Phosphatidylcholines with sn -1 Saturated and sn -2 cis -Monounsaturated Acyl Chains THEIR MELTING BEHAVIOR AND STRUCTURES*

Recently, we have shown by high resolution differen- tial scanning calorimetry that the position of a cis double bond ( (cid:68) -bond) in a series of 1-stearoyl-2-octade-cenoyl- phosphatidylcholines can affect the phase transition temperature ( T m ) or enthalpy ( (cid:68) H ) of the gel-to-liquid crystalline phase transition of this series of lipids in the following manner. The value of T m (or (cid:68) H ) is minimal when the (cid:68) -bond is positioned at C(11) in the sn -2 acyl chain; in addition, this value increases steadily as the (cid:68) -bond migrates toward either end of the acyl chain, resulting in a symmetrical, inverted bell-shaped profile (Wang, Z.-q., Lin, H.-n., Li, S., and Huang, C. (1995) J. Biol. Chem. 270, 2014–2023). In this communication, we have further demonstrated the inverted bell-shaped profile of T m using 1-arachidoyl-2-eicosenoyl-phosphati- dylcholines. In addition, we have extended the lipid series of 1-stearoyl-2-octadecenoyl-phosphatidylcholines to include 1-arachidoyl-2-octadecenoyl- phosphatidylcholines and 1-behenoyl-2-octadecenoyl-phosphatidyl- choline, each series with a (cid:68) -bond at varying carbon position of 6, 7, 9, 11, 12, and 13. Calorimetric with different chain lengths and distinct position of the double bond were purchased from Sigma or Nu Chek Prep, Inc. (Elysian, MN). Lysophosphatidylcholines with var- ious saturated acyl chain lengths were obtained from Avanti Polar Lipids, Inc. (Alabaster, AL). High Resolution DSC Measurements— All DSC studies were per-formed on a Microcal MC-2 microcalorimeter with a DA-2 digital inter- face and data acquisition utility for automatic collection (MicroCal, Inc., Northampton, MA). A constant heating scan rate of 15 °C/h was gen- erally used for the DSC experiments. The T m and (cid:68) H values were taken from the DSC curves after the first heating scans, and an average value for T m or (cid:68) H was reported for each sample (4).

noic lipid relative to the saturated counterpart. Finally, two general equations relating T m with the structural parameters of cis-monoenoic phosphatidylcholines are presented. These equations, formulated primarily on the assumption that the short segment of the sn-2 acyl chain acts as a perturbing element, are shown to have strong predictive power in estimating the T m values of the gel-to-liquid crystalline phase transitions for sn-1 saturated/sn-2 cis-monounsaturated phosphatidylcholines.
Phosphatidylcholines isolated from the plasma membrane of eukaryotic cells are a structurally diverse group of phospholipids. The bewildering variety of membrane phosphatidylcholines originates from the numerous possible combinations of sn-1 and sn-2 acyl chains, most of which are derived biosynthetically from saturated and unsaturated fatty acyl-CoA, respectively. By and large, the acyl chain lengths and chemical structures of the two acyl chains in a membrane phosphatidylcholine molecule are different. A good example is 1-palmitoyl-2-arachidonoyl-phosphatidylcholine, one of the most abundant lipid species found in liver cells. In the plasma membrane, phosphatidylcholine molecules aggregate in the form of the lipid bilayer due to their amphipathic nature, thus constituting the basic structural matrix. In addition, some phosphatidylcholine molecules serve as the metabolic precursors of intrinsic signaling elements, thus conferring some regulatory properties on eukaryotic cells. Consequently, it is important and relevant to investigate the intricate relationships between the structure and properties of the lipid bilayer composed of naturally occurring phosphatidylcholines.
Although the structures of a large number of phospholipids with saturated and identical number of carbon atoms in their two acyl chains have been determined by crystallographic approaches (1), the prevalence of the single-crystal structures of naturally occurring phospholipids is still elusive. However, computer-based molecular modelings for biomolecules have been advanced rapidly in recent years. This approach offers the possibility of simulating the unknown structure of naturally occurring phospholipids based on the single-crystal structures of saturated phospholipids (2). The combination of this computational approach together with calorimetric data, for example, has provided valuable information relating the structure and melting behavior of naturally occurring phospholipids in the bilayer (3,4).
