Higher-Order Cyclodextrin Complexes: The Naphthalene System

Naphthalene excited dimer (excimer) fluorescence is observed in the presence of β- and γ-cyclodextrin (CD) at elevated naphthalene (NAP) concentrations (100 μM) but not at low NAP concentrations (5 μM). This is attributed to formation of 2:2 CD:NAP complexes in the former situation. Complexes of NAP with hydroxypropyl β-CD are exclusively 1:1 and no excimer emission is observed. Complexes of NAP with α-CD do not show excimer emission either but the complex stoichiometry is 2:1 CD:NAP in this case. The formation constants for both the 1:1 and 2:2 β-CD:NAP complexes have been determined and they have been found to depend on the ionic strength of the salting out agent NaCl. K_1:1 = 377 ± 35 M^-1 in the absence of salt and 657 ± 60 M^-1 at 1 M NaCl. The corresponding values for K_2:2 are (1.0 ± 0.2) × 10⁴ and (4.0 ± 0.5) × 10⁴ M^-1, respectively. Stern-Volmer fluorescence quenching studies of the 1:1 and 2:2 species by water-based quenchers (NaI and CsBr) show that both types of complexes protect the fluorophore from the quencher. However, the more completely encapsulated NAP in the 2:2 complex is protected to a greater extent. This is also the case for the 2:2 γ-CD:NAP complex. This protective effect is reflected in the observed rate constants for NAP quenching. For example, k_Q = 7.1 × 10⁹ M^-1 s^-1 for NaI in the absence of CD. This is reduced to 2.1 × 10⁹ M^-1 s^-1 for the 1:1 complex and 1.2 × 10⁹ M^-1 s^-1 for the 2:2 complex when 10 mM β-CD is present. A similar pattern is observed for CsBr as quencher. The 2:2 complexes are disrupted in the presence of additives such as linear alcohols and surfactants. The implications of these results for application of CDs for drug stabilization are discussed.     

Sorption of phenols by single and mixed cyclodextrin polymers

Cyclodextrin (CD) hydrogels were synthesized by a crosslinking reaction with the same cyclodextrin/epichlorohydrin mole ratio (1/11) using αCD, βCD, γCD, and 50:50 mixtures of α/βCD and β/γCD. In order to investigate the sorption capacity of these hydrogels to different solutes, five model molecules have been selected: phenol, 3-nitrophenol, 4-nitrophenol, 1-naphthol, and the antiinflamatory drug diflunisal. The amounts sorbed have been related to the different affinities of the solutes. 1-naphthol shows the highest affinity for these polymers, especially in the case of sorbents containing βCD. The sorption is considerably poorer for phenol than for its nitro derivatives. The two structural isomers 3- and 4-nitrophenol show significant differences in their affinities towards αCD, βCD and α/βCD. Finally, in the case of diflunisal, a bulkier model molecule, remarkable differences were found on the sorption behaviour by polymers whose cyclodextrins have a similar affinity for this solute (βCD, γCD, and β/γCD).     

Solubility and Kinetic Release Studies of Naproxen and Ibuprofen in Soluble Epichlorohydrin-β-cyclodextrin Polymer

Naproxen (NAP) and ibuprofen (IBU) are poor water soluble anti-inflammatory drugs. A water-soluble epichlorohydrin-β-cyclodextrin polymer (β-CDEPI) was synthesized in a highly basic aqueous solution and at a molar ratio β-CD/EPI of 1:12. Drug solubility and kinetic release of NAP and IBU from the inclusion complexes they form with β-CDEPI as host was studied. Water solubility for both drugs in the presence of this polymer increased (NAP 0.28 mmol and IBU 0.40 mmol per gram of β-CDEPI). The apparent inclusion constants for both drugs in β-CDEPI were calculated from the solubility-phase diagrams with K_incl values of 4300 ± 100 L.mol^? 1 for NAP and 5100 ± 300 L.mol^? 1 for IBU. Kinetic release of Ibuprofen gave a pure Fick trend (t^1/2) behavior. However, for Naproxen a zero order was obtained (t). These results indicate that the nature and bulkiness of the drugs are ruling these kinetic behaviors in the environment of a highly branched polymer.     

