Cyclodextrin Molecules Research Articles

Crystal structure of a cyclomaltoheptaose–4-hydroxybiphenyl inclusion complex

The crystal structure of the inclusion complex of cyclomaltoheptaose (β-cyclodextrin) with 4-hydroxybiphenyl was determined by single-crystal X-ray diffraction at 150 K. The complex contains two cyclomaltoheptaose molecules, two 4-hydroxybiphenyl molecules, one ethanol molecule and fifteen water molecules in the asymmetric unit, and could be formulated as [2(C 42H 70O 35)·2(C 12H 10O)·(C 2H 6O)·15(H 2O)]. It crystallized in the triclinic space group P1 with unit cell constants a = 15.257(3), b = 15.564(3), c = 15.592(2) Å, α = 104.485(15)°, β = 101.066(14)°, γ = 104.330(17)°, V = 3343.6(10) Å 3. In the crystal lattice, two β-cyclodextrins form a head-to-head dimer jointed through hydrogen bonds. Two 4-hydroxybiphenyls were included in the dimer cavity with their hydroxyl groups protruding from two primary hydroxyl sides of the cyclodextrin molecules. The guest 4-hydroxybiphenyl molecules linked into a chain via a combination of an O–H⋯O hydrogen bond and face-to-face π–π stacking of the phenyl rings. The crystal structure supports the calculation results indicating that the 2:2 inclusion complex formed by β-cyclodextrin and 4-hydroxybiphenyl is the energetically favored structure.

On the Characterization of Host−Guest Complexes: Surface Tension, Calorimetry, and Molecular Dynamics of Cyclodextrins with a Non-ionic Surfactant

Three host-guest systems have been characterized using surface tension (sigma), calorimetry, and molecular dynamics simulations (MD). The hosts were three native cyclodextrins (CD) and the guest the non-ionic carbohydrate surfactant octyl-beta-d-glucopyranoside. It is shown that, for any host-guest system, a rough screening of the most probable complex stoichiometries can be obtained in a model free form, using only calorimetric data. The sigma data were analyzed using a model that includes a newly proposed adsorption isotherm. The equilibrium constants for several stoichiometries were simultaneously obtained through fitting the sigma data. For alpha- and beta-CD, the predominant species is 1:1 and to a lesser extent 2:1, disregarding the existence of the 1:2. For gamma-CD, the 1:2 species dominates, the other two being also present. In an attempt to confirm these results, 10 ns MD simulations for each CD were performed using seven different starting conformations. The MD stable conformations agree with the results found from the experimental data. In one case, the spontaneous dissociation-formation of a complex was observed. Analysis of the trajectories indicates that hydrophobic interactions are primarily responsible for the formation and stability of the inclusion complexes. For the 2:1 species, intermolecular H-bonds between CD molecules result in a tight packed structure where their original truncated cone shape is lost in favor of a cylindrical geometry. Together, the results clearly demonstrate that the often used assumption of considering only a 1:1 species is inappropriate.

Selective relaxant binding agents for reversal of neuromuscular blockade

Traditionally, reversal of neuromuscular blockade during anaesthesia was achieved by increasing the acetylcholine concentration in the neuromuscular junction using acetylcholinesterase inhibitors. However, this is ineffective against profound blockade. Furthermore, the increase in acetylcholine level is not limited to the neuromuscular junction, resulting in unwanted side effects requiring co-treatment with muscarinic antagonists. Selective relaxant binding agents offer a new approach for the reversal of neuromuscular blockade: encapsulation of the neuromuscular blocking agent, resulting in inactivation. As part of this new approach, cyclodextrin molecules have been designed that selectively encapsulate steroidal neuromuscular blocking agents. Both animal and human experiments have demonstrated that fast, effective and complete recovery from both normal and profound neuromuscular blockade is now possible. Furthermore, these cyclodextrin derivatives do not have the unwanted side effects of acetylcholinesterase inhibitors.

