Reference interaction site model study on the anomeric equilibrium of D-glucose in aqueous solution
The anomeric equilibrium of D-glucose in aqueous solution was studied by the extended reference interaction site model (XRISM) theory. In this study, all of the rotational degrees of freedom were considered upon the exocyclic hydroxyl and hydroxymethyl groups, namely 729 stereoisomers for each anome...
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irk-123456789-1187072017-06-01T03:04:38Z Reference interaction site model study on the anomeric equilibrium of D-glucose in aqueous solution Miyata, T. The anomeric equilibrium of D-glucose in aqueous solution was studied by the extended reference interaction site model (XRISM) theory. In this study, all of the rotational degrees of freedom were considered upon the exocyclic hydroxyl and hydroxymethyl groups, namely 729 stereoisomers for each anomer. The free energy differences between the α and β anomers were calculated from partition functions. The XRISM theory predicts that β-D-glucose is more stable in aqueous solution than α-D-glucose, which agrees with an experimental result qualitatively. It is found that the solvation free energy stabilizes the β anomer more preferably than α, and that the intramolecular electrostatic energy of the β anomer in solution is remarkably higher than that of α. The β anomer in aqueous solution would favor an interaction with water molecules through hydrogen bonds, compared to the α anomer. В рамках розширеної теорiї базисних силових центрiв (XRISM) вивчається аномерична рiвновага D-глюкози у водних розчинах. В цих дослiдженнях всi обертовi ступенi вiльностi розглядаються для ексоциклiчних гiдроксильних та гiдроксометильних груп, зокрема 729 стереоiзомерiв для кожного аномера. Рiзницi вiльних енергiй α та β аномерiв розраховуються на основi функцiй розподiлу. XRISM теорiя передбачає, що β-D-глюкоза є стабiльнiшою у водному розчинi нiж α-D-глюкоза, що якiсно узгоджується з експериментальними даними. Встановлено, що вiльна енергiя сольватацiї краще стабiлiзує β-аномер нiж α-аномер та що внутрiмолекулярна електростатична енергiя β-аномеру в розчинi значно вища нiж у випадку -аномеру. β-аномер у водному розчинi є бiльш схильним до взаємодiї з молекулами води через водневi зв’язки, порiвняно з α-аномером. 2007 Article Reference interaction site model study on the anomeric equilibrium of D-glucose in aqueous solution / T. Miyata // Condensed Matter Physics. — 2007. — Т. 10, № 3(51). — С. 433-439. — Бібліогр.: 19 назв. — англ. 1607-324X PACS: 82.60.-s, 82.60.Lf, 05.20.-y DOI:10.5488/CMP.10.3.433 http://dspace.nbuv.gov.ua/handle/123456789/118707 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
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The anomeric equilibrium of D-glucose in aqueous solution was studied by the extended reference interaction site model (XRISM) theory. In this study, all of the rotational degrees of freedom were considered upon the exocyclic hydroxyl and hydroxymethyl groups, namely 729 stereoisomers for each anomer. The free energy differences between the α and β anomers were calculated from partition functions. The XRISM theory predicts
that β-D-glucose is more stable in aqueous solution than α-D-glucose, which agrees with an experimental result qualitatively. It is found that the solvation free energy stabilizes the β anomer more preferably than α, and that the intramolecular electrostatic energy of the β anomer in solution is remarkably higher than that of α.