Synthesis of an arabinogalactan-type octa- and two isomeric nonasaccharides. Suitable tuning of protecting groups

An arabinogalactan-type double-branched octa- and two isomeric nonasaccharides were synthesized using the (2-naphthyl)methyl (NAP) and the acid sensitive but base stable (methoxydimethyl)methyl (MIP) protecting groups. The β-(1→6)-linked hexagalactan skeleton was synthesized having a benzyl and a (2-naphthyl)methyl (NAP) group at positions 2 of the second and the penultimate galactopyranosyl units, and this made possible sequential introduction of α-l-arabinofuranosyl or α-l-arabinofuranosyl-(1→5)-α-l-arabinofuranosyl side chains.     

Poly(β-amino acid)s. IV. Synthesis and conformational properties of poly(α-isobutyl-L-aspartate)

Poly(α-isobutyl-L -aspartate) was prepared by the polycondensation reaction of p-nitrophenyl ester of α-isobutyl-L -aspartate and the conformation of the poly(β-amino acid) was investigated by X-ray diffraction, polarized infrared, circular dichroism (CD), optical rotatory dispersion (ORD), and NMR spectroscopy. α-Isobutyl β-p-nitrophenyl-L -aspartate hydrochloride and hydrobromide were used as monomers and dimethylformamide, chloroform, and chlorobenzene, as solvents. A high-molecular-weight polymer with [η] 1.0 dl/g (dichloroacetic acid, 25°C) was formed in the polymerization of the hydrochloride in chloroform at 25°C. The X-ray diagram and polarized infrared spectrum of the stretched polymer film obtained from a chloroform solution suggested a cross-β-form as the most probable structure in the solid state. The CD spectra of the polymer in a 2,2,2-trifluoroethanol (TFE) solution and its film cast from the solution showed a peak at 205 nm and a trough at 190 nm which were assigned to a β-structure. The polymer was associated in chloroform. The NMR and ORD spectra in chloroform were similar to those in TFE, which suggests that the polymer also exists in the β-structure in chloroform. The addition of small amounts of dichloroacetic acid and sulfuric acid to chloroform and TFE solutions, respectively, destroyed the β-structure. A random copolymer of α-isobutyl-L -aspartate with β-alanine was also prepared by polycondensation reaction. The copolymer apparently did not form an ordered structure in the solid state or in solution.     

Interaction of naproxen amphiphilic derivatives with biomembrane models evaluated by differential scanning calorimetry and Langmuir-Blodgett studies

Anti-inflammatory drugs represent a potential new strategy for the treatment of Alzheimer's disease (AD). The ability to cross the blood-brain barrier and to reach brain tissues is a critical point for these drugs and is strictly related to their lipophilicity. Naproxen (NAP) is a non-steroidal anti-inflammatory drug (NSAIDs) under active investigation for AD. To improve its lipophilic character, NAP was conjugated through a diethylamine spacer (EDA) to lipoamino acids (LAA), α-amino acids containing a long alkyl side chain, to obtain the NAP-EDA-LAA10 and NAP-EDA-LAA14 prodrugs. The interaction of NAP and prodrugs with dimyristoylphosphatidylcholine phospholipids, forming either multilamellar vesicles or monolayers (at the air/water interface) and used as biomembrane models, was studied by differential scanning calorimetry and Langmuir-Blodgett techniques. Experimental data showed that NAP conjugation with LAA residues was able to enhance the drug interaction with such biomembrane models.     

Investigation of Drug Nanoparticle Formation by Co-grinding with Cyclodextrins: Studies for Indomethacin, Furosemide and Naproxen

Drugs with poor water solubility were co-ground with cyclodextrins (CDs) to create nanoparticles with improved solubility characteristics. Indomethacin (IDM), furosemide (FRM) and naproxen (NAP) were co-ground with β-CD at the molar ratio of 2:1 (CD:drug). Co-grinding of a drug with CD resulted in not only the formation of drug nanoparticles but also the solubilization of the drug by inclusion complex formation with CD in aqueous media. The nanoparticle fraction of IDM, and FRM from ground mixtures prepared with β-CD was as high as 60–70% while the solubilization fraction was less than 10%. In contrast, β-CD–NAP ground mixture showed a large fraction, 48%, for drug solubilization and only 4% for nanoparticle formation. Furosemide ground mixtures prepared with α-CD, β-CD and γ-CD showed comparatively high nanoparticle fraction while the solubilization fraction was around 10%. Both the nanoparticle fraction and the solubilization fraction were greater in the IDM–β-CD system than those in γ-CD and α-CD systems. The nanoparticle formation of NAP depended on the types of CD used as a co-grinding additive. Naproxen nanoparticles could be prepared by co-grinding NAP and α-CD, while the solubilization of NAP tended to improve when β-CD or γ-CD was used.     

