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* Department of Molecular and Integrative Physiology, Department of Biochemistry, University of Illinois at Urbana-Champaign Programs in Biophysics, Neuroscience, and Bioengineering, and Beckman Institute, University of Illinois, Urbana, Illinois; and Department of Biological, Chemical, and Physical Sciences, Illinois Institute of Technology, Chicago, Illinois
Correspondence: Address reprint requests to Hugh L. Scott, Jr., Illinois Institute of Technology, 3101 S. Dearborn, Chicago, IL 60616. Tel.: 312-567-3730; Fax: 312-567-3494; E-mail: scotth{at}iit.edu.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONAPPENDIXACKNOWLEDGEMENTSREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONAPPENDIXACKNOWLEDGEMENTSREFERENCES |
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; Ahmed et al., 1997; Brown and London, 1998). Rafts have been identified as important membrane structural components in signal transduction (Manes et al., 1999; Aman and Ravichandran, 2000; Xavier et al., 1998; Kawabuchi et al., 2000), protein transport (Rozelle et al., 2000; Cheong et al., 1999; Viola et al., 1999), and sorting of membrane components (Manie et al., 2000; Harder et al., 1998; Sönnichsen et al., 2000; Liao et al., 2001). The mechanism for raft formation in the membrane most likely involves differential miscibility of the various lipids, and preferential association of cholesterol with SM over other membrane lipids (Reitveld and Simons, 1998). Although cholesterol is closely associated with SM in most animal cell membranes, it is important to characterize the thermophysical and structural properties of single-component SM bilayers to better understand the properties of mixed lipid-cholesterol systems.
Sphingomyelin consists generally of a sphingosine base with an 18-carbon chain and a double bond at position 4, attached to a phosphorylcholine fatty acid. The fatty acid chains are generally long and saturated or monounsaturated. In bovine brain SM the most abundant fatty acid chains are 18:0 (42%) and 24:0 (27%), whereas in egg SM the dominant fatty acid is 16:0 (66%) followed by 18:0 (10%); see Ramstedt et al. (1999). Recent reviews of organizational and thermophysical properties of sphingolipid bilayers have summarized properties of these systems with and without cholesterol (Brown, 1998; Maggio, 1994; Koynova and Caffrey, 1995). X-ray and scanning calorimetry experiments established that 16:0 SM exhibits a chain melting phase transition at 40.5°C, very close to the phase transition of dipalmitoyl phosphatidylcholine (DPPC) (Calhoun and Shipley, 1979; Maulik and Shipley, 1996). In a comprehensive study using scanning calorimetry and x-ray diffraction, Maulik et al. (1991) analyzed the thermophysical properties of 18:0 SM at various temperatures and levels of hydration. For the highest hydration levels (>25 wt % HO) 18:0 SM has a chain melting phase transition at 45°C. From electron density profiles and assuming the partial specific volume of 18:0 SM to be the same as that of DPPC (Nagle and Wilkinson, 1978), Maulik et al. (1991) calculate the area per molecule, for full hydration, to be 45 Å2 per molecule at 22°C (below the phase transition temperature) and 55 Å2 per molecule at 55°C (above the phase transition temperature). Koynova and Caffrey (1995) have reviewed thermodynamic data for all experimentally studied sphingolipids. Of interest are the facts that 1), the lipid chain melting transition temperature increases slowly with chain length for saturated SM, from 40.5°C for 16:0 SM to 47.5°C for 24:0 SM; and 2), the insertion of a double C=C bond at position 9 in the acyl chain decreases the phase transition temperature by 
15°C, whereas the same substitution reduces transition temperatures in phospholipids by nearly 50°C (Koynova and Caffrey, 1995).
