Long-period Phase Research Articles

Evaluation of molecular interaction between intercellular lipid organization in human stratum corneum and terpenes using time-resolved synchrotron X-ray diffraction

The stratum corneum (SC) presents certain limitations for topical administration of medication, which can be overcome using penetration enhancers (PEs) such as terpene (TP). The SC is also crucial for maintaining the skin barrier and consists of two lamellar structures: the short periodicity phase (SPP) and long periodicity phase (LPP). In this study, we monitored changes in the X-ray diffraction peaks of the human SC, 30 min after TP application (neroridol, 1,8-cineol, and d-limonene). With the application of nerolidol, no significant changes were observed in the small-angle diffraction peak positions for the lamellar structure of SPP, but the integrated intensity decreased. On the contrary, when applying 1,8-cineole and d-limonene, a lower angle peak shift with broadening of the peak width of SPP diffraction peaks was observed for d-limonene than for 1,8-cineole, and the degree of peak shift and width broadening was greater for d-limonene than for 1,8-cineole. The diffraction peaks of LPP disappeared when 1,8-cineole and d-limonene were applied. These results indicate that the degree of interaction between the SC and TP differs depending on the molecular species, and d-limonene and 1,8-cineole exhibit penetration-enhancing via lamellar structure disruption of both SPP and LPP, immediately after application.

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.

The molecular arrangement of ceramides in the unit cell of the long periodicity phase of stratum corneum models shows a high adaptability to different ceramide head group structures

The stratum corneum (SC) lipid matrix, composed primarily of ceramides (CERs), cholesterol and free fatty acids (FFA), has an important role for the skin barrier function. The presence of the long periodicity phase (LPP), a unique lamellar phase, is characteristic for the SC. Insight into the lipid molecular arrangement within the LPP unit cell is imperative for understanding the relationship between the lipid subclasses and the skin barrier function. In this study, the impact of the CER head group structure on the lipid arrangement and barrier functionality was investigated using lipid models forming the LPP. The results demonstrate that the positions of CER N-(tetracosanoyl)-sphingosine (CER NS) and CER N-(tetracosanoyl)-phytosphingosine (CER NP), two essentials CER subclasses, are not influenced by the addition of another CER subclass (N-(tetracosanoyl)-dihydrosphingosine (CER NdS), N-(2R-hydroxy-tetracosanoyl)-sphingosine (CER AS) or D-(2R-hydroxy-tetracosanoyl)-phytosphingosine (CER AP)). However, differences are observed in the lipid organization and the hydrogen bonding network of the three different models. A similar localization of CER NP and CER NS is also observed in a more complex lipid model, with the CER subclass composition mimicking that of human SC. These studies show the adaptability and insensitivity of the LPP unit cell structure to changes in the lipid head group structures of the CER subclasses.

Models of the Three-Component Bilayer of Stratum Corneum: A Molecular Simulation Study.

The construction of the stratum corneum (SC) is crucial to the problems of transdermal drug delivery. SC consists of the keratinocyte layers and the lipid matrix surrounding it. Among them, the lipid matrix is the barrier for many exogenous molecules, mainly composed of ceramides (CERs), free fatty acids (FFA), and cholesterol (CHOL). In this work, we developed single-component (CERs, CER-NS, and CER-EOS) and six three-component models, and each model was simulated by using the GROMOS-54A7 force field. Short-period phase (SPP) and long-period phase (LPP) systems were established separately, and area per lipid (APL), thickness, order of carbon chain (SCD), and density distribution were analyzed. The transition of CER-NS and CER-EOS in LPP was observed. The results of hydrogen bonds in the lipid systems indicated that a strong hydrogen-bond network was formed between the skin-lipid bilayers. Umbrella sampling method simulations were performed to calculate the free energy change of ethanol moving into the skin-lipid bilayer. The results revealed that ethanol molecules pulled some water molecules into the membrane when they passed through SPP-1. Our findings provided some insights and models of the stratum corneum that could be used for the subsequent mechanism of macromolecule permeation through membranes in drugs, cosmetics, and so on.

