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Catalyzed Thermal Isomerization between Previtamin D3 and Vitamin D3 via β-Cyclodextrin Complexation

1995; Elsevier BV; Volume: 270; Issue: 15 Linguagem: Inglês

10.1074/jbc.270.15.8706

1083-351X

Xiao Quan Tian, Michael F. Holick,

Effects and risks of endocrine disrupting chemicals

To examine the effect of microenviroments on previtamin D3 ⇌ vitamin D3isomerization, we have conducted kinetic studies of the reaction in an aqueous solution of β-cyclodextrin. Our results showed that at 5°C, the forward (k1) and reverse (k2) rate constants for previtamin D3⇌ vitamin D3isomerization were increased by more than 40 and 600 times, respectively, compared with those in n-hexane (k1, 8.65 × 10−6versus 1.76 × 10−7s−1; k2, 8.48 × 10−6versus 1.40 × 10−8s−1), the fastest rate of this isomerization ever reported at this temperature. Thermodynamic studies revealed that the equilibrium constant of the reaction was significantly reduced by more than 12-fold when compared to that in n-hexane at 5°C, and the percentage of vitamin D3at equilibrium was increased as the temperature was increased in β-cyclodextrin. When complexed with β-cyclodextrin, the previtamin D3⇌ vitamin D3isomerization became endothermic (Δ Ho= 13.05 kJ mol−1) in contrast to being exothermic in other media. We propose that thermodynamically unfavorable cZc conformers of previtamin D3are stabilized by β-cyclodextrin, and thus the rate of the isomerization is increased. This conformation-controlled process may play an important role in the modulation of previtamin D3⇌ vitamin D3endocrine system in vivo such as in the sea urchin. To examine the effect of microenviroments on previtamin D3 ⇌ vitamin D3isomerization, we have conducted kinetic studies of the reaction in an aqueous solution of β-cyclodextrin. Our results showed that at 5°C, the forward (k1) and reverse (k2) rate constants for previtamin D3⇌ vitamin D3isomerization were increased by more than 40 and 600 times, respectively, compared with those in n-hexane (k1, 8.65 × 10−6versus 1.76 × 10−7s−1; k2, 8.48 × 10−6versus 1.40 × 10−8s−1), the fastest rate of this isomerization ever reported at this temperature. Thermodynamic studies revealed that the equilibrium constant of the reaction was significantly reduced by more than 12-fold when compared to that in n-hexane at 5°C, and the percentage of vitamin D3at equilibrium was increased as the temperature was increased in β-cyclodextrin. When complexed with β-cyclodextrin, the previtamin D3⇌ vitamin D3isomerization became endothermic (Δ Ho= 13.05 kJ mol−1) in contrast to being exothermic in other media. We propose that thermodynamically unfavorable cZc conformers of previtamin D3are stabilized by β-cyclodextrin, and thus the rate of the isomerization is increased. This conformation-controlled process may play an important role in the modulation of previtamin D3⇌ vitamin D3endocrine system in vivo such as in the sea urchin. The photobiogenesis of vitamin D3in the skin consists of two sequential pericyclic reactions (Fig. 1) (Havinga, 1973Havinga E. Experientia. 1973; 29: 1181-1192Crossref PubMed Scopus (210) Google Scholar; Holick et al., 1980Holick M.F. MacLaughlin J.A. Clark M.B. Holick S.A. Potts Jr., J.T. Anderson R.R. Blank I.H. Parrish J.A. Elias P. Science. 1980; 210: 203-205Crossref PubMed Scopus (600) Google Scholar; Moriarty et al., 1980; MacLaughlin et al., 1982MacLaughlin J.A. Anderson R.R. Holick M.F. Science. 1982; 216: 1001-1004Crossref PubMed Scopus (422) Google Scholar). The first step involves the ultraviolet-B- (UV-B, 1The abbreviations used are:UV-Bultraviolet-B7-DHC7-dehydrocholesterolpreD3previtamin D31,25-(OH)2D31,25-dihydroxyvitamin D31,25-(OH)2preD31,25-dihydroxyprevitamin D3HPLChigh performance liquid chromatography. 1The abbreviations used are:UV-Bultraviolet-B7-DHC7-dehydrocholesterolpreD3previtamin D31,25-(OH)2D31,25-dihydroxyvitamin D31,25-(OH)2preD31,25-dihydroxyprevitamin D3HPLChigh performance liquid chromatography. 