Anal. Chem. 1998, 70, 5024-5028
Microcalorimetry of Chiral Surfactant-Cyclodextrin Interactions Alan Cooper,*,† Margaret A. Nutley,† and Patrick Camilleri‡
Chemistry Department, Glasgow University, Glasgow G12 8QQ, Scotland, and SmithKline Beecham Pharmaceuticals, New Frontiers Science Park, Third Avenue, Harlow, Essex CM19 5AW, U.K.
The interactions of the chiral surfactants taurodeoxycholate (TDOCA) and deoxycholate (DOCA) with a range of cyclodextrins in aqueous solution have been investigated by isothermal titration microcalorimetry. In the presence of β-cyclodextrin, the apparent critical micelle concentration (cmc) of taurodeoxycholate is increased, and the enthalpy of demicellization decreased, in a manner consistent with 1:1 complexation of TDOCA with β-CD at low concentrations. There is no evidence for direct interaction of cyclodextrins with surfactant micelles. This is confirmed by more direct binding titrations. Below the cmc, TDOCA forms 1:1 host-guest complexes with β-cyclodextrin (∆H°bind ) -32 kJ mol-1, Kdiss ) 0.38 mM; 25 °C, pH 7), methyl-β-cyclodextrin (∆Hbind ) -13 kJ mol-1, Kdiss ) 0.36 mM), hydroxypropyl-β-cyclodextrin (∆H°bind ) -12 kJ mol-1, Kdiss ) 0.51 mM), and γ-cyclodextrin (∆H°bind ) -7.3 kJ mol-1, Kdiss ) 0.08 mM), but not with the smaller r-cyclodextrin. At higher cyclodextrin concentrations, the calorimetric binding data are more ambiguous, suggesting 2:1 cyclodextrin/TDOCA complexation. Similar results are found with DOCA, though experiments here are limited by the tendency of DOCA to form gels in aqueous buffers. Enhanced chromatographic or electrophoretic chiral resolution observed in mixed chiral surfactant/cyclodextrin phases could be the result of increased solubility and/or the multiplicity of chiral complexes in such systems. Cyclodextrins are used in a wide variety of applications for both analytical and preparative chiral separations,1-3 where the intrinsic chirality of the cyclodextrin binding cavity and the solubility and versatility of chemically modified cyclodextrins can be used to advantage. Combinations of cyclodextrins with bile salts and other chiral surfactants are now increasingly used in chromatographic and electrophoretic chiral separation procedures3-7 * Corresponding author. Phone: (+44) 141-330 5278. Fax: (+44) 141-330 4888. E-mail:
[email protected]. World Wide Web: http://www.chem. gla.ac.uk/∼alanc/alanc.html. † Glasgow University. ‡ SmithKline Beecham Pharmaceuticals. (1) Ward, T. J.; Armstrong, D. W. In Chromatographic Chiral Separations, Zief, M., Crane, L. J., Eds.; Marcel Dekker: New York, 1988; pp 131-163. (2) Lelievre, F.; Gareil; P.; Jardy, A. Anal. Chem. 1997, 69, 385-392. (3) Stalcup, A. M.; Gahm, K. Y.; Gratz, S. R.; Sutton, R. M. C. Anal. Chem. 1998, 70, 144-148. (4) Okafo, G. N.; Bintz, C.; Clarke, S. E.; Camilleri, P. J. Chem. Soc., Chem. Commun. 1992, 1189-1192.