Influence of cyclodextrins on the physical stability of DPPC-liposomes

This paper reports on the physical stability of DPPC-(dipalmitoyl phosphatidyl choline) liposomes in various aqueous dispersions and its control by uncharged polymers. The effect of natural (α-, β-, γ-) cyclodextrins (CDs) on the stability of bare and polymer-bearing liposomes and also, the attachment of the CD molecules and the macromolecules, respectively, to the DPPC-bilayers of small unilamellar vesicles (SUV) were studied. It was found that above a CD/DPPC ratio, each cyclodextrin caused a definite destruction in the phospholipid bilayers. The extent of membrane destabilization due to a cyclodextrin closely related to the amount of the CD molecules bound to the DPPC-bilayers. The polymer-coated liposomes formulated by incorporating a dissolved homopolymer or copolymer into the phospholipid bilayer of the vesicles exhibited higher physical stability. Uncharged polymers effectively hindered the disintegration of the liposomal membranes brought about by the CD molecules. The polymer layers formed around the phospholipid bilayers ensured an enhanced steric stabilization for the DPPC-liposomes. Methylcellulose (MC) with high molecular mass and a polyvinyl alcohol- co-vinyl propional copolymer alike exhibited efficient stabilizing effect.

Action of α-cyclodextrin on phospholipid assemblies

Interactions of α-cyclodextrin (α-CD) with dimyristoylphosphatidylcholine (DMPC) and Egg phosphatidylcholine (Egg-PC) were studied (i) by analyzing surface pressure-area isotherms and surface tension of phospholipid monolayers formed at the interface between air and α-CD aqueous solutions and (ii) by X-ray diffraction performed on fully hydrated α-CD/phospholipid binary mixtures. The cyclodextrin molecules strongly interact with the two-dimension phospholipid assembly. Their addition into the aqueous sub-phase leads to the removal of part of the phospholipids from the air-water interface: the higher the α-CD concentration, the higher the phospholipid depletion. This should preferentially involve interactions between cyclodextrin and the phosphatidylcholine head group as α-CD is water-soluble and not surface-active. At the three-dimension level, the bilayer packing of the phospholipid lamellar phase appears not affected by the presence of cyclodextrin as shown by X-ray scattering at small angles whereas wide-angle diffraction patterns reveal the formation of a crystalline phase organized in a pseudo-hexagonal lattice usually characteristic of α-CD dimers. These results point out that α-CD should interact with bilayer-forming phospholipid molecules but likely according to a process that would preserve intact at least a part of the multilamellar assembly.

Supramolecular crystal structures of per(3,6-anhydro)-α-cyclodextrin grown from KCl or NaI solutions

Crystals of per(3,6-anhydro)-α-cyclodextrin{hexakis(3,6- anhydro)cyclomaltohexaose} ( 1) grown in presence of KCl or NaI evidence the similar distorted conformation of macrocycle and provide the same supramolecular scaffolding of cyclodextrins based on CH⋯O hydrogen bonds. Infinite tubes parallel to symmetry axis 6 are filled by water molecules or by iodine atoms in 1/KCl and 1/NaI crystals, respectively. In 1/KCl crystals an inclusion complex of stoichiometry 1:2 has been found. Coordination polyhedra of the dimeric K units fuse with the coordination polyhedra of one pentacoordinated chloride atom to form an infinite helix along the c direction crossing over a helical organic envelope of cyclodextrin molecules.

Fluorescence studies on the interaction between pyrene‐labelled poly(acrylic acid) and cyclodextrins

AbstractThe interactions, in aqueous media, between a pyrene‐labelled polyelectrolyte poly(acrylic acid) (PAAMePy) with two different degrees of labelling and β‐ and γ‐cyclodextrins (β‐ and γ‐CD) were studied using absorption and fluorescence (steady‐state and time‐resolved) techniques. In addition to qualitative and quantitative parameters obtained from absorption and steady‐state fluorescence spectra, time‐resolved fluorescence data are presented, allowing additional important observations regarding the nature of the interactions. From the overall data it was possible to conclude that in the case of interaction with γ‐CD the efficient encapsulation of two pyrene units into the cavity of the cyclodextrin molecule leads to a decrease in the number of available free monomers and an increase in the number of preformed ground‐state dimers (GSDs) of pyrene. It was also shown that contrary to the situation in water, where only intramolecular interactions are present, the addition of γ‐CD leads to new interpolymeric interactions. The absence of significant changes is noted when the interactions of PAAMePy polymers take place with β‐CD. The excimer‐to‐monomer fluorescence intensity ratio (IE/IM) was found to increase with the added amount of γ‐CD but not with β‐CD. This increase is justified on the basis of the increase of the GSD contribution. The photophysical behaviour was found to be dependent on the pH of the media, but with the absence of relevant interactions between CD and PAAMePy polymer at alkaline values. Copyright © 2007 Society of Chemical Industry

