Full text of DOI:10.1093/glycob/10.6.587

Glycobiology vol. 10 no. 6 pp. 587–594, 2000
Conformational behavior of hyaluronan in relation to its physical properties as probed
by molecular modeling
Katia Haxaire, Isabelle Braccini, Michel Milas,
Marguerite Rinaudo and Serge Pérez1
umbilical cords. It is also produced by some bacteria; for
example, it is a significant component of the extracellular
material of strains such as Streptococcus zooepidemicus,
which is used to produce, on a large scale and with a good
yield, pure HA having a molar mass around 2–3 × 106.
HA participates in a hydrated network with collagen fibers
(e.g., vitreous humor), where it acts as an organizing core in
the intercellular matrix, connecting together and spatially
distributing the cartilage glycoconjugates to form complex
intercellular aggregates (Hardingham, 1981; Hascall, 1981).
HA is a constituent of the pericellular coat of unfertilized eggs,
and a variety of other cells (Goldberg and Tolle, 1984) where
it may act in cell–cell interaction and cell adhesion (Underhill
and Dorfman, 1978; Mikuni-Takagi and Toole, 1980; Turley
and Roth, 1980).
The physical properties and functions of hyaluronan are
based on its ability to form viscoelastic aqueous solutions. In
solid state, x-ray fiber diffraction has been used in a number of
different cationic environments of HA. Left-handed 4-fold
helices were found in sodium and potassium environments,
and left-handed 3-fold helices with calcium (Sheehan and
Atkins, 1983). An extended 2-fold helix has been proposed for
the structure of HA under acidic conditions in presence of most
cations (Atkins et al., 1972), except potassium and ammonium
salts, which form left-handed 4-fold anti-parallel double
helices (Sheehan et al., 1977; Arnott et al., 1983). Despite such
architectural diversity, all these structures are consistent with
the occurrence of intramolecular hydrogen bonds across the
glycosidic linkages (Winter and Smith, 1975), and supported
by preliminary computer simulations (Scott et al., 1991). In
order to get further insight into the hydration features of HA,
molecular dynamics simulations have been performed on its
constituent disaccharides (Almond et al., 1997) and trisaccha-
rides (Kaufmann et al., 1998). Detailed NMR study of the
conformation of one constituting disaccharide has been
performed in water (Sicinska et al., 1993). While these investi-
gations are yielding a detailed description of the dynamics of
HA oligomers with the surrounding water molecules, they do
not offer any comprehensive understanding of the molecular
basis which may underline the occurrence of the numerous
polymorphs that have been observed for HA.
Centre de Recherches sur les Macromolécules Végétales, CNRS (associated
with Université Joseph Fourier, Grenoble), 38041 Grenoble, France
Received on September 24, 1999; revised on November 9, 1999; accepted on
November 14, 1999
Hyaluronan (HA) is a linear charged polysaccharide whose
structure is made up of repeating disaccharide units.
Apparently conflicting reports have been published about
the nature of the helical structure of HA in the solid state.
Recent developments in the field of molecular modeling of
polysaccharides offer new opportunities to reexamine the
structural basis underlying the formation and stabilization
of ordered structures and their interactions with counte-
rions. The conformational spaces available and the low
energy conformations for the disaccharide, trisaccharide,
and tetrasaccharide segments of HA were investigated via
molecular mechanics calculations using the MM3 force
field. First, the results were used to access the configura-
tional statistics of the corresponding polysaccharide. A
disordered chain having a persistence length of 75 Å at
25°C is predicted. Then, the exploration of the stable
ordered forms of HA led to numerous helical conforma-
tions, both left- and right-handed, having comparable ener-
gies. Several of these conformations correspond to the
experimentally observed ones and illustrate the versatility
of the polysaccharide. The double stranded helical forms
have also been explored and theoretical structures have
been compared to experimentally derived ones.