The intriguing molecular dynamics of Cer[EOS] in rigid skin barrier lipid layers requires improvement of the model

Omega-O-acyl ceramides such as 32-linoleoyloxydotriacontanoyl sphingosine (Cer[EOS]) are essential components of the lipid skin barrier, which protects our body from excessive water loss and the penetration of unwanted substances. These ceramides drive the lipid assembly to epidermal-specific long periodicity phase (LPP), structurally much different than conventional lipid bilayers. Here, we synthesized Cer[EOS] with selectively deuterated segments of the ultralong N-acyl chain or deuterated or 13C-labeled linoleic acid and studied their molecular behavior in a skin lipid model. Solid-state 2H NMR data revealed surprising molecular dynamics for the ultralong N-acyl chain of Cer[EOS] with increased isotropic motion toward the isotropic ester-bound linoleate. The sphingosine moiety of Cer[EOS] is also highly mobile at skin temperature, in stark contrast to the other LPP components, N-lignoceroyl sphingosine acyl, lignoceric acid, and cholesterol, which are predominantly rigid. The dynamics of the linoleic chain is quantitatively described by distributions of correlation times and using dynamic detector analysis. These NMR results along with neutron diffraction data suggest an LPP structure with alternating fluid (sphingosine chain-rich), rigid (acyl chain-rich), isotropic (linoleate-rich), rigid (acyl-chain rich), and fluid layers (sphingosine chain-rich). Such an arrangement of the skin barrier lipids with rigid layers separated with two different dynamic “fillings” i) agrees well with ultrastructural data, ii) satisfies the need for simultaneous rigidity (to ensure low permeability) and fluidity (to ensure elasticity, accommodate enzymes, or antimicrobial peptides), and iii) offers a straightforward way to remodel the lamellar body lipids into the final lipid barrier.

Phytosphingosine ceramide mainly localizes in the central layer of the unique lamellar phase of skin lipid model systems

Understanding the lipid arrangement within the skin’s outermost layer, the stratum corneum (SC), is important for advancing knowledge on the skin barrier function. The SC lipid matrix consists of ceramides (CERs), cholesterol, and free fatty acids, which form unique crystalline lamellar phases, referred to as the long periodicity phase (LPP) and short periodicity phases. As the SC lipid composition is complex, lipid model systems that mimic the properties of native SC are used to study the SC lipid organization and molecular arrangement. In previous studies, such lipid models were used to determine the molecular organization in the trilayer structure of the LPP unit cell. The aim of this study was to examine the location of CER N-(tetracosanoyl)-phytosphingosine (CER NP) in the unit cell of this lamellar phase and compare its position with CER N-(tetracosanoyl)-sphingosine (CER NS). We selected CER NP as it is the most prevalent CER subclass in the human SC, and its location in the LPP is not known. Our neutron diffraction results demonstrate that the acyl chain of CER NP was positioned in the central part of the trilayer structure, with a fraction also present in the outer layers, the same location as determined for the acyl chain of CER NS. In addition, our Fourier transformed infrared spectroscopy results are in agreement with this molecular arrangement, suggesting a linear arrangement for the CER NS and CER NP. These findings provide more detailed insight into the lipid organization in the SC lipid matrix.

The importance of ceramide headgroup for lipid localisation in skin lipid models

The stratum corneum's lipid matrix is a critical for the skin's barrier function and is primarily composed of ceramides (CERs), cholesterol (CHOL) and free fatty acids (FFAs). The lipids form a long periodicity phase (LPP), a unique trilayer unit cell structure. An enzyme driven pathway is implemented to synthesize these key lipids. If these enzymes are down- or upregulated as in inflammatory diseases, the final lipid composition is affected often altering the barrier function. In this study, we mimicked down regulation of enzymes involved in the synthesis of the sphingosine and CER amide bond. In a LPP lipid model, we substituted CER N-(tetracosanoyl)-sphingosine (CER NS) with either i) FFA C24 and free sphingosine, to simulate the loss of the CER amide bond, or ii) with FFA C24 and C18 to simulate the loss of the sphingosine headgroup. Our study shows the lipids in the LPP would not phase separate until at least 25% of the CER NS is substituted keeping the lateral packing and conformational ordering unaltered. Neutron diffraction studies showed that free sphingosine chains localized at the outer layers of the unit cell, while the remaining CER NS head group was concentrated in the inner headgroup layers. However, when FFA C18 was inserted, CER NS was dispersed throughout the LPP, resulting in an even distribution between the inner and outer water layers. The presented results highlight the importance of the CER NS headgroup structure and its interaction in combination with the carbon chain invariability for optimal lipid arrangement.