Synthesis and characterization of new phenanthrolinetriether copolymers with rotaxane architecture

AbstractThis paper is devoted to the preparation and characterization of new phenanthroline-triether copolymers with rotaxane architecture by reaction of complexes of α- or β- cyclodextrin and tri(ethylene glycol) ditosylate with 2,9-di(4-hydroxyphenyl)-1,10- phenanthroline, which is large enough to prevent dethreading of cyclodextrin molecules. Comparative 1H-NMR analysis of tri(ethylene glycol) ditosylate complexes and of rotaxane copolymers evidenced the lower cyclodextrin content in rotaxane copolymers as compared to the calculated values. The rotaxane copolymers present bimodal molecular weight distributions attributed to the separation of the fractions with different content of cyclodextrin threaded on the copolymer chain. As evidenced by thermogravimetric analysis, the rotaxane copolymers show higher thermal stability than its non-complexed homologue.

Integrity of liposomes in presence of cyclodextrins: Effect of liposome type and lipid composition

Liposome stability during incubation in presence of cyclodextrins (CDs) is studied. Dried-rehydrated vesicle (DRV), multilamellar vesicle (MLV) and small unilamellar vesicle (SUV) calcein-encapsulating liposomes, composed of different lipids are formulated, and retention of calcein is followed during vesicle incubation in hydroxypropyl-β-CD (HPβ-CD), HPγ-CD or methyl-β-CD (Meβ-CD), for 24 h. Results demonstrate that liposome integrity in cyclodextrins is affected by lipid composition and type. For the same lipid composition calcein release from vesicles is faster in the order: MLV > DRV > SUV. Meβ-CD influences liposome stability most, compared to the other CD's studied. Vesicles composed of saturated phospholipids were found more stable compared to phosphatidyl-choline (PC) liposomes, suggesting that phospholipid saturation and membrane rigidity influences the interaction between liposomal-lipids and CD molecules. Chol (cholesterol) addition in lipid membrane improves PC-liposome integrity, but has opposite or no effect on liposomes consisting of saturated lipids. Decrease of vesicle dispersion turbidity and size distribution in presence of CD, implies that Meβ-CD induces vesicle disruption and solubilization (to micelles). Turbidity measurements confirm that DRV liposomes are affected more than SUV.

Noncovalent polymers based on aromatic derivatives of β-cyclodextrin

6-Monotosyl-and 6-mononaphthyl derivatives of β-cyclodextrin have been synthesized, and their self-association abilities have been compared. The quasi-elastic light-scattering study revealed the occurrence of self-organization of mono-6-naphtyl-β-cyclodextrin in dilute aqueous solutions that is responsible for the formation of nanosized aggregates. It is suggested that the driving forces of self-organization are the combination of hydrophobic interactions between the aromatic group of one cyclodextrin molecule and the cavity of the neighboring macrocycle that lead to the formation of noncovalent polymers and hydrogen bonds between these polymers. The absence of intermolecular interactions in the case of mono-6-tosyl-β-cyclodextrin is apparently related to the discrepancy between sizes of the tosyl moiety and of the β-cyclodextrin cavity. The influence of concentration, temperature, pH of solution, and competing low-molecular-mass agents on the self-assembly and stability of supramolecular polymers has been studied.

Slide-ring gel: Topological gel with freely movable cross-links

The structure of “slide-ring (SR) gel” was investigated by means of small angle neutron scattering (SANS). The SR gel was synthesized by coupling of α -cyclodextrin molecules on polyrotaxane chains. A cross-linking point of SR gel has a shape of “figure-of-eight”. Two-dimensional SANS patterns for uniaxially stretched SR gels showed a “normal” butterfly pattern. This result indicates that the cross-links slide along the polymer chain so as to minimize the local strain as a “pulley”. The pulley effect was found to be significant to reduce spatial inhomogeneities inherent in polymer gels.

