Mucoadhesive Polymer Hyaluronan as Biodegradable Cationic / Zwitterionic-Drug Delivery Vehicle

Mucoadhesive polymers in pharmaceutical formulations release drugs in mucosal areas. They interact and fix to mucus through molecular interpenetration, etc., which increase drug bioavailability. Polymers physicochemical properties affect formulation mucoadhesion, rheological behaviour and drug absorption. Hyaluronan (HA) is selected as a mucoadhesive and biodegradable polymer. Geometric, topological and fractal analyses are carried out with program TOPO. Reference calculations are performed with algorithm GEPOL. Procedure TOPO underestimates molecular volume by 0.7 %. The error results 5 % in surface area and derived topological indices. The solvent-accessible surface is undercalculated by 3 %: from hexamer HA to HA·3Ca and hydrate, the hydrophobic term rises by 42% and decays by 26 %, as well as the hydrophilic part drops by 14% and rises by 58 %, in agreement with the number of H-bonds. The accessibility rises by 9 % and decays by 8 %. The fractal dimension is underevaluated by 1 % and, for HA, it results 1.566; on going to HA·3Ca and hydrate, it rises by 2 % and 1 %. The nonburied-atoms dimension increases by 11 %: for HA, it results 1.725. When going to HA·3Ca and hydrate, it augments by 4 % and 0.3%. Ongoing from HA to HA·3Ca and hydrate, the external minus molecular dimension enlarges by 20 % and decays by 9 %. The hydrate globularity is lower than for water, Ca 2+ and averages of O-atoms in HA. The rugosity of Ca 2+ is smaller than for hydrate, averages of O-atoms in HA and water. The accessibilities of Ca 2+ and water are greater than for hydrate. As cations exchange in HA·3Ca requires Ca 2+ alteration, rises of drug zwitterionic character and acidic pH increase absorption.

Local structure around M 2+ was determined by extended X-ray absorption fine structure (EXAFS) and X-ray absorption near edge structure (XANES) [16,17].Co-ordination polyhedron around Cu 2+ is a distorted octahedron: four O-atoms at a distance of 1.95 Å occupy planar equatorial sites; at axial places O-atoms are present at 2.46 Å.Though O-atoms are preferred at axial locations, N-atoms from NAG cannot be excluded. .
In earlier publications, program TOPO was applied to the valence topological charge-transfer indices for the molecular dipole moment [41,42], as well as fractal dimension of percutaneous absorption enhancer phenyl alcohols [43] and 4-alkylanilines [44].Lysozyme showed hydrolytic activity vs. peptidoglycans [45][46][47][48].A new tool was described for interrogating macromolecular structure [49].In the present report, HA geometric, topological and fractal analyses are performed with TOPO.The aim of this study is to find properties distinguishing HA•3Ca•9H 2 O.The goal is to validate the indices by using HA differentiation.The ultimate reason for modelling is to improve pharmaceutical formulations to release drugs in mucosal areas as HA properties affect mucoadhesion, rheological behaviour and drug absorption with the goal of increasing biodisponibility and decreasing toxicity.The following section describes the experimental in silico computational methods.Next, two sections illustrate and discuss the results.Finally, the last section summarizes our conclusions.

