Exploring conformational energy landscape of glassy disaccharides by CPMAS 13C NMR and DFT/GIAO simulations. II. Enhanced molecular flexibility in amorphous trehalose

Abstract

This paper deals with the comparative use of the chemical shift surfaces to simulate experimental 13C CPMAS data on amorphous solid state disaccharides, paying particular attention to -1-1 linkage of trehalose, to -1,4 linkage between pyranose rings (lactose) and to linkage implying a furanose ring (sucrose). The combination of molecular mechanics with DFT/GIAO ab-initio methods provides reliable structural information on the conformational distribution in the glass. The results are interpreted in terms of an enhanced flexibility that trehalose experiences in amorphous solid state compared to the other sugars. An attempt to relate this property to the balance between intra- and inter-molecular hydrogen bonding network in the glass is presented.

Full text

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Exploring conformational energy landscape of glassy
disaccharides by CPMAS 13C NMR and DFT/GIAO simulations.
II. Enhanced molecular flexibility in amorphous trehalose.


Ronan LEFORT1, Patrice BORDAT2, Attilio CESARO3, and Marc DESCAMPS1


1Laboratoire de Dynamique et Structure des Matériaux Moléculaires, P5, Université de
Lille 1, Cité Scientifique, F-59655 Villeneuve d’Ascq Cedex, France


2Laboratoire de Chimie Théorique et de Physico-Chimie Moléculaire, UMR 5624 - IFR,
LCS, 2, rue Jules Ferry, F-64000 Pau, France


3Laboratory of Physical and Macromolecular Chemistry, University of Trieste, Via
Giorgieri 1, I-34127 Trieste, Italy

Abstract :
This paper deals with the comparative use of the chemical shift surfaces to simulate
experimental 13C CPMAS data on amorphous solid state disaccharides, paying particular
attention to -1-1 linkage of trehalose, to -1,4 linkage between pyranose rings (lactose) and
to linkage implying a furanose ring (sucrose). The combination of molecular mechanics with
DFT/GIAO ab-initio methods provides reliable structural information on the conformational
distribution in the glass. The results are interpreted in terms of an enhanced flexibility that
trehalose experiences in amorphous solid state compared to the other sugars. An attempt to
relate this property to the balance between intra- and inter-molecular hydrogen bonding
network in the glass is presented.

PACS : 61.43.Bn, 61.18.-Fs , 76.60.Cq

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Introduction


The general understanding of the local structure of inorganic amorphous states, like
metallic or oxide glasses, has progressed through giant steps in the last decades, both on the
experimental and theoretical fronts [1-3]. Due to the rather simple form of the elementary unit
in those systems, the details of the local structure can often be very accurately described using
a coordination shell image, and most of the information can be revealed through radial pair-
distribution functions, or their reciprocal counterpart (structure factor) which is accessible
through neutron or x-ray diffraction experiments. This approach rapidly reveals to be
incomplete when molecular dissymmetry or specific and directional interactions like
hydrogen bonding are present. Building a correct structural model of disordered hydrogen-
bonded networks remains today a fascinating challenge. As the archetype system, studies on
water are innumerable (see for example [4-8]). Other hydrogen-bonded glasses like protein
networks, polyalcohols or saccharides have also recently raised considerable interest, since
they meet the frontiers of biophysics, food, pharmacy, and materials science [9, 10]. The rich
complexity of carbohydrate systems compared to model atomic glasses originates from their
large number of intramolecular degrees of freedom. These coordinates necessarily affect the
dynamic properties of the compound near its glass transition, often conferring a fragile
character to the structural relaxation of the glass former [11] and also making the description
of the glass structure a very complicated task. Only very recently, local investigation
techniques like nuclear magnetic resonance (NMR) or numerical experiments by molecular
dynamics (MD) have been proved to be very useful in [12-14].