Supramolecular Species Bearing Quaternary Azaaromatic Moieties

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Polymorphism and isostructurality of cyclodextrins and their inclusion complexes

Broad classification of the crystal structures and packingmodes of cyclodextrins (CDs) and their inclusion complexes into channel and cage types is well known. An example of a more detailed classification is that for dimeric (-CD complexes [1] where channel-, intermediate channel-, screw channeland chessboard arrangements were identified. A survey of available CD inclusion complexes of organic guests led to their systematic classification into ∼17 isostructural series, each with a distinctive PXRDpattern [2]. These patterns have proven useful for definitive characterization of new inclusion complexes.More recently, several reports of polymorphs of CDs and their inclusion complexes have appeared, indicating yet wider structural diversity in this class of compounds. In this report, we review these aspects of CDs and their inclusion complexes, and present data for three crystalline forms of permethylated β-CD and several β-CD inclusion complexes of salts of the anti-inflammatory drug diclofenac and its structural isomer meclofenamic acid. The former series comprises a monohydrate (Form 1), a trihydrate (Form 2) and an anhydrate (Form 3), all crystallizing in the space group P212121. The latter two phases are isostructural and were obtained during failed attempts to obtain inclusion complexes with the drugs bucetin and atenolol [3]. The most striking feature revealed here is the relatively round shape of the host molecule in Forms 2 and 3 that results from inclusion of two primary methoxyl groups of each host into the cavity of a neighbouring CD molecule. This contrasts strongly with the collapsed structure of the host in Form 1, where one of the seven methylated glucose rings was found to adopt the unusual C4 conformation. The β-CD complexes of diclofenac prepared and characterized in our laboratory include those of the sodium, potassium and caesium salts of the drug. Although the mode of inclusion of the drug anion in the host cavity is essentially the same in this series, only the latter two complexes are isostructural, crystallizing in the space group P212121, while the crystal of the sodium analogue is hexagonal, space group P61. We recently prepared the Ca 2+ and Mg salts of both diclofenac andmeclofenamic acid, and attempted their inclusion in β-CD. Surprisingly, no complex formation was detected with either of the salts of diclofenac, but its isomer yielded isostructural crystals with compositions β-CDc(meclofenamate) (M)0.5(17H2O. These were found to be isostructural with the sodium analogue investigated earlier and in all three complexes a common mode of inclusion of the guest is observed. New instances of isostructurality among CDhosts and their inclusion complexes reported here have been incorporated into an updated library which includes their PXRD patterns.

SANS study on pulley effect of slide-ring gel

We have recently developed a novel kind of gel “slide-ring (SR) gel”, based on polyrotaxane consisting of thread-like molecules of poly(ethylene glycol) and rings of α -cyclodextrin (CD) molecules. The SR gel has mobile cross-links. In order to improve the unique properties, i.e., “sliding motion” or “pulley effect” of the SR gels and to suppress the self-aggregation tendency of CD molecules, methylated polyrotaxane was synthesized by substituting hydroxyl group with methyl group on CD molecules. The structure of SR gel having methylated CD molecules was investigated by small angle neutron scattering.

Lysozyme refolding with cyclodextrins: structure–activity relationship

Cyclodextrins (CDs), in the presence or absence of detergents, have been reported to suppress aggregate formation during the refolding of a number of proteins. A structure–activity relationship study between CD chemistry and refolding of lysozyme was performed and compared to carbonic anhydrase, in order to better understand the mechanism of CD-assisted protein refolding and to identify CDs that could function as good protein folding agents. Among the natural CDs, which have only hydroxyl groups, alpha-CD, with a smaller cavity size was more effective than the oligosaccharide with a larger cavity, gamma-CD. Replacement of the hydroxyls with other functional groups did not improve, but could seriously interfere, with the lysozyme refolding ability of alpha-CD. In case of gamma-CD, substitution of its hydroxyls with other groups either enhanced or diminished its refolding capability towards lysozyme. In general, neutral CDs were better refolding agents than the charged sugars. The presence of anionic substituents like carboxyl and phosphate groups actually promoted aggregate formation and completely abolished the sugar's refolding ability. This effect was more pronounced with lysozyme than with carbonic anhydrase. CDs with cationic functional groups did not show any significant effects on lysozyme refolding. The presence of both anionic and cationic substituents on the same CD molecule was found to partially restore its renaturation ability. Electrophoresis data indicate that CDs, which promoted lysozyme refolding, arrested aggregation at the stage of smaller soluble aggregates. Interestingly, the structure–activity relationship observed with lysozyme was quite similar to that reported for a non-disulfide protein, carbonic anhydrase. These results suggest that the effects of CDs on protein refolding are attributed to their ability to suppress aggregation of proteins. CDs may show properties similar to chaotropic agents, which may help explain their anti-aggregation and protein refolding ability. Besides alpha-CD, a number of other neutral CDs were found to be effective protein folding aids.

