13C Nuclear Magnetic Resonance Study of Phase Transitions in a Lipid Bilayer Embedded in a Crystalline Matrix: (C,,H,,NH,),CdCl, and (C,,H,,NH,)CuCl, B Y ROBERT BLINC, MATJA~ KO~ELJ, VENCESLAV RUTAR, IVAN ZUPANICIC AND BO~TJAN ZECg J. Stefan Institute, E. Kardelj University of Ljubljana, Ljubljana, Yugoslavia AND HONZA AREND AND RAYMOND KIND Laboratory of Solid State Physics, Swiss Federal Institute of Technology, Honggerberg, CH-8093 Zurich, Switzerland AND GERHARD CHAPUIS Institute of Crystallography, BSP, University of Lausanne, 101 5 Lausanne, Switzerland Received 10th December, 1979 The hydrocarbon parts of (C10HZ1NH3)LCdC14 and (C10H21NH3)2C~C14 represent smectic lipid bi- layers exhibiting two structural phase transitions analogous to those in biomembranes. A 13C nuclear magnetic resonance study showed that in the Cd compound the low-temperature transition is connected with a disordering of the polar heads whereas the high-temperature transition corresponds to a partial melting of the alkyl chains.In the Cu compound the sequence of the two successive transi- tions is reversed. A Landau theory describing the two transitions in terms of order parameters used in the theory of smectic liquid crystals is presented. The occurrence of phase transitions in cell membranes,'V2 which are one of the principal organizational structures of living matter, has recently attracted a great deal of attention. It has been convincingly demonstrated3p4 that the transitions in living cell membranes are due exclusively to the lipid component of the bilayer mem- brane.Most phase transition studies have therefore been performed on " model lipid membranes " which are similar in their structural properties to biomembranes, but can be much better characterized physically and exhibit sharper phase transitions. Lipid bilayers of dipalmitoyl phosphatidyl choline (DPPC) in particular clearly exhibit two first order-phase transitions,' the so-called main transition at Tc2 = 42 "C con- nected with a melting of the chains and the pretransition at T,, = 33 "C. Below T,, the lipid chains are well ordered and tilted with respect to the bilayer normal. X-ray scattering,6 cal~rimetric,~ n.m.r.'-'O and e.p.r." studies have provided much information on the microscopic nature of these transitions, but several important questions are still unanswered.One of them is the nature of the pretransition at Tcl. Another is the detailed state of motion of the hydrocarbon chains in the high (T > Tc2) and the intermediate temperature phase (Tcl < T < Tc2) and the origin of the differ- ence12 in the values of the nematic order parameter s,, = 3(3 cos2 O,, - 1) where 8, is the angular deviation of the nth C--C bond from its orientation in a hydrocarbonR. BLINC et al. 59 chain oriented parallel to a preferred direction, as measured by n.m.r.9J0 and e.p.r." Here we report on a I3C n.m.r. study of the phase transitions in the pseudo two- dimensional layer structure perovskite l3 (C10H21NH3)2CdC14 (henceforth designated C 10Cd) and (C,oH21NH3)2CuC14 (designated ClOCu) which we believe represent the first known examples of a smectic lipid bilayer embedded in a crystalline matrix. The two first-order phase transitions in ClOCd at T,, = 35 "C and Tc2 = 39 "C are closely analogous to the ones in DPPC whereas the nature of the two successive transitions in ClOCu seems to be reversed (Tcl = 36 "C, T,, = 42 "C). The results obtained yield a detailed microscopic picture of the two phase transitions in bilayer membranes and allow for the construction of a Landau theory of the " melting " of membranes in terms of order parameters used in the theory of liquid crystals.Perovskite-type layer structures of the general formula (C,H2, + 1NH3)2MC14 (short notation CnM) show a large variety of structural and magnetic phase transi- t i o n ~ . ' ~ The inorganic layers contain corner-sharing C16 octahedra with divalent metal ions in their centres (M = Cu2+, Mn2+, Cd2+, .. .) thus forming a rigid two- dimensional crystalline matrix. The NH3 groups of the alkyl ammonium chains are attached to the layers by weak N-H - C1 hydrogen bonds and, depending on the length of the chain, different packings are rea1i~ed.I~ For each packing scheme there are several different equivalent orientations of the keys (i.e. NH, groups) in the octa- hedral cavities. The structural phase transitions observed in these systems can be divided into two classes : (a) order-disorder transitions of the rigid alkyl ammonium chains, (b) con- formational transitions of the chains. For short-chain systems (n \< 3) the hindering potential is mainly