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in efforts to enhance enantiomer selectivity and separation efficiency. Empirically,4,6 it has been found that optimal separations are obtained with nonstoichiometric ratios of cyclodextrin to surfactant above the critical micelle concentration (cmc), but the precise nature of the cyclodextrin-surfactant interaction has been difficult to ascertain, and the molecular basis for enhancement of chiral separation is unclear. Since the separation enhancements seen in cyclodextrin-surfactant mixtures is greater than the sum of the effects of each component alone, additional species in such mixtures must be contributing. Based on our knowledge of the host-guest complexation properties of the cyclodextrins, one might anticipate at least the presence of simple 1:1 complexes between surfactant and cyclodextrin. But other stoichiometries may exist, and it is feasible that cyclodextrins may combine with micellar surfactants to create supramolecular mixed micellar complexes, as suggested indirectly by fluorescent probe studies.4 As a first step to understanding the thermodynamics and mechanism of such processes, we here present data from microcalorimetric studies on mixtures of various cyclodextrins with deoxycholate and taurodeoxycholate under various conditions. Previous calorimetric studies have focused on analysis of the thermodynamics of micelle formation in a range of amphiphiles, including deoxycholate,8 and have demonstrated how cmc’s and demicellization enthalpies may be obtained from calorimetric dilution measurements. Here we extend such measurements to surfactant/cyclodextrin mixtures and, in addition, develop more direct isothermal titration microcalorimetry methods to examine the interactions of cyclodextrins with deoxycholate and taurodeoxycholate in aqueous solutions, above and below the cmc. The advantage of calorimetric methods in this context is that not only do they provide absolute thermodynamic data, but they are a convenient analytical technique applicable where no suitable spectroscopic or alternative indirect probe is available. EXPERIMENTAL SECTION Materials. Cyclodextrins (R-, β-, γ-), deoxycholic acid (DOCA), taurodeoxycholic acid (Na salt) (TDOCA), and related compounds (5) Aumatell, A.; Wells, R. J. J. Chromatogr. A 1994, 688, 329-337. (6) Castelnovo, P.; Albanesi, C. Electrophoresis 1997, 18, 996-1001. (7) Williams, C. C.; Shamsi, S. A.; Warner, I. M. Adv. Chromatogr. 1997, 37, 363-423. (8) Paula, S.; Su ¨ s, W.; Tuchtenhagen, J.; Blume, A. J. Phys. Chem. 1995, 99, 11742-11751. 10.1021/ac9805246 CCC: $15.00
© 1998 American Chemical Society Published on Web 10/29/1998
were obtained from Sigma Chemical Co. Methyl-β-cyclodextrin (avg subst 1.8) and hydroxypropyl-β-cyclodextrin (avg molar subst 0.8) were from Aldrich. Cyclodextrins were normally vacuum desiccated over P2O5 prior to use. Solutions were prepared by weight in ultrapure water or aqueous buffer, pH 7.02, comprising 30 mM sodium phosphate and 10 mM boric acid. Measurements. Isothermal titration calorimetry (ITC) experiments were done at 25 °C using a Microcal OMEGA titration microcalorimeter following standard instrumental procedures9,10 with a 250-µL injection syringe and 400 rpm stirring. A typical binding experiment below the surfactant cmc (in the final mixture) involved sequential addition of small aliquots (usually 25 × 10 µL) of one component (cyclodextrin, ∼15 mM, or TDOCA, ∼10 mM) into the calorimeter cell (∼1.4 mL) containing dilute solution of the other component (TDOCA, ∼1 mM, or cyclodextrin, ∼0.5 mM, as appropriate). Control experiments for heats of dilution and mixing involved injection of TDOCA or cyclodextrin solutions into buffer, or addition of buffer to CD/TDOCA mixtures under identical conditions. Calorimetric dilution experiments to determine cmc were done by addition of concentrated TDOCA solution to the calorimeter cell initially containing buffer alone, following a procedure similar to that in ref 8. Similar techniques were used in experiments with DOCA, except in this case solutions were unbuffered (water alone) because of the tendency for DOCA to form gels in buffers around neutral pH (ref 11 and our own unpublished observations). Integrated heat pulse data, corrected for heats of mixing and dilution, were analyzed by nonlinear regression methods in terms of standard equilibrium binding models, using Microcal ORIGIN software, to give estimates of equilibrium dissociation constant (Kdiss), stoichiometry (n), and enthalpy (∆H°bind) of complex formation. Binding of various cyclodextrins to TDOCA above the cmc was determined by injection of cyclodextrin (15 mM, 10 µL injections) into TDOCA (15 mM). Complete calorimetric titration under these highconcentration conditions is not possible because of the limited solubility of cyclodextrins, but apparent enthalpies of binding (∆Hbind) can be obtained reliably from initial injection heats.9 RESULTS AND DISCUSSION Critical Micelle Concentration and ∆H°demic. It is first necessary to establish the cmc of the surfactants under the conditions of these experiments and to see how this may be affected by the presence of cyclodextrins. Cmc’s of TDOCA in buffer or DOCA in water were determined from ITC dilution experiments involving sequential additions of surfactant to buffer (or water). The initially endothermic heat pulses (e.g., Figure 1) diminish with subsequent injections once the concentration of surfactant in the ITC cell exceeds the cmc, allowing estimation of both the cmc (from the turning point of the differential curve) and the enthalpy of demicellization (from the initial heats of injection).8 For TDOCA in pH 7 buffer at 25 °C, we find a cmc of 2.5 ( 0.1 mM and ∆H°demic ) 2.8 ( 0.1 kJ mol-1 (0.68 ( 0.03 kcal (9) Wiseman, T.; Williston, S.; Brandts, J. F.; Lin, L.-N. Anal. Biochem. 1989, 179, 131-137. (10) Cooper, A.; Johnson, C. M. In Microscopy, Optical Spectroscopy, and Macroscopic Techniques, Methods in Molecular Biology, Vol. 22; Jones, C., Mulloy, B., Thomas, A. H., Eds.; Humana Press: Totowa, NJ, 1994; pp 137150. (11) Jover, A.; Meijide, F.; Nunez, E. R.; Tato, J. V. Langmuir 1996, 12, 17891793.