The β anomer in aqueous solution would favor an interaction with water molecules through hydrogen bonds, compared to the α anomer. |
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Miyata, T. |
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Miyata, T. Reference interaction site model study on the anomeric equilibrium of D-glucose in aqueous solution Condensed Matter Physics |
| author_facet |
Miyata, T. |
| author_sort |
Miyata, T. |
| title |
Reference interaction site model study on the anomeric equilibrium of D-glucose in aqueous solution |
| title_short |
Reference interaction site model study on the anomeric equilibrium of D-glucose in aqueous solution |
| title_full |
Reference interaction site model study on the anomeric equilibrium of D-glucose in aqueous solution |
| title_fullStr |
Reference interaction site model study on the anomeric equilibrium of D-glucose in aqueous solution |
| title_full_unstemmed |
Reference interaction site model study on the anomeric equilibrium of D-glucose in aqueous solution |
| title_sort |
reference interaction site model study on the anomeric equilibrium of d-glucose in aqueous solution |
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Інститут фізики конденсованих систем НАН України |
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2007 |
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http://dspace.nbuv.gov.ua/handle/123456789/118707 |
| citation_txt |
Reference interaction site model study on the anomeric equilibrium of D-glucose in aqueous solution / T. Miyata // Condensed Matter Physics. — 2007. — Т. 10, № 3(51). — С. 433-439. — Бібліогр.: 19 назв. — англ. |
| series |
Condensed Matter Physics |
| work_keys_str_mv |
AT miyatat referenceinteractionsitemodelstudyontheanomericequilibriumofdglucoseinaqueoussolution |
| first_indexed |
2025-07-08T14:29:48Z |
| last_indexed |
2025-07-08T14:29:48Z |
| _version_ |
1837089428385824768 |
| fulltext |
Condensed Matter Physics 2007, Vol. 10, No 3(51), pp. 433–439
Reference interaction site model study on the anomeric
equilibrium of D-glucose in aqueous solution
T.Miyata
Institute for Molecular Science, 38 Nishigo-Naka, Myodaiji, Okazaki, Aichi 444–8585, Japan
Received May 30, 2007, in final form July 3, 2007
The anomeric equilibrium of D-glucose in aqueous solution was studied by the extended reference interaction
site model (XRISM) theory. In this study, all of the rotational degrees of freedom were considered upon the
exocyclic hydroxyl and hydroxymethyl groups, namely 729 stereoisomers for each anomer. The free energy
differences between the α and β anomers were calculated from partition functions. The XRISM theory predicts
that β-D-glucose is more stable in aqueous solution than α-D-glucose, which agrees with an experimental
result qualitatively. It is found that the solvation free energy stabilizes the β anomer more preferably than α,
and that the intramolecular electrostatic energy of the β anomer in solution is remarkably higher than that of α.
The β anomer in aqueous solution would favor an interaction with water molecules through hydrogen bonds,
compared to the α anomer.
Key words: RISM theory, D-glucose, anomeric equilibrium, aqueous solution, free energy
PACS: 82.60.-s, 82.60.Lf, 05.20.-y
1. Introduction
Saccharides play a variety of important roles in a biological system, such as metabolism and bio-
logical recognition [1]. The structural information on saccharides is the basis for understanding their
functions. The most important experimental techniques to analyze the conformation of saccharides
are X-ray crystal structure analysis and NMR [1]. In particular, the latter has a great advantage in
investigating the conformation of saccharides in solution. Theoretical and/or computational studies
regarding conformations of saccharides have also been reported [2], where much attention is still
focused on monosaccharides such as D-glucose [3–7], D-mannose [8] and D-xylose [9,10] as well as
oligosaccharides [11,12].
The computational schemes used in studying the saccharides have been mainly quantum me-
chanical (QM) calculations [4,6,12] and molecular simulations [3,5,7–11] that have included solvent
effects to model solutions, which are of biological interest. In describing the solvent environment
in the above methods, continuum solvent models [4,8] or explicit solvents [3,5–7,9–12] have been
employed. In a continuum solvent model, microscopic details of solvation structure are entirely
neglected, and additional macroscopic parameters must be introduced to describe a solvent envi-
ronment. In an explicit solvent model, on the other hand, numerical results are contaminated by
statistical errors originating from a finite sampling number since solvent configurations must be
statistically averaged. Since the energetic differences among the lowest and other local-minimum
energy conformations of a saccharide molecule are generally very small [1], a computational analysis
of the thermodynamic stability (or conformational stability) of saccharides requires both an accu-
rate method and a consideration of many candidate conformations at the same time. In practice,
this is a very demanding task, especially in solution. This fact makes it difficult to study saccha-
rides based on computational chemical approaches at an atomistic level. As a consequence, even
monosaccharides, which are the simplest in structure among saccharides, are still active objects to
attract many researchers in the field of computational chemistry.