Gels of Hydrophobically Modified Hydroxyethyl Cellulose Cross-Linked by Amylose. Competition with Cyclodextrin

Previous work has shown that amylose (AM) can cross-link hydrophobically modified polymers by inclusion complexation, whereby thermoreversible cold-setting gels are formed. In this work, the competition between AM and cyclodextrin (CD) for the formation of inclusion complexes with hydrophobically modified hydroxyethyl cellulose (HMHEC) is investigated. A detailed study of viscosity, NMR self-diffusion, and chemical shifts of the two-component mixture, CD and HMHEC, was performed. The results imply that 2:1 (CD:polymer hydrophobe) complexes may be formed. The three-component mixtures, HMHEC/AM/CD, were investigated by rheology, NMR self-diffusion, and intensities of the NMR resonance peaks. The CD molecules competed efficiently with the AM molecules, as seen by a decreased storage modulus, an increased self-diffusion of AM and HMHEC, and increased NMR intensities of the HMHEC hydrophobes, as the concentration of CD increased in the solution. A high concentration of CD is needed in the mixtures to inhibit all interactions between HMHEC and AM, and it was shown that there still is an effect of AM at excess CD concentration in the mixtures.

Supramolecular Species Bearing Quaternary Azaaromatic Moieties

In the paper at first rotaxanes are presented; these species are divided into three classes, i.e. those containing electron donor, electron acceptor and cyclodextrin molecules as rings. In following parts examples of catenanes, pretzelanes and molecular clips are described.

A Proton Magnetic Resonance Study of Fexofenadine/β-Cyclodextrin Inclusion Complexes in Aqueous Solution

Fexofenadine hydrochloride (FFN), (±)-4-[1-hydroxy-4[4-(hydroxydiphenylmethyl)-1-piperidinyl]-butyl]-α,α-dimethyl benzeneacetic acid hydrochloride, is a second generation antihistamine that is used to treat allergies. It is a racemate and exists as zwitter ion in aqueous media at physiological pH. It belongs to the group of amine compounds bearing diphenylmethyl functionality. Like other members of this group, the drug is highly hydrophobic and slightly soluble in water. The study of inclusion complexes of cyclodextrins (CDs) is a subject of great interest. CDs are oligosaccharides composed of six to eight glucopyranose units bound by α(14) linkages that are commonly named α-, β-, and γ-CD, respectively. β-CD, in particular, has an internal cavity shaped like a truncated cone. The interior of the cavity is relatively hydrophobic while the outer surface is quite hydrophilic because of the presence of numerous hydroxyl groups. CDs can accommodate a variety of guests into its cavity through non-covalent interactions. These complexes serve as models to mimic enzyme activity and to provide understanding of the molecular recognition. Moreover, the physical properties, such as solubility, stability, volatility, sublimation, etc, of the guest molecule are modified upon complexation with CDs, and the resulting inclusion complexes have found numerous practical applications in pharmaceutical sciences and in several other areas of chemistry ranging from analytical to synthetic chemistry. Inclusion complexes of pharmaceutical compounds with CDs have been extensively studied and utilized to improve the solubility, dissolution rate and bioavailability of poorly water-soluble drugs. Other applications of CD complexes of pharmaceuticals include elimination of undesirable drug properties, such as irritation and unpleasant odor or taste. CDs have also been used to stabilize and protect degradation of unstable compounds. In addition, they have shown a potential for improving the stability of light and oxygen sensitive drugs. Various techniques are used to study the CD inclusion complexes but NMR spectroscopy has been found to be most useful in this type of studies. Evidence for the inclusion of the guest into the CD-cavity is obtained by simple NMR titration experiments. NMR spectra of mixtures of CD and guest molecule are recorded and changes in the chemical shifts of both the host and guest are studied. The formation of the inclusion complex results in upfield shift changes in the CD protons situated inside the cavity, namely H-3' and H-5'. On the other hand, guest protons generally experience downfield shift changes but sometimes upfield shifts are also observed. These shift changes are attributed to the anisotropic ring current effect of the aromatic guests. Moreover, the magnitude of the chemical shift changes for the CD-cavity protons have been shown to be a qualitative measure of the stability of the complex while their ratio, ΔδH-5'/ΔδH-3', gives information about the depth of penetration. Also, information regarding the mode of penetration of the guest into the cavity, i.e. from narrower or wider rim side, can be obtained from these shift changes. A typical inference is that ΔδH-5' > ΔδH-3' if the guest enters the cavity from narrower side and vice versa but there are exceptions and these conclusions can only be drawn when only one complex in formed while in cases where multiple equilibria exist these shift changes can only be used as an evidence for the formation of inclusion complexes. Information regarding the stoichiometry and association and/or dissociation constant of the complex can also be obtained by the treatment of simple H NMR titration data. 2D NMR spectroscopy has recently become an important tool for the investigation of the interactions between CDs and guest molecules since the NOE cross peaks between the protons that are closer than 4 A in space are observed in ROESY spectrum. The relative intensities of these cross peaks depend on the spaces between the corresponding protons. The height and the diameter of the β-CD cavity are about 7.9 ± 0.1 A and 6.0-6.5 A, respectively. Therefore, while the guest molecule is included into the β-CD cavity, NOE correlation peaks between the protons of the guest and protons of the β-CD cavity (H-3' and H-5') are observed by means of ROESY experiment. According to the relative intensities of these cross peaks, it is possible to estimate the orientation of the guest molecule within the CD cavity. In continuation of our work on the NMR studies of inclusion complexes of pharmaceutical compounds with βCD, we report herein our results on the detailed study of the complexation between fexofenadine hydrochloride (FFN) and β-CD in aqueous solution using high resolution NMR spectroscopy.

