The lipid ⁄ protein interface as xenobiotic target site Kinetic analysis of tadpole narcosis Joachim Altschuh 1 , Sebastian Walcher 2 and Heinrich Sandermann, Jr 3,4 1 Institute of Biomathematics and Biometry, GSF – National Research Center for Environment and Health, Neuherberg, Germany 2 Lehrstuhl A fu ¨ r Mathematik, RWTH Aachen, Germany 3 Institute of Biochemical Plant Pathology, GSF – National Research Center for Environment and Health, Neuherberg, Germany 4 ecotox.freiburg, Germany High-resolution X-ray diffraction structures of integral membrane proteins have revealed structurally diverse annular, nonannular, single leaflet and laterally con- nected lipid-binding sites [1–4]. Each of the multiple lipid-binding sites of integral membrane proteins may be, to a certain extent, structurally unique, as best documented for the tightly bound phospholipid, cardio- lipin [1–4]. In spite of their analytical power, spectro- scopic methods have so far failed to resolve the multiple protein-bound lipids. Both ESR [5,6] and fluorescence spectroscopy [2,7] use overall relative macroscopic lipid-binding constants. The similarity of these binding constants among different membrane proteins has led to the conclusion that binding to the annular lipid shell shows relatively little structural specificity [2]. The overall microscopic lipid-binding constants of four integral membrane enzymes also were quite uniform [8]. By contrast, there is evidence for special lipid-binding sites having high structural specificity, or dominating the lipid dependence of func- tional proteins. For example, the mitochondrial b-hyd- roxybutyrate dehydrogenase needs the specific lipid, phosphatidylcholine, in a background of other phos- pholipids [9,10], and a specific requirement for cardio- lipin in a background of other lipids is documented for cytochrome oxidase [11] and processes of oxidative phosphorylation [12]. In order to kinetically resolve protein-bound lipids, an extended Adair-type analysis of tadpole narcosis was performed employing micro- scopic lipid-binding constants. More than a century ago, studies of tadpole narcosis led to the Meyer–Overton rule describing a positive Keywords Adair theory; kinetic modelling; lipid ⁄ protein interface; nicotinic acetylcholine receptor; tadpole narcosis Correspondence H. Sandermann, GSF – National Research Center for Environment and Health, Institute of Biochemical Plant Pathology, Ingolsta ¨ dter Landstraße 1, D-85764 Neuherberg, Germany Fax: +49 89 3187 3383 Tel: +49 89 3187 2285 E-mail: sandermann@gsf.de (Received 16 December 2004, revised 4 March 2005, accepted 10 March 2005) doi:10.1111/j.1742-4658.2005.04657.x High-resolution X-ray diffraction structures of integral membrane proteins have revealed various binding modes of lipids, but current spectroscopic studies still use uniform macroscopic binding constants to describe lipid binding. The Adair approach employing microscopic lipid-binding con- stants has previously been taken to explain the enhancement of agonist binding to the nicotinic acetylcholine receptor by general anaesthetics in terms of the competitive displacement of essential lipid activator molecules [Walcher S, Altschuh J & Sandermann H (2001) J. Biol. Chem. 276, 42191–42195]. This approach was extended to tadpole narcosis induced by alcohols. A single class, or two different classes of lipid activator binding sites, are considered. Microscopic lipid and inhibitor binding constants are derived and allow a close fit to dose–response curves of tadpole narcosis on the basis of a preferential displacement of more loosely bound essential lipid activator molecules. This study illustrates the potential of the Adair approach to resolve protein-bound lipid populations. Abbreviations nAChR, nicotinic acetylcholine receptor; SSD, sum of squared deviations. FEBS Journal 272 (2005) 2399–2406 ª 2005 FEBS 2399 correlation between the lipophilicity of chemicals and their anaesthetic potency [13,14]. The underlying