Key words: hyaluronan/molecular modeling/helical
conformations/persistence length
Introduction
Hyaluronic acid, also called hyaluronan and abbreviated HA,
belongs to the family of glycosaminoglycans (GAG). It is
made up of repeating disaccharide units of 2-acetamido-
2deoxy-β-D-glucose (GlcNAc) and β-D-glucuronic acid
(GlcA) linked 1–4 and 1–3, respectively. HA is the only
nonsulfated GAG. The polysaccharide chains are large with
average molar masses in the range 105 to 107, depending on the
source (Laurent, 1970). HA is found in the intercellular matrix
of mammalian connective tissues, and it was previously
extracted from bovine vitreous humor, rooster combs, and
The purpose of the present study is to further develop our
understanding of the physical properties of HA by a detailed
exploration of the structural behavior; the work reported here
provides, via a series of molecular modeling investigations, a
consistent view of the different levels of structural organiza-
tion and polymorphism that HA can assume. This covers (1)
the characterization of the low energy conformers of each
constituent di-, tri-, and tetrasaccharide, (2) the dimensions of
1To whom correspondence should be addressed
© 2000 Oxford University Press
587

K.Haxaire et al.
Grid search
The available conformational space of the polysaccharides
depends mainly on the glycosidic Φ and Ψ torsion angles and
can, to a first approximation, be described by the potential
energy surface of the disaccharide subunits. Following this
assumption, adiabatic maps were computed for β-D-GlcNAc-
(1→4)-β-D-GlcA (N-G) and β-D-GlcA-(1→3)-β-D-GlcNAc
(G-N) disaccharides. They were constructed from 12 indi-
vidual relaxed maps computed with starting geometries which
take into account the privileged orientations of the hydroxy-
methyl group (ω close to 60°, –60°, and 180°) and of the
secondary hydroxyl groups (clockwise (c) and counter-clock-
wise (r) orientations). The acidic and N-acetyl groups were
positioned in their preferred orientation in all the calculations.
This corresponds to the trans orientation for the acetamido
group and a torsion angle of 130° for the acidic group. In the
computation of a relaxed map, the (Φ, Ψ) torsion angles are
rotated in 10° increment over the whole angular range, and the
resulting conformations are relaxed (with the exception of Φ
and Ψ) using the block diagonal method with a termination
criterion of n * 0.00003 kcal/mol (n: number of atoms).
Fig. 1. Schematic representation of the tetrasaccharide β–D-GlcNAc(1–4)β-D-
GlcA(1–3)β-D-GlcNAc(1–4)β-D-GlcA, considered as repeat fragment of HA.
The GlcNAc residue is abbreviated to as N, whereas the GlcA residue is
abbreviated to as G. The labeling of the main atomic positions is indicated,
along with the torsion angles of interest.
the polymer in the disordered state (characteristic ratio, persist-
ence length), (3) all the helical conformations, either single and
double, that are likely to occur in the solid state, (4) their inter-
action with essential cations.
In order to evaluate long range effects along the chain and
the possible occurrence of an inter-residue hydrogen bond
network, trisaccharides and tetrasaccharides were built using
the results of the preceding conformational study. The confor-
mations of all the local minima of the potential energy surface
of N-G and G-N were combined to build the trisaccharides
N-G-N and G-N-G, and the resulting geometries were mini-
mized. Finally, a relaxed map was computed for the central
N-G and G-N glycosidic linkages of the G-N-G-N and N-G-N-
G tetrasaccharides, respectively. In these calculations, the best
conformation established for the disaccharides G-N and N-G
was applied about the outer glycosidic linkages of G-N-G-N
and N-G-N-G, respectively. The isoenergy contour maps were
drawn using the program XFarbe.
Nomenclature
A representation of the tetrasaccharide subunit of HA is given
in Figure 1 along with the labeling of the atoms and the torsion
angles of interest. For the sake of simplicity and in accordance
with previous works, the 2-acetamido-2deoxy-β-D-glucose
(GlcNAc) is abbreviated to as (N), whereas the β-D-glucuronic
acid (GlcA) is abbreviated to as (G). All these residues are on
their pyranosic form. The conformations around the glycosidic
linkages are described by two sets of torsion angles: Φ1-4
=
O5(N)-C1(N)-O1(N)-C4(G), Ψ1-4 = C1(N)-O1(N)-C4(G)-
C5(G) [N-G linkage] and Φ1-3 = O5(G)-C1(G)-O1(G)-C3(N),
Ψ
1-3 = C1(G)-O1(G)-C3(N)-C4(N) [G-N linkage].
Three other important torsion angles are considered in the
study and are those describing the orientation of the following.