Mapping of the Cyclodextrin Cavity Using the Cylindrical Coordinate System

This paper describes the mapping of the inner cavity of cyclodextrin and the guest molecule using the cylindrical coordinate system. Each cavity structure of alpha-, beta-, and gamma-cyclodextrin was examined using the coordinate system, in which, the Z-axis passes through the molecular axis; a normal of the plane that consists of 6, 7, or 8 C(1) atoms of glucose units was obtained using the least-squares methods and that passes through the center of C(1) atoms. The radius rho is the distance from the Z-axis to the solvent-accessible surface of a cavity. The psi-axis is defined such that the nearest C(1) atom of the glucose unit to the Z-axis is its origin. The atomic character of the inner surface of the cavity was also obtained and plotted in the same coordinates. The guest molecule was plotted with the same coordinate system as cyclodextrin to see atoms with large rho distance of the guest molecule on the solvent-accessible surface map of cyclodextrin. It was confirmed from the map that cyclodextrin molecules have an ellipsoidal shape, have pseudo-n-hold symmetry (n=6 to alpha, 7 to beta, and 8 to gamma) in relation to their molecular axis, and guest molecules are located in relatively hydrophobic regions. It was also confirmed that the maps of this system give insights into the complementary characters of structures between the host and the guest by plotting the guest molecule in the same coordinate system.

Influence of Cyclodextrin Molecules on the Synthesis and the Thermoresponsive Solution Behavior of N‐Isopropylacrylamide Copolymers with Adamantyl Groups in the Side Chains

New results have revealed that some values given in this original contribution are incorrect. The determined cloud point of polymer 5 does not lie over 95 °C as originally reported, but is actually 17 °C. The previously observed high optical transparency of a dispersion of polymer 5 was a result of the very small particle size that resulted from ultrasonic treatment. In light of this new result, the data for cyclodextrin-free polymer 5 presented in Table 1 and Figures 1, 2, and 3 are incorrect. In Table 1, the LCST value of polymer 5 of >95 °C should be replaced by 17 °C, while the monomer ratio (n/m) for polymers 5 and 6 should now read as 20:1 instead of 1:20. In Figures 1 and 3, the plotted data for polymer 5 in the absence of cyclodextrin should be replaced by a function which shows a turbidity point at 17 °C. In Figure 2, the LCST value of >95 °C should be corrected to 17 °C. In the text, all passages that refer to the cloud point of cyclodextrin-free polymer 5 are incorrect. However, all the other presented data as well as the conclusion remain valid.