Macroscopic observations of molecular recognition: discrimination of the substituted position on the naphthyl group by polyacrylamide gel modified with β-cyclodextrin

Macroscopic molecular recognition observations were realized using polyacrylamide-based gels modified with α-cyclodextrin (α-CD), β-cyclodextrin (β-CD), 1-naphthylmethyl (1Np), and 2-naphthylmethyl (2Np) moieties, which are denoted as αCD(x)-gel, βCD(x)-gel, 1Np(y)-gel, and 2Np(y)-gel, where x and y indicate the mol % of CD and Np moieties, respectively. The αCD(5)-gel did not adhere to either the 1Np(5)-gel or 2Np(5)-gel, whereas the βCD(5)-gel interacted with both to form alternating or checkered assemblies. Although the difference in the association constants of β-CD for the model polymers was small, the βCD(x)-gel successfully discriminated between 1Np(y)-gel and 2Np(y)-gel at the appropriate x and y.     

Polycaprolactone and poly-β-cyclodextrin polymer blend: a Biopolymers composite film for drug release

Nowadays, biomedical films containing drug carriers are preferred over conventional ones, since the protection of the injury and the therapy is joined within a single device. In the current work, we prepared polycaprolactone (PCL) composite films with β-cyclodextrin (βCD) or its epichlorohydrin crosslinked polymer (βCDP) as ibuprofen (Ibu) drug carrier. The composite films were prepared at different PCL/additive ratios (2, 5, 10 and 20 wt%). ATR-FTIR spectroscopy and water contact angle (WCA) measurements indicated a scarce presence of the additives on the surface. Cross-section scanning electron micrographs showed the presence of aggregates corresponding to βCD and βCDP in the inner regions of the films. The incorporation of βCD and βCDP into the PCL films did not affect their thermal properties as was determined from differential scanning calorimetry (DSC). PCL-films with 10 wt% of the inclusion complexes Ibu@βCD and Ibu@βCDP were prepared and the release studies were performed. At pH?=?7.2, PCL-Ibu@βCDP composite film released 55% of Ibu within the first six hours; eight times the amount released by PCL-Ibu@βCD within the same time interval. A plausible mechanism for ibuprofen release is discussed based on the cross-section SEM micrographs of composite films.

     

Drug loading in cyclodextrin polymers: dexamethasone model drug

In pharmaceutical formulations cyclodextrins (CDs) are used to improve the aqueous solubility, stability, dissolution rate, bioavailability and/or local tolerance of drugs. Moreover, water-soluble polymers can be used to stabilize drug/CD complexes through formation ternary complexes. Alternative approach is to use CD-polymers, which can both enhance the aqueous solubility of a drug and result in sustained drug release. The aim of this work was to compare the solubilizing effects of ternary drug/CD/polymer complexes with two novel high molecular weight CD-polymers, i.e. poly(ethylene glycol) based ??-cyclodextrin (??CD) polymer (PEG/??CD) and epichlorohydrin-??-cyclodextrin polymer (EPI/??CD) using dexamethasone (Dex) as a model drug, as well as the drug loading capacity of those selected CD-polymers. Hydroxypropyl methylcellulose and carboxymethylcellulose sodium salt were shown to have negligible effect on the solubilizing efficacy of ??CD while hexadimethrine bromide increases the solubilization efficacy. The stability of the polymers was tested and it was adequate for the experimental conditions used. The solubilization efficacy of both CD-polymers was higher than that of the parent ??CD and these ??CD based polymers are able to load greater amount of Dex than the parent ??CD.     

