Molecular Dynamics Simulation Study of Skin Lipids - ACS Publications

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Molecular Dynamics Simulation Study of Skin Lipids: Effects of Molar Ratio of Individual Components Over a Wide Temperature Range Rakesh Gupta, and Beena Rai J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.5b02093 • Publication Date (Web): 14 Aug 2015 Downloaded from http://pubs.acs.org on August 18, 2015

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The Journal of Physical Chemistry

Molecular Dynamics Simulation Study of Skin Lipids: Effects of Molar Ratio of Individual Components over a Wide Temperature Range Rakesh Gupta and Beena Rai* Tata Research Development and Design Centre, Tata Consultancy Services, 54B, Hadapsar Industrial Estate, Pune – 411013, INDIA

ABSTRACT Atomistic molecular dynamics (MD) simulations were employed to systematically investigate the effects of molar ratio of individual components cholesterol (CHOL), free fatty acid (FFA) and ceramides (CER) on the properties of skin lipid bilayer over a wide temperature range (300 - 400K). Several independent simulations were performed for bilayers comprising of only CER, CHOL or FFA molecules as well as those made up of mixture of CER: CHOL: FFA molecules different molar ratios. It was found that CHOL increases the stability of bilayer since the mixed (CER: CHOL: FFA) 1:1:0, 1:1:1 and 2:2:1 bilayer remained stable till 400 K while pure ceramide bilayer disintegrated around ~390 K. It was also observed that CHOL reduces the volume spanned by ceramide molecules thereby leading to a higher area per CER and FFA molecule in mixed bilayer system. The CHOL molecule provided more rigidity to the mixed bilayer and lead to a more ordered phase at elevated temperatures. The CHOL molecule provided fluidity to bilayer below the phase transition temperature of CER and kept the bilayer rigid above the phase transition temperature. The FFA interdigitize with CER molecules and increases the thickness of bilayer while rigid CHOL decreases the bilayer thickness. The presence of CHOL increases the compressibility of the bilayer which is responsible for the high barrier function of skin. The CER molecule does forms inter and intra molecular hydrogen bonds while CHOL only forms intermolecular hydrogen bonds.

Keywords: Skin lipids, area and volume per lipid, phase transition, cholesterol interaction, hydrogen bond, area compressibility.

*To whom correspondence should be addressed. [email protected] ACS Paragon Plus Environment


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INTRODUCTION The accurate prediction of dermal uptake of chemicals is relevant to both transdermal drug delivery as well as topical application of cosmetics. Extensive research has been performed over the last several decades to predict skin permeability of various molecules.1-4 These efforts include the development of empirical approaches such as quantitative structure–permeability relationships5 and porous pathway theories6 as well as the establishment of rigorous structure-based models5. However, a molecular-level understanding of the skin’s surface layer – the Stratum Corneum (SC) which shall ultimately lead to the development of rapid in-silico screens to predict permeability of a molecule, from knowledge of its molecular structure alone, is still not on the horizon. SC, the outer most part of skin epidermis, provides main barrier to penetration of pathogens and against water loss. The SC mainly comprises of corenocytes (brick) and lipid matrix (mortar).

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The extracellular lipid matrix is the key determinant for its

barrier functions and is composed of heterogeneous mixture of long chain ceramides (CER), cholesterol (CHOL) and free fatty acid (FFA) in certain ratios.9-10 The heterogeneous nature of SC arises due to presence of more than 300 different CER species comprising of varying head group and fatty chains.11 Each CER is made up of a sphingoside motif which is bound to a fatty acid chain. CERs can be classified into sphingosines (S), phytosphingosines (P) and hydroxysphingosines (H) according to functional group present in the sphingosine motif. CERs can be further classified as nonhydroxy (N), α-hydroxy (A) and esterified ώ -hydroxy fatty acid CERs according to hydroxyl group attached to the fatty acid chain.12 Detailed structures of different types of ceramides present in the human skin can be found elsewhere.6, 13 There are some approaches proposed for breaching the skin barrier such as chemical penetration enhancers, electroporation, sonophoresis, and micro needles but complete understanding of these molecular processes is still in its infancy due to the limitation associated with experimental techniques.14 Molecular simulation offers a way to yield important physical insight at molecular level resolution. However, the investigation of a realistic skin behaviour and structure at molecular level is challenging because of the heterogeneity of ceramides and free fatty acids present in SC.15-16 In human SC ceramides, the length of sphingo motif is always found to be

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between 16-18 carbons but the length of fatty acid varies from 16 to 34 carbons, thereby leading to asymmetry in the length of ceramides chains.17-18 Atomistic modeling of such a complex system incorporating all possible ceramides and fatty acids found in SC is far away from current computational capabilities. However, to in order to simulate a realistic SC layer19, we have chosen the most abundant ceramide, CER-NS 24:0 and free fatty acid, FFA 24:0. Holtze et al.20 first time reported the simulation of two component mixtures of fatty acid and cholesterol, Pandit and Scott21 studied single component CER-NS (16:0) bilayer, Notman et al.22 investigated effect of DMSO on pure CER-NS (24:0) bilayer. The first study of three component mixtures of CER NS (24:0), free fatty acid (24:0) and cholesterol was performed by Das et al. 23 Authors investigated effect of molar ratio of individual component on structural properties and followed by diffusion and permeability calculation for CER and mixed bilayer.24 Same authors have also reported on the modelling of corneocyte wall and proposed that lamellar layering is induced by the patterned corneocyte wall.13 Recently Guo et al. 25 performed both united atom and all atom molecular dynamics simulation of single component CER-NS (16:0) and CER-NP (16:0) using Berger26 and CHARMM27 force field. They found that OH group in CER-NP aligned itself perpendicular to the bilayer normal as compare to CER-NS, resulting into more hydrogen bonded network, which leads to high gel-to-liquid phase transition temperature in CER-NP. Guo et al. performed simulations for symmetric CER-NS bilayer which leads to a proper ordering of lipids tail in its interior, resulting into a high gel to liquid phase temperature. To the best of author’s knowledge no studies have been reported on the phase transition of mixed skin lipid bilayers. We report on the phase transition of skin lipids in at various compositions along with calculated area per CER molecule in multicomponent bilayers. The effects of CHOL and FFA in ceramide lipid bilayers over wide temperature range is systematically investigated via atomistic molecular dynamics (MD) simulation in constant NVT and NPT condition. In bilayer simulation the area per lipid is a primary parameter which is directly correlated to the molecular organisation of lipid bilayer.28 It can be compared with experiments as well as it gives information about the equilibration of the system in simulation. We have modified the method of Hofsäß et al. 29 to calculate