One of the promising methodologies of studying the conformations of saccharides in solution
is the reference interaction site model (RISM) theory [13], which is an integral equation theory
based on statistical mechanics. The RISM theory gives not only a solvation structure around solute
c© T.Miyata 433
T.Miyata
molecules but also a solvation free energy, which is needed when discussing a thermodynamic stabi-
lity. It should also be noted that the RISM theory is free from any statistical errors. Therefore, the
RISM theory is expected to be advantageous in studying the thermodynamic stability of saccharides
in solution. Up till now, no application of the RISM theory to the “true” saccharide molecules has
been reported. The only example that has been reported so far is its application to 4,6-dimethyl-
2-methoxytetrahydropyran, which was studied as a simple model material of monosaccharides by
Maw et al. [14].
We studied the anomeric equilibrium of D-glucose in aqueous solution using the RISM theory,
as a first step to investigate thermodynamic stabilities of saccharides. The anomeric equilibrium
of D-glucose is one of the major subjects that is intensively investigated [3–5,15]. The physical
quantity that determines the anomeric equilibrium in solution is the free energy difference between
solvated α-D-glucose and β-D-glucose. The simplest expectation based on the geometry is that the
hydrogen-bonding capacity of the anomeric hydroxyl group of β-D-glucose with surrounding water
is relatively high since it is in an equatorial form, which directs toward a relatively open space
from the pyranose ring. On the other hand, the anomeric hydroxyl group of α-D-glucose takes an
axial form, and consequently accesses of water molecules to the group may be relatively hindered
by the rest of the pyranose ring compared to the β anomer [3,6,16]. This paper discusses the
free energy difference between α-D-glucose and β-D-glucose in aqueous solution calculated by the
RISM theory, in comparison with the experimental data. Comparisons of our results with the other
computational methods such as quantum mechanics and molecular simulations are also reported.
2. Method
2.1. Free energy calculation
Figure 1 shows typical molecular shapes of (a) α-D-glucose and (b) β-D-glucose, respectively. In
molecular simulations, free energy perturbation (FEP), thermodynamic integration (TI), locally
enhanced sampling (LES), and so on have been used in order to calculate the free energy difference
between α-D-glucose and β-D-glucose in solution [3,5]. Alternatively, we evaluated the free energy
Figure 1. Molecular shapes of (a) α-D-glucose and (b) β-D-glucose, respectively. Black, gray,
and white spheres represent oxygen, carbon, and hydrogen atoms, respectively. The forms of
pyranose ring depicted in the figures are 4C1 chair structures (see the text).
difference ∆Gα→β via the partition function of aqueous solution of each anomer at an infinite
dilution limit. The formulae we used are as follows:
∆Gα→β = kBT ln(Qα/Qβ), (1)
Qα ≈
∑
i
exp[−(EC,i + ∆µS,i)/kBT ], (2)
434
RISM study on anomeric equilibrium of glucose
where kB, T , Q, EC,i, ∆µS,i represent the Boltzmann constant, temperature, partition function,
conformational energy (i.e. intramolecular interaction energy of solute molecule), and solvation
free energy, respectively. When evaluating the free energy difference in gas phase between both
anomers, a similar strategy to the equations (1) and (2) was used in the past [5]. In our method,
the solvation free energy ∆µS,i is calculated using the RISM theory (See the next section for the
details of the RISM theory). The index, i, seen in the equation (2) identifies the conformation
sampled discretely in the conformational space. Note that the summation in the equation (2) is
taken over all the conformations sampled for the corresponding anomer. Moreover, EC,i + ∆µS,i
is a potential of mean force: it should be noted that the exponential function form that appeared
in the equation (2) is obtained merely by an “incomplete” integration of the original configuration
integral, where the integration should be performed only for the degrees of freedom on the solvent
molecules (The derivation process can be found in the reference [13]).