Production of Cyclodextrins from Cornstarch Granules in a Sequential Batch Mode and in the Presence of Ethanol

The influence of Toruzyme? cyclomaltodextrin glucanotransferase concentration and the presence of ethanol have been studied for the production of α-, β-, and γ-cyclodextrins (CDs) from 15% (w/v) cornstarch, at 65 °C and pH 6, with the aim of increasing CD yield. The selected concentrations for a single batch reactor were 10% (v/v) ethanol and 0.1% (v/v) enzyme, yielding after 12 h, 37% total CDs, of which 52.2% was α-CD, 38.8% β-CD, and 9.0% γ-CD. The enzyme specific activities per unit mass of protein for producing α-, β-, and γ-CD were 37.25, 19.61, and 8.63 U mg(-1), respectively. Total CD yield per milliliter of enzyme was 55 g. To increase CD yield per enzyme charge and thus reduce costs, the production of CDs was tested with two sequential batches in which a single enzyme charge was used. At the end of the first batch, the enzyme was adsorbed either on 65 °C pretreated starch granules or on raw starch, and a second batch was run with this material. The best result, in this case, was obtained for pretreated starch, increasing total CD produced by 57.4%, with 53.2% α-CD, 36.1% β-CD, and 10.7% γ-CD. CD yield per milliliter of enzyme was then 87 g.     

β‐Cyclodextrin‐Platinum Nanoparticles/Graphene Nanohybrids: Enhanced Sensitivity for Electrochemical Detection of Naphthol Isomers

Naphthol isomers, including α‐naphthol (α‐NAP) and β‐naphthol (β‐NAP), are used widely in various fields and are harmful to the environment and human health. The qualitative and quantitative determination of naphthol isomers is therefore of great significance. Herein, β‐cyclodextrin (β‐CD)‐platinum nanoparticles (Pt NPs)/graphene nanosheets (GNs) nanohybrids (β‐CD‐PtNPs/GNs) were prepared for the first time using a simple wet chemical method and characterized by atomic force microscopy, transmission electron microscopy, Fourier transform infrared spectroscopy, and electrochemical methods, and then applied successfully in the ultrasensitive electrochemical detection of naphthol isomers. The results show that the oxidation peak currents of naphthol isomers obtained at the glassy carbon (GC) electrode modified with β‐CD‐PtNPs/GNs are much higher than those at the β‐CD/GNs/GC, PtNPs/GNs/GC, GNs/GC, and bare GC electrodes. Additionally, compared with other electrochemical sensors developed previously, the proposed electrode results in improved detection limits of about one order of magnitude for α‐NAP (0.23 nM ) and three orders of magnitude for β ‐NAP (0.37 nM ).     

Tuning the cavity of cyclodextrins: altered sugar adaptors in protein pores

Cyclodextrins (CDs) have been widely used in host-guest molecular recognition because of their chiral and hydrophobic cavities. For example, β-cyclodextrin (βCD) lodged as a molecular adaptor in protein pores such as α-hemolysin (αHL) is used for stochastic sensing. Here, we have tuned the cavity and overall size of βCD by replacing a single oxygen atom in its ring skeleton by a disulfide unit in two different configurations to both expand our ability to detect analytes and understand the interactions of βCD with protein pores. The three-dimensional structures of the two stereoisomeric CDs have been determined by the combined application of NMR spectroscopy and molecular simulation and show distorted conformations as compared to natural βCD. The interactions of these synthetic βCD analogues with mutant αHL protein pores and guest molecules were studied by single-channel electrical recording. The dissociation rate constants for both disulfide CDs from the mutant pores show ～1000-fold increase as compared to those of unaltered βCD, but are ～10-fold lower than the dissociation rate constants for βCD from wild-type αHL. Both of the skeleton-modified CDs show altered selectivity toward guest molecules. Our approach expands the breadth in sensitivity and diversity of sensing with protein pores and suggests structural parameters useful for CD design, particularly in the creation of asymmetric cavities.     

Thermosensitive mucoadhesive gel formulation loaded with 5-Fu: cyclodextrin complex for HPV-induced cervical cancer

