The Sphingosine and Phytosphingosine Ceramide Ratio in Lipid Models Forming the Short Periodicity Phase: An Experimental and Molecular Simulation Study

The lipids located in the outermost layer of the skin, the stratum corneum (SC), play a crucial role in maintaining the skin barrier function. The primary components of the SC lipid matrix are ceramides (CERs), cholesterol (CHOL), and free fatty acids (FFAs). They form two crystalline lamellar phases: the long periodicity phase (LPP) and the short periodicity phase (SPP). In inflammatory skin conditions like atopic dermatitis and psoriasis, there are changes in the SC CER composition, such as an increased concentration of a sphingosine-based CER (CER NS) and a reduced concentration of a phytosphingosine-based CER (CER NP). In the present study, a lipid model was created exclusively forming the SPP, to examine whether alterations in the CER NS:CER NP molar ratio would affect the lipid organization. Experimental data were combined with molecular dynamics simulations of lipid models containing CER NS:CER NP at ratios of 1:2 (mimicking a healthy SC ratio) and 2:1 (observed in inflammatory skin diseases), mixed with CHOL and lignoceric acid as the FFA. The experimental findings show that the acyl chains of CER NS and CER NP and the FFA are in close proximity within the SPP unit cell, indicating that CER NS and CER NP adopt a linear conformation, similarly as observed for the LPP. Both the experiments and simulations indicate that the lamellar organization is the same for the two CER NS:CER NP ratios while the SPP NS:NP 1:2 model had a slightly denser hydrogen bonding network than the SPP NS:NP 2:1 model. The simulations show that this might be attributed to intermolecular hydrogen bonding with the additional hydroxide group on the headgroup of CER NP compared with CER NS.


S2. Coarse-grained Self-Assembly Procedure
The coarse-grained (CG) simulations were performed with the HOOMD-Blue simulation engine [1] using a 10-fs time step.The simulations were started in the constant-energy, constant-volume (NVE) ensemble at 105 K and run for 10-ps to eliminate molecular overlaps using the Velocity-Verlet integration algorithm.This was followed by another 10-ps run in the NVE ensemble at 305 K, again using the Velocity-Verlet integration algorithm.Next, the system density was equilibrated in the constant pressure and temperature (NPT) ensemble for 10 ns at 305 K and 1 bar, utilizing the Martyna, Tobias, and Klein (MTK) barostat-thermostat for integration.After this, a shape annealing process was employed to expedite self-assembly.This process, initially proposed by Moore et al. [2], entails expansion and compression of the simulation box area based on the expected area per lipid (  ), while holding the box volume constant and operating in the constant-temperature, constant-volume (NVT) ensemble using the Nosé-Hoover thermostat to control temperature.Specifically, the diameter of the box area, a square, at the beginning of the shape annealing step was expanded by a factor of 1.58 (i.e., 2.5 0.5 ) over 200 ns.Next, the area was decreased over 200 ns to the area at the expected diameter (  ) calculated from Eq. S2.1 where   is the number of lipids (2200) and   is the number of leaflets (6) in the box.The expected APL (  ) for the CER:CHOL:FFA 1:0.5:1 molar ratio system is 0.325 nm 2 .In the last step of the shape annealing process, the area diameter is held constant at   for 200 ns.After shape annealing, the semi-isotropic barostat to NPT was re-engaged and the temperature was increased from 305 K to 450 K over 100 ns at a constant rate of heating, and then decreased back to 305 K over 50 ns at a constant rate of cooling.This temperature-annealing step serves to eliminate defects formed during the expansion/compression phase and to further relax the lipids.Finally, the simulation was run for 400 ns under physiological conditions at 305 K and 1 bar, emulating benchtop conditions.A stable equilibrated CG structure was confirmed by a constant volume simulation box over the final 200 ns.The final configuration is reverse-mapped using mBuild to regain atomic detail [3], which is then equilibrated using atomistic simulations.