Experimental
In our program TOPO for the theoretical simulation of crystal-fragment shape [50], structure surface is represented by the external surface of a set of overlapping spheres with appropriate radii, centred on the atomic nuclei [51,52].A crystal fragment is treated as a solid in space defined by tracing spheres about atomic nuclei.It is computationally enclosed in a graduated rectangular box, and the geometric descriptors are evaluated by counting the points within the solid or close to chosen surfaces.The crystal-fragment volume is approximated as V = P•GRID 3 , where P is the number of points within the fragment volume (within a distance R X of any atomic nucleus X) and GRID is the mesh-grid size.As a first approximation, the crystal-fragment bare surface area was calculated as S = Q•GRID 2 , where Q is the number of points close to the bare surface area (within a distance between R X and R X + GRID of any atomic nucleus X).However, the estimate was improved: if a point falls exactly on the surface of one of the atomic spheres it accounts indeed for GRID 2 units of area on fragment bare surface, which is because total surface of atom X can accommodate 4R X 2 /GRID 2 points.When a point falls beyond the surface it represents GRID 2 units of area on the surface of a sphere of radius R > R X , not on the surface of atom X on which it accounts only for a fraction of this quantity: GRID 2 (R X /R) 2 .The total bare surface area is calculated as S = F•GRID 2 , where F is the sum of elements AF = R X 2 /R 2 (I) for those points close enough to the surface of any atom X.The R X 2 is the square radius of atom X and R 2 (I) is the square distance of point I from atomic nucleus X.Two topological indices of crystal-fragment shape are calculated: G = S e /S (S e = surface of an equivalent sphere) stands for the fragment globularity and G' = S/V denotes the fragment rugosity.
The hydrated-system properties are related to the contact surface between solute and water molecules.Another crystal-fragment geometric descriptor was proposed: the solvent-accessible surface area AS [53], which is defined by using a probe sphere that is allowed to roll on the outside while maintaining contact with the bare surface [54].It is calculated in the same way as the bare surface area by using pseudo-atoms whose van der Waals radii [55] were increased by the probe radius R [56].The accessibility is a dimensionless quantity ranged in 0-1 representing the ratio of solvent-accessible surface area in a particular structure to solvent-accessible surface area of the same atom when isolated from the crystal-fragment.The fractal dimension, D, results [57]: It provides a quantitative indication of the degree of surface accessibility towards different solvents [58].Program TOPO allows an atom-to-atom analysis of D on every atom i to obtain an atomic dimension index D i from the atomic contributions to AS i .The D i is weight averaged to obtain a new crystal-fragment dimension index D' = ( i AS i D i )/AS, where AS i are used as weights for D i .If an AS i = 0 for any probe, D i cannot be calculated for atom i and this does not contribute to D', which represents a D averaged for atoms nonburied to any solvent-accessible surface in the range of probe spheres.A version of TOPO was implemented in algorithms AMYR [59], GEPOL [60] and SURMO2 [61].Procedure AMYR performs the theoretical simulation of molecular associations and chemical reactions.Software GEPOL performs a triangular tessellation of the crystal-fragment surface.It is used for reference calculations.Codes TOPO and GEPOL recognize the cavity-like spaces in crystal-fragments and are adequate to study intercalation compounds; however, SURMO2 does not distinguish internal cavities.Combination SURMO2 with TOPO or GEPOL allows characterizing the crystal-fragment surface of the cavities.Our version of SURMO2 was corrected for deviation from the spherical shape, by dividing the contribution of every point by the cosine of the angle formed by the semi-axis and the corresponding normal vector to the surface at this point.The volume and surface areas of the crystal fragments with cavities were corrected by maximizing in every angular orientation the distance of the most distant atom in each semi-axis.