molecular mechanism has remained controversial. General anaesthetics were proposed to act primarily by perturbing the membrane lipid phase [13,14], or by attacking hydrophobic protein pockets [15,16]. The latter hypothesis is favoured by site-directed amino acid exchanges [17–19] and by photoaffinity labelling [19,20]. However, many of the findings supporting lipid or protein target sites can also be interpreted in terms of the lipid ⁄ protein interface as a third candidate target site. We have previously developed a kinetic framework for anaesthetics acting by competitive displacement of essential lipid activators from the lipid ⁄ protein interface [21–23]. This mechanism has been tested with synaptosomal Ca 2+ -ATPase [24] and the Torpedo nicotinic acetylcholine receptor (nAChR) [23]. Subsequent to our report [23], a competitive dis- placement of lipids bound to the nAChR has also been reported for free fatty acids [25] and local anaesthetics [26]. The nAChR is the by far best-characterized mem- ber of the superfamily of ligand-gated ion channel proteins [27], which is currently thought to harbour the true target site(s) of general anaesthesia [15–20]. The lipid ⁄ protein interface of the nAChR and its microscopic binding and inhibition constants are used here as a prototype that allows a close fit to dose– response data for tadpole narcosis. Results Experimental system This study was based on the fact that the reported Hill coefficients of tadpole narcosis are in a diagnostic win- dow that is typical for the activation [28] and inhibi- tion [21] of lipid-dependent functional membrane proteins, namely Hill coefficients in the range 2.5–4.0. Tadpole narcosis has been characterized by Hill coeffi- cients of around 4.0 when 14 different aliphatic alco- hols were tested [29] and of around 3.4 with four different cycloalcohols [30]. The Hill coefficients of the previously analyzed enhanced agonist binding to the nAChR were between 2.3 and 4.0 [23,31], and were thus in the same diagnostic window. The multiple-site kinetic formalism for lipid-dependent proteins has therefore previously been applied to the nAChR [23] and is now applied to tadpole narcosis. General anaes- thetics are well known to also interact with the lipid- free pore region of the nAChR, but this inhibitory effect has much lower kinetic cooperativity (Hill coeffi- cients 1.0–1.3) [32,33]. In order to employ the pre- viously characterized lipid ⁄ protein interface of the nAChR as a prototype target site of tadpole narcosis, the microscopic inhibition constants of narcotic chemi- cals need to be known. The K I -value of 1-hexanol has previously been determined [23]. The additional K I val- ues needed for the present study were derived from other previously determined K I values as described in Experimental procedures and summarized in Table 1. Kinetic modelling A basic task of our kinetic modelling was to explain the ‘leftward shift’ of the dose–response curves of tad- pole narcosis relative to those of nAChR agonist bind- ing enhancement. It is known that the members of ligand-gated channel superfamilies [18–20], and mem- brane proteins generally [1–4], have sequence-specific rough surfaces that are likely to lead to nonuniform binding constants for the multiple essential lipid acti- vators. Therefore, it seemed appropriate to develop a general Adair-type formalism for the case of different binding sites (see Appendix). The more loosely bound lipid ligands have higher microscopic lipid dissociation binding constants, K L , and will more easily undergo displacement by general anaesthetics. The K L -value previously derived for the nAChR [23] is therefore allowed to increase in order to simulate the unknown narcotic receptor(s) of tadpoles, all other parameters characterizing the nAChR lipid ⁄ protein interface remaining constant. The initial analysis assumes a uni- form increase in the microscopic dissociation constant, K L , of all 40 lipid activator sites of the nAChR. This is