MOLECULAR MODELING OF HUMAN HAIR 469 EXPERIMENTAL CONSTRUCTION OF AN EPICUTICLE MOLECULAR MODEL The software used in this work was Cerius2 modeling software for molecular simulation by Accelrys, Inc. Based on the work of Negri et al. (1), we used the beta sheet confi gura- tion for the UHSP in the uppermost part of the epicuticle. The conformation of protein in a model beta sheet, containing two folds (top and bottom) was taken from the Protein Data Bank (PDB) for polyalanine. This strand was reproduced in the molecular modeling graphical package, and the multiple strands thus created were successively connected to form a beta sheet of eight strands with four top and bottom folds in the periodic cell, as shown schematically in Figure 2. The number of strands per periodic cell was such that exactly one polymeric UHSP sequence was fi tted (see Figure 1). The top folds contained cysteine amino acid residues, which are essential for the thioester linkages with 18-MEA. Although the exact protein that 18-MEA is attached to is not Figure 2. Stick model of 18-methyl eicosanoic acid attached to a protein backbone at the angle indicated by the modeling software. The sticks, in varying shades of gray, represent oxygen, hydrogen, nitrogen, the back- bone carbons, and the cysteine sulfur group.

JOURNAL OF COSMETIC SCIENCE 470 known at this time, the amino acid sequence used here is shown in Figure 1 and is for the Yahagi UHSP (9), a protein from the KAP-5 family, a protein family that has been shown to be in the outermost A-layer of wool fi ber by Bringans et al. (10). Rogers and Koike (11) describe its presence in the exocuticle and A-layer of human hair. Once the beta sheet was created using the model protein sequence from polyalanine, the amino acid chemistry was changed to fi t the amino acid sequence of the Yahagi UHSP into the model. The fully constructed sheet was then reproduced (duplicated) to several other sheets and these sheets were stacked parallel to each other in the Y direction (the direction of stacking is perpendicular to the original beta sheet), as shown in Figure 2. Each periodic simulation model cell contained three beta sheets. The overall density of the system (per periodic simulation cell) was set at a value of 1.47 gm/cm3, which is within the range provided by the Allworden membrane isolated by Allen et al. (6) of 1.39 to 1.54 gm/cm3 and close to that of whole fi ber, 1.32 gm/cm3 (12). The length of each strand (top fold to bottom fold, Z direction) was nicely fi tted to 50 Å. The thickness of the epicuticle as measured by Swift and Smith (8) is 13 nm. Since (at this time) we do not use other proteins in our model, we constructed only the uppermost portion of the epicuticle, using only the UHSP as a single layer of 5 nm. We also have a constraint of not exceeding 10,000 atoms in our modeling software. This issue was important in determining the number of sheets and the length of the strands in the beta sheet of our model. The initial model showed numerous interatomic steric hindrances from the amino acid side groups within the single strands and in-between strands in different neighboring or adjacent strands in different folds. To alleviate these non-bonded interactions, the side groups were allowed to move and relax in an energy-minimization procedure, keeping the main back- bones of the strands fi xed in space. Backbone atoms of only three amino acid residues on each of the top and bottom folds were allowed to fully relax and move during the molecular simulation (energy minimization and, later on, the molecular dynamics (MD) simulations with the 18-MEA attached). This procedure allowed relaxation of realistic arrangements while maintaining the essential backbone-ordered structure of the beta sheet. All bonded and non-bonded interatomic interactions were calculated using DreidingII force fi eld, including van der Waals and electrostatic interactions (wherein hydrogen bonding is included). The dielectric constant was set to a value of 1.0 (because at present we do not have the correct value for hair protein systems). Bonded terms such as bond stretching and bond-angle bending, as well as torsion terms, were included. The simulation box cells (each structure thus called) were subjected to an initial energy minimization of 50 steps with the steepest descent method and 750 steps with the conjugate gradient method. Interatomic interactions during energy minimization were calculated until a radius of 13–15 Å (cut-in to cut-off) and interactions were terminated at a cut-off radius using a fi fth order spline function. Convergence of the minimization was noted by total potential energy gradients being less than 0.1 kcal/mol. The energy-minimized structure was then subjected to MD in the NVT ensemble at a temperature of 300 K (room temperature). Interatomic interactions during MD simulations were evaluated within a radius of 9 Å (terminated using a cut-off radius of 11 Å with spline function). A total of 120 ps of MD simulation were run to relax the 18-MEA chains. The fi nal confi gurations of the 18-MEA chains of virgin hair were coiled. This structure is further discussed in the Results section. Having thus obtained the well-relaxed hair protein model, the 18-MEA molecules were chemically attached to the cysteine groups on the top folds of each beta sheet. The initial conformations of the 18-MEA molecules were all-trans (straight and perpendicular to the