In this communication, the thermotropic phase behavior of 26 molecular species of phosphatidylcholine with sn-1 saturated/sn-2 cis-monounsaturated acyl chains was studied by high resolution differential scanning calorimetry (DSC). 1 These lipids were semisynthesized in this laboratory; however, they all resemble strictly the naturally occurring monoenoic phosphatidylcholines. The structures of these cis-monoenoic phosphatidylcholines were simulated using the molecular mechanics method, specifically the MM3(92) force field (5). It is well known that fully hydrated cis-monoenoic phosphatidylcholines can exhibit calorimetrically a characteristic T m of the gel-toliquid crystalline phase transition; moreover, this T m is always far below that of the saturated counterpart (6,7). We have undertaken in this work the combined approach of DSC and MM methods in order to gain a deeper understanding of the difference in T m between the cis-monoenoic phosphatidylcholine and the saturated counterpart. Also, we will show in this work that quantitative equations relating T m with the structural parameters for cis-monoenoic phosphatidylcholines can be developed; these equations allow us to predict the T m values for cis-monoenoic phosphatidylcholines in general.

EXPERIMENTAL PROCEDURES
Semisynthesis of Monounsaturated Phosphatidylcholines-Isomerically pure (Ͼ98 mol %) monounsaturated phosphatidylcholines were semisynthesized at room temperature by acylation of CdCl 2 adducts of lysophosphatidylcholine, in dry chloroform, with cis-monounsaturated fatty acid anhydride that was prepared in situ from unsaturated fatty acid and dicyclohexylcarbodiimide, in the presence of catalyst 4-pyrrolidinopyridine, according to the modified procedure of Mena and Djerassi (8) as described previously (9). All reactions were carried out under an N 2 atmosphere to avoid lipid oxidation. The synthesized lipids were purified by silica gel column chromatography as described elsewhere (9). All monounsaturated fatty acids with different chain lengths and distinct position of the double bond were purchased from Sigma or Nu Chek Prep, Inc. (Elysian, MN). Lysophosphatidylcholines with various saturated acyl chain lengths were obtained from Avanti Polar Lipids, Inc. (Alabaster, AL).
High Resolution DSC Measurements-All DSC studies were performed on a Microcal MC-2 microcalorimeter with a DA-2 digital interface and data acquisition utility for automatic collection (MicroCal, Inc., Northampton, MA). A constant heating scan rate of 15°C/h was generally used for the DSC experiments. The T m and ⌬H values were taken from the DSC curves after the first heating scans, and an average value for T m or ⌬H was reported for each sample (4).
MM Calculations-The MM3 force field (version 92), obtained from Quantum Chemistry Program Exchange, Department of Chemistry, Indiana University, was used as the software package for the MM calculations to simulate the energy-minimized structures and steric energy (E s ) for various cis-monoenoic phosphatidylcholines under study. These calculations were run on IBM RS/6000 computer workstation as described previously (4). It should be emphasized, however, that the MM3(92) was originally developed by Allinger and co-workers for hydrocarbons (5). It should also be noted that hydrocarbon chains are by far the most predominant moieties in membrane phospholipids. Thus, we feel that it is completely justified to use the Allinger's MM3 program for simulating cis-monoenoic phospholipid molecules.
In modeling the various structures of cis-monoenoic phosphatidylcholine molecules, the structure of the diacyl moiety of 1-palmitoyl-2oleoyl-phosphatidylcholine with a type IIIb kink motif (2) was used as the starting point; in addition, the headgroup structure of the monoenoic phosphatidylcholine molecule was assumed initially to be identical to that of the dihydrate of dimyristoyl phosphatidylcholine, Structure B, obtained by x-ray diffraction (10). For instance, the initial crude structural model of 1-arachidoyl-2-gondoyl-phosphatidylcholine was constructed as follows: four methylene units, each being linked by the trans C-C bond, were first added to the sn-1 acyl chain of 1-palmitoyl-2-oleoyl-phosphatidylcholine with a type IIIb kink motif. Then, two methylene units were added to the upper segment of the sn-2 acyl chain to form the C(3)-C(4) segment. The resulting crude structure of 1-arachidoyl-2-gondoyl-phosphatidylcholine was subsequently refined by subjecting to energy minimization using Allinger's MM3 program. In order to ensure that the minimum in the potential energy surface was practically reached, additional rounds of energy minimizations were routinely performed. The application of Allinger's program in determining the structure of lipids and the rotational energy barrier of the C-C bond in lipid acyl chain was discussed in detail elsewhere (2). Here, it is worth pointing out the reason why 1-palmitoyl-2-oleoyl phosphatidylcholine with a type IIIb kink was chosen as the starting point for the construction of other monoenoic lipid molecules. This is due to the excellent agreement between the computational structure obtained by MM approach and the reconstructed structure based on x-ray diffraction data detected for this particular conformation of 1-palmitoyl-2oleoyl-phosphatidylcholine (2).