An atomistic model of the human stratum corneum: permeation through the long periodicity phase—effect of a pro-penetrant

The stratum corneum (SC) layer of the human skin is the outermost and primary barrier against chemical topical exposure. The ability of a chemical to pass the SC is a key point for risk assessment and development of cosmetic ingredients. A simulation model of the skin permeability mechanism is therefore of significant translational importance. From neutron diffraction data, the SC peaks comprise a short periodicity phase (SPP) with a repeat distance of 6 nm, and a long periodicity phase (LPP) with a repeat distance of 13 nm.

Sustainable and efficient skin absorption behaviour of transdermal drug: The effect of the release kinetics of permeation enhancer

At present, how the release kinetics of permeation enhancers affected their enhancement efficacy on drug skin absorption and its molecular mechanisms remained unclear. Herein, the release kinetics of permeation enhancer (Plurol Oleique CC (POCC)) which involved release percent (PR), release duration (RD) and release kinetic constant (k) and its enhancement efficacy on drug skin absorption were investigated with in vitro skin retention study and in vitro skin permeation study, respectively. POCC released from the acidic-drug loading patches followed with the Higuchi release model and had short RD (8–16 h), resulting in its unsustainable enhancement efficiency for acidic drugs. However, POCC released from the basic-drug loading patches followed with zero-order model with long RD (12–24 h), inducing a sustainable and efficient enhancement efficiency for basic drugs. The lower variance of an innovative parameter permeation enhancement coefficient (CPE) represented the relatively sustainable and effective enhancement effect and was listed as followed: 0.20 (Zaltoprofen (ZPF)), 0.31 (Diclofenac (DCF)), 0.27 (Indomethacin (IMC)), 0.07 (Azasetron (AST)), 0.11 (Oxybutynin (OBN)) and 0.06 (Donepezil (DNP)). According to the results of FT-IR, MTDSC, 13C NMR spectra, molecular dynamics simulation, SAXS and Raman imaging, the Higuchi release model was caused by strong interaction between the acid drugs and pressure sensitive adhesive (PSA). This strong interaction induced faster diffusion speed of POCC from acidic-drug loading patches and make the swell degree of long periodicity phase (LPP) of stratum corneum (SC) lipids reached plateau early. The zero-order release model was because the weak interaction between basic drugs and PSA making most of POCC was still bound to PSA, which in turn lead to LPP swelled at a slow but sustainable process. In conclusion, zero-order release kinetic of POCC lead to sustainable and efficient penetration enhancement efficiency on basic drug, while the Higuchi release kinetic showed opposite effect for acidic drugs. A deep understanding of release kinetics of enhancer and its enhancement efficiency may drive the ideal selection of permeation enhancers and rational optimization of transdermal patches.

Stabilization of Lipid Lamellar Bilayer Structure of Stratum Corneum Modulated by Poly (2-methacryloyloxyethyl phosphorylcholine) in Relation to Skin Hydration and Skin Protection.

One crucial factor in skin tissue engineering is to understand the hydration and barrier property of skin. We investigated the skin hydration and stabilization strategy of inter-lamellar structure of stratum corneum (SC) using poly (2-methacryloyloxyethyl phosphorylcholine) (PMPC). The unique hydration and stabilization potency of PMPC on the barrier function of the SC examined using freshly excised hairless mouse skin as a model membrane and the relationship between the stabilization of the lipid lamellar bilayer (LLB) and its enhanced water holding capacity was established. Differential scanning calorimeter based on the phase-transition temperature of lipid domain of SC demonstrated that PMPC stabilized the LLB. The ratio of the heat of lipid phase transition (△H) of SC exposed to water and PMPC for 24h was 1.51. X-ray crystallography showed the presence of well- organized lipids in intercellular membranes exhibiting short and long periodicity of lamellar phases. The peak at 4.4nm attributed to the long periodicity phase (LPP) was missing in water-treated SC, where, the presence of 4.2- 4.4nm peak in PMPC treated SC indicated that PMPC stabilized LPP. Transmission electron microscopy study demonstrated that the LLB structure became more rigid and orderly in PMPC treated SC. The unique ion paired structure of PMPC enhances the barrier function of the SC by stabilizing LLB structure and hydration by inducing weakly bound water. The unique hydration state and stabilization effect from extended water exposure could provide a valuable information to prepare reliable artificial skin matrix and skin tissue.