The special case of disaccharides deserves a particular attention, for which a relatively
small number of geometrical parameters are suspected to give a reasonable picture of their
intramolecular energy landscape [13-18], conferring emphasis to the stereochemistry of these

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compounds. Within this family of carbohydrates, trehalose has focused considerable interest,
mainly because of its exceptional biopreservation properties, with a mechanism that still
remains an open question at the molecular level [19-22]. The same sugar has also been
proposed as a model hydrogen-bond network well described by the axiomatic theory of
ideally glassy network developed by Phillips and co-workers [9, 10]. Molecular modelling by
empirical force-fields is a well adapted technique to explore the conformational properties of
carbohydrates [13, 16, 17, 23-27]. For many species, the large number of parameters that
define the molecular geometry give raise to complicated high dimensional energy maps.
These maps often present several potential wells, that correspond to different preferred
conformations, and the question whether the calculated conformations are actually populated
or not in solution and in pure disordered phases is still a matter of debate [13, 14, 27, 28]. The
comparison of these numerical simulations with experiment is therefore a very important and
demanding step, where local techniques like NMR already prove to be determinant [12, 18,
29, 30].

The aim of the present work is to analyse and compare the conformational space that is
actually accessible to three homologous sugars (trehalose, sucrose and lactose) in their
respective pure amorphous phases. The general method relies on the comparison between the
preferred molecular geometries predicted by classical mechanics via empirical force-fields,
and the actual distribution of conformations that is observed by 13C solid state NMR on
amorphous samples. The scientific background of the method and the simulation set-up have
been discussed in detail elsewhere [18]. After a brief description of the experimental and
computational conditions (section 2), we detail the results obtained by 13C CPMAS NMR
experiments. We then report the results of the simulations, which are then discussed in
relation to the balance between intra- and inter-molecular interactions, and their influence on
the local structure of the hydrogen-bonded glassy network.

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Experiments and methods


Samples. Anhydrous ,-trehalose (T), stable anhydrous -lactose and sucrose
crystalline powders were purchased (Sigma-Aldrich) and used without further purification.
The amorphous samples were obtained by ball-milling 1g of crystalline sugar during 30 hours
under dry nitrogen atmosphere in a planetary grinder PULVERISETTE 7 (Fritsch, inc.). A
DSC thermogram was recorded after grinding in order to check the total character of the
amorphization, and the glassy character of the obtained amorphous sample.


NMR Experiments. The 13C CPMAS experiments were carried out at 100.6 MHz on a
Bruker AV400 solid-state NMR spectrometer. Linear amplitude modulation of the rf field
during the contact pulse (typ. 2 ms), and tppm heteronuclear decoupling during acquisition
were employed. Recycle delays ranging between 200 and 450 s were used. Rotation speed
was set to 5 kHz. A standard digital filter was used for acquisition, and the spectra were
obtained by simple Fourier transform of the induction decay, without data apodization.


Molecular modelling. Molecular modelling was achieved using the Hyperchem Pro 7
(Hypercube, Inc.) software package. Conformations were generated by relaxing all the
degrees of freedom but constraining the two dihedral angles  and , as defined for trehalose,
lactose and sucrose in Table 1. For fixed  and , all other conformational degrees of freedom
were optimized using the molecular mechanics package provided in Hyperchem, including
equivalent implementations of the AMBER and CHARMM empirical force fields. The
parameters version used will be denoted in the text by BIO85 (Reiher, [31]). In order to take

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into account a mean-field contribution of the surrounding molecules in a condensed matter
sample, a standard screening procedure of coulomb interaction was used, through an effective
scaled dielectric constant. The 1-4 Scale Factors were equilibrated between Coulomb and Van
der Waals interactions.

Conformational energy maps. All calculations were started from the molecular
coordinates obtained by the single crystal structure determination on anhydrous trehalose (T)
[32], lactose monohydrate (LH2O) [33] and sucrose [34]. Each of these crystal structures was
relaxed by molecular mechanics in order to define the lowest energy molecular conformation
(LMC) in the BIO85 force field. For each sugar, an adiabatic Ramachandran map E(,) was
calculated by classically mapping the whole (,) space by 324 points separated by 20° steps
[12, 30, 35]. For each (,) point in the map, the  and  values were set starting from the
LMC coordinates, and then were restrained by setting a high value of dihedral angle spring
constants. All other degrees of freedom were then relaxed using the BIO85 force field
parameters.