The acidic group of (G): γ = O5(G)-C5(G)-C6(G)-O6(G). The
hydroxymethyl group of (N): ω = O5(N)-C5(N)-C6(N)-
O6(N). The acetamido group of (N): δ = C1(N)-C2(N)-N2(N)-
C7(N).
The signs of the torsion angles are in agreement with the
IUPAC-IUB commission of Biochemical Nomenclature
(IUPAC-IUB, 1983).
Generation of statistical chains
In order to evaluate the behavior and the dimensions of HA
polymer chains in solution, in θ-conditions, large samples of
disordered chains were generated using the Monte Carlo tech-
nique as implemented in the METROPOL program (Boutherin
et al., 1997). The conformations were selected using the
Metropolis algorithm (Metropolis et al., 1953) and distributed
according to Boltzmann statistics. The detailed description of
the procedure is reported elsewhere (Boutherin et al., 1997). In
these calculations, the polymer chain is constructed residue by
residue and the program uses the (E, Φ, Ψ) triads describing
the conformation about the glycosidic linkages. The usual
approach uses the results of the adiabatic map established for
the disaccharide subunits and therefore does not take into
account all the steric interactions between residues in a longer
segment. In order to consider such effects, polymer chains of
HA were generated using the (E, Φ, Ψ) triads referring to the
relaxed maps of the tetrasaccharide fragments (see above), in
addition to the standard procedure. Statistical samples of
20,000 polymer chains each containing 2000 glycosyl residues
were constructed for HA (mean error deviation not exceeding
5%). The dielectric constant was set to 80 to simulate aqueous
medium, and the following temperatures, 298 K, 323 K, 348 K,
and 373 K, were used.
Computational methods
Molecular mechanics calculations
The general molecular mechanics program MM3(92) (Allinger
et al., 1989, 1990, 1992) was used in this study to compute the
energy of any di- or oligosaccharide conformation. The MM3
force field is highly elaborated and includes cross term effects
along with the classical bonded and nonbonded terms. This
force field is well adapted for the conformational study of
carbohydrates (French et al., 1990) and has earned the reputa-
tion to be the most appropriate one for this class of biomole-
cules (in vacuum). It takes into account the anomeric and exo-
anomeric effects, and uses an explicit term for hydrogen
bonds. The 1992 version includes an angular dependence in the
hydrogen bonding function.
588

Conformational behavior of hyaluronan
The extension and relative stiffness of the chain are
described by the characteristic ratio (C∞) and the persistence
length (Lp) (Lapasin and Pricl, 1995). The average dimensions
(C∞ and Lp) were evaluated from the statistical samples as
follows:
2
2
C
=
lim Cx = lim <r (x)/x.Lo > with r(x) = d(O1(N)–O1(N)[x])
x → ∞ x → ∞
∞
The angular brackets indicate the average of the square end-to-
end distance r2 over all the conformations of polymer chains,
Lo is the bond length connecting two adjacent glycosidic
oxygen atoms, and x is the number of glycosyl residues. The
persistence length (Lp) is defined as the projection of the end-
to-end distance vector r on the first bond of the chain. It repre-
sents the maximum contour length over which a correlation
between monomeric units persists. The asymptotic values of
Cx and Lp(x) when x increases, corresponding to a range of x
where they become independent of the degree of polymeriza-
tion (here x > 500), i.e., C∞ and Lp, can be directly compared
to the experimental parameters in θ-conditions.
Generation of regular helices
All the possible stable single regular helical forms of HA were
established using the program POLYS (Engelsen et al., 1996).
The helices are characterized by the two helical parameters n
and h, where n is the number of repeat units (disaccharide unit)
per turn of the helix and h is the projection of one repeat unit
on the helical axis. The chirality of the helix is described by a
sign attributed to n: a positive value of n corresponds to a right-
handed helix and a negative value to a left-handed helix. The
different single helical forms were extrapolated from the low
energy conformations of the constitutive G-N and N-G subu-
nits. In the POLYS procedure, two sets of (Φ, Ψ) values, corre-
lated to the local minima for G-N and N-G, are applied on the
corresponding (1→3), (1→4) glycosidic linkages of the
polymer chain, and then, POLYS slightly modifies these
values in order to obtain the nearest integral n-fold helical
structure. The regular helices are then constructed using the
optimized (Φ, Ψ) values. Taking into account the results
obtained for the trisaccharides regarding the stability of the
conformers, all the reasonable combinations of the low energy
conformations of the dimer subunits were explored. Finally, all
the optimized single helical structures were minimized (with
ε = 4 to simulate the solid state) with a constraint applied on
the glycosidic linkages in order to preserve the regular helicity.