RESULTS
Before we present our experimental and computational results, it is appropriate to mention first the rules of nomenclature for abbreviating diacyl phospholipids adopted in this study. For a saturated diacyl lipid species, C(X):C(Y)PC denotes a phosphatidylcholine (PC) molecule with X and Y carbon atoms in the sn-1 and sn-2 acyl chains, respectively; hence, the notation C(X) preceding the colon in C(X):C(Y)PC refers to the sn-1 acyl chain with X carbons, and the notation C(Y) succeeding the colon gives the total number of carbons (Y) in the sn-2 acyl chain. The convention for numbering the carbon atom in the acyl chain begins at the carboxyl end. The sn-2 acyl chain of a saturated diacyl C(20):C(18)PC, for instance, has 18 carbon atoms; its carbonyl carbon is C(1) and its terminal methyl carbon is C(18). For a sn-1 saturated/sn-2 monounsaturated phosphatidylcholine molecule, it is abbreviated as C(X):C(Y: 1⌬ n )PC. Here, we designate the position of the cis double bond as ⌬ n , where the superscript n refers to the lower number of the two carbon atoms linked by the double bond. For instance, the double bond at the C(9)ϭC(10) position in the oleoyl chain is designated by ⌬ 9 . The numerical value 1 after the colon in the notation C(Y:1⌬ n ) refers to a single cis carbon-carbon double bond (⌬) at the n position along the sn-2 acyl chain. For 1-arachidoyl-2-gondoyl-phosphatidylcholine and 1-palmitoyl-2oleoyl-phosphatidylcholine, they can thus be abbreviated as C(20):C(20:1⌬ 11 )PC and C(16):C(18:1⌬ 9 )PC, respectively.
The Effect of the ⌬ n -Position on the Phase Transition Behavior of Bilayers Composed of 1-Eicosanoyl-2-eicosenoyl-phosphatidylcholines- Fig. 1A shows four DSC heating thermograms for lipid dispersions prepared individually from C(20): C(20:1⌬ n )PC with n ϭ 5, 8, 11, and 13. Each thermogram is characterized by a sharp, symmetric, and pronounced endothermic phase transition that can be assigned as the gel-toliquid crystalline phase transition or the chain melting transition. The phase transition temperature, T m , is the temperature corresponding to the maximal peak height of the transition curve. The T m values are distinctly different for these four isomers of C(20):C(20:1⌬ n )PC, being 44.9, 30.7, 19.7, and 22.8°C as n ϭ 5, 8, 11, and 13, respectively. Fig. 1B shows the T m value as a function of the ⌬-bond position, ⌬ n , for the series of lipids shown in Fig. 1A. It is evident that a steady migration of the ⌬-bond from C(5) to C (8) and then to C(11) results in a progressive decrease in T m . However, the incremental drop in T m does not correspond proportionally to the stepwise increase in the ⌬ position. Interestingly, as the ⌬-bond migrates further down along the sn-2 acyl chain from C(11) to C(13), the T m value increases slightly. The smooth parabolic curve connecting the four data points seen in Fig. 1B is the least-squares fitting curve. This parabolic character of the T m versus ⌬ n -position curve is in close agreement with previous DSC studies using C(18):C(18:1⌬ n )PC with n ϭ 6, 7, 9, 11, 12, and 13 (4). The transition enthalpy (⌬H) associated with the chain melting transition is calculated from the area under the endothermic peak, and the ⌬H values for aqueous dispersions prepared from the four isomers of C(20):C(20: 1⌬ n )PC under study are summarized in Table I. The change in ⌬H as a function of the ⌬ n position is observed to follow, within experimental errors, the same general trend as that of the T m . However, due to the large scattering of the experimental data, a clear minimum in ⌬H at n ϭ 11 in the ⌬H versus ⌬ n position curve is not discernible (Table I).