Isotropic 13C chemical shift maps. NMR chemical shift calculations were carried out for
each studied disaccharide on the previous 324 relaxed conformations generated by molecular
mechanics. For each conformation, the isotropic magnetic shielding of each carbon of the
sugar was evaluated using the GIAO method on a density functional theory (B3PW91) with
the 3-21+G** basis, as implemented in the Gaussian 03 software (Gaussian, Inc.) [36]. The
324 single point calculations resulted for each sugar in two magnetic shielding maps, that
were converted into chemical shift maps (Cx,,) and (Cy,,), where Cx and Cy represent
the two carbons involved in the glycosidic bond of the disaccharide. The conversion from
rough magnetic shielding to chemical shift comparable to the experiment was carried out by

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simple linear transformation
BSA
calc 
.
.

, where the A and B coefficients are given in Table
2.

Simulation of the CPMAS spectrum. The scientific background leading to the
formulation of the simulated S() CPMAS spectrum was presented and discussed in detail
elsewhere [18]. The numerical evaluation of S() requires integration of constant chemical
shift contours in the map (Cx,,), using equation (1).


 




,
,
.
,
S d d
 
  



 
  
  



(1)



In this equation, (,) represents the probability density of occupation of a given
molecular conformation (,) [18]. This function (,) thoroughly carries the structural
information that can be extracted out of the modelling of the NMR spectrum. The actual
resolution of this map is limited in the present work to 20° angular steps. In order to smooth
the integration contour, cubic spline interpolation was used. The simulated CPMAS spectrum
S() was then evaluated by sampling 1024 different  values, each one corresponding to one
numerical integration over an interpolated (Cx,,)= contour, evaluated by standard
Romberg method. The gradient term in Eq. (1) was calculated by finite difference
approximation using ==0.01° angular steps.

The last step of data processing is the convolution of S() with a lorentzian function, in
order to account for the homogeneous CPMAS linewidth. This was achieved by inverse
Fourier Transform of S() to a free induction decay S(t), then multiplication of S(t) by an
exponential function and back Fourier Transform to S(). A typical line broadening imposed
in this work was 1 ppm HWHM.

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13C CPMAS Spectra


The Figure 1 compares the CPMAS spectra of crystalline and amorphous forms of three
disaccharides. In all cases, the particular resonances assigned to the two carbons linked to the
bridging oxygen are marked.

The spectral feature common to the three sugars in the amorphous state is the relevant
broadening of all NMR signals. These distributions of isotropic chemical shifts reflect the
underlying distributions of molecular conformations in the glass, which largely rely upon the
changes in the glycosidic dihedral angles. For the glycosidic carbons, the observed chemical
shift distributions spread over about 10 ppm for sucrose and lactose. For trehalose, it is highly
asymmetric, tails downfield, and extends over more than 15 ppm. This particularity would
suggest that the trehalose molecules experience enhanced flexibility in the glass compared to
the other disaccharides, if the chemical shift maps are similar. Another remarkable point for
the three sugars is that the NMR spectrum of the amorphous states does not completely
envelope that of their respective crystalline states. This is especially noticeable for the
glycosidic carbons of lactose and sucrose, for which the maxima of the chemical shift
distributions do not coincide with the NMR lines of the crystal. For lactose, we observe an
upfield shift of the NMR distributions, particularly important for the glucose residue C’4
resonance. For sucrose, the observed shift is downfield. For trehalose, this effect is not
pronounced, and the maximum of the distribution in the glass exactly corresponds to one of
the C1/C’1 resonances of the T crystal. These observations support the idea that the most
probable molecular conformation in the glassy state is different, at least for lactose and
sucrose, from the one observed in the crystalline form.