Early 1H-, 31P- (Schmidt et al., 1977), and 14N- (Siminovitch and Jeffrey, 1981) nuclear magnetic resonance (NMR) studies of small single-lamellar vesicles of SM showed that spin-lattice relaxation rates are lower in the polar and the acyl chain regions in SM, linewidths are greater, and chemical shifts are broader compared to phosphatidylcholine bilayers. Schmidt et al. (1977) interpret the data as evidence for intramolecular hydrogen between phosphate ester oxygen atoms and H atoms in the amide or hydroxyl moieties of SM. McIntosh et al. (1992) examined structural and thermal properties of bovine brain SM and 24:0 SM using scanning calorimetry and x-ray scattering, and found that the electron density profile of 24:0 SM is indicative of chain interdigitation between the two leaflets due to the large difference in chain length of the two methylene chains. Maulik and Shipley (1996) obtained electron density plots for 16:0 SM, with a peak-to-peak distance of 46.9 Å at 29°C and 44.4 Å at 50°C.
Pressure-area plots of SM monolayers have also been utilized to characterize these systems, complementing studies of SM in vesicles. Li et al. (2000) have carried out a systematic set of experiments using monolayer films of SM with acyl chain lengths from 12 to 26 carbons. At 20°C and 30 dynes/cm surface pressure, Li and co-workers find that 18:0 SM films have an area of 47.2 Å2 per molecule. As chain length increases (decreases) this value decreases (increases). Introduction of an unsaturated bond in the acyl chain significantly increases the area per molecule at the same pressure, e.g., to 59.4 Å2 per molecule for 18:1 SM at 30 dynes/cm and 20°C. Kuikka et al. (2001) have carried out a series of monolayer experiments comparing 16:0 SM with its 16:0 sphingamine analog, containing a saturated sphingamine rather than sphingosine base (DH-SM). They find that DH-SM generally has lower area per molecule than the corresponding SM at given temperature and pressure. Epifluorescence microscopy images showed the presence of large (10 µm) domains of condensed lipid in 16:0 SM at low surface pressure. The domains changed in size and structure upon addition of cholesterol.
Despite the documented biological importance of sphingolipids, far less is known about their atomic level structure in bilayers than is known for phospholipids. Atomic level simulations can begin to address this problem. The first molecular dynamics simulation to appear is that of Mombelli et al. (2003). This simulation consisted of a bilayer of 128 16:0 SM molecules plus 2864 waters. As we also report below, intramolecular hydrogen bonds were found in the SM polar region. The purpose of the present article is to describe results of molecular dynamics (MD) simulations of bilayers of 18:0 sphingomyelin (SM) in excess water. The simulated system is 20 nm in lateral dimensions, making them similar in size to raft microdomains (26 ± 13 nm; Pralle et al., 2000), and the final MD trajectory after equilibration is 2 ns in length. This length scale allows us to probe molecular structure and whole-bilayer undulations.
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METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONAPPENDIXACKNOWLEDGEMENTSREFERENCES |
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). In calculating molecular-mechanics torsion profiles in the course of parameterization, GROMOS96 MD software (van Gunsteren et al., 1996) was used because of its capability of restraining dihedral angles. Standard GROMOS96 energy functions (van Gunsteren et al., 1996) were used in all cases. GAUSSIAN98 (Frisch et al., 2002) was used to calculate ab initio torsional profiles and to optimize molecular structures at the theoretical level B3LYP/6-31G(d,p). Analysis of the properties of the system was done using a combination of GROMACS utilities and our own analysis code.
Fig. 1 shows the structure of 18:0 SM, and the numbering and labeling scheme we used. Table 1 lists the atom labels and their corresponding atom types as defined in the interaction parameter file. A 18:0 SM bilayer of 1600 lipids (800 per leaflet) plus 50,592 SPCE waters was constructed by the following process: an equilibrated dipalmitoyl phosphatidylcholine (DPPC) bilayer of 100 DPPC molecules was converted to 18:0 SM by making the necessary atomic level changes and additions. This system was hydrated at 32 waters per lipid and equilibrated using our previously published procedure of alternating short (100-ps) MD runs with 20,000 configurational bias Monte Carlo (CBMC) steps (Chiu et al., 1999a). The MD runs were carried out at a temperature of 50°C, a surface tension of 46 dynes/cm (Chiu et al., 1995), and a normal pressure of 1 atm. After this system was equilibrated, as judged by stability of the system energy and area per molecule, it was enlarged to a system of 400 SM plus 12,800 waters by replication. The same MD-CBMC procedure was applied to this system for equilibration, and, after this was complete, replication was again used to construct the system of 1600 SM plus 50,592 waters. Energy minimization was run after each enlargement step, and between MD and CBMC runs. For the large system CBMC was not used due to limitations in the current version of the CBMC code. MD simulations for the large system were run with the pressure set at 1 atm anisotropically. The simulation is sufficiently large that changing the boundary conditions from constant surface tension to constant isotropic pressure (zero surface tension) did not change the area per molecule of the system.
