl chain binding site, esteratic site oxyanion active site directed pseudo substrate inhibitors for both enzymes. Both enzyme inhibition data for carbamates 16-22 are well-correlated with sigma* alone. The negative rho* values for these correlations indicate that the serine residue of both enzymes and carbamates 16-22 forms the tetrahedral species with more positive charges than inhibitors and the enzymes and follow the formation of the carbamyl enzymes with more positive charges than the tetrahedral species. Carbamates 24-31 are also exceptions for active site binding inhibitors and probably the second alkyl chain binding site-directed inhibitors for both enzymes. However, the enzyme inhibition constants for carbamates 24-31 are correlated with values of sigma*, E-s, and pi. The negative rho* values for these correlations indicate that both enzymes and carbamates 24-31 form the tetrahedral species with more positive charges than inhibitors and the enzymes and follow the formation of the carbamyl enzymes with more positive charges than those tetrahedral species. Therefore, carbamates 24-31 may bind to both the active sites and the second alkyl chain binding site and follow the evacuation of the active sites. A comparison of the rho* values for cholesterol esterase and Pseudomona species lipase by carbamates 24-31 indicates that cholesterol esterase is much more sensitive to the sigma* values than Pseudomona species lipase. The negative sensitivity values, 9, for the cholesterol esterase inhibitions by carbamates 24-31 indicate that the enzyme prefers to bind to a bulky carbamyl group rather than bind to a small one. The hydrophobicity of carbamates 24-31 does not play a major role in both enzyme inhibitions

Recovering the Sturm-Liouville Operator with Singular Potential Using Nodal Data

[[abstract]]The paper deals with the Sturm-Liouville operator with singular potential. We assume that the potential is a sum of an a priori known distribution from a certain class and an unknown sufficiently smooth function. The inverse problem is to recover the operator using zeros of eigenfunctions (nodes) as an input data. For this inverse problem we obtain a procedure for constructing the solution.[[notice]]補正完畢[[journaltype]]國外[[incitationindex]]SCI[[ispeerreviewed]]Y[[booktype]]紙本[[booktype]]電子版[[countrycodes]]CH

Demonstration of continuous supercritical carbon dioxide anti-solvent purification and classification of nano/micro-sized precipitates of algal zeaxanthin from Nannochloropsis oculata

This study examined time dependent continuous supercritical anti-solvent (SAS) recrystallization applied for purifying and generating zeaxanthin rich particulates from micro-algal Nannochloropsis oculata. Feed solutions varied from 0.4 to 1.2 mg/ml subjected into a 250 ml SAS crystallizer to yield a few classifications of nano- or micro-sized purified precipitates corresponding to different recrystallization time zones. The effect of operational conditions on amount, recovery of the zeaxanthin and mean size, morphology of the precipitates was obtained from experimentally designed SAS process. The mean size of particles falls within several hundreds of nanometers and the content of zeaxanthin in the particulates range from 65 to 71%, which relies highly upon the recrystallization time. This work demonstrated an environmental benign process in producing nano- or micro-sized particles containing rich-zeaxanthin from algal solution by using supercritical anti-solvent within minutes. (C) 2010 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved

Purification of algal anti-tyrosinase zeaxanthin from Nannochloropsis oculata using supercritical anti-solvent precipitation

This work investigated the changes in content of algal zeaxanthin in submicronized precipitates generated from the supercritical anti-solvent (SAS) process of extracting microalgae Nannochloropsis oculata. Following a reverse phase elution chromatography, the particulates were successfully generated from feed solutions containing zeaxanthin that ranged from 0.4 to 0.8 mg/mL by a SAS process. The precipitation condition was set at 323 K and pressures ranged from 10 to 20 MPa. Experimental results of a three-factor center composite response surface method for the SAS process indicated that the size of the precipitates was significantly affected by the flow rate of carbon dioxide. The purity of zeaxanthin increased with increasing solvent flow rate and with reducing solution concentration. The recovery of zeaxanthin and the morphology of the precipitates was also examined. The content of zeaxanthin in sub-micronsized precipitates increased from 485.9(48.6%) to 673.7 mg/g (67.4%). This work demonstrates that elution chromatography coupled with a SAS process is an environmentally benign method to recover anti-tyrosinase zeaxanthin from Nannochloropsis oculata as well as to generate submicrosized precipitates of the purest zeaxanthin from algal solutions. (C) 2010 Elsevier B.V. All rights reserved

Supercritical carbon dioxide anti-solvent process for purification of micronized propolis particulates and associated anti-cancer activity

This study elucidates the supercritical carbon dioxide (SC-CO(2).) anti-solvent micronization of Brazilian propolis particulates that contain the bioactive compound, 3,5-diprenyl-4-hydroxycinnamic acid (DHCA). The effects of the concentration of propolis solution and flow rate of CO(2) on purity, recovery and mean particle size of DHCA-rich particulates are studied using a two-factor central composite response surface methodology. Experimental results indicate that the purity of DHCA increases as the CO(2) flow rate decreases. The mean particle size increases as the feed concentration exceeds 27 mg/mL The growth of human colon (Colo 205) and breast (MDA-MB-231) cancer cells that were treated with these SC-CO(2) precipitates was inhibited at concentrations from 25 to 250 mu g/mL This work demonstrates that the SC-CO(2) anti-solvent micronization of the propolis solution, activated by these DHCA-rich precipitates, is a feasible means of inhibiting the growth of human colon and breast cancer cells. (C) 2009 Elsevier B.V. All rights reserved