290-315 nm) induced electrocyclic ring opening of 7-dehydrocholesterol (7-DHC) between C9 and C10 to form a seco-sterol, previtamin D3(preD3) (Woodward and Hoffmann, 1965Woodward R.B. Hoffmann R. J. Am. Chem. Soc. 1965; 87: 2511-2513Crossref Scopus (379) Google Scholar; Havinga, 1973Havinga E. Experientia. 1973; 29: 1181-1192Crossref PubMed Scopus (210) Google Scholar; Esvelt et al., 1978; Jacobs and Havinga, 1979Jacobs H.J.C. Havinga E. Adv. Photochem. 1979; 11: 305-373Google Scholar; Holick et al., 1979Holick M.F. Richtand N.M. McNeill S.C. Holick S.A. Frommer J.E. Henly J.W. Potts Jr., J.T. Biochemistry. 1979; 18: 1003-1008Crossref PubMed Scopus (83) Google Scholar, Holick et al., 1980Holick M.F. MacLaughlin J.A. Clark M.B. Holick S.A. Potts Jr., J.T. Anderson R.R. Blank I.H. Parrish J.A. Elias P. Science. 1980; 210: 203-205Crossref PubMed Scopus (600) Google Scholar). PreD3is an obligatory precursor for the biogenesis of vitamin D3. Once formed, preD3begins to thermally isomerize to vitamin D3viaan antarafacial [1,7]-sigmatropic hydrogen shift from C19 to C9(Dauben and Funhoff, 1988aDauben W.G. Funhoff D.J.H. J. Org. Chem. 1988; 53: 5070-5075Crossref Scopus (41) Google Scholar, Dauben and Funhoff, 1988bDauben W.G. Funhoff D.J.H. J. Org. Chem. 1988; 53: 5376-5379Crossref Scopus (14) Google Scholar; Yamamoto and Borch, 1988; Curtin and Okamura, 1991Curtin M.L. Okamura W.H. J. Am. Chem. Soc. 1991; 113: 6958-6966Crossref Scopus (69) Google Scholar). The thermal rearrangement of preD3⇌ vitamin D3is an intramolecular concerted process. Due to the reversibility of this isomerization, vitamin D3and its precursor preD3always coexist and constantly interconvert. This contrasts markedly with all other steroids. ultraviolet-B 7-dehydrocholesterol previtamin D3 1,25-dihydroxyvitamin D3 1,25-dihydroxyprevitamin D3 high performance liquid chromatography. ultraviolet-B 7-dehydrocholesterol previtamin D3 1,25-dihydroxyvitamin D3 1,25-dihydroxyprevitamin D3 high performance liquid chromatography. The relevance of preD3⇌ vitamin D3endocrine system to biological activity was recently implicated in studies (Norman et al., 1993Norman A.W. Okamura W.H. Farach-Carson M.C. Allewaert K. Branisteanu D. Nemere I. Muralidharan K.R. Bouillon R. J. Biol. Chem. 1993; 268: 13811-13819Abstract Full Text PDF PubMed Google Scholar; Dormanen et al., 1994Dormanen M.C. Bishop J.E. Hammond M.W. Okamura W.H. Nemere I. Norman A.W. Biochem. Biophys. Res. Commun. 1994; 201: 394-401Crossref PubMed Scopus (62) Google Scholar) suggesting the existence of different forms of the 1,25-dihydroxyvitamin D3(1,25-(OH)2D3) receptor: the classic nuclear receptor for 1,25-(OH)2D3associated with genomic activity as well as the uncharacterized membrane receptors for both 1,25-(OH)2D3and 1,25-dihydroxyprevitamin D3(1, 25-(OH)2preD3) associated with nongenomic activity. Hobbs et al., 1987Hobbs R.N. Hazel C.M. Smith S.C. Carney D.A. Howells A.C. Littlewood A.J. Pennock J.F. Chem. Scr. 1987; 27: 199-205Google Scholar reported the first example that preD3⇌ vitamin D3isomerization could be altered in vivo in the sea urchin Psammechinus miliaris. There were three remarkable features for the reaction in the sea urchin. First and most important, the equilibrium of the reaction is dramatically altered and shifted toward preD3at equilibrium (45% in the sea urchin versus 8% in n-hexane at 10°C). The second striking feature for the reaction in the sea urchin was that the rate of conversion of vitamin D3 ⟶ preD3was greatly increased. For example, at 10°C less than 5% of vitamin D3converted to previtamin D3in n-hexane after 1 month (Tian et al., 1993Tian X.Q. Chen T.C. Matsuoka L.Y. Wortsman J. Holick M.F. J. Biol. Chem. 1993; 268: 14888-14892Abstract Full Text PDF PubMed Google Scholar). In contrast in the sea urchin at the same temperature, it took only about 1-2 days to convert as much as 30-45% of vitamin D3into preD3(Hobbs et al., 1987Hobbs R.N. Hazel C.M. Smith S.C. Carney D.A. Howells A.C. Littlewood A.J. Pennock J.F. Chem. Scr. 1987; 27: 199-205Google Scholar). Last and most unusual was the percentage of vitamin D3at equilibrium was increased as temperature was increased (72 and 78% at 17.5 and 20°C, respectively), which is in contrast to all other known reaction systems reported to date which showed a decrease in the amount of vitamin D3with increasing temperature (Cassis and Weiss, 1982Cassis Jr., E.G. Weiss R.G. Photochem. Photobiol. 