Article pubs.acs.org/Langmuir
Insights into the Structure of Covalently Bound Fatty Acid Monolayers on a Simplified Model of the Hair Epicuticle from Molecular Dynamics Simulations Daniel W. Cheong,* Freda C. H. Lim,‡ and Liping Zhang‡ Institute of High Performance Computing, Agency for Science, Technology and Research, 1 Fusionopolis Way, #16-16 Connexis, Singapore 138632 ABSTRACT: The epicuticle is the outermost layer of the human hair, and consists of a monolayer of fatty acids that is predominantly 18-methyleicosanoic acid (18-MEA) covalently bound to a protein matrix. Surprisingly, despite the clear scientific and industrial importance, the detailed molecular structure of this fatty acid layer is still poorly understood. In this work, we aim to gain insight into the structure of this socalled F-layer by performing molecular dynamics simulations on a simplified hair surface model consisting of a monolayer of 18-MEA covalently attached to graphene sheets at various separation distances. The relative free energy of the fatty acid layer was calculated as a function of separation distance in order to obtain the optimal packing density of the fatty acids. Conformational properties such as the thickness, tilt angle, and order parameter of the fatty acid layers were also calculated to characterize the structure of the F-layer. Simulations of the structurally similar eicosanoic acid (EA) were also performed as a comparison and to investigate the role of the anteiso-methyl side chain at the 18th position of 18-MEA. The degree of water penetration into the fatty acid layer at the various separation distances was also investigated. Our simulations suggest that the optimal spacing for the fatty acids is between 0.492 and 0.651 nm, in contrast to the generally accepted literature value of around 0.9−1.0 nm. This results in a packing density of between 0.21 and 0.37 nm2 per fatty acid molecule and a thickness of around 2.01−2.64 nm. We also show that, at larger separation distances, the 18-MEA fatty acid provides a slightly better hydrophobic layer than the EA fatty acid, suggesting that the 18-MEA fatty acid may have been naturally selected to provide better protection for the hair when it loses some of the fatty acids due to daily wear and tear. To our knowledge, this is the first attempt to systematically investigate the hair surface structure and properties with molecular simulations.
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INTRODUCTION Hair is a complex composite biomaterial, consisting of mostly proteins and lipids, arranged in several distinct layers of a fiber. During the past decades, extensive investigations have revealed that the hair fiber consists of four basic units: the cuticle, the cortex, the medulla, and the cell membrane complex.1 The cuticle forms the outer protective layer consisting of multiple overlapping scales around the hair fiber. The majority of the fiber mass is contained in the cortex, which consists of fibrous proteinaceous material. In some thicker hairs, a thinner, more loosely packed medulla can be found near the center of the fiber. Finally, the cell membrane complex acts as the glue that binds the cells in the fiber together.1−3 A good overview of the hair structure and morphology can be found in several review papers and books.1−5 As mentioned above, the role of the cuticle is to act as a chemically resistant protective layer for the hair fiber. It is generally made up of 5−10 overlapping sheet-like cuticle cells, which also consists of several layers, typically referred to as the endocuticle, the exocuticle, the A-layer, and a thin outer membrane called the epicuticle. The different layers of the cuticle contains proteinaceous material of varying cystine © 2012 American Chemical Society
content, with the outer layers containing more cystine than the inner layers.4 Being the outermost layer of the hair, the epicuticle would be the first surface to interact with the environment and any chemicals that would be introduced to the hair. As such, it is of vital importance to have a good understanding of the physical, chemical, and structural properties of the epicuticle. Numerous studies have led to several generally accepted understanding of the epicuticle. The epicuticle has been estimated to be around 5−10 nm thick, although measurements in the range of 2.5−25 nm have been reported.1,6 It has also been proposed that the epicuticle contains about 75% of a highly cross-linked protein layer, and 25% fatty acids, predominantly 18-methyleicosanoic acid (18MEA), which are covalently attached to the protein via thioester bonds to the cysteine residues forming the so-called F-layer.7,8 However, despite the abundant information on the hair and its clear scientific and industrial relevance and importance, the detailed molecular structure of the epicuticle Received: May 28, 2012 Revised: August 7, 2012 Published: August 14, 2012 13008
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performed MD simulations with a united atom potential on Langmuir monolayers of 18-MEA and the structurally similar eicosanoic acid (EA), which differs from 18-MEA only in the absence of the anteiso-methyl side chain at the 18th carbon position. More recently, Natarajan and Robbins31 used MD simulations to determine the thickness of the 18-MEA layer. However, they have assumed a separation distance of the 18MEA to be around 0.9 nm while also explicitly considering a protein layer composed of beta sheets of an arbitrary ultra-highsulfur protein. Furthermore, they only performed very short simulations of 120 ps, which may not be sufficient to fully relax the structure of the protein and fatty acids. In this work, we aim to gain insights into the detailed molecular structure of the fatty acid layer on the hair surface using molecular dynamics simulations, without assumption of separation distance. As we are focusing on the structure and properties of the attached fatty acids on the epicuticle, we follow a similar approach to that of Berkowitz28,29 and use graphene sheets as a model substrate to which the fatty acid molecules are covalently attached. The protein is not explicitly considered in this model, since the exact protein and its structure are still not known. The graphene substrate will significantly simplify the model, while the structure of graphene will allow us to attach the fatty acid molecules in a hexagonal array, as is commonly believed.4 The spacing of the fatty acids is varied, and the relative free energy values of the fatty acid layers are calculated and compared to determine the optimal spacing of the fatty acids and the resultant thickness of the fatty acid layer. The tilt angle and order parameter of the chains are calculated to characterize the structure of the molecules in the layer. We also investigate the role of the anteiso-methyl side chain on 18-MEA by performing the same simulations with EA and comparing the free energy and structure. Subsequently, a water layer is added above the fatty acid layers to investigate the degree of water penetration into the fatty acid layers. We hope to gain a better understanding of not only the structure of the F-layer, but also the role of the 18-MEA on the hair surface.