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,b). Parameters for the sphingosine chain polar groups were taken from the GROMOS96 43A1 parameter set (von Gunsteren et al., 1996). Parameters for saturated hydrocarbon chain atoms were taken from our earlier determination of these quantities by fitting to density and heat of vaporization data for hexane, decane, and pentadecane simultaneously (Chiu et al., 1999b). Parameters for the C=C double-bond carbons were determined from simulations of liquid 5-decene (Chiu et al., 1999b). Cutoffs of 20 Å were employed for van der Waals and electrostatic interactions.
After the large bilayer was equilibrated we undertook a re-examination of the force field for the SM polar region. A Hartree-Fock calculation at the HF/6-31G* level was carried out for the SM molecule (carbons below C19 and C41 were truncated). In the last column of Table 1 we list the partial charges used for SM simulation and those derived from HF calculation. The HF/6-31-G* derived charges on the atoms of the amide and hydroxyl groups are much larger than those adopted from the 43A1 parameter set. We also note that in our previous work (Chiu et al., 1999b) the experimental heats of vaporization 
Hvap for (decane and pentadecane) that we used as target values for parameterization are significantly lower than those listed in the CRC Handbook of Chemistry and Physics (Lide, 1990–1991) and the data from TRC Thermodynamic Tables (Texas A & M University System, College Station, TX). We therefore have also recalculated, following the same procedure as Chiu et al. (1999b), 6–12 parameters for hydrocarbon chains using the new values of the heats of vaporization as targets. Details of parameterization and the force-field parameters for SM used in this work are presented in Appendix.
The simulation was then re-started from the beginning snapshot of the previous 1600 SM simulation, and was run for 1 ns for equilibration, and then another 2.8 ns, the last 2.0 ns of which were used for averaging. The particle-mesh Ewald method was used for the long-range electrostatic corrections. We used a cutoff of 1.0 nm in the direct space and a Fourier spacing of 0.15 nm. A sixth-order interpolation was used. For the van der Waal interactions, a twin-range cutoff (1.0/1.6 nm) was applied. The system was run under the NPT condition with semi-isotropic pressure coupling, i.e., pressure coupling which is isotropic in the x- and y-directions, but different in the z-direction (the bilayer normal). The neighbor pairlist was updated every five timesteps. All bond lengths of the lipids were constrained with the LINCS algorithm (Hess et al., 1997). The SETTLE algorithm (Miyamoto and Kollman, 1992) was applied to water molecules for bond length constraint.
Temperature boundary conditions were set using the Nosé-Hoover algorithm (Nosé, 1984; Hoover, 1985). Pressure boundary conditions were set using the Parrinello-Rahman pressure coupling method (Parrinello and Rahman, 1981). The simulation is sufficiently large that changing the boundary conditions from constant surface tension to constant isotropic pressure (zero surface tension) did not change the area per molecule of the system.
Fluctuations of the membrane produce wavevector-dependent undulatory and peristaltic modes (Lindahl and Edholm, 2000). To compute these modes from simulation, we represented the position of each lipid along the membrane normal direction by the z-coordinate, of its carbon C13 atom (Fig. 1 a). For the undulatory spectrum, the instantaneous fluctuations, 
, of the lipid positions from their leaflet average,
, were calculated. The lipids were then binned into cells according to the positions along the xy-plane, and the cell values were defined to be the average of the instantaneous fluctuations of the contributing lipids (each leaflet taken separately). Application of a two-dimensional fast Fourier transform to the cell values provides the undulatory spectral amplitudes and intensities, which were subsequently time-averaged (sampling rate, 0.5 ps) and histogrammed according to wavevector magnitude, q. Note that this method is unreliable at the length scale of individual lipids (toward large q). For the peristaltic spectrum, the instantaneous fluctuations in bilayer thickness, hper = (h - 
h
)/2, where h is the distance between corresponding z-cells from the monolayers and h is the average distance, were analyzed. The calculated Fourier amplitudes u2(q) plotted here are scaled by the area of the system, and the values of the fitting coefficients have been converted to standard units.