Under particular conditions, i.e., pH 3–4 and K+ salt form,
HA has been reported to adopt a double helix conformation
with anti-parallel strands (Arnott et al., 1983). The occurrence
of such a double helix for K+-hyaluronate has been debated and
several models have been proposed and questioned. In the
present study, the feasibility of an anti-parallel double helix for
HA was explored using an extension of a home made program
CHACHA, originally developed to evaluate the chain–chain
interactions (Pérez et al., 1990) and predict crystal structures
(Pérez, 1990). In the procedure used, two identical single
helices are superimposed along their Z-axis. One helix, chain
A, remains unchanged along the procedure. Firstly, chain B, is
reversed along Z (rotation 180° around Y-axis). Then, it is
rotated over all the angular range around Z (µ: 0° to 360° by
10° intervals) and translated over an integral h length (∆Z: 0 to
8.2, by 0.818 Å intervals). All the combinations of µ and ∆Z
Fig. 2. Adiabatic maps of (a) β-D-GlcA(1–3)β-D-GlcNAc (G-N) and
(b) β–D-GlcNAc(1–4)β-D-GlcA (N-G) disaccharides [MM3(92), ε = 80] with
the energetic wells labeled A, B, C, and D. Contours are drawn in 1 kcal/mol
intervals starting from the global minimum. Representation of the low energy
conformers in each well are shown.
were explored and for each geometry, the Van der Waals
energy was computed. The best conformations were finally
relaxed with a constraint applied on the glycosidic linkages. As
the number of atoms in the generated double helices is too high
for a MM3 minimization, TRIPOS force field with additional
PIM parameters (Imberty et al., 1991) were used.
Results and discussion
Conformational properties of the constituent oligosaccharides
The (Φ,Ψ) adiabatic maps of the two disaccharide model frag-
ments, G-N and N-G of HA, computed with a dielectric
constant of 80, are displayed in Figure 2. These maps share
some common features typical of (1→3) di-equatorial and
4
(1→4) di-equatorial linked C1 hexopyranoses. The potential
energy surfaces exhibit roughly three distinct regions: the main
domain, containing the A and B wells, which encompasses
more than half of the energetically stable conformations, and
two separated regions, named C and D (containing the D, E
wells for N-G). The major structural features of the minima of
the different A, B, C, D, E wells are summarized in Tables I
and II for G-N and N-G, respectively. For all the minima, the
hydroxymethyl group of the N residue presents the GT orienta-
tion, which is generally the most represented one in solution
for glucose and glucose-derived sugars (Marchessault and
589

K.Haxaire et al.
Table I. Energy minima of the potential energy surfaces of the disaccharide GN
group invariably adopted the stable trans orientation. As
mentioned previously, dimers are too short to provide pertinent
information about the structural parameters contributing to the
stiffness of HA, the favored conformations of the two trisac-
charides N-G-N and G-N-G were investigated further. Only
the conformations arising from the combination of the low
energy conformers of each disaccharide component were
considered. The fully optimized structures were those main-
taining the conformational features which were observed in the
disaccharides. Thus, at the trisaccharide level, a network of
hydrogen bonds, involving the contiguous ring oxygens,
clearly appeared (Figure 3); the acetamido group did not
participate in this network as it never forms any hydrogen bond
with OH or COOH group of the adjacent residue. Neverthe-
less, for all the trimers generated, the distance between amide
proton and the carboxylate oxygen of the N-G component is
compatible with the inclusion of only one bridging water mole-
cule. As another possible source of stiffening, the relative ener-
gies of the trimers (data not shown), indicated significant
interaction for longer oligomers. The region D, and regions C,
D, E of G-N and N-G components, respectively, became inac-
cessible at the trisaccharide level.