determined by the key (rpolar head): key hole interaction, where- as for long chains (n > 3) the interaction among neighbouring chains becomes more important.The inorganic layers behave like a stable but elastic matrix and affect the phase transitions only indirectly through the coupling between the MCI, octahedra and the NH3 " heads " of the chains. The projection of the structure of ClOCd on the bc plane at room temperature (T< Tcl) is shown in fig. l(a). The structure consists of CdC14 layers sandwiched between well ordered alkylammonium chains which are tilted by 40" with respect to the normal to the layer. The ammonium end of each chain is linked to the layer by N-H*** C1 hydrogen bonds and each chain is coordinated to six others. In ClOCd the chains in subsequent bilayers form a zig-zag arrangement parallel to the crystal c-axis [fig.l(a)], whereas all the chains are parallel to a single direction in ClOCu and ClOMn [fig. l(b)]. In ClOCd the layers consist of nearly ideal, corner- sharing CdCl octahedra, whereas they consist of bipyramids in ClOCu. The entropy change at T,, [AS = (0.9 0.3)R per mole chains] can be explained by an order- disorder transition of rigid chains between two equivalent sites. The entropy change at Tc2, on the other hand, corresponds to A S = 0.8 R per R-C-C-R bond and can be only explained by a " melting " of the chains, or equivalently, by rapid chain isomerization via kink diffusion. In the intermediate phase of ClOCd the polar NH3 groups are flipping between two possible orientation^,'^ p = 5 1.The alkyl chains also flip by 90" around their chain axes so that neighbouring chains move in opposite directions like a 2-dimensional array of connected gears. The onset of the disordering of the polar heads in the low-temperature phase of ClOCd can be quantitatively followed l4 by measuring the temperature dependence of the I4N quadrupole coupling constant e2gQ/h and asymmetry parameter q. Since the motion between the two sites with e.f.g. tensors T(l) and T(2) is fast on the n.q.r.60 PHASE TRANSITIONS IN A L I P I D BILAYER a c (2) c (3) r B --l C FIG. 1 .-Projection of the low-temperature structure of (CloHz7NH3)zCdCl, (a) and (C10H21NH3)2- CuCl, (b) on the bc plane. The projection of the electron density map of ClOCd on the ac plane in the high-temperature phase is shown in fig.l(c). Due to 90" flips there is a dynamical dkorder between the two displayed positions of the chain which are occupied with a 50% probability.R. BLINC et al. 61 40 time-scale, the 14N n.q.r. spectrum is determined by the time averaged value of the e.f.g. tensor: (W)) = 3(1 + P)T(l) + 30 - p)T(2) - (1) - Knowing the e.f.g. tensors T(1) and T(2) from the completely ordered state, the temperature dependence of p = ( p ( t ) ) can be determined from (T(t)). The Fourier map in the high-temperature phase of ClOCd [fig. l(c)] shows in addition to the CdC1, octahedra well defined N and C( 1) positions whereas the remain- ing part of the chain is parallel to the c-axis and splits symmetrically on both sides of the mirror plane with a statistical weight 0.5 for each chain due to the 90" flipping.The average positions of C(2) and C(3) are weakly defined, whereas the terminal part of the chain [C(4) to C(lO)] forms a continuous distribution parallel to the c-axis. There is no evidence for a cone-like motion around the layer normal. The I3C spectra of the low-temperature and the intermediate-temperature phases of ClOCd are nearly identical but there is a sharp change in the 13C spectrum on going into the high-temperature phase. The angular dependence of the -CH, group spectra in the low-temperature phase is characteristic of two sets of rigid -(CH2)n- chains which are tilted by &40" with respect to the layer normal. The chain methylene groups display the full chemical shift anisotropy similar to that observed in n-eicosan15 or polyethylene.lb In the intermediate-temperature phase the chains are still tilted by &40" and almost rigid (fig.2). The bulk of the data can be described by an axially symmetric 13C chemical shift tensor: a1 = +(Sll + S,,) = 43 3 p.p.m., 811 = S,, = 15 + 5 p.p.m. with respect to TMS. is parallel to the chain direction. The axial symmetry of the l3 C tensor is due to the 90" flips around the chain axis which result in a rapid exchange of Sll and a,, but do not The symmetry axis 611 = 0 90 180 0 45 90 13 5 180 Ull" FIG. 2.