Figure 1. Calorimetric dilution data illustrating the determination of critical micelle concentrations. (A) Raw data for successive 10-µL injections of TDOCA (49 mM) into buffer at 25 °C. The positive heat pulses indicate endothermic dissociation of micelles. (B) Integrated heat energies for each injection (symbols) and the differential curve (line) with the cmc estimate indicated. The enthalpy of micelle dissociation (∆Hdemic) is determined from the heats of initial injections.
mol-1), in good agreement with previously published data.12,13 (Literature values range from 1 to 4 mM for the cmc of TDOCA, determined by different methods,12,13 and +2.57 kJ mol-1 for the enthalpy of demicellization under similar conditions.12) The corresponding figures found here for DOCA in water are 7.4 ( 0.5 mM (cmc) and 1.1 ( 0.04 kJ mol-1 (0.26 ( 0.01 kcal mol-1) (∆H°demic), again consistent with previous observations.8,12 Literature cmc data are somewhat more variable in this case because of the less cooperative nature of deoxycholate micelle formation,8 and values in the range 2-70 mM have been reported, depending on the type of measurement employed.12 ∆H°demic for DOCA depends quite strongly on temperature and is close to zero at 25 °C,8 consistent with the rather small heat effect observed here. Addition of cyclodextrins to the surfactant solution has a marked effect on both cmc and heat of demicellization. ITC dilution experiments with mixtures of TDOCA and β-cyclodextrin give thermograms qualitatively similar to those in the absence of cyclodextrin but with apparent cmc values increasing approximately linearly with total cyclodextrin concentration (Figure 2). The apparent heat of demicellization falls in a similar manner. This indicates that complexation between β-CD and (free) TDOCA shifts the micellar equilibrium in favor of monomer, at least at low concentrations. These data below the TDOCA cmc are (12) Jana, P. K.; Moulik, S. P. J. Phys. Chem. 1991, 95, 9525-9532. (13) Funasaki, N.; Ueshiba, R.; Hada, S.; Neya, S. J. Phys. Chem. 1994, 98, 11541-11548.
Analytical Chemistry, Vol. 70, No. 23, December 1, 1998
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Figure 2. Variation in (A) apparent cmc and (B) enthalpy of micelle dissociation (∆Hdemic) of TDOCA in the presence of β-cyclodextrin. Linear regression of the cmc data in (A) is shown with a slope of 0.87 ( 0.11 and intercept of 2.6 ( 0.1 mM, consistent with simple complexation of cyclodextrin with nonmicellar TDOCA monomer (see text). Linear regression of enthalpy data (B) gives ∆Hdemic ≈ (3.0 ( 0.1) - (0.75 ( 0.15)[CD] kJ mol-1.