is still poorly understood. The specific proteins that make up the protein layer in the epicuticle is still not known. It has been suggested that the protein layer should contain a high cysteine content, with these cysteine residues arranged in a pseudohexagonal array on the surface. It has also been suggested that the cysteine residues are separated by an average center-to-center distance of around 0.936 nm, which is believed to correspond to the surface area of the 18-MEA molecule on its end.4 To date, it has not been possible to analyze and determine the proteins attached to 18-MEA to confirm the suggestions. The thickness of the 18-MEA layer has also not been consistently reported. Various transmission electron microscope (TEM) measurements4,7,9 have reported thicknesses between 2.5 and 6.0 nm. The lower and higher values of the range would be more consistent with a lipid monolayer or bilayer, respectively, since an extended 18-MEA molecule would be approximately 2.4 nm.9 An X-ray photoelectron spectroscopy (XPS)10 study, however, measured the thickness to be only 0.9 nm. Explanations for this low value of the thickness have included suggestions that the 18-MEA molecules may be folded back on themselves11 or that it is merely an artifact of the high vacuum conditions of XPS.12 The apparent inconsistencies in these measurements highlight the fact that the experimental determination of the hair surface structure is not trivial. The situation is exacerbated by the fact that the epicuticle is very thin relative to the hair fiber, and that variations in the structure and composition of the hair surface are inherent across gender, ethnicity, age, and environmental conditions. Furthermore, while the presence of covalently bound 18-MEA on the hair surface has been known for quite some time,13 the specific role of the branched 18-MEA fatty acid on the hair epicuticle is still uncertain.9 While branched fatty acids are common in biological systems, they are usually found in smaller quantities among other straight chain saturated and unsaturated fatty acids.9,14−16 The presence of a very specific branched fatty acid on a surface membrane, as found on the hair epicuticle, is highly unusual, suggesting that it may in fact serve a specific function.9 In recent years, computer simulations are becoming more widely used to study the properties of complex biomaterials, and they are proving to be an excellent tool to gain detailed molecular understanding of a system. In particular, molecular dynamics (MD) simulations have been an especially useful tool to understand the basic physical structure, conformational behavior, and thermodynamics of monolayers of chain molecules.17−22 These simulations can often provide a fundamental understanding of molecular interactions and dynamical processes involved. MD simulations are also commonly used to study complex biological systems, although due to the inherent complexity, simplified model systems are frequently used to investigate the most important effects in these systems.23−29 For example, Choudhury and Pettitt23−25 carried out simulations on a system containing two graphene sheets immersed in water to study the hydrophobic interactions between model nanoscale particles. Lu and Berkowitz26,27 performed simulations to study the hydration force between two hydrophilic graphene plates with fixed charges as a simple model for lipid bilayers with dipoles. Eun and Berkowitz28,29 improved the model and used similar graphene sheets decorated with phosphatidylcholine headgroups as model bilayers to understand the origin of the hydration force between two lipid bilayers in water. Simulation studies on hairrelated systems are much fewer. McMullen and Kelty30 have
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MODEL AND METHODOLOGY Hair Surface Model. In this work, we adopt a very simplified model for the hair epicuticle. The protein layer is simplistically represented by 11 graphene sheets separated by an intersheet distance of 0.335 nm,32 creating a graphite block of thickness 3.35 nm. The fatty acid molecules are covalently attached to both the topmost and bottom-most graphene sheets, resulting in 2 identical surfaces. The lateral size of the graphene sheets are determined by the spacing between the fatty acids such that 90 molecules can be attached to each surface. Six separation distances were considered, and the number of atoms, simulation box size, and the corresponding area per molecule at each separation distance are given in Table 1. A schematic diagram depicting the 6 separation distances is shown in Figure 1. Each graphene sheet is periodic in the 2 lateral directions, effectively creating 2 infinite surfaces. The height of the simulation box was set to 12 nm, which means the 2 surfaces are separated by at least 8−9 nm, to avoid any interactions between the fatty acid molecules of separate layers. A typical initial configuration of the model is shown in Figure 2. The Optimized Potential for Liquid Simulations (OPLS) allatom force field33,34 has been used to describe all interatomic interactions for the graphene, 18-MEA, as well as the EA molecules. The OPLS force field was developed and parametrized for organic molecules, making it suitable to model our 13009
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Table 1. Separation Distances, the Number of Atoms, the Initial Simulation Box Size, and the Resultant Area per Moleculea d
Natoms
x
y
z
area/molec.
0.426 0.492 0.651 0.738 0.851 0.984
17460 19440 25380 29340 35280 43200
3.69 4.428 5.6375 6.642 7.38 8.856
3.834 4.26 5.8581 6.39 7.668 8.52
12.0 12.0 12.0 12.0 12.0 12.0
0.157 0.21 0.367 0.472 0.629 0.838
a
All dimensions are given in nm and the area per molecule is given in nm2.