illustrated for 1-hexanol in Fig. 1. An approximation to the data points for tadpole narcosis and the ‘left- ward shift’ is achieved by increasing K L 8.2-fold to 387 nm. This overall increase is within the $ 10-fold range of average macroscopic lipid-binding constants of various membrane proteins as documented by ESR [5] and fluorescence spectroscopy [2]. A 10-fold range of overall macroscopic binding constants for different lipids has recently also been documented by ESR- spectroscopy for the nAChR [26]. In the case of b-hydroxybutyrate dehydrogenase there was a 15-fold difference in macroscopic binding constants between the specific lipid activator, phophatidylcholine, and the nonactivating lipid, phosphatidylethanolamine [10]. The curve fits to the data points for tadpole narcosis by the additional alcohols of Table 1 are shown in Fig. 2 along with the theoretical curves for the enhancement of agonist binding to the nAChR. The latter curves were calculated with the K I values of Table 1 and Eqn (1) of Walcher et al. [23]. As discussed above it is unlikely that all lipid-bind- ing sites of a sensitive target protein differ by the same Lipid ⁄ protein interface J. Altschuh et al. 2400 FEBS Journal 272 (2005) 2399–2406 ª 2005 FEBS factor from closely related nontarget members of the same superfamily. We therefore applied our general- ized Adair-type formalism to differentiate between two lipid-binding classes (Appendix). A fixed number, m, of the total of 40 lipid-binding sites of the receptor is allowed to have increased K L values. For example, if m ¼ 4 lipids are assumed to be more loosely bound, a factor of 270 is required to achieve a fit to the data points for 1-hexanol. The results of a more extensive analysis of assuming two lipid-binding classes are sum- marized in Table 1. The corresponding dose–response curves are shown in Fig. 1 for 1-hexanol and in Fig. 2 for the other tested alcohols. Statistical quality Although the focus of the mathematical approach is on the ‘leftward shift’, illustrated in Figs 1 and 2, a statisti- cal analysis was performed for additional justification. The sums of squared deviations (SSD) for a uniform increase in K L were between 0.022 and 0.38 but were higher for small values of m. All SSD values are listed in Table 1. It should be noted that the SSD values of tadpole narcosis are of poorer quality than of agonist binding enhancement [23]. However, a survey of the lit- erature on tadpole narcosis showed that the two studies used [29,30] were among the best documented. The curve fits of Figs 1 and 2 were obtained by varying only Fig. 1. Fitted dose–response curves for 1-hexanol. The principle (upper) is to mathematically transfer the dose–response curve for the nAChR [23] to the data set for tadpole anaesthesia [29]. This ‘leftward shift’ of the whole-animal response is achieved by increasing the microscopic lipid dissociation constant, K L , of the nAChR over all binding sites: m ¼ 40 (solid line), or over part of the binding sites: m ¼ 10 (dotted line), and m ¼ 4 (dashed line). The data points for enhancement of agonist binding (s) were taken from Miller et al. [31] and those for tadpole narcosis (d) from Alifimoff et al. [29]. Table 1. Results of regression analyses. Values of log K OW , K I , K L ¢ and SSD for all alcohols analysed. In addition to the fitting procedure des- cribed in the Results, the data were also fitted using the standard two-parameter fits of the Gauss and logistic procedures; the correspond- ing SSD values are shown in the last two columns. Chemical log K OW a K I b (mM) No. receptors m with K L ¢ c K L ¢ c (lM) SSD d,e SSD d,f SSD d,g 1-Hexanol 2.03 h 0.069 j 40 0.387 0.22 0.21 0.21 10 1.85 0.25 4 12.7 0.37 1-Octanol 3.00 h 0.011 k 40 0.642 0.38 0.23 0.22 10 3.16 0.46 4 26.6 0.70 Cyclohexanol 1.23 h 0.25 k 40 0.182 0.022 0.0092 0.011 10 0.723 0.031 4 3.36 0.062 Cycloheptanol 1.88 i 0.080 k 40 0.214 0.022 0.028 0.029 10 0.899 0.024 4 4.74 0.046 Cyclooctanol 2.53 i 0.026 k 40 0.244 