The Importance of Free Fatty Chain Length on the Lipid Organization in the Long Periodicity Phase.

The skin’s barrier ability is an essential function for terrestrial survival, which is controlled by intercellular lipids within the stratum corneum (SC) layer. In this barrier, free fatty acids (FFAs) are an important lipid class. As seen in inflammatory skin diseases, when the lipid chain length is reduced, a reduction in the barrier’s performance is observed. In this study, we have investigated the contributing effects of various FFA chain lengths on the lamellar phase, lateral packing. The repeat distance of the lamellar phase increased with FFA chain length (C20–C28), while shorter FFAs (C16 to C18) had the opposite behaviour. While the lateral packing was affected, the orthorhombic to hexagonal to fluid phase transitions were not affected by the FFA chain length. Porcine SC lipid composition mimicking model was then used to investigate the proportional effect of shorter FFA C16, up to 50% content of the total FFA mixture. At this level, no difference in the overall lamellar phases and lateral packing was observed, while a significant increase in the water permeability was detected. Our results demonstrate a FFA C16 threshold that must be exceeded before the structure and barrier function of the long periodicity phase (LPP) is affected. These results are important to understand the lipid behaviour in this unique LPP structure as well as for the understanding, treatment, and development of inflammatory skin conditions.

Molecular Simulation of Properties of the Long Periodicity Phase in the Stratum Corneum

The stratum corneum (SC) layer of the human skin is the outermost and primary barrier against chemical topical exposure including cosmetics. The ability of a chemical to pass the SC is a key point for risk assessment as well as for drug development. Thus a simulation model of the skin permeability mechanism is of significant translational importance. From neutron diffraction data, the SC peaks comprise a long periodicity phase (LPP) with a repeat distance of 13 nm and a short periodicity phase (SPP) with a repeat distance of 6 nm. The LPP captures long-scale dynamics and can be adequately assigned to a molecular construct termed a sandwich model by Bouwstra, which comprises two bilayers surrounding a fluid interior slab with lipid headgroups pointing in both directions, i.e. a bilayer-slab-bilayer arrangement. A long ceramide-1 (CerEOS) populates only the outer leaflet of the bilayer, penetrating into the inner bilayer leaflet. A systematic study of transdermal solute penetration through the LPP has not yet been performed. Here, we employ microsecond MD simulations in combination with a non-equilibrium pulling methodology to calculate free-energies and permeabilities of transdermal penetration of a set of compounds (e.g. caffeine) through a model of the LPP studied by Groen et al. composed of Ceramide-1 (CerEOS), Ceramide-2 (CerNS), Ceramide-3 (CerNP), Chol, and free-fatty acid (LA), with an equimolar ratio of ceramide, cholesterol and free-fatty acid.

Probing the Unique Role of Ultralong-Chain Omega-Acylceramide Cer[EOS] in a Stratum Corneum Lipid Model Matrix using 2H NMR

The stratum corneum (SC) as the outermost layer of the human skin prevents the body from excessive water loss as well as xenobiotics. At the moment, the LPP(long periodicity phase) is estimated as essential for the barrier function of the human skin, but the exact molecular structure is still unknown. Therefore, we studied a LPP model of the intercellular lipids of the SC consisting of Cer[EOS], Cer[NS], a free fatty acid-mixture (FFA-mix, C16-C24 saturated) and cholesterol at a molar mixing ratio of 0.3:0.7:1:0.45.

Arrangement of Ceramides in the Skin: Sphingosine Chains Localize at a Single Position in Stratum Corneum Lipid Matrix Models.

Understanding the structure of the stratum corneum (SC) is essential to understand the skin barrier process. The long periodicity phase (LPP) is a unique trilayer lamellar structure located in the SC. Adjustments in the composition of the lipid matrix, as in many skin abnormalities, can have severe effects on the lipid organization and barrier function. Although the location of individual lipid subclasses has been identified, the lipid conformation at these locations remains uncertain. Contrast variation experiments via small-angle neutron diffraction were used to investigate the conformation of ceramide (CER) N-(tetracosanoyl)-sphingosine (NS) within both simplistic and porcine mimicking LPP models. To identify the lipid conformation of the twin chain CER NS, the chains were individually deuterated, and their scattering length profiles were calculated to identify their locations in the LPP unit cell. In the repeating trilayer unit of the LPP, the acyl chain of CER NS was located in the central and outer layers, while the sphingosine chain was located exclusively in the middle of the outer layers. Thus, for the CER NS with the acyl chain in the central layer, this demonstrates an extended conformation. Electron density distribution profiles identified that the lipid structure remains consistent regardless of the lipid’s lateral packing phase, this may be partially due to the anchoring of the extended CER NS. The presented results provide a more detailed insight on the internal arrangement of the LPP lipids and how they are expected to be arranged in healthy skin.