Well GN
A
B
C
D
Φ
Ψ
γ (°)
δ (°)
∆E (kcal/mol)
H bond (Å)
1–3 (°)
1–3 (°)
-79.7
111.6
127.3
136.5
0
-91.4
81.1
127.4
144.4
0.28
-91.8
-69.2
56.3
128.8
126.8 126.2
87.6
1.88
_
96.6
3.38
_
O5(G)…O4(N)
2.72
O5(G)…O4(N)
2.70
Pérez, 1979). The general behavior of both disaccharides is
similar with respect to their respective conformational space.
The minima of A and B regions, which are extended conforma-
tions with optimal exo-anomeric effects, are very close in
energy. The minimum of the C well is less than 2 kcal/mol
higher in energy; this weak energy difference compared with
the conformations of the main region A-B, in addition to an
energy barrier less than 7 kcal/mol between the two domains,
suggests the contribution of conformations from the C region
in solution. The D well is isolated from the main region and
contains conformations significantly higher in energy, espe-
cially for the (1→4) linked N-G disaccharide. Such a well is
not likely to be populated in solution.
Intrinsic viscosity measurements have indicated that, in
aqueous salt solutions, sodium hyaluronate behaves as a semi-
rigid polymer (Morris et al., 1980). This stiffness has been
proposed to arise partly from the presence of an extended
network of intramolecular hydrogen bonds (Atkins et al.,
1980). A first type of H bonds (2 per trisaccharide) involving
the ring oxygen atoms is commonly accepted. Both the slow
periodate oxidation of the glucuronic residue (G) in HA (Scott
and Tigwell, 1978) and the dramatic decrease of the dimen-
sions in highly alkaline solutions strongly suggest their occur-
rence.
In contrast, the hydrogen bonds involving the acetamido
group are still debated. The trans orientation of this group
established in water by NMR (Cowman et al., 1984; Sicinska
et al., 1993) is incompatible with the direct hydrogen bond
between the NH (N) and COO– (G) groups, originally
proposed by Atkins and coworkers (Atkins et al., 1980). In the
present study, the results of the conformational search
performed on the disaccharides indicate that the conformations
of the lowest A, B energy regions are stabilized by the presence
of the hydrogen bonds involving the ring oxygen atoms (see
Tables I, II). In contrast, none of the two hydrogen bonds
involving the acetamido group were observed. This exocyclic
Conformational properties of HA chains
Because of the important biological functions of hyaluronan,
particular interest has been focused on the hydrodynamic and
rheological properties of hyaluronate solutions, especially their
viscoelasticity. From several experimental studies, solution
properties have been interpreted by a stiffened random coil
(Cleland and Wang, 1970; Morris et al., 1980). NMR (Darke et
al., 1975) and viscosity (Morris et al., 1980) studies indicated
the occurrence of ordered domains in solution. Recent investi-
gations carried out on HA of bacterial origin led to the conclu-
sion that the polymer is best represented as a wormlike
polymer perturbed by ionic effects (Fouissac et al., 1992) and
characterized by an intrinsic persistence length in the range of
70–80 Å (Fouissac et al., 1992)
Theoretically, configurational characteristics can be calcu-
lated from statistical samples of disordered chains using mole-
cular mechanics. In the present study, the disordered chains were
generated for different temperatures, from the energetic data of
the disaccharide and tetrasaccharide segments, using the corre-
sponding (Φ,Ψ) energy maps. The usual approach consists of
using the (E, Φ, Ψ) triads referring to the disaccharide subunits
and thus, the calculated dimensions refer to the unperturbed state
of the polymer, experimentally observed in the θ-conditions.
Using this procedure, a persistence length of 55 Å is predicted,
which represents a value below the recent experimental ones
Table II. Energy minima of the potential energy surfaces of the disaccharide NG
Well NG
A
B
C
D
E
Φ
Ψ
γ (°)
δ (°)
∆E (kcal/mol)
H bond (Å)
1–4 (°)
1–4 (°)
-90.9
-169.6
6.3
-70.1
-120.1
0.2
-98.3
54.1
115.9
139.1
0.06
52.1
-120.3
-8.3
153.9
5.20
_
73.5
-92.1
-97.5
140.5
5.52
_
139.9
0
131.4
0.22
O5(N)…O3(G)
2.70
O5(N)…O3(G)
2.85
O5(N)…O3(G)
2.96
590

Conformational behavior of hyaluronan
Fig. 3. Lowest energy conformers of the trisaccharides G-N-G and N-G-N
showing the hydrogen bonds involving the ring oxygens and connecting the
consecutive residues.