CH O OH
In gel Ca alginate used for wound dressing, Ca 2+ releasing helps in healing and exchanges exuded Na + .Stable cationic colloids were elaborated by using chitosan (CS):HA polyelectrolyte complexation [64].Ag + /Ag 3 PO 4 nanoparticles:HA/CS complexes (cf. Figure 4) resulted antimicrobial [65,66].Hydrogels are used in medical applications, e.g., implants, tissue engineering and contact lenses.The HA was selected as a mucoadhesive and biodegradable polymer.Polar molecules (cf.Table 1) administered with HA show high dipole moment.Notice the low MW of metronidazole, etc. and the low human skin permeability of caffeine used as transdermal anticellulite.Some small, lipid-soluble drugs cross the blood-brain barrier (BBB) simply by diffusion through the cell membrane and others, e.g., caffeine, enter successfully through specialized transporter proteins.
A model showed that the decimal logarithm of 1-octanol-water partition coefficient (log P) positively correlated and MW negatively associated with log K p [67]: where n is the number of points and r, correlation coefficient.Table 2 shows the administration routes of drug metronidazole for bacterial, fungal and protozoal vaginitis [68,69].) , e P: 1-octanol-water partition coefficient, f Kp: human skin permeability (cm•s -1 ).An HA comparative analysis was performed in three forms: hexamer (trimer of heterodimers) HA (cf. Figure 5), HA•3Ca and HA•3Ca•9H 2 O.The geometry of the systems was taken from the Protein Data Bank code 4HYA (X-ray fibre diffraction).In 4HYA, nine crystallization water molecules are included most strongly bound in the first hydration shell (cf. Figure 6).The 4HYA consists of six saccharide residues (126 atoms, cf.Table 3) with MW = 1123g•mol -1 .The glycosaminoglycan hexamer co-ordinates three Ca 2+ ions also surrounded by at least nine water molecules.The 11 N/O-H…O H-bonds include one N-H…O and 10 O-H…O, e.g., three pairs of H-shared H-bonds.Many H-bonds are formed because of the polyanionic nature of HA main chain.).Geometric and topological analyses were performed with our program TOPO (cf.Table 4).Reference calculations were performed with our version of GEPOL.Algorithm TOPO underestimated the molecular volumes V and surface areas S by 0.7% and 5 %, respectively.Surface-derived molecular globularities G were overestimated by 5% and rugosities G' resulted underestimated by 5 %. ).
Figure 9a shows the wire-frame molecular structure of HA. Figure 9b   Surface CPK + of HA (cf. Figure 10) shows more open cavities than HA•3Ca•9H 2 O (Figure 9d), which could be accessed by a water molecule.Program TOPO allows the atom-to-atom partition analysis of all geometric descriptors.Water solventaccessible surface analysis (cf.Table 5) shows that the solvent-accessible surface (AS) area was underestimated by 3 %.When going from hexamer HA to HA•3Ca and HA•3Ca•9H 2 O the hydrophobic solvent-accessible surface (HBAS) area rose by 42% and decayed by 26 %, respectively.On the other hand, the hydrophilic solvent-accessible surface (HLAS) area dropped by 14 % and increased by 58 %.It resulted the most sensitive geometric descriptor for the presence of Ca 2+ and, especially, water, in agreement with the highest number of H-bonds in the hydrated co-ordination complex (Table 3).Ongoing from HA to HA•3Ca and HA•3Ca•9H 2 O, the accessibility enlarged by 9% and decreased by 8%.The fractal dimension D was underevaluated by 1 %.The fractal dimension of HA turned out to be 1.566.When going to HA•3Ca and HA•3Ca•9H 2 O, it rose by 2 % and 1 %.The low accessibility and relatively low dimension of HA•3Ca•9H 2 O suggest that its reaction requires water or Ca 2+ exchange, in agreement with the closed character of CPK +/++ surfaces (Figure 9).The fractal dimension averaged for nonburied atoms D' increased by 11% with regard to the molecular dimension.In particular, for HA the external dimension resulted 1.725.Ongoing to HA•3Ca and HA•3Ca•9H 2 O it augmented by 4% and 0.3%.When going from HA to HA•3Ca and HA•3Ca•9H 2 O, the difference nonburied minus molecular dimensions (D'-D) enlarged by 20 % and decayed by 9 %.It resulted greatly sensitive to Ca 2+ and water incidences.), e Accessibility (%), f Molecular fractal dimension, g Molecular fractal dimension averaged for nonburied atoms.
Atom-to-atom partition analyses of HA•3Ca•9H 2 O topological indices and fractal dimension, cf.Table 6, show that globularity G of hydrated co-ordination complex was lower than for O-atoms in water, Ca 2+ and averages of O-atoms in HA in 2.0-2.4.Rugosity G' of Ca 2+ was smaller than for hydrate, O-atom averages in HA in 1.2-1.3Å - and O-atoms in water.Hydrate accessibility lay in the range of O-atom averages in HA (5.9-11.9%);however, accessibilities of Ca 2+ and O-atoms in water (34%) were much greater.On the other hand, the fractal dimensions of hydrate, Ca 2+ and O-atoms in water lay in the range of averages of O-atoms in HA (1.1-3.6).In particular, maximum fractal dimension corresponds to GCU O-atoms for which the utmost reactivity is expected, in agreement with M z+ -interchange and Ag + reactions (Figure 4).), c Molecular fractal dimension.

Discussion
Natural polysaccharide HA gelifies at pH < 4. It is characterized by its regenerative properties on different mucous zones, e.g., GI, oral, vaginal, etc.The HA is mainly used in medical and cosmetic applications.Among the many benefits HMW-HA holds in medicine are: (1) the maintenance of tissue space for surgery, (2) protection of cells and tissue and (3) therapeutic effectiveness.Healing efficiency of HA depends critically on MW: the higher the MW, the longer its benefit.The use of HA in cosmetics presents an impact on public health because of the risk of ingredient penetration into the deeper skin layers, which are cleared by systemic circulation (systemic absorption is more likely to occur in injured skin, e.g., sunburnt, atopic, eczematous, psoriatic skin).The problem is important in the case of anticellulite creams as the tissue target is on the dermis.Caffeine, Coleus forskohlii and Nelumbo nucifera extracts are efficacious ingredients of anticellulite cosmetics.In order to develop formulations, it is interesting to enhance their low skin permeabilities (Table 1).However, care should be taken concerning toxicity.Finally, it is proposed that (1) polymer COOHs react completely with matrix OHs to give esters, (2) polymer reaction with drugs begins with water or, even, Ca 2+ exchange, (3) matrix rheological properties, e.g., pHdependent gelification, etc., are important and (4) caffeine is a potential lead structure in drug design.