quantitatively consistent with a 1:1 complex formation between β-CD and free TDOCA, as can be seen more clearly from direct titration experiments (below). In particular, as shown below at these cmc and β-cyclodextrin concentrations in the ITC cell, approximately 87% of the cyclodextrin molecules will be complexed with monomeric surfactant. Consequently, we might expect
cmc (apparent) ) total nonmicellar surfactant concentration ) cmc0 + 0.87[CD] where cmc0 is the cmc of the surfactant in the absence of cyclodextrin complexation. Linear regression of the data in Figure 2 gives
cmc (apparent) ) (2.6 ( 0.1) + (0.87 ( 0.11)[CD] mM entirely consistent with this model. Interaction with Cyclodextrins below the Surfactant Cmc. More direct data on complex formation are obtained by calorimetric titrations of TDOCA solutions with cyclodextrins at concentrations below the surfactant cmc in the final mixture, which give isotherms typical of 1:1 complex formation (Figure 3). Analysis of such experiments in terms of a simple single-site binding model yields the apparent stoichiometries and thermodynamic data listed in Table 1. No binding was observed with R-cyclodextrin, presumably because the small size of the host 5026 Analytical Chemistry, Vol. 70, No. 23, December 1, 1998
Figure 3. Typical calorimetric titration showing binding of β-cyclodextrin to TDOCA at 25 °C in pH 7 buffer, below the cmc. (A) (1) Raw data for sequential 10-µL injections of β-cyclodextrin (15.0 mM) into TDOCA (1.02 mM; ITC cell volume ) 1.3963 mL). The negative heat pulses indicate exothermic interaction effects in this case. Control heats of dilution data are shown for similar injections of buffer into TDOCA (2) and β-cyclodextrin solution into buffer alone (3). (B) Integrated heat pulse data (open symbols), corrected for dilution controls and fit (solid line) to a simple single-site binding model with parameters given in Table 1.
cavity precludes incorporation of the bulky TDOCA group. Significant binding, with stoichiometric ratios close to 1 in all cases at these low concentrations, is observed with larger cyclodextrins, with the highest affinity being shown by γ-cyclodextrin. β-Cyclodextrin and its modified versions show similar binding affinity (Kdiss and ∆G°), though there are significant differences in ∆H°bind and ∆S°bind. Binding of TDOCA to cyclodextrins is exothermic in all cases, with a large favorable entropy contribution (positive ∆S°bind) except with β-CD. Despite these relatively large variations in ∆H° and ∆S°, the effects are in opposite directions and tend to cancel and give relatively small changes in ∆G°. Such enthalpyentropy compensation is typical of interactions involving a multiplicity of weak noncovalent interactions14,15 such as might be expected here, involving complex changes in solvation/ hydration of both cyclodextrin and TDOCA molecules as well as direct interactions between host and guest. Very similar data are obtained for the binding of deoxycholate to β-cyclodextrin in water (Table 1), though the tendency for aqueous deoxycholate mixtures to form gels at these concentrations,11,16 particularly in buffered solutions as we observed here, precluded more extensive study. (14) Dunitz, J. D. Chem. Biol. 1995, 2, 709-712. (15) McPhail, D.; Cooper, A. J. Chem. Soc., Faraday Trans. 1997, 93, 22832289. (16) Terech, P.; Smith, W. G.; Weiss, R. G. J. Chem. Soc., Faraday Trans. 1996, 92, 3157-3162.
Table 1. Thermodynamic Data for Binding of TDOCA and DOCA below the cmc to Various Cyclodextrins at 25 °C, pH 7 n ( SDa
Kdiss ( SDa/ mM
Rβmethyl-βhydroxypropyl-βγ-
1.02 ( 0.07 1.01 ( 0.01 0.99 ( 0.08 1.07 ( 0.13
ndc 0.38 ( 0.10 0.36 ( 0.06 0.51 ( 0.06 0.082 ( 0.01
β-
1.0 ( 0.1
0.22 ( 0.04
cyclodextrin
a
∆H°bind ( SDa/ kJ mol-1
∆G°bind ( SDa/ kJ mol-1
∆S°bind ( SDa/ J K-1 mol-1
no.b
-31.6 ( 2.4 -12.9 ( 0.4 -11.7 ( 0.0 -7.3 ( 1.3
-19.5 ( 0.6 -19.8 ( 0.5 -18.8 ( 0.3 -23.3 ( 0.3
-40.4 ( 10.1 23.4 ( 2.8 23.8 ( 0.9 53.7 ( 5.3
2 12 2 2 4
DOCA -33.0 ( 2.8
-20.8 ( 0.7
-41.0 ( 11.3
5
TDOCA
Standard deviation from multiple experiments. b Number of experiments. c nd ) no detectable binding.