Of the four heating thermograms shown in Fig. 1A, the one exhibited by the aqueous dispersion of C(20):C(20:1⌬ 8 )PC shows a single transition with the sharpest endothermic peak centered at 30.7°C and a peak width at half-height (⌬T1 ⁄2 ) of 0.3°C. On cooling, however, the exothermic transition of the same lipid sample gives rise to a peak centered at 30.7°C with a discernible shoulder at 31.1°C (DSC curve not shown). The molecular origin of the shoulder is uncertain; nevertheless, it seems that an obligatory and transient intermediate state  (Fig. 1B). These two series of cis-monoenoic phosphatidylcholines have a common structural feature, namely, the total numbers of carbon atoms in the two acyl chains being identical. Hence, the chain length difference between the two acyl chains (⌬C) for each lipid species is the same. In order to examine the possible effect of the sn-1 acyl chain on the parabolic character of the T m values of cis-monoenoic phosphatidylcholines with different ⌬-bond position in the sn-2 acyl chain, two additional series of monoenoic phosphatidylcholines with different ⌬C values were synthesized. These two series of lipids, C(20):C(18:1⌬ n )PC and C(22):C(18:1⌬ n )PC with n ϭ 6, 7, 9, 11, 12, and 13, were then studied by DSC. Fig. 2 shows the representative DSC heating thermograms for C(20):C(18:1⌬ n )PC and C(22):C(18:1⌬ n )PC with n ϭ 6, 7, 9, 11, 12, and 13. Most thermograms are characterized by a highly cooperative endothermic transition, which can be readily assigned as the chain melting or the gel-to-liquid crystalline phase transition. Of those with two endotherms, the larger transition always occurs at a higher temperature, which is assigned as the gel-to-liquid crystalline phase transition. This assignment is supported by the observation that transition characteristics of this high temperature endotherm are reproducible after repeated cooling/heating cycles, whereas those of the low temperature transition are thermal-history dependent. For example, the C(20):C(18:1⌬ 11 )PC dispersion exhibits two overlapped transitions (Fig. 2). The high temperature transition peaked at 8.5°C and is reproducible upon repeated heatings or coolings. The low temperature transition, however, has a peak at 7.2°C upon heating; this peak is shifted to 7.0°C upon cooling. We, therefore, assign the high temperature transition as the gel-to-liquid crystalline phase transition for fully hydrated C(20):C(18:1⌬ 11 (4) are also included in the same plot. Structurally, these three series of monoenoic lipids differ in their sn-1 acyl chain lengths. Several distinct features are immediately evident from this plot. First, the parabolic T m -⌬ n curve shifts to higher temperatures as the sn-1 acyl chain length increases. Second, the ⌬ n point corresponding to the minimal T m in each curve is upshifted slightly as the sn-1 acyl chain length increases. In fact, the value of ⌬ n corresponding to the minimal T m is calculated by the least-squares analysis to occur at n ϭ 10, 10.4, and 10.8 as the sn-1 acyl chain length increases from 18 to 20 and then to 22, respectively. In each of these least-squares analyses, an equation of T m ϭ a 0 ϩ a 1 (⌬ n ) ϩ a 2 (⌬ n ) 2 has been used to fit the experimental date, where a 0 , a 1 , and a 2 are the coefficients. In addition, the difference in T m between any pair of the three curves (⌬T m ) shown in Fig. 3 decreases as the ⌬-bond migrates from C(10) toward either the carboxyl or the methyl end. Interestingly, the decrease in ⌬T m is more pronounced toward the chain methyl terminus. Finally, it is evident from Fig. 3 that all experimental T m values for monoenoic lipids with the ⌬-bond at C(13) are virtually superimposable. The ⌬H values for these lipids are, within experimental errors, also virtually identical ( Table I) sitions of these three series of monoenoic lipids with a common ⌬ n position at C(13) are presented in Table I. In Fig. 4A, the plot of T m as a function of the total number of carbon atoms in the sn-2 acyl chain (Y) is presented. Within the narrow range of Y from 18 to 22; the T m is observed to be a linear function of Y for all three series of cis-monoenoic lipids with constant values of X and n. The sn-2 acyl chain of a monoenoic lipid in the gel-state bilayer can be considered to consist of two linear segments separated by the cis double bond (vide post). As the Y value increases, the sn-2 acyl chain length of the lipid molecule in the gel-state bilayer increases; in particular, only the lower or the shorter segment of the sn-2 acyl chain increases due to the fixed position of ⌬-bond at C (13). In addition, the thickness of the hydrocarbon core of the transbilayer dimer (N) and the effective chain length difference between the two acyl chains (⌬C) also change as the Y values increase in these cis-monoenoic lipids. The quantitative definitions of N and ⌬C in terms of X, Y, and n for cis-monoenoic phosphatidylcholines are given in the next section; nevertheless, the data shown in Fig. 4A indicate that the net effect of the length of the shorter segment of the monounsaturated sn-2 acyl chain, the bilayer thickness, and the acyl chain length difference can result in a situation in which the T m value of the lipid bilayer is linearly related to Y.