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the area per lipid in the mixed bilayer.

1. Simulation details 1.1. Force field The potential function and interaction parameters for CER were taken from Berger force field 26, which is properly parameterized for Palmitoylsphingomyelin (PSM) bilayers and phospholipids. The PSM’s have similar structure as CER-NS except for head group geometry. The head group size and partial charges in PSM are very high as compared to CER.30 The polar hydrogen’s were included explicitly and charges on polar groups were taken from earlier simulations reported in the literature.22-24 The Ryckaert-Bellemans dihedral potential was used for lipid hydrocarbon tails. 31 The topology for free fatty acid and cholesterol were same as used by Holtze et al.20 The simple point charge (SPC) model was used for water molecule.

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The united atom carbon in all components had

zero partial charge.

1.2. Simulation setup All simulations were carried out in NVT and NPT ensemble using the latest GROMACS molecular dynamics package.33-35 The temperature was controlled by Berendsen thermostat with a time constant of 0.5 ps for initial equilibration, later it was changed to Nose-Hoover thermostat with same time constant. Pressure was maintained at 1 bar using Berendsen barostat for initial equilibration with a time constant of 0.5 ps and compressibility of 4.5 x 10-5 bar-1, later in production run it was changes to ParrinelloRahman barostat with a time constant of 5 ps and compressibility of 4.5 x 10-5 bar-1. The semi isotropic coupling (coupled separately in xy and z direction) of barostat was used to simulate tension less bilayer. All the bonds in lipid molecules were constrained using LINCS algorithm36 while for water SETTLE37 algorithm was used. A time step of 2 fs was used for simulation below 360 K and 1 fs for higher temperature. It has been shown earlier that cutoff for electrostatic interaction leads to some artifacts in phospholipids bilayer simulation.38 A cut off of 1.2 nm was used for van der Waals and electrostatic interactions. Long range electrostatic interaction was computed using particle mesh Ewald (PME) method. Equilibration time for all the systems was 10 ns (NVT) followed


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by 100 ns (NPT) equilibration. The final 10 ns run of NPT simulation was used for calculation of equilibrium properties (production run). The configuration was sampled at every 0.5 ps in production run. All the properties were averaged over 5 blocks of 2 ns.

1.3. Initial bilayer structures Molecule structure of individual component used in this simulations, are shown in Figure1. We have used hairpin configuration of CER molecules.23 To remove bad contacts between molecules, energy minimization was carried out in vacuum using steepest decent and conjugate gradient method. For single component bilayer system, an individual molecule was first minimized and then replicated using “genconf” (Gromacs) in X and Y direction to obtain single layer. This single layer was then replicated in Z direction to obtain initial bilayer configuration followed by energy minimization. This minimized bilayer was placed in a bigger box and the box was filled with SPC water molecules. Further, the system was energy minimized and subjected to 10 ns NVT MD run at 300 K, by keeping lipid molecules fix for proper hydration. For mix bilayer, initial random configurations were generated using the tool- PACKMOL.39-40 Initial and final configurations of mix bilayers mostly correlated in gel phase simulations.20 We further performed simulated annealing to remove these artifacts. All the minimized structures were heated till 360 K and cooled back again to 300 K in 1 ns run. Structures obtained from the simulated annealing, were equilibrated for 100 ns at 300K. These equilibrated structures were further used as a starting structure for a given temperature and ran for another 80-100 ns at 1 bar. The final 10 ns run of these simulations was used for analysis and computation of properties. Same procedure was followed for the simulations of pure CHOL and FFA bilayers. Table 1 shows the molar ratio used in the simulations and corresponding number of individual molecules. The ratios in the article should be considered in the order of CER: CHOL: FFA until unless it is specified specifically.

2. Area and Volume per molecule In an MD simulation of single component bilayer which has normal along the z direction, the volume per lipid (VPL) could be calculated by subtracting volume of water molecule from the total volume,


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V  Lx Ly Lz

Vlipid 

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............ (1)

V  NW VW N lipid

........... (2)

Where Vlipid is volume per lipid, V is total volume of box calculated by simulation, Nw is number of water molecule, Vw is volume span by single water molecule at similar simulation conditions such as temperature, van der Waals and columbic cutoffs. Hofsäß et al.29 calculated volume per dipalmitoylphosphatidylcholine (DPPC) molecule in mixed bilayer of DPPC and CHOL by assuming constant volume of CHOL at all concentration. We have used the similar procedure but modified the above equations for mix component system by assuming that volume of cholesterol and FFA molecule do not change with their number (molar concentration) although it changes with temperature. We also assumed that all the volume has been occupied by molecules i.e. there is no free volume in bilayer. Considering above assumption the volume per CER molecule in a mix bilayer system can be written as:

Vcer 

V  NW VW  N cholVchol  N ffaV ffa N cer

…………..…. (3)

where Nffa and Nchol are number of FFA and cholesterol molecules in the mix bilayer respectively. Vchol, Vffa are volume per lipid for pure cholesterol and FFA bilayer respectively, which were calculated by separate individual simulations of pure cholesterol and FFA system in NPT ensemble at each temperature

using identical simulation

condition such as time steps and cut-offs. The area per lipid (APL) is a primary parameter which describes the molecular packing of lipid bilayer. It can be compared with experiments as well as it gives information about the equilibration of the system in simulation. In a molecular dynamics simulation of pure lipid bilayer which has normal along the z direction, the APL can be calculated using following equation


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A

2 Lx Ly

............... (4)

N lipid

Where Lx , Ly is the box length in X and Y direction respectively and N

lipid

is total

number of lipids in the bilayer. Some methods have been proposed for calculating the area per phospholipid molecule and area per CHOL in mix bilayer system at different temperature and CHOL mole fractions.41-42 Chiu et al.42 assumed area per lipid molecule to be independent of mole fraction of CHOL and calculated area per lipid by simple linear regression. Hofsäß et al.29 used volume per lipid and common bilayer thickness to compute individual area per molecule at different mole fraction of CHOL. We have employed similar approach to calculate area per molecule in our mix bilayer system. We have assumed that all the available volume was occupied by lipid molecules that mean there is no free volume inside the bilayer. Average thickness of a bilayer is given by:

havg 

V  NW VW A

…........ (5)

where V and A are the volume and area given by the equation 1 and 4 respectively. Therefore the area per ceramide (APC) molecule can be written as:

Acer 

Vcer havg

............ (6)

using equation (3), (5) and (6)

Acer 

 V  NW VW  N cholVchol  N ffaV ffa  A   V  NW VW  N cer 

Acer  Achol  Affa 

N chol Vchol  N ffaV ffa  A  1   N cer  V  NW VW 

AVchol V  NW VW

……... (7)

............ (8)

AV ffa

…....... (9)

V  NW VW

Where Achol and Affa are the area per molecule of pure cholesterol and FFA bilayer


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respectively. Ncer , Nchol and Nffa are the number of ceramide, cholesterol and FFA molecules in the mix bilayer. Vchol , Vffa are the volume per molecule calculated from the pure CHOL and FFA bilayer simulation.

3. Results and discussion 3.1. Heating run Initially equilibrated bilayer structures at 300 K were used for the heating run. All the bilayers were heated from 300K to 450K slowly at the rate of 5K/ns with time step of 1 fs. Figure 2 shows the evolution of temperature, area per lipid and box volume with simulation time. The constant slope of the temperature curve confirmed the uniform heating. Due to rigid structure of the CHOL the pure CHOL bilayer was stable for whole heating run and pure FFA disintegrated near 380 K. The bilayers disintegrated in the order of (CER: CHOL: FFA) 0:0:1, 1:0:1, 1:1:0, 1:0:0, 1:1:1, 2:2:1, 0:1:0.

3.2. Structures Figure 3 shows snapshot of pure CER bilayer and tails arrangement at each temperature. At physiological temperatures bilayer was found to be in gel phase with proper ordering of lipid tails in both of the leaflets. The lipids tails were found to be in hexagonal phase which are in agreement with earlier experimental studies.43-45 At higher temperature this hexagonal phase disappears and we observe a phase change around 360 - 370 K. Earlier simulations20,21 and experimental studies43,46 have shown that CER-NS exhibits a gel to liquid crystalline phase transformation over a temperature range of 353-363 K. It is important to note that in the centre of bilayer almost liquid like phase was observed due to asymmetric chain length of CER tails (Figure 3). Figure 4 and 5 show the individual component structure of 1:1:1 and 2:2:1 bilayer at each temperature. At lower temperature (< 340 K), all the components are in proper order for both the systems. Since FFA has lower melting point (~ 357 K) and CER has gel to liquids phase transformation temperature of ~ 365 K, near the 380 K more disordering is observed in both the systems. Due to its rigid nature, CHOL provides stability to bilayer, which is apparent from the structure of CHOL in both the systems at each temperature.


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3.3. Volume per lipid The pure bilayer of FFA and CHOL were simulated to get the volume per FFA and CHOL molecules and the results are presented in Table 2. We have obtained volume and area per FFA (APF) of 0.604 nm3 and 0.206 nm2, respectively for a pure FFA system, which is in close agreement with the earlier experimental value47-48 of 0.20-0.21 nm2 and simulation studies20 of palmitic fatty acid at 303 K. We have obtained area per cholesterol molecule of 0.365 nm2 at 300 K in pure cholesterol system, which is closer to experimental value49-50 of 0.36-0.37 nm2 and simulation value

20

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of ~0.37 nm . The melting point of

FFA (lignoceric acid, 24:0) and cholesterol are found to be around ~ 357 K51 and 423 K52, respectively. We also noticed that pure FFA bilayer system was not stable at temperature more than 370 K. Volume per CER molecule calculated using equation 3 for each bilayer system has shown in Figure 6a. The Vcer was least in 1:1:0 bilayer and it increases in presence of FFA.