0.038 0.012 0.011 10 1.04 0.049 4 5.60 0.092 a Logarithms of octanol ⁄ water partition coefficient. b Microscopic inhibition constant. c Microscopic lipid dissociation binding constant of a class of more loosely bound activator molecules binding to a number m of receptor binding sites. d Sum of squared deviations. e For nonlinear regression with the present kinetic model. f Gauss fit. g Logistic fit. h From Hansch et al. [43]. i Estimated with ALOGP 2.1 [45]. j From Walcher et al. [23]. k From regression analysis, see Experimental procedures. J. Altschuh et al. Lipid ⁄ protein interface FEBS Journal 272 (2005) 2399–2406 ª 2005 FEBS 2401 a single parameter, K L . Curve fits with comparable SSD values were obtained when the data sets were sub- jected to the standard two-parameter fits of the Gauss and logistic procedures [34]. As expected, two variable parameters generally produced a better fit, but the mechanism-related model was, at least for m ¼ 40, of comparable quality. Overall, statistical quality was determined by the quality of the data sets used. Discussion Animal narcosis Narcosis is assessed by some all-or-none quantal response of individuals in an animal test population. Theoretically, if all members of the population were equally responsive, the dose–response curve would be a sharp step-function with infinite steepness [18,35]. Hill coefficients for anaesthesia of mice, rats, dogs and humans have been derived and were found to be between 10 and 22 [15,18,36]. Similarly, high slope val- ues were reported in a recent study with several mouse strains when either the loss of righting reflex or a tail clamp assay was employed [37]. High Hill coefficients of around 13 were also reported for narcosis of brine shrimps exposed in artificial sea water [38]. Uniquely low slope values of narcosis have been reported for tadpoles. The two independent studies [29,30] re-ana- lysed here used different tadpole species and experi- mental conditions. Loss of the righting reflex was assessed in one study [29], whereas the second study [30] measured the lack of sustained swimming. Hill coefficients of around 4.0 [29] and 3.4 [30] were in a diagnostic window for lipid-dependent enzymes and receptors [21–23,28] so that our analysis became possible. The quantal responses of tadpoles seem to reflect the titration of some as yet unidentified lipid- embedded target site(s). The much higher slope values of narcosis obtained with other animal species and man are attributed to population heterogeneity [35] and ⁄ or synaptic-block [36] or threshold sensing [18] mechanisms. It seems unlikely that the low Hill coeffi- cients for tadpoles can be explained by population heterogeneity alone, because this would imply an extre- mely high heterogeneity for tadpoles in contrast to all other animal species. A search for a particular mech- anism therefore seems reasonable. Role of loosely bound lipid activators The above analysis shows that loosely bound essential lipid activator molecules could act as an anaesthetic Fig. 2. Fitted dose–response curves for the straight-chain and cyclic alcohols of Table 1. Only the microscopic lipid-binding constant K L was allowed to vary, all other parameters describing the lipid ⁄ protein interface [23] remaining constant. The curves for the nAChR shown on the right were calculated as described in the Results. The following fitted curves to the data points (d)for tadpole narcosis [29,30] are shown on the left: m ¼ 40; (solid line), m ¼ 10 (dotted line), and m ¼ 4 (dashed line). Lipid ⁄ protein interface J. Altschuh et al. 2402 FEBS Journal 272 (2005) 2399–2406 ª 2005 FEBS target site as an alternative to lipid-free hydrophobic protein pockets which are currently favoured in the lit- erature [18,20]. So far, there is only indirect experimen- tal evidence for such loosely bound lipid activator molecules. X-Ray and electron diffraction studies have well documented the opposite situation, namely the existence of particular tightly bound