The same nine experimental T m values shown in Fig. 4A are replotted in Fig. 4B as a function of the number of carbons in the sn-1 acyl chain (X). It should be noted that the increase in X from 18 to 20 and then to 22 for the three series of cismonoenoic lipids shown in Fig. 4B results in a corresponding increase of two C-C bond lengths in both ⌬C and N values. Here, each curve in Fig. 4B reflects the subtle change in the net effect of the simultaneous increase in ⌬C and N on T m , which varies from one lipid series to the next.
Based on the experimental curves illustrated in Fig. 4, A and B, it is evident that the T m of the gel-to-liquid crystalline phase transition for cis-monoenoic phospholipids can be influenced by X, Y, and ⌬ n , which, in turn, can be related to the structural parameters ⌬C, N, and the length of the shorter segment of the sn-2 monounsaturated acyl chain. The unique value of T m for bilayers of a given cis-monoenoic phosphatidylcholine can thus be considered as a net result of the fine interplay of the three structural parameters.
Molecular Structures of Phosphatidylcholines with sn-1 Saturated/sn-2 cis-Monounsaturated Acyl Chains as Simulated by the Molecular Mechanics Method-Since x-ray crystallographic structures of phosphatidylcholines with sn-1 saturated/sn-2 cis-unsaturated acyl chains do not exist, we have employed in this study the computer graphics-aided computational approach to simulate the structures of various cis-monoenoic phosphatidylcholines. As described under "Materials and Methods," this computational approach utilizes the MM method; specifically, the MM3(92) force field developed by Allinger and co-workers is used to generate the energy-minimized lipid structure and to calculate the steric energy of the energy-minimized lipid structure. The energy-minimized structure, however, represents the molecular structure of the lipid packed in the bilayer assembly in the crystalline state.  Fig. 5. Here, lipids in both the monomeric and dimeric states are orientated in the same manner with the zigzag plane of the all-trans sn-1 acyl chain lying on the paper (or x-y) plane. The sn-2 acyl chain of each phospholipid molecule is seen to contain two linear segments separated by a ⌬-bond-containing sequence, g ϩ s ϩ ⌬s ϩ , where g ϩ and s ϩ are gauche (ϩ) and skew (ϩ) conformations, respectively. The zigzag planes of the two segments in the sn-2 acyl chain align perpendicularly to the paper plane; however, the long axes of the two segments run in parallel with the directionality of the sn-1 acyl chain.
If we take the chain length difference between the sn-1 and sn-2 acyl chains of C(20):C(20:1⌬ 13 Ϫ 2), respectively, in terms of C-C bond lengths along the long chain axis. In fact, the value of ⌬C for a mixed-chain C(X):C(Y:1⌬ n )PC can be generalized as follows: ⌬C ϭ X Ϫ Y ϩ ⌬C ref . Furthermore, the chain length of the sn-1 acyl chain is X Ϫ 1 carbon-carbon bond lengths, and the chain length of the monounsaturated sn-2 acyl chain, in terms of C-C bond lengths, from the point corresponding to the carbonyl carbon of the sn-1 acyl chain to the methyl terminus is X Fig. 5A that this linear portion of the sn-2 acyl chain can be considered to consist of two segments separated by the ⌬-bond. The length of the lower segment (LS), which extends from the olefinic carbon C(n ϩ 1) to the terminal methyl carbon is (Y Ϫ n Ϫ 1), and the length of the upper segment (US) Finally, let us define the thickness of the hydrocarbon core of the trans-bilayer dimer (N), which is taken to be the length separated by the two carbonyl oxygens of the sn-1 acyl chains along the long chain axis. The value of N can be related to X and Y as follows: VDW is the van der Waals' distance between the two opposing terminal methyl groups from the sn-1 and sn-2 acyl chains and is taken to be 3 C-C bond lengths.