Figure 2. Typical initial configuration of the model in a simulation box. The protein layer is simplistically represented by 11 graphene sheets, and 90 18-MEA molecules are attached to each of the 2 outermost graphene sheets via thioester bonds. Only the backbone carbon atoms of the 18-MEA molecules are shown for clarity.
free energy of the fatty acid layer at various spacing will be more important, which should be less sensitive to the exact parameter values used for the thioester bond. When water is introduced to the simulations, the SPC/E water model is used,36 which has been found to give the best bulk water properties out of the three-site water models.37 It has also been found to work well with several force fields, including OPLS, in calculating hydration properties.38 Simulation Method. MD simulations were performed using Gromacs v 4.0.7.39 Simulations were performed with time steps of 2 fs. Periodic boundary conditions were applied in all three directions. Cut-off radii were set at 0.9 nm for electrostatic interactions and 1.4 nm for Lennard-Jones interactions. Long-range electrostatic interactions were treated using the Particle-Mesh Ewald (PME) summation method.40 Simulations in the canonical (NVT) ensemble were used in systems without water, while the isothermal−isobaric (NPT) ensemble was used in systems containing water. Temperature coupling was done with a Berendsen thermostat but with an additional stochastic term to ensure a correct kinetic energy distribution and produce a correct canonical ensemble.41 Pressure coupling was achieved using the Berendsen barostat.42 Relaxation times of 1 and 2 ps were used for the temperature and pressure coupling, respectively. All simulations were performed for 15 ns, but all results were taken only from the last 10 ns of the simulations. Equilibration was tested by checking that the average potential energy and entropy are no longer changing with time. Calculation of Free Energy. In order to determine the optimal spacing between the fatty acids in the hair epicuticle, we compared the free energy of the fatty acid layer at various spacings. The simulations of the epicuticle model without water were performed using the canonical (NVT) ensemble, and thus the relevant free energy would be the Helmholtz free energy, A, given by the familiar thermodynamic relationship
Figure 1. Schematic diagram depicting the arrangement of the attached fatty acid molecules in the six separation distances considered in this work. The black dot is the position of the reference molecule. Blue dots represent distances of 0.426 nm, red dots represent distances of 0.492 nm, green dots represent distances of 0.651 nm, orange dots represent distances of 0.738 nm, pink dots represent distances of 0.851 nm, and gray dots represent distances of 0.984 nm. Only the first 6 repeat units at each distance are shown. The fatty acids are then replicated according to this arrangement to obtain 90 fatty acids on each layer.
system. In fact, a recent comparative study of force fields also showed that OPLS performed well when modeling organic monolayers.35 On the two outermost graphene sheets, the fatty acids are attached to the graphene via thioester bonds. The carbon atoms to which the fatty acids are attached have been modified to be described by an sp3 carbon, while the rest of the atoms in the graphene sheet are described by an sp2 carbon. Since the thioester bond is not explicitly defined in the OPLS force field, we have adapted the parameters from other defined carbon−sulfur bonds as well as the parameters for esters. The charges on the sulfur and oxygen atoms are slightly modified to −0.32 and −0.43, respectively, and the entire system is maintained as charge neutral. While the parameters for the thioester bond may affect the results, we believe that the structure and thermodynamic behavior of the fatty acid layer will depend largely on the lipid−lipid interaction along the rest of the chain.18 Furthermore, as we are interested in determining the optimal separation distance for the fatty acids, the relative 13010
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Table 2. Energies of 18-MEA Fatty Acid Layer at Different Separation Distancesa d
ELJ −3.0 −10.4 −8.1 −6.3 −5.4 −4.3
0.426 0.492 0.651 0.738 0.852 0.984 a
± ± ± ± ± ±
Ecoul 0.1 0.1 0.1 0.1 0.1 0.1
1.48 1.13 0.78 0.45 0.48 0.49
± ± ± ± ± ±
Ebond
0.01 0.01 0.04 0.03 0.03 0.03
24.7 20.7 20.3 21.9 21.8 21.7
± ± ± ± ± ±
Epot
0.2 0.2 0.2 0.2 0.2 0.2
23.1 11.4 12.9 16.0 16.9 17.9
± ± ± ± ± ±
TS 0.2 0.2 0.2 0.2 0.2 0.2
33.6 38.2 40.4 41.2 41.2 40.6
± ± ± ± ± ±
A 0.1 0.4 0.5 0.1 0.3 0.4
−10.4 −26.8 −27.5 −25.2 −24.3 −22.7
± ± ± ± ± ±
0.3 0.4 0.5 0.2 0.3 0.4
All energies are given in 103 kJ/mol.
A = U − TS
(1)
distances, the exact value of the entropy is of secondary importance. The relative entropy and free energy should still be valid and are used to determine the optimal separation distance of the fatty acids.