A novel long-period phase in Mg97Yb2Cu1 alloy

A Mg80Yb12Cu8 (CY) phase was found in a Mg97Yb2Cu1 alloy quenched after being annealed at 873 K for 10 min; the unit cell dimensions of the CY phase are described as 43×43×2 with respect to those of the original hcp-Mg lattice. The a-axis lattice constant of the CY phase well matches 43 times the a-axis length of the α-Mg phase. In the present work, the c-axis of the CY phase and the dendrite-like α-Mg phase in the precipitate zone are coaxial, i.e., the basal planes are coherent. This result is attributed to the good match between the lattice constants of the fundamental a-axis of the CY phase and the α-Mg phase. According to compression tests, the CY phase is responsible for the increase in strength observed in both the elastic and work-hardening regions in the Mg97Yb2Cu1 alloy. As far as our investigations of Mg97Yb2M1 (M = Al, Ni, Co) alloys, the phase similar to the CY phase have not found. Our discovery of this phase might provide a new path to the discovery of long-period superlattice in various Mg alloys.

Regularities of the formation and features of the influence of a fine structure on the properties of a new-generation magnesium alloy

An approach to creating high-strength deformable magnesium alloys for developing a fine-grained structure and a favourable phase composition is considered. The possibility of a noticeable improvement in the characteristics of magnesium alloys by introducing REEs in certain ratios for the formation of long-period phases (LPSO phases) is considered. The regularities of formation and features of the influence of a fine structure on the properties of a new-generation magnesium alloy of the VMD16 brand are studied.

Molecular Structure of the Long Periodicity Phase in the Stratum Corneum.

All-atom models of the long periodicity phase (LPP) in the stratum corneum (SC) are studied using bilayer-slab-bilayer (sandwich) structures and multi-microsecond simulations. Linoleate promotes melting of the interior slab, which contains ceramide (Cer) in the posturing chain conformation, a structurally distinct conformation from full chain extension. The mechanism of Cer transitioning into full extension is characterized by initial anchoring of the head-proximal carbons and occurs over tens of nanoseconds. Free fatty acids translocate through the interior over hundreds of nanoseconds, while Cer and cholesterol take around a microsecond or longer to translocate. Electron density and neutron scattering length density profiles from simulation agree with experiment, and the high disorder of linoleate in CerEOS supports experiments with infrared spectroscopy and nuclear magnetic resonance. Lateral organization demonstrates dependence on lipid composition and bilayer thickness. To further validate the LPP model, umbrella sampling was used to calculate ethanol permeability in comparison with experiment (log(P) values obtained from modeling the SC's multiple LPP layers are -7.6 and -6.6 cm/s, and that from experiment on cadaver skin is -6.65 cm/s). A "leapfrog" mechanism for ethanol permeation is proposed which is associated with its role as a topical enhancer. These models, the first experimentally verified atomistic sandwich models of the LPP, will aid in the design and optimization of transdermal drug delivery.

Molecular Structure of the Long Periodicity Phase in the Stratum Corneum

The long periodicity phase (LPP) of the stratum corneum (SC) is studied using all-atom molecular dynamics simulations of sandwich models on the microsecond timescale. The interior of the sandwich structure is fluid but transitions into the gel phase due to free fatty acid (FFA). Ceramides (Cer) transition from hairpin to extended conformations, and the mechanism is characterized by initial anchoring of the head-proximal carbons. FFA translocates through the interior on the hundred-nanosecond timescale, and cholesterol (Chol) is oriented perpendicular to the normal at the bilayer-monolayer interface. Strong agreement with experiment is noted based on electron density and neutron scattering length density (NSLD), and the high disorder of Cer linoleate supports infrared spectroscopy. Cer preferentially clusters over Chol and FFA in the outer leaflet. To further validate the model, ethanol permeability was calculated using umbrella sampling, which agrees excellently with experiment (logP of −6.5 cm/s vs. −6.7 cm/s in experiment) and suggests that the limiting factor is the LPP. Furthermore, a leapfrog mechanism of ethanol permeation into the skin is proposed. These are the first experimentally verified sandwich models of the LPP and will aid the design and optimization of transdermal drug delivery systems.