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Simulations


This section illustrates the steps leading to the simulations of the CPMAS spectra. First,
the relaxed molecular conformations are generated by molecular mechanics, minimizing the
corresponding potential energy surfaces E(,), for each pair (,). Then, for each
conformations the corresponding (Cx,,) maps for the glycosidic carbons are calculated.

Energy and Chemical shift surfaces

Figure 2 presents the potential energy maps obtained by relaxing a single molecule
(starting form the conformation of the molecule in the crystal) by CHARMM-type molecular
mechanics with the BIO85 parameters. Rather that the global minimum, here the minimum
energy conformation of the molecule constrained in each given , pair is searched. Only the
region of the map around the lowest energy basin is shown. It appears clearly from Table 3
that the preferred conformation of lactose and sucrose in the crystal is not located in the centre
of the region with the lowest energy but differs significantly from the calculated one
(although still in the low energy basin). It clearly means that the single molecule geometry is
affected by the intermolecular interactions in the crystalline field, in the order lactose >
sucrose > trehalose. At least qualitatively, this difference accounts for the shifts observed in
Figure 1 between the spectra for amorphous and crystalline disaccharides. One may wonder
whether the information provided by the comparison between NMR data for amorphous and
crystalline forms and that obtained by the conformational energy maps provide any hints
about the validity of the computational procedure.
Single molecule approach should be considered simplistic as it neglects the potential mean
field generated by the random distribution of other sugar molecules. Undoubtedly,

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intermolecular interactions, which are relevant in the periodic crystalline field, may have less
significance in a merely statistical distribution. Furthermore, slow dynamics averages may
hamper the effectiveness of the calculation, while the difference in the internal conformational
population may result less significant.

In the case of trehalose the calculated and crystallographic torsional angles defining the
geometry of the glycosidic bond remain close together. These observations are consistent with
the analysis of the experimental NMR spectra, and suggest that a structural description of
amorphous forms of disaccharides based only on single molecule properties could be valid in
a first order approximation.

Following this hypothesis, the simulation of the CPMAS spectra was carried out based on
such a single molecule approach.

Figure 3 shows the chemical shift surfaces, calculated over the molecular conformations
shown in the E(,) maps. As a consequence of the molecular symmetry of trehalose, the
equivalence E(,)=E(,)T and (C1,,)= (C’1,,)T are evident in Figures 3 and 4. This
characteristic property has been profitably used to average the small fluctuations of the
calculations.


Results and discussion


Figure 4 presents the simulated regions of the CPMAS spectra corresponding to the
glycosidic carbons of ,-trehalose, -lactose and sucrose. Simulations were carried out
according to equation 1, and calculated over the contours of the chemical shift maps presented
in

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Figure 3 by using the appropriate (,) functions. Two different forms of the (,)
molecular conformational probability were tested. First, a Boltzmann partition on the E(,)
maps presented in Figure 2 has been assumed, see equation (2), by using the the temperature
TB as an adjustable parameter for fitting:





RT

,
, exp
.B
E
 
  







(2)

A second procedure assumed a Gaussian partition of conformations, with maximum centred
on (g,g) and width parameters  and  defined by equation (3):




22
22
, exp
22
gg
 



  











(3)

where g, g, and  =  were adjustable parameters for the simulations. This second
procedure was included to formulate a set of “equivalent” energy basins that provides the
quantitative comparison for flexibility.


As shown in Figure 4, the simulations with Boltzmann populations (,) of the E(,)
maps (Figure 2), i.e. with reference to a single molecule energy landscape model, poorly
describe the experimental data, except in the case of trehalose. However, a very large
temperature value had to be assumed in the equation (2) for this system. We shall return to
this point in the discussion. It has been already showed [18] that the most important parameter
in those calculations is rather the position of (,) than its very detailed shape. As a
consequence, simulations seem to indicate that either the conformational populations resulting

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from molecular mechanics modelling or the chemical shift surfaces contain approximation.
Given the procedure followed which assigns the highest accuracy to the calculation of the
(Cx,,) maps, attempts have been made to search for a more effective fit of the chemical
shift distributions by adjusting the energy maps. As a matter of fact, although the obvious
choice would have been a novel, but time consuming, calculation including the potential mean
field generated by the random distribution of other sugar molecules, a satisfactory agreement
between experiments and calculations were obtained by using a simple gaussian
conformational occupation (,), slightly shifted apart from the minima of E(,), as
reported in Table 4. Although not necessarily realistic, this result once more reveals the great
influence of the highest probability region on the (Cx,,) map. With such artificial
conformational distribution a good description of the experimental line shapes is obtained,
except for the lactose C’4 NMR line.