(Rinaudo et al., 1999). One considers that some longer range
interactions between sugar units are not completely taken into
account when the disaccharide unit is used; so, calculations were
performed in a second step using the energy maps corresponding
to the central N-G and G-N glycosidic linkages of the G-N-G-N
and N-G-N-G tetrasaccharides, respectively. In these conditions,
a value of 75 Å is calculated for the persistence length at 25°C
using a dielectric constant of 80; this value characterizes a semi-
rigid polymer with moderate extension. This value agrees well
with the experimental one and confirms the presence of signifi-
cant interaction between sugar units in larger oligomers. Snap-
shots of typical polymer conformations are presented in Figure
4a, illustrating the moderately extended and sinuous character of
HA chains. The variations of the persistence length (Lp vs. x) at
different temperatures are shown in Figure 4b. Asymptotic
behavior was reached for values of about 500 glycosyl residues
at 298 K. It corresponds to a characteristic ratio of about 22.
Increasing the temperature regularly decreases Lp and C∞, but
Figure 4b indicates a moderate effect of the temperature on these
parameters. Despite the intrinsic limitations of the theoretical
calculations (lack of water, counterions, problems arising from
excluded volume effects), the agreement obtained between theo-
retical and experimental values, in θ-conditions, suggests that
the conformational behavior of the polysaccharide chain may be
properly simulated using reasonable approximations.
Fig. 4. (a) Snapshot of the disordered chains of HA at 25°C. (b) Persistence
length, Lp(Å), calculated as a function of the number of glycosyl residues, x,
of the HA chain and varying with temperature. The values are averaged over a
statistical sample of 20,000 polymer chains generated using the (E, Φ, Ψ) triad
data of the tetrasaccharide fragments N-G-N-G and G-N-G-N.
The ordered chain conformations
From the combination of minima of both N-G and G-N poten-
tial energy surfaces, HA oligomers exhibiting regular helical
conformations have been extrapolated and minimized. Consid-
ering the oligomerization effects observed on the trisaccha-
rides (see above), only the minima from the A, B, C regions for
G-N and from the A-B region for N-G were used. The struc-
tural and energetic parameters of the helices generated are
reported in Table III. Side and top views of the corresponding
structures are given in Figure 5.
The main result arising from the data in Table III is that HA
polysaccharide can assume a wide range of energetically stable
integral helices, ranging from the left handed 4-fold symmetry
591

K.Haxaire et al.
Fiber studies and refinements have effectively identified
numerous allomorphs which are all left-handed 3- and 4-fold,
and 2-fold helices with axial rises per disaccharide in the range
of those calculated in the present study. It has been established
that these helical conformations of HA strongly depend on the
nature of the counterions and on the pH, and more moderately
on the temperature and relative humidity (RH). Above pH 4.0,
at room temperature and 80–85% RH, sodium (Sheehan and
Atkins, 1983; Mitra et al., 1985–1986) and potassium
(Sheehan and Atkins, 1983; Mitra et al., 1985–1986) hyaluro-
nates adopted pseudo left-handed 4-fold conformations in an
orthorhombic unit cell, with an axial rise per disaccharide
being 8.4 and 9.0 Å, respectively. On drying or heating these
samples, slight rearrangements occur; a more extended confor-
mation is obtained on heating (70°C) Na-hyaluronate (h = 9.3
Å) (Sheehan and Atkins, 1983) and on drying K-hyaluronate
(h = 9.6 Å) (Sheehan and Atkins, 1983; Mitra et al., 1985–
1986). A tetragonal unit cell is obtained on drying Na-HA
(Guss et al., 1975; Sheehan and Atkins, 1983) (0% RH)
without changes in the helical parameters. Below pH 4.0, very
different helical conformations are obtained, with a different
effect for the two ions. In the presence of sodium (Sheehan and
Atkins, 1983), the conformation of the chain is that of a two-
fold helix, with an axial rise/disaccharide of 9.8 Å; this confor-
mation is the most extended form of hyaluronate trapped in the
solid state. Concerning K-HA, an antiparallel double-stranded
helix is observed (Arnott et al., 1983); the backbone of indi-
vidual chains is a contracted left-handed 4-fold helix with an h
value of 8.2 Å. This helical conformation has been debated and
detailed model buildings and structure analysis have been
presented for this form. The HA duplex with 43 symmetry was
first trapped at low pH by Sheehan et al. (1977) in oriented
Fig. 5. Stable regular helical conformations of single strand of HA chains. The
helices are represented using projection parallel and orthogonal to their axes.