The features of behavior of the Lyapunov's exponents from the symmetry of thermodynamic potential described by lifshitz invariant

The influence of the thermodynamic potential ( n ) symmetry on the behavior of the Lyapunov exponents is investigated. The calculation of the system of second-order differential equations was performed by a multi-step variable-order BDF method. The Lyapunov coefficients were calculated using Python software using Skipy, JiTCODE libraries. It is established that for values of n ≥ 5, the dynamics of the incommensurate superstructure is determined by the spatial change in the amplitude of the order parameter (the first integral of the motion of the incommensurate superstructure). For n < 5, the dynamics of a incommensurate superstructure is determined by the spatial change of the phase of the order parameter and its perturbation. It is shown that the dynamics of the superstructure is not affected by the ferroelectric or ferroelastic nature of the incommensurate superstructure. In order to obtain a detailed picture of the dynamics of the incommensurate superstructure, phase portraits were investigated in the coordinates R , R `, and φ at different values of the anisotropic interaction of the superstructure and the initial phase values of the order parameter φ 0 . It is established that the dynamics of this system is determined by the cascades of transition to chaos and areas of self-organization of the superstructure. It is shown that at the final stage of the transition to chaos, the system is characterized by the emergence of a chaotic attractor, which has a more complex phase portrait structure. The projection of such an attractor consists of two symmetrical parts with respect to the axis of the abscissa. The movement of a typical trajectory of a chaotic attractor can be divided into two phases. In the first phase of the trajectory, chaotic movements are made along the turns of the upper (lower) part of the attractor from time to time, passing to the boundary of the localization region where the stability of the upper (lower) symmetric boundary cycles is lost. At an unpredictable time, the trajectory moves from the upper (lower) part of the attractor to its upper (lower) part. This process is repeated infinitely many times. Thus, the transition to chaos has features characteristic of the Feigenbaum scenario (infinite cascade of bifurcations of doubling cycles), and for mixing (unpredictable mixing between the upper and lower parts of the emerging chaotic attractor). The self-organization process can be associated with the localization of a wave vector of incommensurate superstructure at a commensurate higher order value. It is shown that the distortion of the order parameter phase at the edge of the crystal can be related to boundary conditions in the first approximation. According to the authors, such cascading transitions to chaos are related to the modes of existence of a incommensurate superstructure. The emergence of chaos in the third stage is caused by the transition of a incommensurate superstructure to its stochastic mode of existence. In a stochastic mode of existence of a incommensurate superstructure, a chaotic, possibly incommensurate phase arises, which is a prototype of this chaotic state. It should be noted that the initial conditions (boundary conditions) stabilize the system, thereby leading to the removal of the degeneracy of the system, and the transition of a incommensurate superstructure to a state characterized by the existence of long-period proportional phases. Key words: incommensurate superstructures, phase portraits, Lyapunov’s exponents.

Preferential arrangement of lipids in the long-periodicity phase of a stratum corneum matrix model

The lipid matrix of the stratum corneum, the outermost skin layer, consists primarily of ceramides, cholesterol, and FFAs. These lipids form a trilayer long-periodicity phase (LPP) that is unique to this barrier. Knowledge about the LPP is essential in understanding the barrier function. Previous studies of LPP lipid models have identified the position of the major lipid classes and suggested that a large fraction of FFAs and the ceramide acyl chain are present in the central region. However, the precise arrangement, such as lipid subclass mixing (isolated or mixed) and ceramide conformation (extended or hairpin), remains unknown. Here, we deuterated FFAs and the ceramide acyl chain to study CD2 and CH2 interactions with Fourier-transform infrared spectroscopy. The ceramide and FFAs of various chain lengths were not in separate domains but had mixed together. The larger number of CD2-CD2 lipid chain interactions in the LPP than in a symmetrical bilayer structure implied that the ceramide had primarily adopted an extended conformation. Shorter FFAs were present in the central region of the LPP. This model explores the biophysical properties of the stratum corneum's LPP to improve the understanding of the barrier function of this layer.