At this point, it is instructive to compare the angular features of the conformational states
that provide a reasonable fit to the experimental NMR chemical shift data (compare Table 3
and Table 4). The best-fit gaussian minima remain close to the energy minima of the single
molecule E(,) maps, and are therefore significantly shifted apart from the conformations
observed in the crystalline forms. It is interesting to note that the most important angular
shifts do correspond to the most important shifts observed in the NMR spectra for amorphous
and crystal states, respectively. As an example, g=-10° for amorphous sucrose compared to a
c=-44.8° in the crystal, and it corresponds to an important shift in the CPMAS spectrum for
the C’2 fructose carbon. On the other hand, still for sucrose, the angle  seems less affected
(g=100°, c=107.8°) by amorphization, and correlatively, no important shift is evidenced in
the NMR spectrum assigned to the glucose C1 carbon. Similar angular and NMR shifts are
also observed for lactose, but the poor quality of the best-fit obtained for the C’4 glucose
carbon prevents any conclusive quantitative results for this sugar.

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This observation confirms the hypothesis made on the basis of the scrutiny of the
experimental spectra. In other words, the average molecular conformation of disaccharides in
glassy state is closer to a single molecule property than to that of the corresponding crystalline
form, where long-range interactions prevail. This rather trivial observation should however be
counterbalanced by noticing that the single molecule image is valid as a first approach, but is
obviously not sufficient to completely account for the actual experimental CPMAS spectra of
the glasses. While the (Cx,,) surface can confidently be assumed to be an intramolecular
property, this is not true anymore for the (,) conformational occupation probability
density, that can be influenced by long range interactions. As a consequence, a suitably
“fitted” gaussian (,) gives better results than the probability function provided by force-
field based intramolecular E(,) .

Another result of our simulations is the relevant difference between the relative width of
the (,) functions for trehalose and the other sugars. As reported in Table 4, and illustrated
in Figure 4, the standard deviation of the probability curves for  and  torsional angles is as
large as 50° for trehalose, and about 20° for lactose and sucrose. A similar conclusion has also
been reached by using the Boltzmann probability function based on the calculated E(,)
surface, for which a quite unrealistic high temperature of 1800 K had to be adopted for
trehalose (Table 4). Therefore, both the gaussian and the Boltzmann fits suggest that the
conformational space explored by trehalose molecules in the amorphous phase should be
larger than that calculated for the other two sugars, as well as for the single trehalose
molecule. At a second order level, as already discussed in the previous paper [12, 18] and
mentioned in another study on model trehalose molecule [12, 18] the unrealistic temperature
value that has to be assumed suggests that a pure single molecule energy landscape model is
not correct in case of amorphous trehalose, and that border-conformations in the higher
energy regions could be equally made accessible.

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On the basis of the convergent evidence, this result should be considered as model-
independent, and mainly of intramolecular origin. Indeed, it is easily recognised that
intramolecular hydrogen bonds are present in the crystal forms as well in solution of both
lactose and sucrose [32-34, 37, 38], while these interactions are mostly absent in ,-
trehalose [32-34, 37, 38]. Our work therefore suggests that these intramolecular hydrogen
bonds persist in glassy lactose and sucrose, stabilizing the molecular conformations close to
the most probable one, while the intramolecular interactions that stabilize the single trehalose
molecule may be easily balanced by the surrounding interactions providing comparatively
enhanced flexibility around its glycosidic bond. Higher flexibility of trehalose in comparison
with maltose and sucrose has also been deduced by Lerbret et al. [39] on the basis of
molecular dynamics simulations of water solutions of these disaccharides.