For saturated identical-chain phosphatidylcholines such as C (14):C(14)PC packed in the gel-state bilayer, the sn-1 acyl chain is effectively longer than the sn-2 acyl chain along the long molecular axis. In fact, the methyl groups of sn-1 and sn-2 acyl chains within the same lipid molecule in the gel-state bilayer are separated from each other by about 1.5 C-C bond lengths (11). In the presence of a cis C-C double bond, the sn-2 acyl chain is further shortened by about 0.8 C-C bond lengths when a sequence g ϩ s ϩ ⌬s ϩ is taken into consideration (2,4). Consequently, the value of ⌬C ref can be reasonably assumed to be 2.3 C-C bond lengths for C(X):C(X:1⌬ n )PC packed in the gel-state bilayer. The various structural parameters for C(X): C(Y:1⌬ n )PC packed in the gel-state bilayer involving the ⌬C ref term, as discussed in the above paragraph, can thus be ex-pressed as follows: ⌬C ϭ X Ϫ Y ϩ 2.3; US ϭ n Ϫ 2.3, and N ϭ X ϩ Y Ϫ 1.3. All of these terms have the unit of C-C bond lengths. The calculated values of the various structural parameters for all the cis-monoenoic lipids under study are summarized in Table II. DISCUSSION It is well known that the gel-to-liquid crystalline phase transition behavior exhibited by fully hydrated phosphatidylcholines is modulated by many internal factors, most notably the variation in the chain length and the chemical structure of the hydrocarbon chain (12). In addition, the T m and ⌬H values of the main phase transition for aqueous dispersions of monoenoic phosphatidylcholines depend critically on the position of the cis carbon-carbon double bond (⌬ n ) in the sn-2 acyl chain (4). For example, a parabolic T m Ϫ ⌬ n curve with the minimal T m at C(11) is obtained after a single ⌬-bond is introduced into the sn-2 acyl chain at different positions in C(18):C(18)PC. This parabolic character of the T m Ϫ ⌬ n curve has been attributed primarily to the preferentially favorable interactions between the longer linear segment of the sn-2 acyl chain with the neighboring saturated sn-1 acyl chains in the gel-state bilayer (4).
In this study, the parabolic nature of the T m Ϫ ⌬ n curve observed originally for C(18):C(18:1⌬ n )PC is confirmed by C(20):C(20:1⌬ n )PC (Fig. 1). In addition, we have expanded the subclass of the lipid series used in the earlier work by including synthetic mixed-chain phosphatidylcholines in which the total number of carbon atoms in the sn-1 acyl chain is different from that in the sn-2 acyl chain. Our DSC results shown in Fig. 3 indicate that the T m -lowering effect of the ⌬-bond in the sn-2 acyl chain is clearly influenced by the length of the sn-1 acyl chain when the ⌬-bond is located near the center of the chain. By contrast, the T m -lowering effect of the ⌬-bond at C(13) is unchanged as the saturated sn-1 acyl chain increases from 18 to 22 carbon atoms (Fig. 3). The questions of exactly how the increase in the sn-1 chain length can affect the T m (or ⌬H) of mixed-chain monounsaturated phosphatidylcholine when the cis ⌬-bond is near the center of the sn-2 acyl chain and how the effect is abolished when the cis ⌬-bond is at C(13) are discussed in the following paragraphs.
For C(X):C(18:1⌬ n )PC packed in the gel-state bilayer, the thickness of the hydrocarbon core of the trans-bilayer dimer (N) and the ⌬C value of the monomeric lipid increase with increasing chain length of the sn-1 acyl chain, since both N and ⌬C values are linearly related to X when Y in C(X):C(Y:1⌬ n )PC is kept constant (N ϭ X ϩ Y Ϫ 1.3 and ⌬C ϭ X Ϫ Y ϩ 2.3). As both N and ⌬C values increase simultaneously and as the ⌬C value is greater than the van der Waals' distance separating the two opposing methyl groups near the bilayer center, the chain methyl ends of two sn-1 acyl chains in the trans-bilayer dimer will interact laterally, at T Ͻ T m , giving rise to a more stable bilayer structure. For instance, as C(18):C(18:1⌬ 9 )PC is lengthened to C(20):C(18:1⌬ 9 )PC, the N and ⌬C values are each increased by two C-C bond lengths. The van der Waals' distance between two methyl groups is 4.0 Å or 3.0 C-C bond lengths; consequently, the two sn-1 acyl chains of the transbilayer C(20):C(18:1⌬ 9 )PC are laterally overlapped by about 1.3 C-C bond lengths, which can give rise to an additional favorable van der Waals' energy that is absent in the trans- The total numbers of carbons in the sn-1 and sn-2 acyl chains are identical; hence, the effective chain length difference between these two acyl chains projected on the long molecular axis is defined as ⌬C ref . In this packing motif, the sn-2 acyl chain has a sequence g ϩ s ϩ ⌬s ϩ around the cis double bond. In this graphics display, the zigzag planes of the two segments of the chain separated by the sequences g ϩ s ϩ ⌬s ϩ are oriented perpendicularly to the zigzag plane of the sn-1 acyl chain. The most striking feature of this packing motif is the complementary van der Waals' interactions between the all-trans sn-1 acyl chain and the two segments of the sn-2 acyl chain. The length of the upper segment starting from the point corresponding to the carbonyl oxygen position of the sn-1 acyl chain is