where U is the internal energy, T is the temperature, and S is the entropy. The internal energy U is the sum of the potential and kinetic energy of the system, and is readily obtained from the MD simulations. The entropy S, however, is not so trivial to calculate from simulations. In this work, we have used the quasiharmonic approximation,43−45 which allows the estimation of the entropy from the covariance matrix of the atomic coordinates. The quasiharmonic analysis is based on the assumption that fluctuations in the motion of the system can be approximated using a Gaussian probability distribution. As such, quasiharmonic frequencies ωi can be obtained from the diagonalization of the mass weighted covariance matrix calculated during an MD simulation. The molar entropy can then be approximated from the entropy of the harmonic oscillator according to S = R∑ i
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RESULTS AND DISCUSSION Optimal Spacing of 18-MEA on the Hair Surface. As discussed in the Introduction, the detailed atomic structure of the fatty acid layer on the hair epicuticle is still poorly understood. In particular, the separation distance between the fatty acids, and the thickness of this layer, has not been conclusively determined. It is frequently assumed that the separation distance of the fatty acids is 0.936 nm as described by Swift,4 as it is thought to be consistent with the surface area that an 18-MEA molecule would occupy on its end. One of our primary goals in this work is to test the validity of this separation distance by determining the thermodynamically most favored separation distance using MD simulations. We have thus calculated the potential energies, the entropy, and the Helmholtz free energy as described in the Model and Methodology section, and the results are presented in Table 2. From Table 2, we see that the nonbonded potential energy of the 18-MEA fatty acid layer is largely dominated by the short-range Lennard-Jones (LJ) interactions. Since 18-MEA has a largely nonpolar chain with a polar headgroup covalently bonded to the substrate, it is not surprising that the coulomb interactions make a relatively small contribution to the overall potential energy. The LJ energy, ELJ, shows a big decrease between the distances of 0.426 and 0.492 nm. At larger separation distances, ELJ slowly increases again, although it never goes higher than the energy at the closest separation distance. The high ELJ at 0.426 nm indicates that the fatty acids are packed too tightly, resulting in steric overlaps, while the large decrease at 0.492 nm indicates that the fatty acids are now able to arrange themselves without any overlaps. The coulomb energy, Ecoul, decreases monotonically as the separation distance is increased until 0.738 nm. Since the polar headgroup of the 18-MEA molecules are all like-charged, it is reasonable that the resulting energies from the electrostatic interactions are repulsive and will decrease as the distance between the charges is decreased. However, we also see that, beyond a distance of 0.738 nm, the electrostatic interactions remain roughly constant, suggesting that the effect of the electrostatics will be negligible beyond this separation distance. The bonded energy, Ebond, is much larger relative to the nonbonded energy, and exhibits a similar trend to the LJ energy. Ebond is also highest at the closest separation distance of 0.426 nm, due to the constrained conformation of the chains at such close packing. Ebond decreases significantly at 0.492 nm and has a minimum at 0.651 nm, before increasing slightly at larger distances. Also, similar to Ecoul, Ebond remains roughly constant beyond a distance of 0.738 nm. The sum of the bonded and
ℏωi /kT − ln[1 − exp( −ℏωi /kT )] exp(ℏωi /kT ) − 1 (2)
While this equation for the entropy is exact in the harmonic limit, its accuracy for real systems would depend on the accuracy of the quasiharmonic approximation for the system. More details on the method can be found in references by Karplus et al.43,44 Practically, this can be done using the built-in tools g_covar and g_anaeig within the Gromacs package. g_covar will calculate and diagonalize the mass-weighted covariance matrix from the simulation trajectory, while g_anaeig will analyze the resulting eigenvectors and calculate the entropy using the quasiharmonic approximation. Since the simulation is coupled to a fixed temperature, and the number of fatty acid molecules is the same in each simulation, the kinetic energy contribution of the fatty acids to the internal energy should be invariant, and only the potential energy needs to be considered. The contributions of the bonded, Lennard-Jones, and Coulomb interactions from the fatty acids are determined by selectively “turning off” the charges and bonds of the appropriate molecules and recalculating the potential energy. These are then summed to give the total potential energy of the fatty acids, and the Helmholtz free energy is readily calculated using eq 1. The free energy is calculated independently for the two fatty acid layers present, and the average value from the two layers is reported. We must stress that, due to degrees of freedom inherent in the fatty acid molecules, the entropy calculated using the harmonic approximation is a rough estimate at best. However, the quasiharmonic approximation has been tested on several organic molecules and applied to ligand binding, and it has been found to perform reasonably well.45 Furthermore, since we are interested in comparing the free energy of the fatty acid layer at various separation 13011