In what follows, we describe the conformations considered in this study, which are related to the
summation in the equation (2). The intramolecular degrees of freedom of D-glucopyranose include
the forms of pyranose ring (i.e. puckering), vibrations on each bond length and on each angle, the
rotational freedom around the C–C bond of the exocyclic hydroxymethyl group (hereafter, this
bond is referred to as C5–C6 bond), and the rotational freedom of five exocyclic hydroxyl groups
(hereafter, the bonds corresponding to this freedom are referred to as C–O bond). Concerning
the forms of pyranose ring, the 4C1 chair structure is known to be the most stable among the
forms of D-glucopyranose ring: for instance, it was reported that the free energy of the 4C1 chair
structure of β-D-glucopyranose is lower than that of 1C4 chair form by as much as 8 kcal/mol,
which was evaluated by a quantum mechanical calculation [17]. In this work, we considered only
the 4C1 chair form, and the other ring forms were not treated since they are expected to be
insignificant in the analysis of thermodynamic stability of D-glucose. All the vibrational degrees
of freedom were frozen in this study, related with the bond lengths and angles. We considered
the remaining rotational degrees of freedom around the C5–C6 bond and five C–O bonds, which
become six degrees of freedom in total. Since each rotational degree of freedom produces three
stable rotamers, i.e. gauche-trans conformers, the final number of conformations we treated for
each anomer is 36 = 729: that is, in the equation (2), the summation was taken over 729 conformers
for each anomer.
2.2. RISM theory
In the evaluation of solvation free energy, an extended reference interaction site model (XRISM)
integral equation was employed in this study. The details of the XRISM theory have been described
elsewhere [13]. Here, we show only basic equations. The XRISM integral equation for solute-solvent
correlation functions reads
huv
αγ(r) =
∑
η
∑
ν
wuu
αη ∗ cuv
ην ∗ χvv
νγ(r), (3)
where h, c, w are the total correlation function, the direct correlation function and the intramolec-
ular correlation function, respectively. χ represents the pure solvent site density pair correlation
function, and is evaluated from the dielectrically consistent RISM (or DRISM) theory (DRISM
formalism can be found in [13] and references therein). “u” and “v” stand for solute and solvent,
respectively. The asterisk, ∗, represents the convolution integral. The equation (3) can be solved
with coupling the closure equations. We used the HNC closure and the KH closure, which are given
by the equations (4) and (5), respectively [13]: namely,
1 + huv
αγ(r) = exp
[
−βuuv
αγ(r) + huv
αγ(r) − cuv
αγ(r)
]
, (4)
and
1 + huv
αγ(r) =
{
exp[duv
αγ(r)] for duv
αγ(r) 6 0,
1 + duv
αγ(r) for duv
αγ(r) > 0,
duv
αγ(r) = −βuuv
αγ(r) + huv
αγ(r) − cuv
αγ(r).
(5)
435
T.Miyata
Here, uuv
αγ(r) is the interaction potential energy, and β is defined as β = 1/kBT . Hereafter, the
coupling between the equations (3) and (4) is referred to as the XRISM/HNC theory, and that
between (3) and (5) as the XRISM/KH theory, respectively.
The solvation free energy for the XRISM/HNC theory and that for the XRISM/KH theory are
expressed by the equations (6) and (7), respectively [13]:
∆µHNC
S = −kBT
∑
α
∑
γ
4πργ
∫
dr
[
cuv
αγ(r) −
1
2
huv
αγ(r)2 +
1
2
huv
αγ(r)cuv
αγ(r)
]
, (6)
and
∆µKH
S = −kBT
∑
α
∑
γ
4πργ
∫
dr
[
cuv
αγ(r) −
1
2
Θ
(
−huv
αγ(r)
)
huv
αγ(r)2 +
1
2
huv
αγ(r)cuv
αγ(r)
]
, (7)
where ργ represents the solvent site density, and Θ(x) is the Heaviside step function. The solvation
free energy is calculated for each conformer from equations (6) or (7), and substituted into the
equation (2).
2.3. Computational details
Both the conformational energy and the solvation free energy were calculated for 729 conformers
in each anomer, molecular structures of which can be searched by rotating C5–C6 bond and five
C–O bonds one by one with the grid size of 120◦. Then, they were substituted into the equation (2).
For the calculation of conformational energy of D-glucose, OPLS-AA parameters [18] were used.
As to the solvent water, SPC/E model [19] was employed. The temperature was set as 298.15
K. The number of grid points and the grid separation we used are 512 and 0.05Å, respectively.
The convergence of the XRISM calculation was accelerated by means of the MDIIS [13]. In this
study, both the XRISM/HNC theory and the XRISM/KH theory were numerically solved 1458
times, which corresponds to two anomers, and all calculations were converged without using the
techniques such as “charge up” or “temperature lowering.”