designated as US, while the length of the lower segment starting from the olefinic C(nϩ1) carbon is designated as LS. The relationship between US (or LS) and other structural parameters is defined in the text and is shown in A. B, the trans-bilayer dimer of C(20):C(18:1⌬ 13 )PC. The effective chain length difference between the sn-1 and sn-2 acyl chains within the monomer is the structural parameter ⌬C. The distance along the long molecular axis separating the two carbonyl oxygens in the two opposing sn-1 acyl chains is the thickness of the hydrophobic core (N), another structural parameter. former are 2.0 C-C bond lengths longer than those of the latter. Experimental data presented in Table I  It should be reiterated that the presence of a cis double bond in a hydrocarbon chain reduces the rotational barriers for adjacent C-C single bonds, thus promoting the conformational variability of the hydrocarbon chain (2). For a cis ⌬-bond located near the center of a hydrocarbon chain such as the sn-2 acyl chain of C(18):C(18:1⌬ 9 )PC, the energy barrier for rotating the C(10)-C(11) bond between two energy minima can be calculated by MM calculations to be 2.21 kcal/mol. As the ⌬ n in the sn-2 acyl chain of C(18):C(18:1⌬ n )PC is downshifted from C(9) to C(13) toward the methyl end, the height of the energy barrier is reduced to 1.88 kcal/mol for rotating the C( acyl chains for these three monoenoic lipid species are 1.88, 2.21, and 2.31 kcal/mol, respectively, when these monoenoic lipids are in the highly ordered conformations. At higher temperatures close to T m , the lipid chains are more disordered near the methyl ends, and the differences in the energy barriers for rotating the C(14)-C(15) bond in the sn-2 acyl chains among these three lipid species are expected to be further reduced. Our basic assumption stated above is thus not unreasonable.
Another intriguing question about the effect of cis ⌬-bond on the phase transition behavior of fully hydrated phosphatidylcholine concerns the strikingly large reduction in T m . For example, the T m value of the C(22):C(18)PC bilayer is 58.6°C (13), whereas that of the C(22):C(18:1⌬ 13 )PC bilayer is 16.3°C (Table I). Before we offer an answer to this intriguing question, we need to first identify what structural modifications take place in the cis-monounsaturated phosphatidylcholines in comparison with the saturated counterparts and to consider the difference in T m in relation to the structural differences.

TABLE II
The T m and the structural parameters of gel-state monounsaturated phosphatidylcholines with a cis ⌬-bond in the sn-2 acyl chain The definitions of various structural parameters (⌬C, US, LS, and N) are given in the text and Fig. 5. T m cal values are obtained from Equations 2 and 3 for group I and II lipids, respectively. The difference between the experimental T m (column 2) and the calculated T m (column 8) values are listed in column 9 as ⌬T m . In calculating T m , C(18):C(22:1⌬ 13 )PC is not considered, since the length of sn-1 acyl chain is shorter than of sn-2 acyl chain with a negative ⌬C value, and it is thus classified as group IЈ cis-monoenoic lipid. The basic structure of saturated C(X):C(Y)PC packed in the gel-state bilayer with a partially interdigitated motif can be specified by two structural parameters ⌬C and N, each of which is related to X and Y as follows (14): ⌬C ϭ ͉X Ϫ Y ϩ 1.5͉ and N ϭ X ϩ Y Ϫ 0.5. For monounsaturated C(X):C(Y:1⌬ n )PC packed in the same motif of gel-state bilayer, the presence of a structural modification of ⌬ n -bond in the sn-2 acyl chain increases the number of structural parameters to four (⌬C, N, US, and LS). These structural parameters are illustrated in Fig. 5.
Based on the calorimetric results obtained with 50 molecular species of saturated mixed-chain phosphatidylcholines, it has been demonstrated that the two structural parameters, N and ⌬C, for a given type of saturated mixed-chain phosphatidylcholine molecules packed in the gel-state bilayer can be correlated with the T m value of the lipid bilayer (13,14). Specifically, the T m values are related to N and ⌬C as follows (14): T m ϭ a 0 Ϫ a 1 (1/N) Ϫ a 2 (⌬C/N), where the first term (a 0 ) in the right-hand side of the equation corresponds to the extrapolated maximal T m value, which can be obtained with a lipid bilayer containing an infinitely large value of N; the second term with a negative sign indicates that the T m value of a bilayer increases with increasing values of N; the last term, also with a negative sign, is regarded as the chain-end perturbation term, expressed as a normalized ⌬C value, which shows that the larger the chainend perturbation, the smaller the T m and that the perturbation becomes insignificant as N Ͼ Ͼ ⌬C. More recently, this equation of T m has been refined to include a correction term (13); however, this modified equation does not significantly change our general interpretation of T m . In summary, the basic idea underlying this equation is that the T m increases with increasing N and that the T m decreases with increasing ⌬C for saturated mixed-chain phosphatidylcholines.