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acid layers go from a more ordered layer to a more disordered layer. Such melting transitions have also been observed in simulations of Langmuir monolayers.22 We will address this phenomenon a little more in the next section in the context of the structure of the fatty acid layers. The minimum free energies of both fatty acid layers occur at a separation distance of 0.651 nm. However, the free energy at 0.492 nm is only slightly higher. As such, it is possible and likely that the true minimum free energy and hence the optimal separation distance of the 18-MEA on the hair epicuticle will occur somewhere between 0.492 and 0.651 nm. This is in contrast to the generally accepted separation distance of 0.936 nm as described by Swift.4 This distance was thought to represent the surface area that an 18-MEA molecule would occupy on its end. However, our free energy results show that an 18-MEA molecule does not need such a large surface area. If an 18-MEA molecule in fact occupies a surface area of 0.688 nm2, corresponding to a diameter of 0.936 nm, the free energy at separation distances less than this diameter would be very high due to the steric overlaps. Instead, the free energy results suggest that, while a separation distance of 0.426 nm will indeed result in significant overlaps, a distance of 0.492 nm is sufficient to accommodate the 18-MEA molecules. In fact, the molecules prefer to be more densely packed, as evidenced by the minimum free energy at 0.492−0.651 nm. Structure of 18-MEA F-layer. Subsequently, we proceeded to investigate the structure of the fatty acid layer at the different separation distances. We characterized the structure of the fatty acid layer by 3 properties, namely, the thickness of the layer, the tilt angle of the fatty acids, and the order parameter of the fatty acid chains with respect to the axis normal to the graphene sheets. We first show snapshots from the final configuration of the 18-MEA and the EA layer at the various separation distances in Figure 4. At the closest separation distance of 0.426 nm, the 18-MEA fatty acid chains are all perpendicular to the graphene layer, and are well-ordered. However, the ends of the 18-MEA fatty acids are very tightly packed and are relatively disordered. In contrast, the EA layer is extremely well-ordered throughout and perfectly perpendicular to the graphene sheet. At a slightly larger separation distance of 0.492 nm, the 18-MEA chains are still largely perpendicular, but regions of disorder can be found within the layer. The EA chains are still fairly ordered, but now exhibit a larger tilt angle with respect to the graphene sheet. At an even greater distance of 0.651 nm, both fatty acids now exhibit a larger tilt angle with respect to the graphene sheet, but appear to still be aligned to each other. Beyond this distance, both fatty acid chains are no longer aligned and form a disordered layer. These snapshots visually confirm what we had inferred from the energies, that the fatty acid layer undergoes a melting transition from a more ordered to a more disordered conformation between 0.651 and 0.738 nm. The thicknesses of the fatty acid layers are measured from the average density profiles of the backbone atoms of the fatty acids over the last 10 ns of the simulation. The additional methyl side chain in 18-MEA could bias the mass density profile of 18-MEA in comparison to EA. Therefore, to maintain consistency between the density profiles of the two fatty acids, only the backbone atoms are considered. The thicknesses of the top and bottom fatty acid layers are measured independently, as the thickness in which the fatty acids backbone atoms exhibit a mass density of at least 1 kg/m3 throughout the 10 ns simulation considered, to avoid counting the small probability
nonbonded energies gives the total potential energy, which is also highest at 0.426 nm, is minimum at 0.492 nm where it is less than half of the highest energy, and increases beyond 0.492 nm. Consistently, the entropy is at a minimum at a distance of 0.426 nm. Since the fatty acids are tightly packed at such a small separation distance, it is reasonable that the entropy is the lowest at this distance. As expected, the entropy increases as the separation distance is increased and shows a maximum at 0.738−0.852 nm. The entropy then decreases slightly at 0.938 nm but remains roughly constant at distances of 0.728 nm and beyond. While the entropy may be expected to continue to increase at large separation distances, we will explore the reasons for the decrease when we discuss the structure of the fatty acid layer in the next section. From the potential energy and the entropy, the free energy is readily calculated. Similarly, the free energy A is highest at 0.426 nm, is lowest at 0.651 nm, and increases at larger distances. Since the absolute energy values obtained from a simulation are irrelevant, we have shown the relative Helmholtz free energy of the 18-MEA layer with respect to the value at the closest separation distance in Figure 3. Additionally, we have
Figure 3. Relative Helmholtz free energy of the fatty acids with respect to the free energy at the closest separation distance d = 0.426 as a function of separation distance. Blue circles are for 18-MEA and red circles are for EA. Lines are only guides to the eye. The minimum free energy occurs at a separation distance of d = 0.651 nm, although the true minimum can be between 0.492 and 0.651 nm.
included the relative Helmholtz free energy of the EA layer with respect to the free energy at the closest separation distance in Figure 3 as a comparison, although the individual contributions to the free energy of the EA fatty acid layer are not shown. The overall trend of the free energy for both fatty acids layer is very similar, with a minimum at around 0.492−0.651 nm and increasing free energy at larger distances. The biggest difference occurs at a distance of 0.426 nm, where 18-MEA exhibits a large increase in the free energy, while EA only shows a very small increase in the free energy. As discussed previously, the high energy is a result of steric overlaps when the 18-MEA are packed too tightly together. This is caused by the ante-isomethyl side chain on 18-MEA, which does not have enough space at a separation distance of 0.426 nm. On the other hand, the absence of this side chain on the EA molecule allows it to be packed more closely without the steric overlaps, resulting in a much lower free energy compared to 18-MEA. Another observation that can be made is that, between the region of 0.651 and 0.738 nm, the free energy is seen to increase more sharply and then continues to increase only very slightly after 0.738 nm. This can be explained when we see that the bonded energy, Coulomb energy, and the entropy all remain relatively constant after 0.738 nm. It is likely then that there is some sort of transition that occurs around this distance where the fatty 13012
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Figure 5. Thicknesses of the 18-MEA and EA fatty acid layers. Blue circles are for 18-MEA and red circles are for EA. Lines are only guides to the eye.