S3. Simulation Data Analyses and Results
Three Bilayer (Six Leaflet) Membrane

Area Per Lipid
Area per lipid (APL) is calculated as where   and   are the dimensions of the simulation box in the x and y direction, respectively, and   is the number of lipid head groups within the selected number of leaflets (  ).CERs in the three-bilayer membrane are present in hairpin (with both tails in the same leaflet) and linear (with tails in adjacent leaflets) conformations.Therefore, to include both tails of every CER in the APL calculation, while excluding lipids that might be affected by contact with bulk water (i.e., those in the two outer leaflets), the APL is calculated for the four inner leaflets.

Bilayer Thickness
Bilayer thickness is calculated from the mass density profile of the three-bilayer stack, created as a histogram by binning the mass along the z-coordinate.The mass density profile for each simulation trial is the average of the profiles from 200 frames of data collected over the last 2 ns of simulation time.The bilayer thickness is the distance between the maximum of two peaks in the average profile that are associated with the head group region of the innermost bilayer (designated as A and B in Figure S3.2) calculated using the SciPy find_peaks function [4].Reported values of the bilayer thickness are the average of three independent simulation trials.Table S3.1.Structural properties calculated at 32 °C (305 K) from the reverse-mapped atomistic simulations for CG self-assembled three-bilayer membrane with CER NS:NP molar ratios matching the two SPP models in a mixture of CER, CHOL and FFA C24 with a 1:0.5:1 molar ratio.All properties were calculated for the central bilayer, except for the area per lipid, which was calculated for the four inner leaflets.Results are reported as the mean and standard deviation of three replicated simulations.

Identifying CER Molecules in the Linear Conformation
For convenience, the fraction of CERs in the four inner leaflets that are in the linear conformation was determined by converting the atomistic CER structures back to CG bead mapping shown in Figure S3.3 for CER NS.A CER molecule is considered to be in the linear conformation if the angle between the TAIL-A bead on the acyl tail, the AMIDE bead in the head group, and the TAIL-S bead in the sphingosine tail is greater than 100 degrees.For each of the three simulation trials, the numbers of CER NS and NP molecules in the linear conformation, alone and together, in each of the 200 frames of data were averaged and then divided by the average number of that type of CER head groups in the inner four leaflets.The results reported in Table S3.2 are the average and standard deviation of the three simulation trials.Table S3.2.The percent of CERs NS and NP that are in the linear conformation reported as the mean and standard deviation of three replicated simulations.Results are for the four inner leaflets of the threebilayer membrane from the reverse-mapped atomistic simulations of the CG self-assembled membrane with CER:CHOL:FFA at a 1:0.5:1 molar ratio for CER NS:NP molar ratios that match the two SPP models.a

Model System
Linear CER NS (%) Linear CER NP (%) Total Linear CERs (%) SPP NS:NP 2:1 34 ± 5 39 ± 2 37 ± 3 a Differences between the two NS:NP ratios were not statistically significantly different for CER NS, CER NP, or CERs NS and NP combined; also, differences between CER NS and CER NP were not statistically significantly different for either NS:NP ratio (P<0.5).