3.4. Area per lipid Figure 6b shows area per CER (Acer) molecule for each bilayer at different temperature calculated using equation 7. The APL increases with temperature because of more thermal energy which loses the packing of lipid tails. Acer value of ~0.39 nm2 for pure CER bilayer at 300K matches very well with x-ray experiment value of ~0.4 nm2 obtained by Dahlen et al.53 as well as literature.23,24 Acer increases gradually with temperature in all systems. The Acer values are found to be higher in case of mixed 2:2:1 bilayer and lower for 1:0:1 bilayer at each temperature studied. Figure 6c shows area spanned by each cholesterol (Achol ) molecule in the bilayer, calculated from equation 8. It is interesting to note that CHOL spanned less area in each of the mixed bilayer as compare to pure cholesterol bilayer. Figure 6d shows area per free fatty acid (Affa) molecule calculated by equation 9. We found that more of the cholesterol present in the bilayer leads to more of Acer and Affa values. Overall effect of CHOL is to provide more area to CER and FFA in mixed bilayer system.

3.5. Tail order parameter


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This parameter is used to characterize the order in lipid bilayers and can be measured by deuterium NMR. An order parameter for every CH2 group in the chains is defined as:

SZ 

3 1 cos 2 d    2 2

............ (10)

where dθ is the angle between the bilayer normal (z axis) and vector connecting cn-1 to cn+1 CH2 atom. The value of Sz = 1 represents tails are oriented parallel to bilayer axis, while a value of -0.5 represents orientation perpendicular to bilayer normal. Figure 7 shows the comparison of order parameter in each bilayer system below and above the phase transition temperature. The profiles for all the system are almost similar but order parameter decreases with temperature. Chain sn1 (C1-C16) has little bit more ordering as compare to chain sn2 (C27-C49). The order parameter of chains are very low near the interface (C24 and C16) and increases as we move further down to high lipid density region and decreases towards the centre of the bilayer. The asymmetry in ceramide tails leads to more disordering of sn2 chain length in low lipid density region. The similar chain length of FFA leads to a proper inter-digitization thereby increasing the ordering of ceramide tails. CHOL induces fluidity in phospholipid lipid membranes by decreasing the chain ordering below the gel to liquid crystal transition temperature while it increases the rigidity of bilayers above the transition temperature. This phenomenon has been observed both in experiments54-55 and simulations studies.56-57 Mizushima et al. 58

performed differential scanning calorimetry (DSC) experiments on ternary mixture of

CER, FFA and CHOL and found that CHOL increases the fluidity of alkane chains by reducing ordering. This phenomenon has also been observed in recent simulation study.22 We have noticed both these effects in our simulations as shown in Figure 7. Below the phase transition temperature of CER (~365 K), the order parameter is found to be little bit higher in 1:1:1 system as compare to 2:2:1 system. While at higher temperature (>~365 K) reverse phenomena is observed. The order parameter is little bit more in 2:2:1 system as compare to 1:1:1 system. The order parameter for 1:0:1 is highest for both of the chains at each temperature. The same effect of CHOL is also seen in fatty acid chain as shown in Figure 8. It follows the similar trends as CER chains, below the melting point of FFA (~357 K), the order parameter is higher in 1:1:1 system while above this temperature


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reverse phenomena is observed. Another interesting point to note is that the phase transition temperature is found to be lowest in the pure 0:0:1 bilayer and highest in 0:1:0 bilayer. This can be explained by CHOL’s high melting temperature and its rigid structure. 3.6. Lipid density In Figure 9, the densities of lipid components are plotted along the bilayer normal (zaxis) for ceramide bilayer at different temperature. The profile is similar to the four region model as proposed by Marrink et al.59-60 Density from z ~ -6.0 (not shown in Figure) to z ~ -3.2 is constant and this flat region is called bulk water, as we move further near the interface the density of water decreases and head groups density increases ( z~ 3.2 to z ~ -2.0). Next region from z ~ -2.0 to z ~ - 0.8, has very ordered and tightly packed lipid tails, which is mainly responsible for barrier properties of skin. In the last region total lipid density has minimum value because of loose and random packing of lipid tails. There is a sharp peak in ceramide density near the water - lipid interface and all the head group sit just below the water-lipid interface. The interfacial width is found to be smaller than those of phospholipids membrane because of small size and low partial charge of head group. Next to this region, lipid tail density is very high because of proper ordering of tails, the density in this region is found to be around of ~ 1.3 g/cm3. In the middle of bilayer there is dip in lipid density because of asymmetric chain length, this region has more and more free volume and has density of ~ 0.7 g/cm3. The temperature induces disorder in the system which leads to a small tail density in liquid crystalline phase (~360-370 K) as compare to gel phase (300K). The head group density profile gets broader with temperature because of more fluidity in liquid crystalline phase. Figures 10 shows the density profiles of each component of mix 1:1:1 and mix 2:2:1 bilayer. The density profile is almost similar at all the temperature studied. It is worth noting that the peaks of CER and FFA density are near the interface indicating that head groups of both of the component sit just below the lipid -water interface. The CHOL mostly sits in highly dense region of bilayer. Due to smaller size and low partial charge of head groups in ceramide bilayer as compare to phospholipid CHOL molecules sit much below the head group region, almost between the lipid tails. The CER and FFA profile


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shows a small peak at the centre of lipid bilayer at low temperature which was absent in pure ceramide bilayer. This confirms that similar chain length of CER and FFA leads to proper inter-digitization. These peaks get distorted with increase in temperature because higher thermal energy leads to disordering in the tails enabling fluid like environment. The lipid tail density decreases with increase in temperature because bilayer moves from gel to liquid phase at higher temperature. Figures 11a and 11b show density profile of individual components along the bilayer normal in each bilayer at 300 K and 360 K, respectively. Overlapping of FFA and ceramide density peak and inter-digitization between them can easily be seen. FFA induces more and more ordering in lipid tails and increase the thickness of bilayer but CHOL reduces the ordering as well as thickness of bilayer.16 The lipid density profile shows the similar behaviour at all the temperature studied. Peak to peak distance between lipid density was found to be highest in ceramide bilayer and lowest in mix 2:2:1 bilayer. Also, overall density reduction can be seen in FFA and CHOL with increasing temperature as illustrated earlier. Figure 12 shows the electric density of lipid bilayers along the bilayer normal in each bilayer system at different temperature. The shape of electron density in individual bilayer is almost similar for all the temperature but density gets lower with increase in temperature. It is interesting to note the mixed bilayers which comprise CHOL have two peaks while single peak was observed in CHOL free mixed bilayer. This confirms that CHOL mostly sits in between the CER and FFA chains.