acids are tilted farther away from the normal axis as compared to 18-MEA. This will naturally result in a thicker layer for 18MEA. Simulations of Langmuir monolayers of EA and 18-MEA at packing densities up to 0.25 nm2/molecule (d ≈ 0.53 nm) also show that 18-MEA form thicker layers than EA.30 Beyond 0.651 nm, the thicknesses for both 18-MEA and EA are very similar, and within the simulation uncertainty. At these distances, the fatty acids are no longer sterically hindered and have sufficient space to rearrange themselves. As a result, the thicknesses of the two fatty acid layers do not differ much. Around a separation distance of 0.651 and 0.738 nm, we see a kink in the thickness curve for both fatty acids. This is likely due to the melting of the monolayers which we discussed previously. This is accompanied by a larger uncertainty in the thickness at 0.651 nm, which is expected when such a transition occurs. On the basis of our free energy results, the optimal spacing of the fatty acids is between 0.492 and 0.651 nm. This in turn results in a monolayer thickness of between 2.01 and 2.64 nm, which roughly corresponds to the length of an extended 18MEA molecule, and in agreement with very early TEM measurements.6 However, the thickness of the monolayer has not been consistently reported in the past, with values ranging from 0.9 to 6.0 nm to be found in literature.4,6,7,9,10 Our simulations show that, if the 18-MEA molecules were to be separated by a distance of 0.936 nm as reported by Swift,4 the monolayer thickness will be around 1.3 nm, consistent with the measured value of 0.9 ± 0.4 nm using X-ray photoelectron spectroscopy.10 Our results are also consistent with previous simulation results31 that estimate the thickness of the 18-MEA monolayer separated by a distance of around 0.9 nm to be around 1.08 ± 0.2 nm. At this large separation distance, the fatty acids are mostly laying down on the hair surface, resulting in the very thin layer, as proposed by Zahn et al.11 The agreement of the results from our simplified model with that of Natarajan and Robbins,31 which include an explicit protein layer, also supports our assumption that a simplified model is sufficient to gain insights into the structure of the fatty acid layer. One possibility to reconcile the inconsistent experimental measurements may be to consider the role of free lipids on the hair surface. It is known that, besides the bound fatty acids, there are also free lipids on the hair surface, with estimates ranging from 4% to 12% existing in the top 3 nm of the hair.31,46,47 It is possible that the surface of the protein layer does not or cannot contain sufficient cysteine residues to serve as binding sites for the thioester linkages of the 18-MEA to form such a dense layer. Therefore, free lipids could exist between the bound fatty acids to achieve the most favorable conformation. Removal of these free lipids could result in a less
Figure 4. Snapshots of the resulting fatty acid layer at the various separation distances. The left column shows snapshots of 18-MEA layers, and the right column shows snapshots of EA layers. The separation distances represented are 0.426, 0.492, 0.651, 0.738, 0.852, and 0.984 nm from top to bottom. Only the backbone carbon atoms of the fatty acids are shown for clarity.
of the fatty acid extending beyond the measured thickness. The chosen density cutoff is completely arbitrary, but the qualitative results will not change should a different cutoff be used. The reported thicknesses in Table 3 and Figure 5 are taken as the Table 3. Thicknesses of the 18-MEA and EA Fatty Acid Layersa
a
d
18-MEA
EA
0.426 0.492 0.651 0.738 0.852 0.984
2.76 2.64 2.01 ± 0.12 1.98 1.56 1.26
2.64 2.49 ± 0.04 1.89 ± 0.12 1.98 1.56 1.23 ± 0.04
All values are given in nm.
average of the top and bottom layers, and uncertainties are reported as the standard deviation of the two thicknesses where applicable. As expected, the thickness of the layers generally decreases as the separation distance of the fatty acids is increased, as can also be observed visually in Figure 4. At close separation distances, the 18-MEA fatty acid forms a slightly thicker layer than EA. This is most likely due to the fact that, because of the presence of the side chain on 18-MEA, they are packed more densely in comparison to EA. In order to minimize the steric overlaps at such a high packing density, 18MEA would be stretched longer than EA, resulting in the slightly thicker layer. At 0.492 nm, it is clear that the EA fatty 13013
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50°. Beyond 0.651 nm, the tilt angle decreases again as the monolayer melts and becomes a disordered layer. The maximum in the tilt angle and the melting of the monolayer are consistent with previous simulations of Langmuir monolayers,22 although the maximum value of the tilt angle and the separation distance at which the melting occurs are much higher than those calculated from the Langmuir monolayers. This can perhaps be attributed to the fact that our fatty acids do not exist as free-standing monolayers and that different force fields used in different simulations could lead to different quantitative results. Since one end of the fatty acid is covalently attached to a solid surface, it is possible that the ordered conformation of the monolayers is stabilized, delaying the melting transition. At separation distances of 0.738 nm and above, the tilt angle varies greatly with large uncertainties. Since the monolayer has melted at this point, the fatty acids no longer exhibit a uniform tilt. The exact value of the tilt angle is no longer significant or reliable, as evidenced by the large fluctuations. To further characterize the fatty acid layer, we have also calculated the order parameter of the fatty acid chains, relative to the normal z-axis, according to the equation
dense and thinner fatty acid layer. However, the free energy results clearly support the densely packed layer to be the most favorable structure. The thicknesses of the fatty acid layers are, not surprisingly, related to the tilt angles of the fatty acid chains. To calculate the tilt angle θ, each fatty acid layer is divided into 5 regions. The angle formed by the vector between the centers of mass of the first and last carbon atoms in each region and the normal axis is measured. The tilt angle is taken as the average of the angles formed from the 10 regions (5 on the top layer and 5 on the bottom layer), and simulation uncertainties are taken as the standard deviation from the 10 values (Figure 6). We see that,
Figure 6. Tilt angles of the 18-MEA and EA fatty acid molecules. Blue circles are for 18-MEA and red circles are for EA. Lines are only guides to the eye.