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RESULTS |
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0.6 Å2 over 2.8 ns, the simulation time for this raft-size SM bilayer may not be long enough. To conclude, the system will stabilize with a molecular area of 53 Å2. However, a plot of the molecular area versus time for a small SM bilayer (100 SM molecules and 3162 waters) over 38 ns, run under identical boundary conditions, as shown in Fig. 2 b, shows that the bilayer stabilizes with an average molecular area of 52 Å2. These results are in close agreement with the experimental data of Maulik et al. (1991), despite their estimate of 55 Å2 for the area per molecule; one contribution to the difference between experiment and simulation comes from the Maulik group's assumption that the molecular volume for 18:0 SM is the same as that for DPPC, i.e., 1232 Å3 (for this, see Nagle and Tristram-Nagle, 2000). From the dimensions of our simulation box, and assuming a molecular volume for water of 30.4 Å3 (Armen et al., 1998), we find the average molecular volume for an SM in an equilibrated bilayer to be 1182 Å3. If we use this value of the molecular volume and the d-spacing measured by Maulik and Shipley (1996), we find an area per molecule of 52.7 Å2 for the experimental data, in excellent agreement with the simulation prediction. The low area per molecule for 18:0 SM, above its phase transition temperature, is in contrast to the molecular areas of phospholipids above their transitions (e.g., 64 Å2 for DPPC; Nagle and Tristram-Nagle, 2000). The relatively low area per molecule indicates that the fluid phase of SM is considerably more ordered than that of phospholipids, a conclusion supported by the small (compared to phosphatidylcholine values) change in enthalpy for sphingomyelins compared to phosphatidylcholine values (a factor of 2/3; Koynova and Caffrey, 1995).
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obtain a value of 41 Å for 18:0 SM at 50°C, at all hydration levels between 20 and 50 wt %. Our calculated profile shows methylene "shoulders" more distinctively than does the experimental profile. A possible explanation for this is longer time- and length-scale undulation fluctuations in experimental systems, which could "wash out" the shoulder locations in an electron density plot.
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0.3 near the top of the chains, and decrease to 0.1 for the acyl chain and 0.15 for the sphingosine chain at the lowest methylene positions. For comparison, the order parameters for both chains of DPPC at a similar temperature begin at 0.18–0.2 in the upper part of both chains, and are 0.06 for the lowest methylene (Chiu et al., 1999a).
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1.7 Å is due to hydrogen bonding between H15 and O17 on different molecules (for this calculation atoms on the same molecule were excluded). The amide hydrogen is also capable of hydrogen-bonding to neighboring hydroxyl oxygen. Fig. 6 shows the RDF for these atoms, and the 1.75 Å peak reveals hydrogen bonding between these moieties as well.
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to account for chemical shift data in their NMR data. The most likely candidates for participation in intramolecular hydrogen bonding are the phosphate oxygens and the hydroxyl and amide hydrogens. Fig. 7 shows the RDF calculated between the ester oxygen OS11 and the hydroxyl hydrogen, H37. The plot has a very sharp peak at 1.6 Å, which is due to intramolecular hydrogen bonding. This hydrogen bonding is extensive, existing in 57% of the SM molecules in our simulation cell. The implication is that over half of the SM molecules in the bilayer essentially have a six-membered ring (including the hydroxyl hydrogen, H37, and closed by the H37-OS11 hydrogen bond) in the polar regions of their sphingosine chains. Fig. 8 is a plot of the RDF between the ester oxygen OS7 and the hydroxyl hydrogen H37. This RDF has a small, sharp peak at 1.7 Å indicative of some hydrogen bonding but far less than in the case of the OS11 oxygen. Similar RDF values calculated between phosphoryl oxygens (OM9 and OM10) and the hydroxyl hydrogen show almost no intramolecular hydrogen bonding. Table 2 summarizes the hydrogen-bonding data we have found in our simulation, from RDF calculations. Fig. 9 shows a typical SM molecule, with an intramolecular hydrogen bond.