Table 2. Apparent Enthalpies of Binding of Cyclodextrins to TDOCA above the Cmc cyclodextrin
fraction bound (φ)
∆H°obsa/ kJ mol-1
∆H°obs(calc)b/ kJ mol-1
βmethyl-βhydroxypropyl-βγ-
0.87 0.87 0.83 0.97
-22.8 -7.5 -5.0 -8.4
-25.1 ( 2.5 -8.8 ( 0.5 -7.1 ( 0.1 -4.2 ( 1.4
a Per mole of cyclodextrin, typically (1.0 kJ mol-1. Determined from initial injections of cyclodextrin (10 µL, 15 mM) into 15 mM TDOCA. b ∆H° obs(calc) ) φ(∆H°bind + ∆H°demic), calculated as described in the text assuming [cmc]TDOCA ) 2.5 mM, ∆H°demic ) 2.8 kJ mol-1, with other parameters from Table 1.
Interaction with Cyclodextrins above the Surfactant Cmc. ITC experiments with TDOCA above the cmc are potentially more difficult to interpret because dissociation of micelles by dilution or by complexation with cyclodextrin gives additional heat effects that distort the calorimetric titration curves (not shown). Moreover, the relatively low solubilities of cyclodextrins limit the concentration range over which complete calorimetric titrations can be obtained. Nevertheless, estimates of the apparent enthalpy of cyclodextrin-surfactant complexation above the cmc can be obtained from calorimetric injections of cyclodextrin into high concentrations of TDOCA, and such data are shown in Table 2. With the exception of γ-CD, the binding enthalpies observed in such cases are all consistently less exothermic than those observed for similar complexation below the cmc. This is partly to be expected, since binding of each TDOCA to cyclodextrin would require the (endothermic) dissociation of the TDOCA molecule from the micelle. However, for simple 1:1 complexation, this should only give rise to a difference of around 2.8 kJ mol-1 (i.e., ∆H°demic for TDOCA), compared to somewhat larger differences observed here. At first sight, this might indicate nonstoichiometric or more complicated binding schemes above the cmc, though it is difficult to find any such model that fits the data. More careful consideration of the concentration-buffering action of the surfactant micelles, however, rationalizes these differences without resort to more complex schemes. Assuming that cyclodextrins (CD) complex only with monomeric surfactant (S), the equilibria above the cmc may be represented by
CD + (S)micelle h CD + S h CD-S with Kdiss ) [CD][S]/[CD-S]. Insofar as the pseudo-phase
separation model holds for the surfactant micellar equilibrium,8,13 (S)micelle h S, whenever micelles are present the concentration of free monomeric surfactant [S] will be equal to the cmc. In other words, the micellar phase will act as a buffer to the free surfactant concentration such that [S] ) [cmc] throughout. Consequently, under these conditions, Kdiss ) [CD][cmc]/[CD-S], and the fraction (φ) of the total cyclodextrin forming a complex will be given by
φ ) [CD-S]/([CD] + [CD-S]) ) (1 + Kdiss/[cmc])-1 which will be constant regardless of the total surfactant concentration. In cases where the surfactant cmc is comparable to the surfactant-cyclodextrin dissociation constant (Kdiss), this can mean that a significant fraction of the cyclodextrin remains uncomplexed even in the presence of a large excess of surfactant micelles. For TDOCA, assuming [cmc] ) 2.5 mM (see above) and with Kdiss given by measurements below the cmc (Table 1), the fraction of β-cyclodextrins bound in equilibrium mixtures above the cmc lies in the range 80-90%, rising to 97% for the more tightly binding γ-cyclodextrin (Table 2). As a consequence, in calorimetric titrations of cyclodextrins into micellar TDOCA mixtures, the observed heat of mixing will be less than anticipated for complete complexation:
∆H°obs ) φ(∆H°bind + ∆H°demic) Calculated values are shown in Table 2. Bearing in mind the cumulative errors in such calculations and the approximations inherent in the model, the calculated enthalpies are in reasonable agreement with observed values, suggesting that calorimetric data from these experiments above the TDOCA cmc are consistent with simple 1:1 complex formation between cyclodextrins and free monomeric TDOCA, with no significant population of nonstoichiometric complexes under these conditions ([TDOCA]tot . [CD] tot). The data described so far at relatively low cyclodextrin concentrations have given no indication of interactions other than simple 1:1 host-guest complexation between cyclodextrin and monomeric surfactant, even at very high surfactant concentrations where cyclodextrin-micelle interactions might have been anticipated. The situation is different, however, in the reverse situation when [CD] tot . [TDOCA] tot, as illustrated in Figure 4. Here we Analytical Chemistry, Vol. 70, No. 23, December 1, 1998
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Figure 4. Comparison of heat of binding of β-cyclodextrin to TDOCA at low and high relative cyclodextrin concentrations in the final reaction mixture. (A) Raw calorimetric data for sequential 10-µL injections of β-cyclodextrin (14.8 mM) into TDOCA below the cmc (1.07 mM). (B) Raw data for sequential 10-µL injections of TDOCA (1.07 mM) into β-cyclodextrin (14.8 mM). (C) Integrated heat pulse data from A (closed symbols) and B (open symbols), corrected for heats of dilution (negligible). The data from (A) fit to a single-site binding model (solid line) as in Figure 3. In (B), the TDOCA concentration is too low to achieve saturation of cyclodextrin binding sites, but the heat effects are significantly more exothermic than in (A). Heat of dilution effects are negligible.