1982; 35: 439-444Crossref Scopus (20) Google Scholar; Yamamoto and Borch, 1985Yamamoto J.K. Borch R.F. Biochemistry. 1985; 24: 3338-3344Crossref PubMed Scopus (24) Google Scholar; Tian et al., 1993Tian X.Q. Chen T.C. Matsuoka L.Y. Wortsman J. Holick M.F. J. Biol. Chem. 1993; 268: 14888-14892Abstract Full Text PDF PubMed Google Scholar, Tian et al., 1994Tian X.Q. Chen T.C. Lu Z. Shao Q. Holick M.F. Endocrinology. 1994; 135: 655-661Crossref PubMed Scopus (55) Google Scholar). The shell tissue of sea urchin has been found to have the greatest ability to alter the rate and equilibrium of preD3⇌ vitamin D3isomerization (Hobbs et al., 1987Hobbs R.N. Hazel C.M. Smith S.C. Carney D.A. Howells A.C. Littlewood A.J. Pennock J.F. Chem. Scr. 1987; 27: 199-205Google Scholar). However, the active agent within the shell has not been identified. It is known that more than 90% of mollusk shell consists of inorganic salts, mainly calcium carbonate, and the remainder are proteins and polysaccharides (Rieke et al., 1992Rieke P.C. Tarasevich B.J. Bentjen S.B. Fryxell G.E. Campbell A.A. Bein T. Supramolecular Architecture: Synthetic Control in Thin Films and Solids. Maple Press, York1992: 61-75Google Scholar). Both protein component and pure mineral salts fail to catalyze the isomerization, and the effect of saccharides has not been examined (Hobbs et al., 1987Hobbs R.N. Hazel C.M. Smith S.C. Carney D.A. Howells A.C. Littlewood A.J. Pennock J.F. Chem. Scr. 1987; 27: 199-205Google Scholar). Cyclodextrins, the naturally occurring, truncated cone-shaped oligosaccharides, have received increasing attention in recent years for their ability to complex a variety of guest molecules including steroids into their hydrophobic cavities in aqueous solution (Saenger, 1984Saenger W. Atwood J.L. Davies J.E.P. MacNicol D.D. Inclusion Compounds. Vol. 2. Academic Press, New York1984: 231-259Google Scholar; Liu et al., 1990Liu F.Y. Kildsig D.O. Mitra A.K. Pharmacol. Res. 1990; 7: 869-873Crossref Scopus (55) Google Scholar; Albers and Muller, 1992Albers E. Muller B.W. J. Pharm. Sci. 1992; 81: 756-761Abstract Full Text PDF PubMed Scopus (46) Google Scholar). These microheteroenvironments have been shown to modify both energetics and dynamics of many chemical reactions (Ueno and Osa, 1991Ueno A. Osa T. Ramamurthy V. Photochemistry in Organized and Constrained Media. VCH Publishers, Inc., New York1991: 739-782Google Scholar; Pitchumani and Ramamurthy, 1994Pitchumani K. Ramamurthy V. Photochem. Photobiol. 1994; 59: 399-401Crossref Scopus (2) Google Scholar). Of great importance is their ability to catalyze reactions of a wide variety of guest molecules (Breslow, 1984Breslow R. Atwood J.L. Davies J.E.P. MacNicol D.D. Inclusion Compounds. Vol. 3. Academic Press, New York1984: 473-508Google Scholar; Tabushi, 1984Tabushi I. Atwood J.L. Davies J.E.P. MachNicol D.D. Inclusion Compounds. Vol. 3. Academic Press, New York1984: 445-471Google Scholar; Chen and Pardue, 1993Chen E.T. Pardue H.L. Anal. Chem. 1993; 65: 2563-2567Crossref PubMed Scopus (15) Google Scholar). It is known that β-cyclodextrin is capable of forming 2:1 (host/guest) inclusion complexes with vitamin D3(Szejtli et al., 1980Szejtli J. Bolla . Szabó P. Ferenczy T. Pharmazie. 1980; 35: 779PubMed Google Scholar; Szejtli, 1984Szejtli J. Atwood J.L. Davies J.E.P. MacNicol D.D. Inclusion Compounds. Vol. 3. Academic Press, New York1984: 331-390Google Scholar; Bogoslovsky et al., 1988Bogoslovsky N.A. Kurganov B.I. Samochvalova N.G. Isaeva T.A. Sugrobova N.P. Gurevich V.M. Valashek I.E. Samochvalov G.I. Vitamin D. Molecular, Cellular and Clinical Endocrinology. Walter de Gruyter & Co., Berlin1988: 1021-1023Google Scholar). Therefore, we evaluated β-cyclodextrin as a possible model to mimic the preD3⇌ vitamin D3reaction in the sea urchin and investigated the mechanism by which the reaction kinetics was modulated by this constrained medium. Crystalline β-cyclodextrin, methyl-β-cyclodextrin (mean degree of substitution, 10.5-14.7), α-cyclodextrin, vitamin D3(>99%), and 7-DHC (98%) were purchased from Sigma and were used as received without further purification. n-Butanol (>99%) was obtained from Aldrich. High performance liquid chromatography (HPLC) grade n-hexane and 2-propanol were obtained from EM Science (Gibbstown, NJ). PreD3was chemically synthesized by photolysis of 7-DHC solution according to a previous reported method (Tian et al., 1993Tian X.Q. Chen T.C. Matsuoka L.Y. Wortsman J. Holick M.F. J. Biol. Chem. 1993; 268: 14888-14892Abstract Full Text PDF PubMed Google Scholar, Tian et al., 1994Tian X.Q. Chen T.C. Lu Z. Shao Q. Holick M.F. Endocrinology. 1994; 135: 655-661Crossref PubMed Scopus (55) Google Scholar). PreD3in n-hexane solution was stored in argon-flushed glass ampoules at −70°C until use, and the purity was checked by HPLC analysis and its UV absorption spectrum. The inclusion complex was prepared by a modified method described by Duveneck et al., 1989Duveneck G.L. Sitzmann E.V. Eisenthal K.B. Turo N.J. J. Phys. Chem. 1989; 93: 7166-7170Crossref Scopus (63) Google Scholar, i.e. addition of one volume of 1 m M 7-DHC in ethanol to 50 volumes of aqueous β-cyclodextrin solution (15 mg/ml). The prepared solutions were stirred at room temperature for at least 4 h and then filtered to remove possible precipitates to obtain a clear solution. The formation of the inclusion complex was verified by the appearance of characteristic UV absorption spectrum of 7-DHC (MacLaughlin et al., 1982MacLaughlin J.A. Anderson R.R. Holick M.F. Science. 1982; 216: 1001-1004Crossref PubMed Scopus (422) Google Scholar). Due to 7-DHC's very low water solubility, no UV absorption for 7-DHC could be detected when using pure water as the solvent. The same procedure was used to prepare the inclusion complexes of 7-DHC with α-cyclodextrin and methyl-β-cyclodextrin in aqueous solution. Solutions of 7-DHC inclusion complex were placed in argon-flushed quartz tubes and irradiated on ice by UV-B Medical Sunlamps (National Biological Corp., Cleveland, OH) for 1 min (40 mJ cm−2) (Tian et al., 1993Tian X.Q. Chen T.C. Matsuoka L.Y. Wortsman J. Holick M.F. J. Biol. Chem. 1993; 268: 14888-14892Abstract Full Text PDF PubMed Google Scholar). For kinetic studies, triplicate exposed solutions were incubated at 5, 30, 37, and 50°C for various durations. Aliquots sampled at each time interval were immediately extracted with a precooled n-butanol/ n-hexane solution (15:85, v/v). The amount of vitamin D3and preD3in each sample was quantified by a previously described HPLC method (Tian et al., 1993Tian X.Q. Chen T.C. Matsuoka L.Y. Wortsman J. Holick M.F. J. Biol. Chem. 1993; 268: 14888-14892Abstract Full Text PDF PubMed Google Scholar, Tian et al., 1994Tian X.Q. Chen T.C. Lu Z. Shao Q. Holick M.F. Endocrinology. 1994; 135: 655-661Crossref PubMed Scopus (55) Google Scholar). Due to high excess of β-cyclodextrin (host/guest = 660:1) and the virtual insolubility of free 7-DHC in water, it was expected that 7-DHC, preD3, and vitamin D3were completely complexed with β-cyclodextrin forming readily water-soluble inclusion complexes (Szejtli et al., 1980Szejtli J. Bolla . Szabó P. Ferenczy T. Pharmazie. 1980; 35: 779PubMed Google Scholar; Szejtli, 1984Szejtli J. Atwood J.L. Davies J.E.P. MacNicol D.D. Inclusion Compounds. Vol. 3. Academic Press, New York1984: 331-390Google Scholar). Therefore, the following reversible thermal isomerization existed in the exposed solutions: preD3-(β-cyclodextrin)2 ⇌ vitamin D3-(β-cyclodextrin)2(Eq. 1) In analogy to the thermal interconversion between free preD3and vitamin D3in solutions, rate constants (k1and k2), equilibrium constant (K), and thermodynamic activation parameters were calculated by using standard methods for reversible first-order reactions (Tian et al., 1993Tian X.Q. Chen T.C. Matsuoka L.Y. Wortsman J. Holick M.F. J. Biol. Chem. 1993; 268: 14888-14892Abstract Full Text PDF PubMed Google Scholar, Tian et al., 1994Tian X.Q. Chen T.C. Lu Z. Shao Q. Holick M.F. Endocrinology. 