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90.0° with a width at half-maximum of 61°. Surprisingly, the peak in the P–N dipole vector distribution for DPPC bilayers, calculated by Smondryev and Berkowitz (1999) is similarly located, broadly spread between 80° and 90°. For DPPC, however, the distribution of P–N dipole vector angles is much wider, 100°, at half the maximum, compared to SM. We have also calculated the average P–N orientation for a DPPC bilayer consisting of 400 DPPC and 12,800 waters (unpublished data; cutoff-based simulation at constant surface tension). We find that the distribution of P–N angles again peaks at 80°. But in contrast to Smondryev and Berkowitz we find the width to be narrower than the width of the SM distribution, 52.3°.
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287 mV, with the interior of the bilayer positive. The membrane potential (interior of the bilayer relative to the bulk water) was calculated to be 540 mV.
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),
 | (1) |
is the membrane surface tension, and p,und is a molecular protrusion energy density for undulations. Equation 1 admits two regimes,
 | (2) |
p,und is a microscopic surface tension term that is interpreted as a lipid protrusion restoring force per unit area. Lindahl and Edholm (2000) have carried out the same analysis for large (1000 lipids) DPPC.
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q-4 regime in q (small q), and I q-2 (large q). Here we have taken the membrane surface tension term in Eq. 2 as zero ( = 0) due to the boundary conditions applied in the simulation. We then applied a least-squares fit to each regime independently. From the slope of the small-q line, we obtain a leaflet bending modulus of kc = (41.2 ± 1.9) x 10-20 J and lipid restoring force p,und = 79 mN m-1. For comparison, Lindahl and Edholm obtain, for DPPC, kc = 4 x 10-20 J with p,und 
50 mN m-1. The reported experimental value of the bending modulus for DPPC is kc = 5 x 10-20 J (Evans and Rawicz, 1990). Given the smaller area per molecule, we observe that, in the SM bilayer, it is not surprising that SM bilayers have a larger bending modulus than DPPC bilayers.
The power spectrum for peristaltic modes is presented in Fig. 12 b. The peristaltic fluctuation power spectrum is expected to obey the expression (Lindahl and Edholm, 2000)
 | (3) |
p,per is the restoring force for peristaltic molecular protrusions. In general, p,per for peristaltic and undulatory molecular protrusions differ. Since the peristaltic modes are limited in amplitude by the thickness of the bilayer, the spectrum is proportional to q-2 for large q but becomes asymptotically a constant as q approaches zero. This behavior leads to the two regimes:
 | (4) |
= 0 and performing a least-squares fit to each regime independently resulted in three converging solutions. In Fig. 12 b we show, for clarity, just one of these solutions and obtain the values kd = 24 x 10-20 J, ke = 1.3 x 10-7 mN nm-3, and p,per = 150 mN m-1. (The ranges of fitting constants were found to be kd = 0.78 x 10-20 to 2.4 x 10-20 J; ke = 1.3 x 10-7 to 1.7 x 10-7 mN nm-3; and p,per = 84–165 mN m-1.)
To calculate the area compressibility modulus, KA, we used ensemble fluctuation theory (Allen and Tildesley, 1987), predicting that 
, where 
A is the area fluctuation of the system. This calculation includes fluctuations from undulatory and peristaltic modes, and we obtained the value
 | (5) |
Since SM bilayers are more ordered, compared to phospholipid bilayers under comparable conditions, and since SM molecules have two chains with different structures, it is natural to examine the question of interdigitation of terminal methyls and near-terminal methylenes between the two leaflets. To this end we calculated atom distributions for each leaflet separately. We found that the distributions of terminal methyls for the two leaflets overlap to an extent that 23% of all methyls are in the overlap region in the center of the bilayer. We found that only 2% of all methylenes overlap in the bilayer center. Interdigitation is thus not an important property of the SM bilayer in our simulation.
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DISCUSSION |
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400 nm. This size approaches the lower end of estimates for the size of lipid rafts in membranes. Although sphingolipids apparently reside mainly in the outer monolayer of most membranes in which they are found, this study of a hydrated SM bilayer provides atomic level insights into the structure and interactions of SM in membranes. In a subsequent article we will describe simulations of SM monolayers of the same size.