compare the heat effects observed by mixing relatively high concentration β-cyclodextrin (14.8 mM) with nonmicellar TDOCA solution (1.07 mM) in two different ways. Figure 4A shows the heat pulses from addition of β-cyclodextrin to TDOCA in the ITC cell, giving the normal calorimetric titration curve as described above, with binding parameters from Table 1. However, in the reverse situation (Figure 4B), injection of aliquots of TDOCA solution into the more concentrated β-cyclodextrin gives a sequence of essentially constant exothermic heat pulses corresponding to the formation of complexes in the presence of a large molar excess of cyclodextrin. Although such experiments cannot show saturation of cyclodextrin binding sites, because of the low surfactant concentration available in the injection syringe, and therefore cannot yield complete titration data, the magnitude of (17) Cooper, A.; Nutley, M. A. J. Chem. Res. (S) 1982, 218-219.
5028 Analytical Chemistry, Vol. 70, No. 23, December 1, 1998
the initial heat pulses does give the apparent enthalpy of complexation.9 These heat pulses, corresponding to an enthalpy change of -36.4 ( 0.1 kJ mol-1 of surfactant injected, are significantly more exothermic than the heat of 1:1 complexation of around -32 kJ mol-1 found at lower β-cyclodextrin concentrations (Table 1). Since the surfactant concentration in these experiments (Figure 4) is always below the cmc, no additional heat effects can arise from micelle processes, and no significant heat of dilution effects were seen in any of the appropriate control experiments. Consequently, the additional exothermic interaction heat observed at the higher relative cyclodextrin concentrations must be a reflection of some additional exothermic interaction between the cyclodextrin and surfactant molecules, over and above the 1:1 complexation already characterized. The simplest interpretation is the possible formation of some ternary 2:1 cyclodextrin/surfactant complexes when β-cyclodextrin is in excess, as previously observed in other systems.17 The overall picture emerging from these calorimetric studies can, therefore, be visualized as follows. At high surfactant concentrations (above the cmc), there will be an equilibrium population of (chiral) micelles and free monomeric surfactant. Cyclodextrins will bind to the free monomeric surfactant molecules and shift the equilibrium away from the micellar phase. At high cyclodextrin concentrations, the equilibrium will be further shifted by formation of 2:1 complexes between cyclodextrin and monomeric surfactant. The net effect will be to “solubilize” the surfactant (as host-guest complexes) and also to solubilize the cyclodextrin above the concentration levels normally seen in the absence of surfactant.4 Although the absolute surfactant and cyclodextrin concentrations used for optimal chiral resolution (typically 20 mM:50 mM β-cyclodextrin/taurodeoxycholate4) are somewhat higher than those studied here (for technical reasons), it is reasonable to assume that the same range of molecular species will be found under such conditions. It is not yet clear which of these various species might be potentially responsible for interactions with chiral analytes in separation processes, nor how the distribution of species might be affected by the presence of additional components in the mixture. The nonadditive resolution enhancement effects seen in such mixtures might be simply a consequence of the higher surfactant/cyclodextrin concentrations possible in such mixed systems and/or the increased multiplicity of additional chiral species present in the solution environment. ACKNOWLEDGMENT The Biological Microcalorimetry Facility at Glasgow University is supported by funds from BBSRC and EPSRC.
Received for review May 13, 1998. Accepted September 2, 1998. AC9805246