Table III. Structural and energetic parameters of the stable single strand
helical conformations of hyaluronan
polycrystalline fibers containing K+, NH4 , Rb+ or Cs+ ions.
+
These ions are known to disrupt “water structure” (Frank and
Evans, 1945) and the double helical structure is a general
response to their presence. The model established by the
authors (abbreviated as X1) provided acceptable x-ray discrep-
ancy indices but proposed an helical conformation of the indi-
vidual chains quite different from that described by Guss et al.
(1975) for HA single helix with the same 43 symmetry and
comparable axial advance/disaccharide. Later, Arnott et al.
(1983) reinvestigated the hyaluronan double helix. They
proposed a crystal model (abbreviated as X2) with a mutual
arrangement of the chains comparable to that of the first
model, but with different helical conformation. Even if this
refined model is more likely because of the helical conforma-
tion, close to that of the single helix, it is difficult to reject the
first structure as both models provided comparable R factors.
The present work provides the way to explore the occurrence
of double helical structures for HA. Starting from the helical
structure optimized to reproduce both the experimental 4-fold
left-handed chirality and axial advancement (h = 8.2 Å), all
possible associations in double helix have been explored with
respect to the relative orientation (parallel and anti-parallel)
and position (rotation: µ, translation: ∆Z). The anti-parallel
arrangement of the chains appeared to be significantly favo-
rable compared to the parallel arrangement; this is in agree-
ment with experimental data suggesting such arrangement as a
result of chain folding. The calculations indicate that there is
roughly only one way to associate the chains in double helix:
all the viable anti-parallel duplexes differ from each other by
helix
n
(1)
(2) (3)
–3
9.8 9.9
(4)
2
(5)
–3
(6)
2
(7)
3
(8)
4
(9)
5
–4
2
h dim
9.5
0.61
10.0 10.0 10.1 7.4
5.9
4.0
∆Edim
(kcal/mol)
0
0.66 0.90 1.15 1.64 0.65 2.12 1.88
to the right-handed 5-fold symmetry. Helical structures gener-
ated from the lowest A-B regions of both G-N and N-G disac-
charide subunits have extended 4-, 3-, or 2-fold conformations
with a rise per dimer, h, ranging from 9.51 to 10.13 Å. The
helices constructed from the energy of the minimum C, for N-
G component, are right-handed hollow helices (Figure 5:
helices 7–9). It can be seen that the left-handed models are
lower in energy than the corresponding right-handed models.
The results indicate that small variations in glycosidic torsion
angles may have a significant influence on the symmetry and
pitch of the resulting helices without any noticeable energetic
cost. Such variations are expected to occur through interactions
of HA with counterions and water, and with variations in pH
and temperature adopted for the preparation of the fibers.
Consequently, important polymorphism may be expected for
HA, and indeed, the three lowest theoretical helical conforma-
tions, which present a different symmetry: 2-fold helices and
left-handed 3- and 4-fold helices illustrate well the versatility
of HA in the solid state.
592

Conformational behavior of hyaluronan
Table IV. Geometrical and helical parameters of the best optimized duplex
along with those of two minimized x-ray models
a
b (X2)
–70
c (X1)
–121.2
117.9
–120.9
118
Φ1–3(°)
Ψ1–3(°)
Φ1–4(°)
Ψ1–4(°)
–75.0
114.8
–79.2
–117.7
0
116.4
–79.5
–89.5
66.5
∆E(kcal/mol)
122.1
helix as any contamination of sodium or potassium hyaluro-
nate by this divalent cation (even at substochiometric levels)
changes the dominant conformation to that of the 3-fold helix
typical of a pure Ca-form. This particular conformational
behavior related to the presence of calcium ions suggests
specific interaction between HA and Ca2+. Nevertheless,
screening ion-chain interaction for the three helical forms,
(Figure 5: helices 1 to 7) and Na+, K+, and Ca2+ ions using the
GRID MD program (Goodford, 1985) failed to identify any
specific structural features in the 32 conformation for calcium
binding with respect to the two other forms, and did not bring
a satisfying explanation concerning the behavior of HA in the
presence of calcium. This procedure was successfully used in a
preceding similar study realized on four polyuronides (Brac-
cini et al., 1999) known to form complex bonds with calcium
in solution or gel. The lack of water in the procedure and the
inherent approximation of the GRID calculations probably
represent too strong limitations to get meaningful results for a
system such as hyaluronate. Indeed, the fiber diffraction
studies indicated that water is essential to coordinate the
cations and maintain the ordered environment.