Conclusions
From the present results and discussion the following conclusions can be drawn: 1.The advantage of program TOPO with respect to GEPOL is that the former allows an atom-to-atom partition analysis of the geometric, topological, fractal indices and their combination: hydrophobic and hydrophilic solvent-accessible surface areas.The latter was detected as the most sensitive geometric descriptor for the presence of Ca 2+ and, especially, water, in agreement with the number of H-bonds, which were calculated with TOPO.Ongoing from hyaluronan to Ca 2+ co-ordinated to hydrate, accessibility rose by 9 % and decayed by 8 %.The relative error with program TOPO is 0.7 % in volume, as well as 5 % in surface area and its derived indices.3. The hydrate globularity was lower than for O-atoms in water, Ca 2+ and O-atom average in hyaluronan.The rugosity of Ca 2+ was smaller than for hydrate, O-atoms average in hyaluronan and O(water).The accessibility of Ca 2+ and O(water) was much greater than for hydrate.The maximum fractal dimension corresponds to D-glucuronic-acid O-atoms for which the utmost reactivity is expected, in agreement with M z+ interchange and Ag + reactions.
4. As cations exchange in hyaluronan co-ordination compound and action requires Ca 2+ alteration, the reinforcement of drug cationic/zwitterionic character and acidic pH increases absorption.
Hyaluronan is an articular-cartilage component where it is present as coat around chondrocytes.When aggrecan monomers bind to it in link-protein presence, large, anionic aggregates form, which are responsible for cartilage resilience.Its water interaction, represented by 10-15 H-bonds per disaccharide repeat, indicates binding capacity and importance for cartilage viscoelastic properties.
In mucosas, a need for the elimination of pathogens and prophylaxis exists.The hyaluronan rheological behaviour in pH 4-7 did not differ.However, pH < 4 generated gels because of hydrophobic interactions and H-bonds, which resulted promising for drug administration on mucous membranes and skin.
Further work will analyze polymer reactions with alcohols in the matrix/drugs (eugenol, metronidazole, betamethasone, etc.), matrix rheological properties and caffeine as a potential lead structure in drug design.Caffeine, etc. are efficacious ingredients of anticellulite cosmetics.However, care should be taken concerning toxicity, especially for injured skin.Work is in progress on the prediction of chromatographic retention times and molecular classification of (1) tea compounds and (2) methylxanthines (caffeine and its metabolites) and nicotine-metabolite cotinine in human plasma.

Figure 2 .
Chemical modifications in synthetic procedures for the fabrication of HA HGPs and DXNs.

Figure 4 .
Figure 4. Suggested structure of complex of hyaluronic acid (HA) and silver Ag + .

Figure 7
Figure 7 illustrates four out of 11 N/O-H…O H-bonds in HA•3Ca•9H 2 O: one N-H…O and three out of 10 O-H…O.

Figure 8 )
shows some small open cavities.
Figure9ashows the wire-frame molecular structure of HA.Figure9breveals the ball-and-stick (B&S) molecular model of HA•3Ca•9H 2 O.The Corey-Pauling-Koltun (CPK) molecular structure of HA•3Ca•9H 2 O (Figure 9c) defines the van der Waals molecular surface area S. Notice some small open cavities on CPK surface in agreement with Figure 8.The water-accessible surface CPK + of HA•3Ca•9H 2 O (Figure 9d) delimits the solvent-accessible surface area AS.Most open cavities on CPK (Figure 9c) close on CPK + surface meaning that they are not accessible to a water molecule (radius R = 1.25 Å).The CPK ++ of HA•3Ca•9H 2 O (Figure 9e) denotes the surface accessible by a protein side chain (R = 3.50 Å) and is used to calculate the fractal dimension D. Again, most open cavities on CPK (Figure 9c) close on CPK ++ , which are not accessed by a protein side chain.Structures comparison suggests that HA•3Ca•9H 2 O reaction with a molecule or drug begins with water and, even, Ca 2+ exchanges in the co-ordination compound.As many drugs are either cationic or zwitterionic, e.g., 65 % of orally available drugs are charged or zwitterionic, Ca 2+ exchange is favoured by electrostatics at acidic pH; e.g., drugs metronidazole and minoxidil are ionic pairs.

2 .
The fractal dimension was underevaluated by 1 %.Ongoing to Ca 2+ co-ordinated and hydrate, fractal dimension of hyaluronan (1.566) rose by 2 % and 1 %, respectively.The fractal dimensions of nonburied atoms increased by 11 % with regard to molecular fractal indices.Ongoing to Ca 2+ co-ordinated to hydrate, fractal dimension of external atoms (1.725) augmented by 4 % and 0.3 %.Nonburied minus molecular fractal dimension enlarged by 20 % and decayed by 9 %.It was sensitive to Ca 2+ and water occurrences.

Table 1 .
Molecular dipole moments of water, theophylline and polar molecules administered with HA.

Table 2 .
Administration routes of drug metronidazole for bacterial, fungal and protozoal vaginitis.

Table 3 .
Number of atoms, hydrogen bonds and molecular weight of hyaluronic acid (HA).

Table 4 .
Geometric descriptors and topological indices of hyaluronic acid (HA).
a V Ref. b S c S Ref. b G d G Ref. b G' e G' Ref.

Table 5 .
Geometric descriptors and fractal dimensions of the solvent-accessible surface of HA.
b HBAS c HLAS d Accessibility e D f D Ref. b D'