Sz =
3 1 ⟨cos2 θz⟩ − 2 2
(3)
where θz is the angle between the molecular axis under consideration and the normal z-axis. The molecular axis is defined as the vector from Cn−1 and Cn+1 for a given carbon atom Cn on the chain backbone. Since both 18-MEA and EA each have 20 backbone carbon atoms, the order parameter is defined for the 18 intermediate carbon atoms excluding the first and last carbon atoms. As defined in eq 3, the order parameter can vary between 1 and −0.5, where the former represents full order along the reference axis (θz = 0°) and the latter represents full order perpendicular to the reference axis (θz = 90°). A value of 0 represents a random, isotropic orientation of the chain molecules. The order parameter is calculated for the 2 layers independently, and each is averaged over the 90 molecules in each layer and over the last 10 ns of the simulation. The reported order parameters shown in Figure 7 are the average of the order parameters from each layer. As we have already observed visually, at 0.426 nm, the 18MEA molecules are highly ordered with an order parameter close to 1 and the EA molecules exhibit very high order along the normal axis with an order parameter that is practically 1. At 0.492 nm, the 18-MEA molecules are a little more disordered toward the tip of the molecule, while the central region of the molecules still exhibits high order, comparable to that at a distance of 0.426 nm. The EA molecules show a more uniform
at 0.426 nm, both chains are practically aligned with the normal axis with a tilt angle of about θ ≈ 1°. At 0.492 nm, EA exhibits a very clear tilt angle relative to the normal axis. For Langmuir monolayers of straight-chained molecules similar to EA, a tilt transition is expected to occur at a packing density of around 0.2 nm2/molecule,22,48−50 in which the molecules shift from being aligned perpendicularly to a more tilted conformation. This is consistent with the separation distance of 0.492 nm in our simulations, which translates to around 0.21 nm2/molecule. The measured tilt angle of the EA molecules (θ ≈ 20°) is also comparable to the tilt angle of the Langmuir monolayers, which has been reported to be between 13° and 20° from experiments and simulations.22,48 On the other hand, the 18-MEA fatty acids still maintain a relatively perpendicular orientation at 0.492 nm, with an average tilt angle of θ ≈ 5°. The branched geometry of 18-MEA appears to delay the tilt transition. This can most likely be understood by the additional interactions from the ante-iso-methyl side chains. Due to the side chains, the terminal ends of the 18-MEA monolayers are more densely packed. This will likely stabilize the monolayer in the perpendicular orientation, thus delaying the transition to a tilted orientation. At 0.651 nm, both fatty acids exhibit a large tilt angle of around
Figure 7. Order parameters in the z direction for 18-MEA (left) and EA (right). Blue circles represent d = 0.426 nm, red circles represent d = 0.492 nm, green circles represent d = 0.651 nm, orange circles represent d = 0.738 nm, pink circles represent d = 0.852 nm, and gray circles represent d = 0.984 nm. 13014
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the various separation distances. To do so, we have added a layer of water above the equilibrated fatty acid layer and performed a 15 ns MD simulation in the isothermal−isobaric (NPT) ensemble. A semi-isotropic pressure coupling scheme was used since it is more appropriate for interfacial systems, where the normal pressure was set to 1 bar, and the lateral dimensions are kept constant. The amount of water that penetrated into the fatty acid layer is then measured from the average density profiles of water and fatty acid backbone atoms in both layers independently over the last 1 ns of the simulation. Using the same density cutoff of 1 kg/m3 as before to define the thickness of the fatty acid layer, the density of water within the fatty acid layers are summed and then divided by the thickness of the layers, resulting in the density of water penetrated into the layers. The values obtained from both layers are averaged and the standard deviation is taken to be the simulation uncertainty. This result is shown in Figure 8.
disorder along the entire chain. Both molecules have order parameters close to zero at separation distances of 0.651 and 0.738 nm. An order parameter of zero generally represents molecules which are isotropically orientated, indicating that the chains show no preference in orientation. This is what we observe in the molecules at 0.738 nm. However, we see in Figure 4 that, at 0.651 nm, the molecules are generally oriented about 50° to the normal axis which, based on this definition of the order parameter, will also result in an order parameter close to zero. As the separation distance is further increased, the order parameter further decreased and approaches a value of −0.5. This can be understood from the fact that, at larger separation distances, the fatty acids begin to lay flat on the graphene sheet, resulting in a perpendicular orientation with respect to the normal axis. This could also explain why the entropy of the fatty acids decreases slightly at 0.938 nm, as observed in Table 2. At distances of 0.738−0.852 nm, the fatty acid chains are spaced far enough apart that they are able to adopt a highly disordered conformation, resulting in a maximum in the entropy. While the entropy could be expected to continue to increase as the separation distance between the fatty acids is increased, the chains in fact become slightly more ordered at a distance of 0.938 nm when they adopt the perpendicular orientation flat on the surface, resulting instead in a decrease in entropy. Another interesting observation is that, for the 18-MEA molecules, the order parameter for the terminal carbon seems to converge to a value close to zero at separation distances of 0.651 nm and above. This is not observed for the EA molecules. This behavior has also been observed in simulations of Langmuir monolayers of EA and 18-MEA at packing densities up to 25 Å2/molecule (d ≈ 0.53 nm).30 The terminal ends of the 18-MEA molecules at the smaller separation distances also tend to be more disordered than that of EA. This is clearly a result of the ante-iso-methyl side chain of 18-MEA, which increases the mobility of the terminal methyl groups, and allows them to arrange themselves in a similar, disordered structure, independent of the separation distance and the orientation of the rest of the chain. As mentioned earlier, the unique structure of 18-MEA and its abundance as a bound fatty acid on the hair epicuticle suggests that it serves a specific function on the hair surface, although that function is yet to be clearly understood. Some possibilities of the role of 18-MEA include the inhibition of micelle or bilayer formation, providing an improved hydrophobic protection for the hair surface, and making this hydrophobic layer more biologically resistant.9 The disordered ends of the 18-MEA molecules at almost all separation distances would support the idea of inhibiting micelle or bilayer formation, since it would prevent the assembly of any ordered structures. Our results also suggest that 18-MEA could help minimize the effect of weathering and damage on the hair surface. As fatty acids are stripped from the hair surface from daily wear and tear, the remaining fatty acids appear to be able to arrange themselves such that the structure of the terminal ends of the fatty acids remain relatively unchanged. This will also likely provide an improved hydrophobic protection for the hair. We will explore the degree of water penetration in the fatty acid layer at the different separation distances in the next section. Water Penetration into the Fatty Acid Layers. The fatty acid layer on the hair epicuticle serves as a protective hydrophobic layer for the hair fiber. In the following, we have investigated the penetration of water into the fatty acid layers at
Figure 8. Density of water that has penetrated into the fatty acid layers at various separation distances. Blue circles are for 18-MEA and red circles are for EA. Lines are only guides to the eye.