1994; 135: 655-661Crossref PubMed Scopus (55) Google Scholar). In brief, the rate constants were obtained from the slopes of the plots of ln[(De - Do)/(De - Dt)] versus reaction time t. The equilibrium constants were equal to the ratios of forward rate constants (k1) over reverse rate constants (k2). The standard enthalpy change (Δ Ho) for the reaction was calculated from the van't Hoff plot, and activation energy (Ea) was obtained from Arrhenius plot. Finally, the activation parameters were calculated from Eyring's equation. Incubation of purified preD3in β-cyclodextrin aqueous solution at 37°C for 30 min resulted in the conversion of 60% of preD3into vitamin D3, in contrast to only 1% of conversion in n-hexane (Fig. 2, A and B). For the reverse reaction, in β-cyclodextrin, 19% of vitamin D3was converted into preD3at 37°C within 30 min, whereas in n-hexane no conversion of vitamin D3into preD3was detected at the end of 1 h of incubation (Fig. 2, C and D). The integrated rate equation for the thermal interconversion between preD3and vitamin D3inclusion complexes (Eq. 1) was expressed as ln[(De − Do)I(De − Dt)] = (k1 + k2)t = kt(Eq. 2) where k was the total rate constant, k1 and k2 were the rate constants for the preD3 → vitamin D3 reaction and vitamin D3 → preD3 reaction, respectively. De, D0, and Dt were vitamin D3 concentration at time t reached equilibrium, t = 0 and t = t, respectively. Based on Equation 2, it was expected, and demonstrated (Fig. 3) that the plot of ln [(De - D0)/(De - Dt)] versus reaction time t was linear, and the total rate constant was calculated from the slope of the straight line by least-squares analysis. The determined total rate constants in β-cyclodextrin at 5, 30, 37, and 50°C were 0.0000171 ± 0.0000028 s-1 (correlation coefficient r = 0.973), 0.000246 ± 0.000003 s-1 (r = 0.985), 0.000477 ± 0.000017 (r = 0.992) and 0.00210 ± 0.00021 s-1 (r = 0.993), respectively. The kinetic values (k1, k2, and K) for the preD3 ⇌ vitamin D3 reaction in n-hexane (Tables I and II) were determined at 5 and 37°C (Fig. 3), and at other temperatures, they were calculated based on previously reported data (Tian et al., 1993Tian X.Q. Chen T.C. Matsuoka L.Y. Wortsman J. Holick M.F. J. Biol. Chem. 1993; 268: 14888-14892Abstract Full Text PDF PubMed Google Scholar). Compared to the preD3 ⇌ vitamin D3 reaction in n-hexane at 5°C, complexing with β-cyclodextrin dramatically accelerated the thermal isomerization rates between preD3 and vitamin D3 resulting in a 49- and 606-fold catalysis for the forward preD3 → vitamin D3 conversion and reverse preD3 → vitamin D3 conversion, respectively (Table I), the highest isomerization rate for the reaction reported to date. At equilibrium the percentage of preD3 in β-cyclodextrin was shifted from less than 8% in n-hexane at 5°C to 49% in β-cyclodextrin.Table I:Temperature dependence on the rate constants of preD3⇌ vitamin D3isomerization in an aqueous solution of β-cyclodextrin (A) and in n- hexane (B)Table I:Temperature dependence on the rate constants of preD3⇌ vitamin D3isomerization in an aqueous solution of β-cyclodextrin (A) and in n- hexane (B)Table II:Temperature dependence on the equilibrium constants of preD3⇌ vitamin D3isomerization in an aqueous solution of β-cyclodextrin and in n- hexaneTable II:Temperature dependence on the equilibrium constants of preD3⇌ vitamin D3isomerization in an aqueous solution of β-cyclodextrin and in n- hexane The temperature dependence of the rate constant was defined by Arrhenius' equation k = A exp(−Eα/RT) or lnk = −Eα/RT + lnA(Eq. 3) where Eα was the activation energy of the reaction, lnA was an integration constant, and A was defined as the frequency factor. Arrhenius plot (Ink against l/T) for the preD3 ⇌ vitamin D3 interconversion was linear over the experimental temperature range (5-50°C), with Ea1 = 82.37 kJ mol-1, Eα2 = 69.34 kJ mol-1, correlation coefficients r1 = -0.998 and r2 = -0.999 (Table III). Compared to the reaction in n-hexane, the activation energies were reduced by 2.53 and 31.16 kJ mol-1 for the forward and reverse process, respectively.Table III:Arrhenius rate parameters and thermodynamic values for preD3⇌ vitamin D3isomerization in an