3.7. Interfacial and bilayer width The interface (bilayer/water) width was estimated as the distance over which water density drops to 1/e of its bulk value.22,

23

The bilayer thickness could be defined in

several ways such as distance between phosphate atom in each leaflet in phospholipid membrane61, or distance between peaks of electron density profile.62 As shown in Figures 10 and 11, since CHOL sits in the interior space of bilayer, it is not convenient to calculate bilayer thickness by calculating distance between some of the head group atoms. We have used two different methods to calculate bilayer thickness. Schematic of the first approach has shown in supplementary information. Second approach is based on


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volume per CER and area per CER using equation 6. Results for bilayer thickness of each system estimated by above methods are summarized in Table 3. The bilayer thickness was found to be highest in 0:0:1 and lowest in 0:1:0 layers at all temperature studied. The bilayer thickness in mixed bilayer was found to be lowest in 1:1:0 bilayer and maximum in 1:0:1 bilayer. This shows that the same chain length fatty acid interdigitize with ceramide molecules chain and increases the chain length on other side being small in size CHOL reduces the bilayer thickness. This phenomenon has also been observed experimentally by Schroeter et al.63 The bilayer thickness decreases with increasing temperature because percentage in area expansion is larger than that of volume. The interfacial width (~0.5 nm) is smaller than that of sphingomyelin bilayers (~0.9 nm) because of small head group of ceramide layer.30 Figure 13 shows the distance between the head group atoms of CER (N23), CHOL (O6) and FFA (O1) in two leaflets. Inclusion of fatty acid increases the distance of N23 between the two leaflets while CHOL decreases this distance. Minimum distance was found in 1:1:0 bilayer while maximum distance was found in 1:0:1 system. Another interesting thing we noticed that above the phase transition temperature of CER, in mixed bilayer distances between these atoms in two leaflets were more in high CHOL containing bilayer which supports the fact that above the phase transition temperature CHOL provides more ordering to the bilayer.

4.7 Area Compressibility Area compressibility of a bilayer whose normal oriented along the Z axis is calculated as K A  kbT

 A  A    A 2 2

………………………………………….. (12)

where A = Lx x Ly, is area of the bilayer in XY plane, kB is Boltzmann constant and T is temperature. The angular brackets denote the ensemble averages taken over the course of simulation Figure 14 shows the area compressibility of each bilayer at different temperature. The compressibility was found to be highest in the pure CHOL bilayer which supports the fact of rigidity of cholesterol and less permeability of the skin. The pure FFA bilayers are softer than pure CER and CHOL bilayers. Presence of FFA reduces the area


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compressibility and makes bilayer soft in nature. The compressibility increases with increase in the CHOL concentration for a fixed temperature. Additional bigger bilayer patches were simulated to check the effect of system size over the area compressibility. The details are given in table S1 (supplementary information). The KA decreases with the increase in system size in tensionless bilayer system. This has also been observed in earlier studies of phospholipids bilayer.64

3.8 Hydrogen bond The numbers of hydrogen bonds present in bilayer systems were calculated based on the geometrical criteria. A hydrogen bond exists if the distance between the donor and acceptor atom is ≤ 0.35 nm and acceptor-donor -hydrogen angle is ≤ 60◦. Table 4 shows the number of hydrogen bonds between individual components of the bilayer at different temperature. Earlier study shows that the number of hydrogen bonds per water molecule in liquid water is around 3.5-3.8 at 300K.65 In all lipid bilayer system this number decreases to between 1.5-1.7 at 300K since at the interface CER forms the hydrogen with water. Being having small head group and small partial charge, CHOL is unable to form hydrogen bond with other CHOL molecules although it does forms hydrogen bonds with water molecules at interface. CER molecules form more intramolecular hydrogen bonds as compare to CHOL and FFA. The number of hydrogen bonds decreases for each bilayer system with increase in temperature because of high kinetic energy (thermal fluctuation) at elevated temperature.

Conclusion The effect of temperature on skin lipid bilayers has been studied at molecular scale. We have performed molecular dynamics simulations for different composition ratio of main constituent (CER-NS 24, CHOL and FFA 24:0) of skin's stratum corenum lipid matrix. We have found that CER bilayer exhibits hexagonal gel phase at normal skin temperature which gets converted into liquid crystalline phase at ~365 K. The asymmetric chain length of CER tails induces fluid like environment in the centre of bilayers. The presence of symmetric chain length FFA induces more and more inter-digitization and increases the ordering of CER tails. The CHOL molecule sits in the interior of lipid tails and


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provides more rigidity to bilayer at higher temperature. CHOL molecules shows duel nature, it decreases the chain ordering mixed bilayer below the phase transition temperature of CER and increases the ordering above the phase transition temperature. The fatty acids of similar chain length of CER, increases the thickness of the bilayer while short and rigid CHOL molecule decreases the thickness of the bilayer. Presence of CHOL increases the area compressibility of bilayer which is responsible for the barrier function of skin while FFA reduces the compressibility. CER molecule forms intra and inter molecule hydrogen bonds while CHOL only forms inter molecule hydrogen bonds. In real, human skin lipids comprise of heterogeneous mixture of poly disperse FFA (in terms of chain length) and ceramide acid motif (in terms of chain length and functional head group). This work is only related to the most abundant ceramide (CER-NS) and fatty acid found in the human skin. We are currently working on incorporating the effect of polydispersity in our simulations and results will be presented in a later communication.