To further explore and possibly corroborate the above reported idea, resort is made to an
implicit concept that is beyond the influence of the surrounding random molecules on the
intramolecular potential. Indeed, Scopigno et al. [40] found a correlation between the fragility
of a glass-forming liquid, m, and the temperature coefficient of the non-ergodicity factor, f,
given in the relation:




1
0,1
g
T
T
fQT


  
(4)



This factor, in the low T limit, is related to the vibrational properties of the glassy
dynamics. In other words, Scopigno et al. claim that properties deriving from the curvature of
the potential energy landscape are related to properties deriving from the viscosity increase
upon super cooling [41]. They have found experimentally that the parameter  is proportional
to the fragility m usually defined as

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
1
log( )
T
T

g
T
T
g
m








(5)

Moreover, in a recent paper [41], Bordat et al. have reproduced numerically the
proportionality between  and m and have demonstrated that a large fragility is correlated to
the increase of anharmonicity and capacity for intermolecular coupling of the potential
describing the interactions within the system considered.

Whether this correlation is a very general property of all materials or confined to
“flexible” and “sticky” molecules like H-bond rich polyols is to be clarified. In our context,
however, this parallel implies that, at least for homologous molecules, the change in the -
 values points to both the fragility and the non-ergodicity factor. The exploitation of this
point is given in Figure 5, where the evolution of the inverse non-ergodicity parameter
 ), 0
1
TQf


obtained from MD simulations of glassy trehalose and sucrose is plotted as a
function of the temperature scaled to the glass transition temperature, Tg (see ref [42] for
details).

The two curves of Figure 5 can be fitted according to equation (4) in the very low
temperature domain, well below Tg, to get =0.3582 and 0.1718 for trehalose and sucrose
respectively.

Therefore, we can state that the larger fragility of the trehalose glass compared to the
sucrose glass is a signature of enhanced intermolecular interactions. These enhanced
intermolecular interactions take place in anharmonic potentials favouring then the flexibility
of trehalose. So, a similar conclusion is reached on the flexibility of trehalose and its
intermolecular coupling with surrounding molecules on the basis of different independent
approaches, experimental NMR and simulations data, MD simulation [23, 39] and fragility
analysis [41]. At that stage, it should be very interesting to compare the results of the present

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study to models that take into account the cooperativity in such glassy hydrogen-bonding
networks at a longer length scale. In that sense, the tandem bilayer model proposed by Phillips
[10] for trehalose is one of the possible sketches that are compatible with our experimental
and simulation data.
Some other comments appear also necessary as far as it concerns the bioprotectant role
of trehalose, that is the main reason for the converging interest in the properties of this
molecule. Even not going to the several hypotheses made along the last years, the central
question lies in the evolution of the intermolecular interactions that trehalose is able to
develop upon increasing concentration from the dilute or semi-dilute solution to the
eventually formed solid state surrounding the biosystems to be protected. All findings from
dilute and semi-dilute solutions support a privileged interaction between sugar (trehalose in
particular) and water, by displacing the “water-like structure” in favor of a “sugar-solvation
structure” [26, 39]. Average conformational fluctuations around glycosidic dihedral angles for
different solution composition at 200 K show little variance within the energy basin leading
Sokolov et al [42] to argue little influence of intramolecular hydrogen bondings on the
dynamics of the system. This work provides also a reinterpretation of the “folding” of
trehalose onto a biomolecule and substituting water molecules during drying by rearranging
its conformation [43]. However, the presence of at least one water molecule strongly bound to
trehalose molecule in solution and in hydrated mixtures seems univocally assessed by several
experimental and computational investigations. Although it has been previously suggested a
possible pathway in the mechanism by which water hydration is substituted by sugar-sugar
interaction [22], unfortunately, the consequence of this behaviour in the formation of the
anhydrous sugar phase has not been fully exploited.
On the molecular level, fast rotational motions and higher vOH at Tg have been taken as
indication that trehalose glass is less densely packed than sucrose glass, although these