Human Papilloma Virus (HPV) infections are the major cause of cervical cancers. To achieve a better therapeutic efficacy and patient compliance in the treatment for HPV-induced cervical cancers, anticancer agent 5-fluorouracil has been formulated in a vaginal gel using the thermosensitive polymer Pluronic^® F127 together with alternative mucoadhesive polymers e.g., hyaluronic acid, Carbopol 934 and hydroxypropylmethylcellulose. To increase its aqueous solubility and to achieve the complete release of 5-FU from the gel, the drug was incorporated as its inclusion complex with 1:1 molar ratio with either β-cyclodextrin or hydroxypropyl-β-cyclodextrin. Following the characterization of drug:CD complexes, thermosensitive gel formulations containing different mucoadhesive polymers and the drug in free or complexed form were characterized in vitro by determining the gelation temperature and the rheological behavior of different formulations along with the in vitro release profiles of these formulations in pH 5.5 citrate buffer. It was observed that complexation with cyclodextrin accelerated the release of 5-FU with the exception of formulation containing Carbopol 934 as mucoadhesive polymer. As far as rheological properties are concerned, favorable thermosensitive in situ gelling properties were obtained with formulations containing HPMC as mucoadhesive polymer. Complete release of 5-FU from gels were obtained with both complexes of β-CD and HP-β-CD and cytotoxicity studies against HeLa human cervical carcinoma cells demonstrated that 1% 5-FU:CD complexes were equally effective as 1% free 5-FU indicating better therapeutic efficacy with lower dose.     

Nucleic-Acid Analogs with Restricted Conformational Flexibility in the Sugar-Phosphate Backbone (‘Bicyclo-DNA’). Part 5. Synthesis,Characterization, and Pairing Properties of Oligo-α-D-(bicyclodeoxynucleotides) of the Bases Adenine and Thymine (α-Bicyclo-DNA)

A conformational analysis of the (3′S,5′R)-2′-deoxy-3′,5′-ethano-α-D -ribonucleosides (a-D-bicyclodeoxynucleosides) based on the X-ray analysis of N⁴-benzoyl-α-D -(bicyclodeoxycytidine) 6 and on ¹H-NMR analysis of the α-D -bicyclodeoxynucleoside derivatives 1 - 7 reveals a rigid sugar structure with the furanose units in the l′-exo/2′-endo conformation and the secondary OH groups on the carbocyclic ring in the pseudoequatorial orientation. Oligonucleotides consisting of α-D -bicyclothymidine and α-D -bicyclodeoxyadenosine were successfully synthesized from the corresponding nucleosides by phosphoramidite methodology on a DNA synthesizer. An evaluation of their pairing properties with complementary natural RNA and DNA by means of UV/melting curves and CD spectroscopy show the following characteristics: i) α-bcd(A₁₀) and α-bcd(T₁₀) (α = short form of α-D )efficiently form complexes with complementary natural DNA and RNA. The stability of these hybrids is comparable or slightly lower as those with natural β-d(A₁₀) or β-d(T₁₀)( β = short form ofβ-D ). ii) The strand orientation in α-bicyclo-DNA/β-DNA duplexes is parallel as was deduced from UV/melting curves of decamers with nonsymmetric base sequences. iii) CD Spectroscopy shows significant structural differences between α-bicyclo-DNA/β-DNA duplexes compared to α-DNA/β-DNA duplexes. Furthermore, α-bicyclo-DNA is ca. 100-fold more resistant to the enzyme snake-venom phosphodiesterase with respect to β-DNA and about equally resistant as α-DNA.     

Modelling of molecular interactions and inclusion phenomena in substituted β-cyclodextrin: From simple probes to proteins

The ability of β-cyclodextrin (βCD) to form stable complexes with α-interferon was investigated. By using simple molecular mechanics approach interaction energy profiles of simple probes passing the center of βCD ring cavity along the main molecular symmetry axis were evaluated first. A computational study of host-guest inclusion complexes between βCD and L-α-aminoacids and some selected pentapeptides was also carried out and aimed at understanding the nature of the driving forces and mechanism, leading to their formation. Relative complexation energies for the complexes and the solvation Gibbs free energies for single L-α-aminoacids were calculated. Both the aminoacid residue inside the βCD cavity and neighbouring residues were found to contribute to the stabilization of βCD complexes with the side-chain of aminoacids present on the surface of α-interferon. The most appropriate number of host βCD molecules for the encapsulation in the first shell of one α-interferon molecule resulted to be 25.     