-Angular dependence of the 13C spectra in the high temperature (42 "C) and intermediate temperature (36 "C, insert) phases of ClOCd. v, stands for the angle between the c axis and the direction of the external magnetic field.vP3C) = 67.9 MHz, a I H.62 PHASE TRANSITIONS I N A LIPID BILAYER 1.0 0.8 s 0.6 0.4 0.2 affect ~ 3 ~ ~ . The nematic order parameter S with respect to t,he preferred chain direction, 0 = &40°, is here about one, S x 0.95-0.99. There is another set of I3C lines belong- ing to the less rigid terminal methylene groups which is also axially symmetric and can be described by S x 0.75. The angular dependence of the 13C spectra in the high-temperature phase is com- pletely different (fig. 2) from that in the low- and intermediate-temperature phases. It shows that all chains are equivalent and normal to the layers. Three different sets of 13C lines can be resolved. The most intense line belongs to the bulk of the -CH2 groups.It can be described by 611 = 20 2 p.p.m. and d1 = &S,, + dz2) = 34 p.p.m. The anisotropy of the chemical shift tensor is only partially removed by the molecular motion (chain isomerization via fast kink diffusion) and the nematic order is still significant : I ---o--- I I I la) n - - I I I - I< I - I I (bl I , 1 1 - 1 I - - lcl I ----- Another weak line belongs to the terminal methylene group, -CH2-CH3, and can be described by 611, = 20 p.p.m., 61, = 25 & 1 p.p.m. The third line is due to the methyl group. Here ( T I I ~ ~ ~ = 10 & 1 p.p.m., BICHs = 14 It 1 p.p.m. With the help of the rigid lattice 13C shift tensors of n-eicosane l5 (n-C20H42) we find that S(cc-CHJ x 0.25 & 0.05 and S(-CH3) - 0.20 x 0.05. The above results and the absence of a significant flexibility gradient along the main part of the chain is at vari- ance with the more " liquid like " picture of the bilayer interior suggested by e.p.r.spin label studies,11 but agrees with the deuteron resonance data.9 The interpretation of the high-resolution 13C spectra of ClOCu is complicated by the fact that the paramagnetic contribution of the Cu2+ ions is superimposed on the 13C chemical-shift anisotropy. The contribution of the Cu2+ ions to the magnetic field at a given 13C position has been evaluated and subtracted from the experimental data to yield the I3C chemical-shift tensors. In the high-temperature phase the results agree with those of ClOCd within the limits of experimental error. This demonstrates that, as far as the chain dynamics is concerned, the high-temperature phase is the same in both ClOCd and ClOCu.On cooling down through T,, = 42 "C into the intermediate temperature phase r c 2 I IR. BLINC etal. 63 the spectra change only very little. The angular dependence is the same as in the high temperature phase at Tc2 > 46 "C > Tcl. This result is significantly different from the case of ClOCd where the chains are well ordered and tilted in the intermediate temperature phase. At Tc2 = 36 "C the I3C spectra of ClOCu abruptly change. The lines broaden and the angular dependence of the 13C chemical shifts qualitatively agrees with the data obtained in the low temperature phase of ClOCd if we suppose that all chains are parallel to a single direction and tilted by 40" with respect to the c-axis.The temperature dependence of the nematic order parameter S of ClOCu is plotted as a function of temperature in fig. 3 for the bulk -CH2 groups, the terminal methylene group and the methyl group (fig. 3). The hydrocarbon parts of ClOCd and ClOCu thus represents a smectic liquid crystal with structure similar to the interior of the bilayer lipid membrane^.'^-'^ Let us therefore try to describe the two phase transitions in ClOCd and ClOCu by a Landau type expansion of the non-equilibrium free energy P in terms of order parameters 8, S - Sc andp, used in the theory of smectic liquid crystals: l7 I; = +AB2 + $B04 + u(T - Tc2)(S - Sc) - $c(S - SC)' + $d(S - Sc)4 + + +ap2 + $bp4 - 5;A'Q2(S - Sc) - +ap2(S - Sc). (3) S S ClOCd \! FIG. 4.-Schematic temperature dependences of the order parameters S, p and 8 for ClOCd and ClOCu.The d.t.a. curves for these two systems are shown for comparison.64 PHASE TRANSITIONS I N A LIMPID BILAYER Here S stands for the average nematic order parameter and A , B, a, c, d, b, A' and a' are all positive constants whereas a = p(T-T,). The smectic-C order parameter 8 gives the average tilt of the molecules with respect to the layer normal whereas p is the orientational order parameter for the 90" flipping of the chains and the terminal NH3 groups between the two equilibrium orientations corresponding to p = rt 1. S, is the critical value of the average nematic order parameter S, i.e., the arithmetic average of S in the melted and rigid phase coexisting at the first-order transition tem- perature Tc2 (fig.4). In deriving expression (3) we assumed that there are two import- ant driving mechanisms which induce the transitions: the melting of the chains and the disordering of the keys. If T,, & T,., as seems to be the case in ClOCd, a z const. > 0 and the melting of the chains is the important driving mechanism which induces the transitions in S as well as in 8 and p. In contrast to the isotropic-nematic transi- tion, here S is not a symmetry-breaking order parameter and is not zero, both above and below Tc2. Because of that the linear term in the expansion of F in powers of (S - S,) is not identically equal to zero as in the case of nematic liquid crystals l7 but has the same structure as the free energy at liquid-gas phase transitions.The first coupling term -&A'02(S - Sc) accounts for the fact that rigid chains show a stronger tendency for tilting because of the attractive van der Waals interaction between the chains. The second coupling term -3a'p2(S - S,) describes the fact that " melted " molecules are axially symmetric and the potential hindering the rotation around the long axis is smaller above T,, than in the completely rigid state. Minimizing the total free energy with respect to p and 8 we obtain the following stable solutions for the symmetry-breaking order parameters 8 andp as functions of S : (i) 9 = 0, S < S, = A/A' + Sc (4) and (iii) p = 0, S < S2 = a/a' + S, (6) The temperature dependence of S is obtained by inserting expressions (4)-(7) into eqn (3) and minimizing with respect to S.The observed sequence of phases in ClOCd is obtained by choosing S, > S1, i.e., a/a' > 0 so that - Inthiscasewehavefor: T > T C 2 : S < S , < S c , 8 = O , p = 0 , (94 T,, < T < Tc2:S > s,, 0 # 0 , p = 0 (9b) T < T,,:S> s,, B # 0 , p # 0. (94 and for The high-temperature transition at Tc2 corresponds to a partial melting of the chains which simultaneously destroys the tilting of the molecules, whereas the low-tempera- ture transition at T,, corresponds to an orientational transition and a disordering of the polar " heads " in analogy to DPPC and biomembranes. If, however, a/a' < 0, so that S2 < S, andR. BLINC et al. 65 we get the reversed order of the two phase changes. With increasing temperature we get first the chain melting, and at still higher temperatures the disordering of the keys as observed in ClOCu (fig.4). Here we have: T < T c , : S < S 2 < S c , 8 = 0 , p = 0 (1 la> Tc, < T < Tc, : S < Sc, 8 = 0, p # 0 (1 1 4 T < Tc2: S > Sc, 0 # 0 , p + 0 . (1 1 4 The reversed order of successive phase transitions in ClOCd and ClOCu is thus the result of a difference in the key-key-hole interaction. Until now we have analysed only one bilayer. To get the observed ordering of the whole crystal one has to introduce an interaction between the two neighbouring hydrocarbon bilayers on the opposite sides of the same MC14 layer. The additional term in the free energy can be written as F' = (12) where 0, and 82 are the smectic-C order parameters on the opposite sides of the MC14 layer.For K > 0 one obtains 8, = 8, as observed in ClOCu and for K < 0, 8, = -02 as observed in ClOCd (fig. I). D. Chapman, Quart. Rev. Biophys., 1975, 8, 185. J. F. Nagle, J . Membrane Biol., 1976, 27, 233; J . Chem. Phys., 1973, 58, 252; Proc. Roy. SOC. A, 1974,337, 569. D. L. Melchior and J. M. Stein, Biochim. Biophys. Acta, 1977, 466, 148. S. MarEelja, Biochim. Biophys. Acta, 1974, 367, 165. A. Tardieu, V. Luzzati and F. C. Reman, J . Mol. Biol., 1973, 75, 71 1 . M. C. Philips, R. M. Williams and D. Chapman, Chetn. ghys. Lipids, 1969, 3, 234. J. Charvolin, P. Manneville and B. Deloche, Chem. Phys. Letters, 1973, 23, 345. A. Seelig and J. Seelig, Biochemistry, 1974, 13, 4839. B. J. Gaffney and H. M. McConnell, J. Magnetic Resonance, 1974, 16, 1 . N. 0. Petersen and S. I. Chan, Biochemistry, 1977, 16, 2657. ' E. Sackmann, Ber. Bunsenges. phys. Chem., 1978, 82, 891 and references therein. lo J. Urbina and J. S . Waugh, Proc. Nut. Acad. Sci., 1974, 71, 5062. l3 R. Blinc, B. ZekS and R. Kind, Phys. Rev. B, 1978, 17, 3409 and references therein. l4 J. Seliger, R. Blinc, H. Arend and R. Kind, 2. Phys., 1976, B25, 189. l6 S. J. Opella and J. S. Waugh, J . Chem. Phys., 1977, 66,4919. l7 P. G. de Gennes, The Physics of Liquid Crystals (Clarendon Press, Oxford, 1974). D. L. Van der Hart, J. Chem. Phys., 1976, 64, 830. R. Kind, S. PleSko, H. Arend, R. Blinc, B. ZekS, J. Seliger, B. Loiar, J. Slak, A. Levstik, C. FilipiE, V. Zagar, G. Lahajnar, F. Milia and G. Chapuis, J. Chem. Phys., 1979, 71, 2118. l9 R. Blinc, M. I. Burger, V. Rutar, B. &kS, R. Kind, H. Arend and G . Chapius, Phys. Rev. Letters, 1979, 43, 1679.