lipid molecules such as cardiolipin [1–4]. The lipid-binding sites of the nAChR or other ligand-gated channel proteins have not been resolved into subclasses by direct measure- ment although the sum of the available evidence is strongly in favour of heterogeneous lipid-binding sites [19,26,27]. Indirect support comes from the case of a K + -channel-associated peptide, in which mutation of a single amino acid has been shown by ESR-spectro- scopy to change lipid specificity [39]. The lipid ⁄ protein interface of the nAChR was used here as a prototype to explain tadpole narcosis by assu- ming a preferential displacement of loosely bound lipid activator molecules. This analysis employed Adair-type kinetics and microscopic lipid and inhibitor binding constants. Recent reviews on high-resolution X-ray and electron diffraction structures agree with a picture of high diversity in lipid-binding modes [1–4]. The func- tional importance of individual lipid ⁄ protein binding sites is illustrated by site-directed amino acid exchan- ges along transmembrane helices [40]. Amino acid exchanges near the interface region, or in the lipid hydrocarbon region, have been shown to influence the orientation and function of transmembrane proteins [19,40]. The existence of multiple lipid ⁄ protein binding sites has led to different conclusions. On the one hand, it was stated that a full description of binding to such a heterogeneous surface is an impossibly difficult task [2]. On the other hand, functional assays of reconstituted proteins are proposed to be most crucial to yield infor- mation on the specificity of binding of particular vs. bulk lipids, the number of their binding sites and the occupancies and the cooperativity of their potential interactions [1]. In these proposed functional assays, Adair-type kinetics and the use of microscopic binding constants appear to be one of the tools to achieve the required resolution. Methods to directly determine microscopic lipid-binding constants still remain to be developed. However, an indirect support of the present analysis is provided by molecular dynamics simulation that has recently identified the lipid ⁄ protein interface as anaesthetic target site of the gramicidin ion channel [41]. Experimental procedures This study is based on two independent data sets for tad- pole narcosis by various alcohols [29,30]. The previously published characterization of the lipid ⁄ protein interface of the nAChR [23] including the total number of n ¼ 40 lipid- binding sites of the nAChR [19,42] was adopted, as were the other kinetic constants previously derived [23]. This concerns in particular the microscopic lipid dissociation constant, K L , of the nAChR under the first-order assump- tion of identity of lipid-binding sites. In terms of ‘two- dimensional’ kinetics, K L amounted to 3.75 lipid molecules per receptor molecule. This corresponded to a bulk lipid concentration of 46.9 nm [31]. The previously determined K I value of 1-hexanol (5500 molecules per receptor mole- cule, corresponding to 68.7 lm) [23] is adopted here, while the K I values of the other straight-chain and cyclic alcohols studied were calculated from a regression equation of the logarithms of K I values [23] vs. the logarithms of octa- nol ⁄ water partition coefficients, log K OW [43]. The regres- sion is based on data of ethanol, ether, 1-hexanol, isoflurane, and methoxyflurane: log K I ¼ )0.759Ælog K OW )2.67 (N ¼ 5, r 2 ¼ 0.76, SD ¼ 0.44). The higher alcohols studied in tadpole narcosis [29,30] had log K OW values out- side the range of applicability of the regression and were therefore not included in the analysis. mathematica 4.1 software was employed for all calculations. References 1 Pebay-Peyroula E & Rosenbusch JP (2001) High-resolu- tion structures and dynamics of membrane protein– lipid complexes: a critique. 