Electrospinning of cyclodextrin functionalized polyethylene oxide (PEO) nanofibers

By means of the electrospinning technique we have successfully synthesized cyclodextrin (CD) functionalized polyethylene oxide (PEO) nanofibers (PEO/CD) with the ultimate goal to develop functional nanowebs. Three different types of CDs; α-CD, β-CD and γ-CD are incorporated individually in electrospun PEO nanofibers. The aqueous solutions containing different amount of PEO (3%, 3.5% and 4% (w/v), with respect to solvent) and CDs (25% and 50% (w/w), with respect to PEO) are electrospun and bead-free nanofibers are obtained. The presence of the CDs in the PEO solutions is found to facilitate the electrospinning of bead-free nanofibers from the lower polymer concentrations and this behavior is attributed to the high conductivity and viscosity of the PEO/CD solutions. The presence of CDs in the electrospun PEO nanofibers is confirmed by Fourier transform infrared (FTIR) spectroscopy studies. The 2-D X-ray diffraction (XRD) spectra of PEO/CD nanowebs did not show any significant diffraction peaks for CDs indicating that the CD molecules are distributed within the polymer matrix without any phase separated crystalline aggregates.     

The Effect of the Molecular Weight of Polyvinylpyrrolidone and the Model Drug on Laser-Induced In Situ Amorphization

Laser radiation has been shown to be a promising approach for in situ amorphization, i.e., drug amorphization inside the final dosage form. Upon exposure to laser radiation, elevated temperatures in the compacts are obtained. At temperatures above the glass transition temperature (T_g) of the polymer, the drug dissolves into the mobile polymer. Hence, the dissolution kinetics are dependent on the viscosity of the polymer, indirectly determined by the molecular weight (M_w) of the polymer, the solubility of the drug in the polymer, the particle size of the drug and the molecular size of the drug. Using compacts containing 30 wt% of the drug celecoxib (CCX), 69.25 wt% of three different M_w of polyvinylpyrrolidone (PVP: PVP12, PVP17 or PVP25), 0.25 wt% plasmonic nanoaggregates (PNs) and 0.5 wt% lubricant, the effect of the polymer M_w on the dissolution kinetics upon exposure to laser radiation was investigated. Furthermore, the effect of the model drug on the dissolution kinetics was investigated using compacts containing 30 wt% of three different drugs (CCX, indomethacin (IND) and naproxen (NAP)), 69.25 wt% PVP12, 0.25 wt% PN and 0.5 wt% lubricant. In perfect correlation to the Noyes–Whitney equation, this study showed that the use of PVP with the lowest viscosity, i.e., the lowest M_w (here PVP12), led to the fastest rate of amorphization compared to PVP17 and PVP25. Furthermore, NAP showed the fastest rate of amorphization, followed by IND and CCX in PVP12 due to its high solubility and small molecular size.     

Study of inclusion complex formation between a cationic surfactant, two cyclodextrins and a drug

In this study inclusion of hexadecyltrimethylammonium bromide (HTAB) with α-, and β-cyclodextrin (CD) in the presence and the absence of bromhexine (BH) was investigated using ion-selective electrode method. The association constants of HTAB with CDs were determined by potentiometry and were close to literature values. The obtained results indicated that α-CD formed 1:1 and 1:2 inclusion complexes, but β-CD formed only a 1:1 inclusion complex. In the presence of drug, the interaction between CDs and HTAB decreased, because both drug and HTAB could interact with CDs. The results showed that the interaction between drug and CDs are greater than HTAB and CDs. The stoichiometry of the inclusion complexes, the critical aggregation concentration (CAC), the monomer surfactant concentration of HTAB, [HTAB]_f, and also the effect of the inclusion complex on the micellization process of the HTAB were determined by conductivity measurements.     

A spectroscopic and molecular modeling studies of the inclusion complexes of orciprenaline and terbutaline drugs with native and modified cyclodextrins

The inclusion complexation behavior of orciprenaline (ORC) and terbutaline (TER) with α-CD, β-CD, HP-α-CD and HP-β-CD are examined by absorption, fluorescence, life time and molecular modeling methods. ORC and TER forms 1:1 (CD/drug) inclusion complexes in lower CD concentrations and 1:2 (CD/drug) inclusion complexes with higher CD concentrations. The inclusion of both drugs with HP-CDs was stronger than that of native CDs. Both drugs exhibit dual emission (excimer) in the CD solution, whereas in water single emission is seen. The hydrogen bonding and van der Waals interaction between the drugs and the CD plays an important role in the inclusion complexes. Computational results show the side chain of the drugs encapsulated in the CD cavity. The molecular modeling results by PM3 were in good agreement with the experimental results.