Perhaps the most interesting result of our simulations is the observation that nearly 57% of the SM molecules participate in intramolecular hydrogen bonding between one of the phosphate ester oxygens (primarily OS11) and the hydroxyl hydrogen. This hydrogen bond does not seem to greatly inhibit the conformational freedom of the polar group, as evidenced by the similarity in P–N dipole angular RDF for SM and DPPC. The most important consequence of this intramolecular hydrogen bond is that it produces a reduced probability for hydrogen bonding with water, thus reducing the hydration of the polar region. This observation is consistent with a recent experimental study of the hydration state of the interfacial region of DPPC and 16:0 SM vesicles using fluorescence spectroscopy (Nyholm et al., 2003). The higher bending modulus, relative to DPPC, calculated for SM, is consistent with increased inter- and intramolecular hydrogen bonding. The reduced number of hydrogen-bonding sites will also have implications for SM interactions with cholesterol. We have observed significant differences between SM-cholesterol and DPPC-cholesterol interactions in simulations (unpublished data). Inter- and intramolecular hydrogen bonding in SM also implies that the phase transition temperatures of SM bilayers are more dependent on interactions in the polar groups than is the case for phospholipids. Indeed, the transition temperatures for saturated sphingomyelins do not vary as strongly with acyl chain length as do the transition temperatures for phospholipids.
Given the increased ordering of the hydrocarbon chains, and the restricted polar group mobility from intramolecular hydrogen bonding, it is not unreasonable to expect a reduced molecular volume for SM compared to DPPC. This reduced volume may in fact be responsible for phase separation of sphingolipids from more fluid phospholipids in membranes, which leads to the formation of lipid rafts. The reduced volume also has implications for the interactions of SM with cholesterol, which should not be the same as is found for DPPC (Chiu et al., 2002). This important problem is currently under investigation in our lab.
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APPENDIX |
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). Since the charges we adopted for the amide group and the -COH fragment in SM are very different from those used for protein in the 43A1 parameter set, torsional parameters for the dihedral angles involving these atoms were also reparameterized. Our parameter development for atom types CHn*, CH1', and C0 followed the general methods utilized by several groups (Chiu et al., 1999b; Berger et al., 1997). The procedure outlined by Reiling et al. (1996) was followed to obtain an accurate set of torsional parameters for the dihedral angles involving the atoms of the hydroxyl and amide groups as well as the unsaturated carbon atoms. Some torsional profiles calculated at the B3LYP/6–31G(d,p) level were taken from Langley and Allinger (2002). In this work, the torsional parameters for the dihedral C38–C35–O36–H37 was approximated by fitting to the ab initio torsional profile for isopropanol. Force-field parameters for SM used in this work are presented in Tables A1–A8.
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). Manual adjustments of the atom charges was performed to maintain the neutrality of the headgroup. The aliphatic and alkenic carbons of the two hydrophobic tails were individually assigned with zero charges. The final charge set used for SM simulation is listed in Table 1.
The van der Waals (VDW) parameters
All were taken from the 43A1 parameter set (van Gunsteren et al., 1996) except those for the atom types CH1*, CH2*, CH3*, CH1', and C0. Tables A1 and A2 list the normal C6(i,j) and C12(i,j) parameters, respectively. The 1–4 parameters for third-neighbor interactions are presented in Table A3.
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n) terms used in SM bilayer simulation. The n values defined for the two tetrahedral centers (the last two rows of Table A6) define the naturally occurring configuration, (2S, 3R) of the sphingosine base. Table A7 lists the proper dihedral angle assignments and their corresponding force-field parameters. Kuwajima-type (Kuwajima et al., 1994; Fang et al., 1999) potential functions are used instead of the normal trigonometric functions for those with force constants KWn (n = 1–5) as listed in column 2 of Table A7. The coefficients Cn for the corresponding KW potentials are listed in Table A8.
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ACKNOWLEDGEMENTS |
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FOOTNOTES |
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Submitted on March 8, 2003; accepted for publication August 20, 2003.
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