aqueous solution of β-cyclodextrin (A) and in n- hexane (B) The equilibrium constant for preD3⇌ vitamin D3interconversion depends strongly on temperature. The effect of temperature on the equilibrium constant K was given by the van't Hoff equation lnK = − ΔH°/RT + C(Eq. 4) where ΔH˚ was the standard enthalpy change or the heat of the reaction at 25°C, R was the gas constant, and C was an integration constant. Plotting InK against the reciprocal of the absolute temperature (1/T) gave a straight line (r = -0.982) (Fig. 4). The slope of the line (-ΔH˚/R) was -1570, and thus the ΔH˚ was 13.05 kJ mol-1. Therefore, the determined van't Hoff equation for the isomerization between preD3 and vitamin D3 in β-cyclodextrin was expressed as lnK = − 1570/T + 5.63(Eq. 5) Whereas the reported van't Hoff equation (Tian et al., 1993Tian X.Q. Chen T.C. Matsuoka L.Y. Wortsman J. Holick M.F. J. Biol. Chem. 1993; 268: 14888-14892Abstract Full Text PDF PubMed Google Scholar) for the reaction in n-hexane was lnK = 1882/T − 4.24(Eq. 6) in which ΔH˚ was -15.65 kJ mol-1 These results demonstrate for the first time that whereas in n-hexane and other media the preD3 ⇌ vitamin D3 reaction is exothermic, when the reaction was carried out in β-cyclodextrin solution this isomerization became endothermic (ΔH˚ > 0) (Equations 4 and 5). Fig. 4 compared the effects of temperature on equilibrium constants K in n-hexane and in the β-cyclodextrin solution. It was apparent from Fig. 4 that there existed two distinct mechanisms by which the equilibrium were affected by the changes of temperature. The preD3 ⇌ vitamin D3 interconversion in n-hexane followed the classic mechanism, i.e. as temperature was increased the percentage of vitamin D3 at equilibrium was decreased (Fig. 4 and Equation 6). On the contrary, the isomerization in β-cyclodextrin solution represented a novel mechanism, i.e. the percentage of vitamin D3 at equilibrium was increased as temperature was increased (Fig. 4 and Equation 5). The determined values of standard thermodynamic parameters Δ Go, Δ Ho, and Δ Sofor preD3⇌ vitamin D3interconversion in β-cyclodextrin solution are given in Table III together with the reported values for the reaction carried out in n-hexane (Tian et al., 1993Tian X.Q. Chen T.C. Matsuoka L.Y. Wortsman J. Holick M.F. J. Biol. Chem. 1993; 268: 14888-14892Abstract Full Text PDF PubMed Google Scholar). According to transition-state theory, the rate of a reaction at any given temperature depends solely on the concentration of the high energy activated complex. Eyring's equation relates the rate constant to quasithermodynamic parameters by the following expressions k=(kBTκ/h)exp(−ΔG‡/RT)=(kBTκ/h)exp(ΔS‡/R−ΔH‡/RT)(Eq. 7) where kB was Boltzmann's constant, h was Planck's constant, and κ was the transmission coefficient and its value was assumed to be unity during the calculations. The enthalpy and entropy of activation ΔH‡ and ΔS‡ are measures of the heat and entropy changes when reactants are converted to activated complexes, and the determined values for the reaction in β-cyclodextrin solution are listed in Table IV and compared with the reported values for the reaction in n-hexane (Tian et al., 1993Tian X.Q. Chen T.C. Matsuoka L.Y. Wortsman J. Holick M.F. J. Biol. Chem. 1993; 268: 14888-14892Abstract Full Text PDF PubMed Google Scholar). The free energies of activation, ΔG1‡ (preD3 → vitamin D3) and ΔG2‡~ (vitamin D3 → preD3) were smaller for the reaction carried out in β-cyclodextrin than those in n-hexane (Table IV), which means less energy was needed to bring the reactants to their transition states, and therefore the rate constants were increased for the reaction in β-cyclodextrin solution compared to those in n-hexane (Equation 7 and Table I).Table IV:Activation parameters for preD3⇌ vitamin D3isomerization in an aqueous solution of β-cyclodextrin (A) and in n- hexane (B) Compared to the rate constant in β-cyclodextrin at 37°C, the determined k values in α-cyclodextrin ((2.18 ± 0.0035)×10−5 s−1) and in methyl-β-cyclodextrin ((7.66 ± 0.038) × 10−5 s−1) were decreased by more than 20- and 6-fold, respectively. Whereas the