When a cis ⌬-bond is incorporated into the sn-2 acyl chain of C(22):C(18)PC at C (13), the N value of the gel-state bilayer of C(22):C(18:1⌬ 13 )PC, 38.7 C-C bond lengths, is reduced by 0.8 C-C bond lengths; hence, it is slightly longer than the N value (38.5) of C(22):C(17)PC. In contrast, the chain-end perturbation or ⌬C value of C(22):C(18:1⌬ 13 )PC is smaller than that of C(22):C(17)PC (6.3 versus 6.5). Interestingly, the T m value of the monoenoic lipid is remarkably smaller than the saturated one (16.3°C versus 53.2°C). Obviously, the marked difference in T m exhibited by C(22):C(18:1⌬ 13 )PC and C(22):C(17)PC bilayers cannot be explained completely by the structural parameters N and ⌬C. Other structural parameters must, therefore, be taken into consideration when the T m of cis-monoenoic lipids is discussed. In fact, two additional structure parameters, US and LS, exist for C(X):C(Y:1⌬ n )PC packed in the gel-state bilayer, each of which can represent the length of the longer or the shorter segment of the sn-2 acyl chain, depending on the position of the ⌬-bond. Here, we propose that the entire length of the shorter segment of the sn-2 acyl chain in the gel-state bilayer of C(X):C(Y:1⌬ n )PC acts as a structural perturbing element; hence, it is regarded as an important structural parameter that can modulate effectively the T m of cis-monoenoic lipids. The shorter segment is chosen because, at temperatures slightly below the T m , it may have already, at least in part, transformed into a disordered state.
Of the four structural parameters associated with C(X):C(Y: 1⌬ n )PC packed in the gel-state bilayer, three (N, ⌬C, US or N, ⌬C, LS) are independent variables. Since the shorter segment corresponds to the US when ⌬ n is less than C(11) for a C(18): C(18:1⌬ n )PC molecule and it is then switched to the LS as ⌬ n Ն C(11), we will then divide the monoenoic C(X):C(Y:1⌬ n )PC into two general groups: group I with a longer upper segment and group II with a longer lower segment in the sn-2 acyl chain. Within each general group, lipid molecules with a longer effec-tive saturated sn-1 acyl chain should be treated differently from those with a longer effective monounsaturated sn-2 acyl chain. This is due to the recognition that the perturbing effect of the smaller segment of the sn-2 acyl chain is intrinsically different from that of ⌬C. In this investigation, all but one of the cis-monounsaturated lipids under study have longer effective sn-1 acyl chains. The discussion will thus focus on those with longer effective sn-1 acyl chains. Now, we can proceed to discuss the relationship between the T m and the three independent structural parameters (N, ⌬C, and LS) for group I sn-1 saturated/sn-2 cis-monounsaturated phosphatidylcholines. Specifically, we analyze how the individual contribution of the three structural parameters affects the T m value, and from these analyses we can then arrive at a quantitative equation relating T m to all three structural parameters.
First of all, it is worth noting that the T m values appearing on the right-hand side of each parabolic curve in Figs (Table II). The units for all three structural parameters are the C-C bond lengths along the long chain axis. It is important to recognize that all of the T m values exhibited by this group of cis-monoenoic phosphatidylcholines decrease with increases in LS (Table II); hence, the structural parameter LS may be regarded as a perturbing element for the gel-to-liquid crystalline phase transition. Next, we can identify two pairs of group I cis-monoenoic phosphatidylcholines in Table II that Table II. The T m values exhibited by these two pairs of monounsaturated lipids have an inverse relationship with their ⌬C values, indicating that the perturbing nature of the end effect increases with increasing ⌬C, leading to a decrease in T m for the gel-to-liquid crystalline phase transition. A similar reciprocal relationship between the T m and the ⌬C has also been observed for saturated mixedchain phosphatidylcholines with a common value of N such as the following pairs of positional isomers: C(18):C(16)PC/C(16): C(18)PC and C(18):C(14)PC/C(14):C(18)PC (16,17). Such a reciprocal relationship, however, applies only to position isomers that can form, in excess water, partially interdigitated bilayers at T Ͻ T m (17).
Based on the three relationships discussed above between the T m of the gel-to-liquid crystalline phase transition of a given cis-monoenoic phosphatidylcholine and the underlying three structural parameters of the given molecule, a general equation can be formulated for group I sn-1 saturated/sn-2