Fig. 6. Models for double helical conformations of HA with anti-parallel
strands. (a) calculated model; (b) second model derived from x-ray
experiment, X2, proposed by Arnott and coworkers (Arnott et al., 1983);
(c) first model derived from x-ray experiment, X1, proposed by Sheehan and
coworkers (Sheehan et al., 1977).
maximum 10° in relative rotation (µ) and ∼2 Å in relative
translation. The geometrical and helical parameters of the best
optimized duplex along with those of the two minimized x-ray
models (the three models are minimized under the same condi-
tions) are reported in Table IV, and the three models are illus-
trated in Figure 6. From these results, one can immediately see
that the first x-ray model, X1, exhibits a very high energy,
arising mainly from glycosidic torsion angles of the individual
chains far from the favorable ones (see Tables I and II and
Figures 2a,b). The reinvestigated x-ray model, X2, is energeti-
cally much more stable. Examination of the geometrical
features of the chains indicates that the best theoretical struc-
ture and X2 model have very similar glycosidic and exocyclic
(acetamido and carboxyl groups) torsion angles, with a notice-
able exception for Ψ1–4. We are fully aware that our modeling
study provides an estimate of the internal energy of the macro-
molecular system rather than the free-energy, and it is this
latter that determines the most favored conformations in solu-
tion. Nevertheless, the conformation of the first x-ray model is
so far from the most stable ones that it can be discarded, even
though the influence of the solvation and salt effects were not
considered. The two x-ray models exhibit an inter-chain network
of hydrophobic interactions, via the methyl groups of the aceta-
mido moieties. X2 model exhibits an important network of intra-
and inter-chain hydrogen bonds (Arnott et al., 1983). Despite
being absent from our theoretical calculation, this network may be
very appealing. It is nevertheless questionable, as it results from a
particular chain conformation with a ψ1–4 torsion angle 30° above
a stable value (see Table II, B well) and glycosidic C-O-C valence
angles (C1-O4-C4 = 118.8°[NG linkage]) which deviate from the
usually observed ones.
Conclusion
The present study provided a set of conformational informa-
tion allowing for a better understanding of the specific
behavior of hyaluronan in both solution and solid states.
Important oligomerization effects have been observed in the
energetic evaluation of the trisaccharides N-G-N and G-N-G.
These effects reduce noticeably the accessible conformational
space established on the basis of the N-G and G-N disaccharide
subunits. They could represent a contribution to the inherent
stiffness of hyaluronan, in addition to the network of intra-
molecular hydrogen bonds involving the ring oxygens. This
characteristic feature of HA is also suggested by the evaluation
of the dimensions of the polysaccharide: the persistence length
calculated from a statistical sample of disordered chains is
properly predicted, 75 Å at 25°C, only when using (E, Φ, Ψ)
data corresponding to tetrasaccharides in the procedure; it is
also predicted that Lp decreases when the temperature
increases.
Another characteristic feature probed in this theoretical
study is the polymorphism of HA observed in the solid state.
The versatility of the polysaccharide, illustrated by three
different helical conformations 32, 43, 21, is well predicted
here; it is explained by weak energetic costs (<0.7 kcal/
mol·dimer) associated to small variations in Φ, Ψ glycosidic
torsion angles leading to the different types of helix. Finally,
we investigated the feasibility of a double helix with anti-
parallel strands for HA, and evaluated the two models derived
A particular behavior of HA is observed in the presence of
calcium ions (Winter and Arnott, 1977; Sheehan and Atkins,
1983). At pH > 4, Ca-HA crystallizes in an hexagonal unit cell
and adopts a left-handed 3-fold conformation with h = 9.5 Å;
this helical form is stable to changes in temperature, humidity
and ionic strength. The effect of calcium is to initiate the 3-fold
593

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