S4. Hydrogen Bond Analysis of the Simulations
The number of intermolecular hydrogen bond interactions at 305 K were calculated for the four inner leaflets of the self-assembled three-bilayer membranes (each bilayer contains two leaflets; see Figure S3.1).CER, CHOL and FFA molecules can form hydrogen bonds associated with the eight atoms that are identified in Figure S4.1.Five of these are in the CER head groups (N1, O4, O80, O84, and O88 (in only CER NP)); two are in the FFA head group (O25 and O27), and one is in the CHOL head group (O3).Hydrogen bonds with the carbonyl (C=O) and with the N-H (nitrogen atom) in the CER molecules were assumed to be related to the observed vibration shifts in the amide I and amide II FTIR spectrum, respectively.Results reported for amide I hydrogen bonding are the sum of all hydrogen bonds with the CER C=O (i.e., O4).Amide II related hydrogen bonding results are the sum of all hydrogen bonds with CER N-H (i.e., N1).Hydrogen bonds between CER C=O and CER N-H (i.e., CER-CER N1-O4 hydrogen bonds) are included in the hydrogen bond totals for both amide I and II.The ~ 0.4 water molecules/lipid in the head group regions of the four inner leaflets (Table S4.1) were included in the hydrogen bonding calculations.Table S4.2 lists the number for each of the 42 possible hydrogen bonding pairs in the NS:NP 1:2 and 2:1 models: 33 are between lipids, eight are between water and a lipid, and one is between two water molecules.Tables 4 and 5 in the paper report the number of hydrogen bonds for each lipid class (i.e., for CER, CHOL, and FFA) and for water normalized by the number of molecules in that lipid class and water, respectively.Thus, for CER as the designated hydrogen bonding molecule, the number of CER hydrogen bonds with lipids (i.e., with itself, CHOL, and FFA) and with water are normalized by the total number of CER NS and NP molecules in the four inner leaflets.Lipid compositions of the four inner leaflets differed slightly from the nominal lipid composition.The actual numbers for each lipid class and water are listed in Table S4.1;these numbers were used to normalize the hydrogen bonding results presented in Tables 4 and 5.  S4.2.Number of each hydrogen bond pair calculated at 305 K for the four inner leaflets of the three-bilayer membrane (i.e., leaflets which do not contact bulk water) from the reverse-mapped atomistic simulations of the CG self-assembled membranes.Results are listed by those that are and are not associated with the amide I and II vibrations measured with FTIR (identified as Amide I, Amide II, and Other) and the sum of all hydrogen bonds reported as the mean and standard deviation of three replicated simulations.a

. 1 .
Figure S1.1.The molecular structure of the CERs used in this study.The deuterated moieties are depicted in red (the acyl chains of CER NS and CER NP and the terminally deuterated sphingosine chain of CER NS).

Figure S1. 2 .
Figure S1.2.Linear fitting of the structure factors as a function of the percentage of D2O in the D2O/H2O buffer for the SPP NS:NP 2:1 model and SPP NSd7:NP 2:1 models.The four diffraction orders are indicated by different symbols and colors: first (circle, blue), second (square, red), third (upwardpointing triangle, green), fourth (downward-pointing triangle, orange).

Figure S1. 4 .
Figure S1.4.Proposed schematic model for the arrangement of the SPP unit cell.CHOL is shown in black, FFA C24 is indicated as a single acyl chain in blue and the CER is depicted in blue, in a linear conformation (the acyl chain and sphingoid base on each side of the head group).The asymmetric structure mirrors itself within the lamellar structure, resulting in a symmetric structure of the SPP unit.

Figure S3. 1 .
Figure S3.1.Simulation snapshot of a three-bilayer (six leaflet) membrane from the reverse-mapped atomistic simulation of the CG self-assembled CER:CHOL:FFA system at a 1:0.5:1 molar ratio representing the NS:NP 1:2 model.CER NS C24 is depicted in blue, CER NP C24 in green, CHOL in yellow, FFA C24 in purple, and water in gray on the top and bottom of the simulation box.Oxygen atoms in the lipid head groups are denoted in red, respectively.The box (black dashed line) identifies the four inner leaflets, which do not contact bulk water.The four inner leaflets were analyzed for hydrogen bonding, the number of CERs in the linear conformation, and the scattering length density profiles.The central bilayer is also shown; it was analyzed for the bilayer thickness, tilt angle, and the nematic order parameter.

Figure S3. 2 .
Figure S3.2.Mass density profile of all lipids in a NS:NP 2:1 model system.Points A and B identify the maximums of the inner bilayer head groups found using the SciPy find_peaks function.

Figure S3. 3 .
Figure S3.3.Coarse-grained mapping of CER NS C24.If the angle formed between the TAIL-A (acyl chain), AMIDE, and TAIL-S (sphingosine chain) CG beads is greater than 100 degrees, the CER is considered to be in a linear conformation.

Figure S4. 1 .
Figure S4.1.Nomenclature for the atoms in the CERs, CHOL, FFA, and water molecules that can form hydrogen bonds are specified.For the CERs, atoms participating in hydrogen bonding are N1, O4, O80, O84 and O88 (only CER NP).The O3 atom in CHOL and the O25 and O27 atoms in FFA can form hydrogen bonds.The oxygen in water is denoted as 'O'.