percentage of vitamin D3at equilibrium at 37°C were increased from 64.2 ± 1.8 in β-cyclodextrin to 96.7 ± 0.2 in α-cyclodextrin and 96.6 ± 0.2 in methyl-β-cyclodextrin (Fig. 5). A change in the reaction medium such as polarity, viscosity, etc., can have a substantial influence on the kinetics of chemical reactions. However, from a chemical point of view, these parameters usually do not have a major impact on an intramolecular concerted process. It has been assumed that the rate and equilibrium of preD3⇌ vitamin D3interconversion was only affected by temperature (Hanewald et al., 1961Hanewald K.H. Rappoldt M.P. Roborgh Jr., X. Recl. Trav. Chim. Pays-Bas Belg. 1961; 80: 1003-1014Crossref Scopus (55) Google Scholar; Schlatmann et al., 1964; Sanders et al., 1969). However, in a biological system, the conventional chemical media have been replaced with diversified physiological environments, such as lipid bilayers, micelles, proteins, nucleic acids, and polysaccharides. In contrast to isotropic solutions, these organized and constrained media have the unusual ability to dramatically modulate the conformational equilibrium of guest molecules that may ultimately lead to catalysis or inhibition by favoring or disfavoring particular conformations. PreD3is conformationally flexible and undergoes rotation around C5-C6single carbon bond to create cZc (s- cis,s- cis) and tZc (s- trans,s- cis) conformations (Fig. 1) (Dauben and Funhoff, 1988aDauben W.G. Funhoff D.J.H. J. Org. Chem. 1988; 53: 5070-5075Crossref Scopus (41) Google Scholar, Dauben and Funhoff, 1988bDauben W.G. Funhoff D.J.H. J. Org. Chem. 1988; 53: 5376-5379Crossref Scopus (14) Google Scholar; Norman et al., 1993Norman A.W. Okamura W.H. Farach-Carson M.C. Allewaert K. Branisteanu D. Nemere I. Muralidharan K.R. Bouillon R. J. Biol. Chem. 1993; 268: 13811-13819Abstract Full Text PDF PubMed Google Scholar). In isotropic solutions cZc conformation is energetically less stable due to steric interactions between C19 methyl group and C/D rings. The cZc conformers are able to undergo alternative reaction pathways. They can either thermally isomerize to vitamin D3or photochemically convert to lumisterol, whereas the tZc conformers are the precursors solely responsible for the photoproduction of tachysterol (Dauben and Funhoff, 1988aDauben W.G. Funhoff D.J.H. J. Org. Chem. 1988; 53: 5070-5075Crossref Scopus (41) Google Scholar, Dauben and Funhoff, 1988bDauben W.G. Funhoff D.J.H. J. Org. Chem. 1988; 53: 5376-5379Crossref Scopus (14) Google Scholar; Terenetskaya et al., 1992Terenetskaya I.P. Perminova I.P. Yeremenko A.M. J. Mol. Struct. 1992; 267: 93-98Crossref Scopus (6) Google Scholar). We hypothesize that the complexation of preD3with β-cyclodextrin shifts its conformational equilibrium in favor of formation of cZc conformation, and therefore the rate constant is increased. This hypothesis is supported by the finding that irradiation of 7-DHC˙β-cyclodextrin complex results in marked increase in the formation of lumisterol with a concomitant decrease in the amount of tachysterol compared with the reaction carried out in isotropic solutions. 2X. Q. Tian and M. F. Holick, unpublished results. The thermodynamics and kinetics of preD3⇌ vitamin D3reaction in β-cyclodextrin solution medium showed striking similarities to those in the sea urchin. First, the equilibrium of the reaction was greatly shifted to preD3, i.e. from 8% in n-hexane to 48% in β-cyclodextrin solution at 10°C, which agrees well with the reported value in the sea urchin (more than 45%) (Hobbs et al., 1987Hobbs R.N. Hazel C.M. Smith S.C. Carney D.A. Howells A.C. Littlewood A.J. Pennock J.F. Chem. Scr. 1987; 27: 199-205Google Scholar). Second, like the reaction in sea urchin, the rate of the isomerization in β-cyclodextrin solution is among the fastest ever known, i.e. more than 40- and 600-fold increases in k1and k2, respectively (Table I). Third, the percentage of vitamin D3at equilibrium in β-cyclodextrin solution is increased as the temperature is raised (Fig. 4), which is determined by the negative slope of the van't Hoff plot (Δ Ho> 0) (Equations 4 and 5). And this is in contrast to all other reported reaction media to date (Schlatmann et al., 1964; Cassis and Weiss, 1982Cassis Jr., E.G. Weiss R.G. Photochem. Photobiol. 