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Appendix The Adair approach employing microscopic lipid-bind- ing constants has previously been taken to explain the enhanced agonist binding to the nAChR in terms of the competitive displacement of essential lipid activator molecules [23]. We generalize and extend this approach by allowing for different lipid-binding constants in this study. Thus we consider a macromolecule P with a number n of bind- ing sites for lipid L as well as for inhibitor I. Because the sites may no longer be identical for lipid, we have micro- scopic lipid dissociation constants K L1 , K L2 , , K Ln . However, we assume that the sites are identical for small inhibitor molecules that are assigned a uniform micro- scopic lipid dissociation constant K I . According to the basic model of lipid dependence [28], there is an integer a < n with the following prop- erty: a macromolecule is not functional if fewer than n ) a binding sites are occupied by lipid, and fully functional if at least n ) a sites are occupied by lipid. We derive a formula for the fraction r of functional macromolecules. To begin, we give an expression for the total concen- trations. Consider a fixed binding site (say, of number j) and denoted by [P j0 ] the concentration of macromol- ecules with empty site j. According to the mass-action law, the concentration of molecules with lipid bound to site j is given by P j0 ÂÃ Á ½L K Lj and the concentration of molecules with inhibitor bound to site j is given by P j0 ÂÃ Á ½I K I Therefore the total concentration is given by P j0 ÂÃ Á 1 þ ½L K Lj þ ½I K I  Because the sites are independent, the total concentra- tion is equal to the product P 0 ½Á1 þ L½ K L1 þ I½ K I  Á 1 þ L½ K L2 þ I½ K I  ::: 1 þ L½ K Ln þ I½ K I  with [P 0 ] the concentration of ‘empty’ molecules (with no binding site occupied). This expression may be rear- ranged as ½P 0 Á X n k¼0 Q k Á L½ k with Q k ¼ 1 þ ½I K I  nÀk Á S k 1 K L1 ; 1 K L 2 ::: 1 K Ln  and S k denoting the k-th elementary symmetric poly- nomial in n variables, thus S 0 ðx 1 ; x 2 ; ; x n ¼ 1; S 1 ðx 1 ; x 2 ; ; x n Þ¼x 1 þ x 2 þÁÁÁx n . . . S n ðx 1 ; x 2 ; ; x n Þ¼x 1 Á x 2 ÁÁÁÁÁx n Generally, S k (x 1 , , x n ) is formed by taking all possible products of k distinct factors among the x 1 , , x n , and then summing these up. For more information see Lang [44]. To verify this expression, note 1 þ I½ K I þ L½ K Lj ¼ 1 K Lj L½þK Lj Á 1 þ I½ K I  and use the algebraic identity L½þx 1 ðÞL½þx 2 ðÞÁÁÁL½þx n ðÞ ¼ L½ n þ X nÀ1 k¼0 S nÀk x 1 ; ; x n ðÞL½ k The biochemical interpretation of this rearrangement is the following: The term P 0 ½ÁQ k Á L½ k is equal to the concentration of those macromolecules to which exactly k lipid molecules are bound. Thus the fraction of functional molecules is given by J. Altschuh et al. Lipid ⁄ protein interface FEBS Journal 272 (2005) 2399–2406 ª 2005 FEBS 2405 r ¼ P n k¼nÀa Q k ½L k Q n j¼1 1 þ ½L K Lj þ ½I K I  because [P 0 ] cancels in numerator and denominator. For practical computations (with a usually quite small compared with n) another transformation is useful: Divide numerator and denominator by [L] n , and set S ¼ 1 ⁄ [L]. Then r ¼ P a k¼0 Q nÀk S k Q n j¼1 1 K Lj þ S þ S Á ½I K I  Here the numerator is just the degree a Taylor poly- nomial of the denominator, which can be deter- mined using built-in functions of symbolic computation systems. If all the K Lj ¼ K L are equal, we recover the for- mula from Walcher et al. [23] (with q ¼ 1). In this study we discuss the scenario when there are two classes of lipid-binding sites, i.e. there is a number m,0<m £ n, such that m sites have dissociation con- stant K 0 L , and the remaining n ) m sites have dissoci- ation constant K L for lipid. Lipid ⁄ protein interface J. Altschuh et al. 2406 FEBS Journal 272 (2005) 2399–2406 ª 2005 FEBS . The lipid ⁄ protein interface as xenobiotic target site Kinetic analysis of tadpole narcosis Joachim Altschuh 1 , Sebastian Walcher 2 and. of the findings supporting lipid or protein target sites can also be interpreted in terms of the lipid ⁄ protein interface as a third candidate target site.