Acknowledgement Authors would like to thank High Performance Computing at Tata Consultancy Services (TCS) for providing access to EKA Super computer. We would also like to thank Mr. K Ananth Krishanan, CTO, TCS and Dr. Pradip, Vice president and Head Process Engineering Innovation Labs, TCS-TRDDC, Pune for their constant encouragement and support during this project.


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Figures

Figure 1. Molecular structure of individual skin lipid molecules used in simulations. From left: Ceramide-NS (CER), cholesterol (CHOL) and free fatty acid (FFA). Chain sn1, chain sn2 and Ffa chain sn1 represents lipid tails of CER and FFA respectively. Colour red, blue, white and cyan represents oxygen O, nitrogen N, hydrogen H and carbon C (united atom) respectively.


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Figure 2. Evolution of a) temperature b) area per lipid and c) box volume with simulation time in heating run. Colour black, red, green, blue, yellow, cyan and magenta represents system at composition (CER: CHOL: FFA) 1:0:0, 0:1:0, 0:0:1, 1:1:0, 1:0:1, 1:1:1 and 2:2:1 respectively. Please refer to online article for the colour code.


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Figure 3. Snapshot of pure ceramide bilayer at different temperature (top), arrangement of ceramide tails at plane ~ 1.2 nm above the bilayer centre (below). Ceramide head group, tails and water are shown in blue, cyan and red respectively.

Figure 4. Snapshots of individual components and lateral packing of lipid tails in the upper leaflet (at plane ~ 1.4 nm above the bilayer centre) of mixed (CER: CHOL: FFA) 1:1:1 bilayer at different temperature. From top snapshots are at 300 K, 340K, 360K,


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370K, 380K and 400K respectively. CER, CHOL and FFA are shown in light green, pink and yellow colour respectively

Figure 5. Snapshots of individual components and lateral packing of lipid tails in the upper leaflet (at plane ~ 1.4 nm above the bilayer centre) of mixed (CER: CHOL: FFA) 2:2:1 bilayer at different temperature. From top snapshots are at 300 K, 340K, 360K, 370K, 400K, 410K and 420 K respectively. CER, CHOL and FFA are shown in light green, pink and yellow colour respectively.


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Figure 6. a) volume per CER Vcer molecule calculated by equation 3 b) area per CER Acer molecule calculated by equation 7 c) area per cholesterol AChol molecule calculated by equation 8 d) Area per free fatty acid Affa molecule calculated by equation 9 in each system at different temperature. The 1:0:0, 0:1:0, 0:0:1, 1:1:0, 1:0:1, 1:1:1 and 2:2:1 represents the molar ratio of CER: CHOL: FFA in the bilayer.


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Figure 7. Tail order parameter Sz of CER sn1 and sn2 chains at 300K and above the phase transition temperature of 370K. The chain sn1 and sn2 are shown in Figure 1. The 1:0:0, 1:1:0, 1:0:1, 1:1:1 and 2:2:1 represents the molar ratio of CER: CHOL: FFA in the bilayer.

Figure 8 Order parameter (Sz) of FFA chain in mixed 1:1:1 and 2:2:1 bilayer at different


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Page 22 of 38

temperature. FFA chain is shown in Figure 1. The 1:1:1 and 2:2:1 represents the molar ratio of CER: CHOL: FFA in the bilayer.

Figure 9. Density of individual component of pure ceramide bilayer along the bilayer normal at 300 K (from top), 340 K, 360 and 370 K. System, water, head group, tail and ceramide densities are shown in brown, black, cyan, violet and magenta colour respectively. Please refer to online article for the colour code.


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Figure 10. Density of individual component of mixed (CER:CHOL:FFA) 1:1:1 and 2:2:1 bilayer along the bilayer normal at 300 K (from top), 340 K, 360K , 380 K and 400 K. CER, CHOL, FFA, lipid, water and system densities are shown in black, violet, cyan, magenta , yellow and red colour respectively. Please refer to online article for the colour code.


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Figure 11. Density of a) CER b) CHOL c) FFA and d) lipid along the bilayer normal in each bilayer system at 300 K (left) and 360 K (right). Please refer to online article for the colour code.


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Figure 12. Electron density of each bilayer system along the bilayer normal z at different temperature. The 1:0:0, 0:1:0, 0:0:1, 1:1:0, 1:0:1, 1:1:1 and 2:2:1 represents the molar ratio of CER: CHOL: FFA in the bilayer. Please refer to online article for the colour code.


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Figure 13. Distance between the head group atoms of a) CER (N23) b) CHOL (O6) and c) FFA (O1) in two leaflets. N23, O6 and O1 are shown in Figure1. The 1:0:0, 1:1:0, 1:0:1, 1:1:1 and 2:2:1 represents the molar ratio of CER: CHOL: FFA in the bilayer.

Figure 14. Dependence of Area compressibility kA over the temperature for each bilayer system. The 1:0:0, 0:1:0, 0:0:1, 1:1:0, 1:0:1, 1:1:1 and 2:2:1 represents the molar ratio of CER: CHOL: FFA in the bilayer.