1982; 35: 439-444Crossref Scopus (20) Google Scholar; Yamamoto and Borch, 1985Yamamoto J.K. Borch R.F. Biochemistry. 1985; 24: 3338-3344Crossref PubMed Scopus (24) Google Scholar; Tian et al., 1993Tian X.Q. Chen T.C. Matsuoka L.Y. Wortsman J. Holick M.F. J. Biol. Chem. 1993; 268: 14888-14892Abstract Full Text PDF PubMed Google Scholar, Tian et al., 1994Tian X.Q. Chen T.C. Lu Z. Shao Q. Holick M.F. Endocrinology. 1994; 135: 655-661Crossref PubMed Scopus (55) Google Scholar). Since Δ Ho= Ea1- Ea2, the mechanism responsible for the positive Δ Hois that the activation energy for the reverse reaction (Ea2) is markedly reduced and becomes smaller than Ea1(Table III), i.e. Ea1- Ea2= ΔHo> 0. Based on Arrhenius' equation (Equation 3) it is evident that the rate constant can be increased either by lowering the activation energy (Ea) through the formation of inclusion complex, or by increasing frequency factor (A) through properly orienting C19 and C9of the preD3and vitamin D3molecules, or a combination of both. For the forward reaction, preD3 ⟶ vitamin D3both effects exist and are additive, with Ea1 being lowered by 2.5 kJ mol−1and A1being increased by 17-fold. By this mechanism, the forward rate constant k1for the reaction carried out in β-cyclodextrin solution was increased more than 40 times compared to that in n-hexane at 5°C (Table I). However, the dramatically increased k2is a consequence of a significantly lowered Ea2 being offset by a smaller A2 (Table III). If A2were not decreased, we could have expected that at 5°C, k2for the vitamin D3 ⟶ preD3isomerization in β-cyclodextrin would be increased by a million fold. To examine the effects of cavity size of cyclodextrin on the reaction rate of preD3⇌ vitamin D3isomerization, kinetic studies were carried out in α-cyclodextrin. We found that when the cavity diameter of cyclodextrin was decreased from 6.2 Å (β-cyclodextrin) to 4.9 Å (α-cyclodextrin), the rate constant was decreased by more than 20 times. These results indicate that similar to an enzymatic reaction, the size of the hydrophobic cavity had a great influence on the reaction rate. To assess the influence of outer surface hydroxyl groups of cyclodextrin on the reaction rate, comparisons were made between the reactions in β-cyclodextrin and in methyl-β-cyclodextrin. It was found that reaction rate in β-cyclodextrin was six times faster than that in methyl-β-cyclodextrin. Since partial permethylation had no effect on the cavity size and basic conformation of the cyclodextrin (Myles et al., 1994Myles A.M.C. Barlow D.J. France G. Lawrence M.J. Biochim. Biophys. Acta. 1994; 1199: 27-36Crossref PubMed Scopus (29) Google Scholar), these data suggest for the first time that the host hydroxyl groups can accelerate the reaction rate of the [1,7]-sigmatropic hydrogen shift between preD3and vitamin D3. It is interesting to note that the degree of the acceleration of the reaction rate by intermolecular hydroxyl groups is similar to the reported values for intramolecular hydroxyl-directing effects (π-facial selectivity) on the reactions involving [1,7]-sigmatropic hydrogen shift (Hoeger et al., 1987Hoeger C.A. Johnston A.D. Okamura W.H. J. Am. Chem. Soc. 1987; 109: 4690-4698Crossref Scopus (65) Google Scholar, Wu and Okamura, 1990Wu K.-M. Okamura W.H. J. Org. Chem. 1990; 55: 4025-4033Crossref Scopus (20) Google Scholar; Curtin and Okamura, 1991Curtin M.L. Okamura W.H. J. Am. Chem. Soc. 1991; 113: 6958-6966Crossref Scopus (69) Google Scholar). The observation that either changing cavity size or masking host hydroxyl groups resulted in a dramatic increase in the percentage of vitamin D3at equilibrium revealed a novel mechanism by which the equilibrium of preD3⇌ vitamin D3isomerization can be modulated by constrained media. A similar mechanism may exist in vivo by which the preD3⇌ vitamin D3endocrine system is modulated to meet various physiological requirements. We thank David Jackson for his assistance in preparing the graphics.