Similarly, while the value of the density cutoff may change the quantitative results, the qualitative behavior of the water penetration remains unchanged should a different cutoff value be used. At the closest separation distances of 0.426 and 0.492 nm, the fatty acid layer is, not surprisingly, practically impermeable, with almost no water to be found in the layer. Beyond a distance of 0.492 nm, the fatty acids are spaced far enough apart that a significant amount of water is able to penetrate into the layer, increasing as the separation distance is increased. A similar amount of water appears to be able to penetrate the two different fatty acids up to a separation distance of 0.738 nm, whereas at larger distances of 0.852 nm and above, slightly less water seems to be able to penetrate the 18-MEA fatty acid layer compared to the EA layer. Since the 2 fatty acids are identical in structure, except for the additional methyl side chain on 18MEA, the difference in water penetration has to be related to this additional side chain. It appears then that the presence of this additional methyl group provides a slightly better hydrophobic layer when the fatty acids are spaced further apart. This is likely related to the way that the terminal end of the fatty acids are arranged, as discussed previously. Due to the side chain, the terminal ends are arranged in a similar, disordered structure regardless of separation distance. This implies that, even as the hair surface undergoes damage and loses some of the bound 18-MEA, the randomly oriented and denser terminal ends of 18-MEA could provide a slightly better hydrophobic protection for the hair surface, allowing less water to penetrate through compared to EA. This highlights the unique role that 18-MEA plays on the hair epicuticle. 13015
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CONCLUSIONS The investigation and characterization of the F-layer in the hair epicuticle is very difficult experimentally, partly because the epicuticle is very thin relative to the hair fiber, but also because variations in the structure and composition of the hair surface are inherent across gender, ethnicity, age, and environmental conditions. To this end, molecular simulations can provide a useful tool to systematically investigate the structural and thermodynamic properties of the F-layer. In this work, we have performed molecular dynamics simulations on a simplified model of the hair epicuticle, consisting of fatty acids covalently bound to graphene sheets, in order to investigate the optimal separation distance of the fatty acids and the structure of the fatty acid layer. We have calculated the free energy of the fatty acid layers as a function of the separation distance, and characterized the structure of the layers by calculating the thickness, the tilt angle, and the order parameter of the chains. We have also investigated the amount of water penetration into the fatty acid layers at each separation distance. The results from this work lead to several new insights into the structure of the hair epicuticle, and address several outstanding questions about the hair surface. We have shown that the most thermodynamically favorable conformation for the fatty acids is a densely packed layer with a thickness roughly equivalent to the length of an extended molecule. Our results are consistent with the epicuticle model of Negri and coworkers,7 but we have shown that the optimal separation distance between the 18-MEA molecules is between 0.492 and 0.651 nm, much smaller than the frequently cited value of 0.936 nm.4 It also addresses the inconsistent and conflicting results that have been reported to date on the thickness of the fatty acid layer. We show that, at the optimal separation distance, the fatty acids will be extended and form a layer of thickness between 2.01 and 2.64 nm, consistent with results from early TEM measurements.6 On the other hand, if the fatty acids are spaced further apart at around 0.9−1.0 nm, the fatty acids will lie much closer to the surface and form a thin layer of around 1.3 nm, consistent with results from XPS measurements.10,11 This apparent inconsistency can be reconciled if we consider the presence of free lipids in the epicuticle. It is conceivable that free lipids exist between the bound fatty acids on the surface of virgin hair to achieve the thermodynamically favored densely packed F-layer conformation. Removal of these free lipids, whether advertently or inadvertently during the experimental process, could result in a less dense and thinner F-layer, producing inconsistent results. Furthermore, we have also shown that the unique structure of 18-MEA appears to mitigate the effects of damage on the hair surface by being able to adopt a similar, disordered conformation on the terminal ends of the chains, regardless of the separation distance. This in turn is seen to slightly improve the hydrophobic protection of the hair surface when the fatty acids are spaced further apart. Despite being a very simple model with no explicit protein layer, our results are consistent with existing data and support the idea that even a simple model can be used to gain understanding of very complex systems. To our knowledge, this is the first systematic study of the hair surface structure using molecular simulations. We believe that our simple model, together with molecular dynamics simulations, can serve as a useful tool to systematically investigate other properties of the hair surface, such as the role of free lipids, the effect of damage
and surface charges, as well as interactions of the hair surface with small molecules.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Author Contributions ‡
Contributed equally to this work.
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the Science and Engineering Research Council of A*STAR (Agency for Science, Technology and Research), Singapore. We gratefully acknowledge the provision of computing facilities by the A*STAR Computing Resource Center (A*CRC).
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REFERENCES
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