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Tables Table1. Number of individual molecules used in simulation for each molar ratio. System*

CER

CHOL

FFA

Water

1:0:0

128

0

0

5120

0:1:0

0

128

0

5120

0:0:1

0

0

512

9020

1:1:0

64

64

0

5120

1:0:1

84

84

168

5120

1:1:1

52

50

52

5120

2:2:1

56

56

32

5120

*The 1:0:0, 0:1:0, 0:0:1, 1:1:0, 1:0:1, 1:1:1 and 2:2:1 represents the molar ratio of CER: CHOL: FFA in the bilayer.

Table 2. Volume# and area$ per FFA/CHOL molecule at different temperature calculated from pure FFA (0:0:1) and CHOL (0:1:0) bilayer simulations respectively. System

Nlipids

Nwater

Temp

Vw*

Vchol, Vffa

Affa, Achol

K

nm3

nm3

nm2

FFA

512

9020

300

0.0302

0.604

0.206

FFA

512

9020

340

0.0313

0.634

0.217

FFA

512

9020

360

0.0319

0.643

0.221

FFA

512

9020

370

0.0323

0.663

0.253

CHOL

128

5120

300

0.0302

0.626

0.366

CHOL

128

5120

340

0.0313

0.631

0.370

CHOL

128

5120

360

0.0319

0.632

0.372

CHOL

128

5120

370

0.0323

0.636

0.375

CHOL

128

5120

380

0.0327

0.638

0.377

CHOL

128

5120

400

0.0336

0.640

0.380

*The water volume Vw was calculated from the separate simulations of 2048 water molecules at the same simulation condition used for respective bilayer system. # calculate using equation 2. $ calculated using equation 4.


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Table3. Distances between head group atoms# in between the two leaflets of the bilayer and average bilayer thickness of each bilayer at different temperature. System

havg1 & (method 1) Nm

havg2 & ( method 2) Nm

Temp

CER O21*

CHOL O6*

FFA O1*

K

Nm

Nm

Nm

1:0:0

300

5.182

-

-

5.65

5.55

1:0:0

340

5.136

-

-

5.61

5.53

1:0:0

360

5.135

-

-

5.59

5.52

1:0:0

370

5.123

-

-

5.57

5.44

0:1:0

300

-

3.378

-

3.423

3.36

0:1:0

340

-

3.367

-

3.411

3.342

0:1:0

360

-

3.355

-

3.401

3.324

0:1:0

370

-

3.354

-

3.396

3.321

0:1:0

380

-

3.346

-

3.389

3.319

0:1:0

400

-

3.326

-

3.372

3.318

0:0:1

300

-

-

5.635

5.866

5.796

0:0:1

340

-

-

5.54

5.847

5.787

0:0:1

360

-

-

5.528

5.826

5.726

0:0:1

370

-

-

5.497

5.240

5.612

1:1:0

300

4.413

4.1

-

4.693

4.583

1:1:0

340

4.372

4.089

-

4.683

4.573

1:1:0

360

4.305

4.083

-

4.644

4.554

1:1:0

370

4.263

4.001

-

4.645

4.545

1:1:0

380

4.240

3.911

-

4.631

4.511

1:1:0

400

4.101

3.815

-

4.662

4.492


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1:0:1

300

5.275

-

5.827

5.926

5.896

1:0:1

340

5.176

-

5.711

5.829

5.879

1:0:1

360

5.171

-

5.747

5.888

5.858

1:0:1

370

5.156

-

5.711

5.856

5.836

1:1:1

300

4.681

4.334

5.005

5.119

5.095

1:1:1

340

4.592

4.27

4.962

5.071

4.98

1:1:1

360

4.541

4.257

4.913

5.033

4.94

`1:1:1

370

4.491

4.089

4.925

4.962

4.90

1:1:1

380

4.355

3.96

4.662

5.023

4.85

1:1:1

400

4.179

3.86

4.578

4.889

4.85

2:2:1

300

4.542

4.186

4.831

4.957

4.83

2:2:1

340

4.470

4.166

4.838

4.911

4.80

2:2:1

360

4.425

4.125

4.823

4.929

4.78

2:2:1

370

4.459

4.068

4.729

4.859

4.77

2:2:1

380

4.425

4.021

4.704

4.829

4.76

2:2:1

400

4.325

3.922

4.645

4.758

4.66

*CERO21, CHOLO6 and FFAO1 represents the atom name O21, O6 and O1 in ceramide, cholesterol and fatty acid molecules respectively. Atoms are shown in the Figure 1. # The error in the data is around of ± 0.05% (T < 350 K) to ±0.15 % (T > 360 K). & The havg1 and havg2 are calculated from volume to area per lipid ratio and drop in water density profile respectively. Details of the methods are given in the supplementary information (figure S5).


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Table4. Number of hydrogen bonds* formed in different components of each bilayer system at different temperature. System$

Temp

CERCER

CERCHOL

CERFFA

CERW#

CHOLCHOL

CHOLFFA

CHOLW

FFAFFA

FFAW

W-W

300

1.52

0

0

2.13

~0

0

0

0

0

1.70

340

1.42

0

0

2.01

~0

0

0

0

0

1.60

360

1.36

0

0

1.95

~0

0

0

0

0

1.55

370

1.34

0

0

1.90

~0

0

0

0

0

1.51

380

1.27

0

0

1.88

~0

0

0

0

0

1.50

300

0

0

0

0

~0

0

2.03

0

0

1.70

340

0

0

0

0

~0

0

1.92

0

0

1.60

360

0

0

0

0

~0

0

1.86

0

0

1.55

370

0

0

0

0

~0

0

1.82

0

0

1.52

380

0

0

0

0

~0

0

1.78

0

0

1.49

400

0

0

0

0

~0

0

1.71

0

0

1.44

300

0

0

0

0

~0

0

0

0.28

1.66

1.67

340

0

0

0

0

~0

0

0

0.27

1.56

1.57

360

0

0

0

0

~0

0

0

0.24

1.49

1.52

370

0

0

0

0

~0

0

0

0.20

1.45

1.49

300

0.78

0.293

0

3.35

~0

0

0.74

0

0

1.69

340

0.75

0.280

0

3.00

~0

0

0.64

0

0

1.59

360

0.72

0.272

0

2.94

~0

0

0.56

0

0

1.54

370

0.68

0.265

0

2.82

~0

0

0.50

0

0

1.51

380

0.66

0.256

0

2.72

~0

0

0.48

0

0

1.49

400

0.64

0.247

0

2.51

~0

0

0.43

0

0

1.43

300

1.24

0

0.59

2.0

~0

0

0

0

0.26

1.71

K 1:0:0

0:1:0

0:0:1

1:1:0

1:0:1


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1:1:1

2:2:1

340

1.19

0

0.57

1.84

~0

0

0

0

0.24

1.61

360

1.14

0

0.54

1.75

~0

0

0

0

0.23

1.57

370

1.08

0

0.50

1.64

~0

0

0

0

0.20

1.54

300

0.76

0.31

0.19

2.93

~0

0.12

0.88

1.06

1.78

1.69

340

0.72

0.28

0.15

2.59

~0

0.10

0.79

1.44

1.76

1.59

360

0.71

0.25

0.14

2.56

~0

0.10

0.77

1.61

1.71

1.54

370

0.73

0.23

0.12

2.49

~0

0.10

0.76

1.54

1.69

1.51

380

0.66

0.23

0.14

2.43

~0

0.08

0.72

1.68

1.63

1.48

400

0.65

0.22

0.13

2.38

~0

0.07

0.69

1.62

1.61

1.46

300

0.80

0.34

0.13

2.72

~0

0

0.86

0.85

1.81

1.67

340

0.75

0.33

0.11

2.68

~0

0

0.83

0.71

1.75

1.59

360

0.71

0.33

0.09

2.63

~0

0

0.76

0.61

1.68

1.54

370

0.69

0.29

0.08

2.61

~0

0

0.74

0.62

1.67

1.52

380

0.65

0.26

0.08

2.59

~0

0

0.72

0.65

1.66

1.48

400

0.63

0.25

0.07

2.47

~0

0

0.63

0.59

1.57

1.44

* The error in the data is around of ±1 % (T < 350 K) - ±3 % (T > 360 K) # W stands for the water molecule. $ The 1:0:0, 0:1:0, 0:0:1, 1:1:0, 1:0:1, 1:1:1 and 2:2:1 represents the molar ratio of CER: CHOL: FFA in the bilayer.

Supplementary Information Figure S1 (equilibration of area per lipid), Figure S2 (equilibration of volume per lipid), Figure S3 (equilibration of potential energy), Figure S4 (Structures of equilibrated bilayer at 300 K), Figure S5 (method of calculation of bilayer width) and Table S1 (Effect of system size on the bilayer properties). This material is available free of charge via the Internet at http://pubs.acs.org.

ABBREVIATIONS CER, ceramide ; CHOL, cholesterol, FFA, free fatty acid; VPL, volume per lipid; APL, area per lipid; APC, area per ceramide;


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Page 32 of 38

AUTHOR INFORMATION Corresponding Author Email: [email protected]

Phone: +91-02066086203

References 1) Michaels, A. S.; Chandrasekaran, S. K.; Shaw, J. E. Drug Permeation through Human Skin: Theory and In-Vitro Experimental Measurement. AIChE J. 1975, 21, 985-996. 2) Christian, U.; Hansen, C. M.; Dyk, V.; John, W.; Jensen, P. O. Permeability of Commercial Solvents through Living Human Skin. American Industrial Hygiene Association Journal. 1995, 56(7), 651-60 3) Baratosova, L.; Bajgar, J. Transdermal Drug Delivery In-Vitro Using Diffusion Cells. Current Medical Chemistry. 2012, 19, 4671-4677 4) Huzil, J. T.; Sivaloganathan, S.; Kohandel, M.; Foldvari, M. Drug Delivery through the Skin: Molecular Simulations of Barrier Lipids to Design More Effective Noninvasive Dermal and Transdermal Delivery Systems for Small Molecules, Biologics, and Cosmetics. WIREs NanomeNanobiotechnol. 2011, 3, 449-462. DOI: 10.1002/wnan.147 5) Jepps, O. G.; Dancik, Y.; Anissimov, Y. G.; Roberts, M. S. Modeling the Human Skin Barrier- Towards a Better Understanding of Dermal Absorption. Advanced Drug Delivery reviews. 2013, 65, 152-168 6) Mitragotri, S. et al. Mathematical Models of Skin Permeability: An Overview. International Journal of Pharmaceutics. 2011, 418 (1), 115-129 7) Williams, M. L.; Elias, P. M. The Extracellular Matrix of Stratum Corneum: Role of Lipids in Normal and Pathological Function. CRC Critical Reviews in Therapeutic Drug Carrier Systems.1987, 3, 95-122 8) Wertz, P. W.; Downing, D. T. The Nature of the Epidermal Barrier: Biochemical Aspects. Adv. Drug Del. Rev. 1996, 18, 283-294


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9) Norlen, L.; Nicander, I.; Rozell, B. L.; Ollmar, S.; Forslind, B. Inter- and IntraIndividual Differences in Human Stratum Corneum Lipid Content Related to Physical Parameters of Skin Barrier Function In Vivo. J. Invest. Dermatol. 1999, 112, 72-77 10) Weerheim, A.; Ponec, M. Determination of Stratum Corneum Lipid Profile by Tape

Stripping

in

Combination

with

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