3. Results and discussion
Table 1 shows the free energy differences ∆Gα→β between α-D-glucose and β-D-glucose in
aqueous solution calculated on the basis of the XRISM/HNC and XRISM/KH theories. Here,
∆Gα→β indicates the free energy change when an α-D-glucose is transformed into a β-D-glucose, as
can be seen from the equation (1). The free energy difference in gas phase is also shown in table 1,
which was evaluated by the same procedure as equations (1) and (2) except for the assumption of
∆µS,i = 0 in the equation (2). Experimental data and the other computational results reported to
date are also listed in table 1. The difference between the XRISM/HNC theory and the XRISM/KH
theory was insignificant with regard to the free energy difference. The XRISM theory combined
with the equations (1) and (2) predicts that the β anomer is more stable than α in aqueous
solution. This result agrees with the experimental data qualitatively [15]. However, the present
method overestimated the magnitude of the free energy difference in aqueous solution (i.e. the
relative stability of the β anomer) by about 1.3 kcal/mol, compared with the experimental data.
In gas phase, the β anomer was predicted to be more stable than α, which is contrary to the
quantum mechanical result by Barrows et al. [4] and the one of molecular dynamics simulation by
Simmerling et al. [5]. As an integral tendency, our method overestimated the relative stability of the
β-D-glucose. We shall point out, nevertheless, that the difference between ∆Gα→β in gas phase and
that in solution is about 1.0 kcal/mol in our study, which is close to the results reported by Barrows
et al. (i.e. 0.6 kcal/mol) [4] and Simmerling et al. (i.e. 0.98 kcal/mol) [5]. This fact implies that
the solvation effect itself can be treated with a satisfactory accuracy in our calculation. Therefore,
the above overestimation observed in our study may be attributed to an incomplete sampling
in the conformational space, e.g. a lack of vibrational flexibilities of D-glucose. There remain the
436
RISM study on anomeric equilibrium of glucose
Table 1. Free energy difference [kcal/mol] between α-D-glucose and β-D-glucose. The values are
in the form of a free energy change when an α-D-glucose is transformed into a β-D-glucose.
method ∆Gα→β(gas) ∆Gα→β(water)
XRISM/HNC (this work) (–0.59) –1.62
XRISM/KH (this work) (–0.59) –1.64
experiment [15] –0.3
QM [4] 0.4 –0.2
FEP and TI [3] 0.31±0.43
LES [5] 0.80±0.03 –0.18±0.06
possibilities that a structural optimization related to the bond lengths and bond angles as well as
dihedral angles may improve the numerical accuracy in describing the free energy surfaces.
Here, we show each component of potential of mean force (i.e. energy decomposition) such as
van der Waals (i.e. vdw or Lennard-Jones) term, electrostatic term and so on, in order to explore
physical origins of the fact that the β anomer is more favored in aqueous solution than α. Table 2
lists the conformational energy EC,α→β , intramolecular vdw energy Evdw,α→β , intramolecular elec-
trostatic energy Eelec,α→β , torsion energy Etors,α→β , and solvation free energy ∆µS,α→β , where
the numerical values shown in the table were evaluated as averages over all conformations using
a Boltzmann weight factor, and presented in the form of an energy gain when an α-D-glucose was
transformed into a β-D-glucose. In table 2, we observe again an insignificant difference between the
XRISM/HNC theory and the XRISM/KH theory. It is found that the principal factor to stabilize
the β anomer in aqueous solution is the solvation free energy, which stabilizes β by as much as 2.5
kcal/mol better than α in solution. It is also interesting to note that in terms of the intramolecular
electrostatic energy, a slightly higher stability of β-D-glucose than α-D-glucose in gas phase (ca –0.4
kcal/mol) is drastically reversed when the surrounding environment is changed into aqueous solu-
tion (ca 1.3 kcal/mol): that is, the intramolecular electrostatic contribution favors the α anomer
better than β in aqueous solution. On the one hand, both anomers are stabilized by forming in-
tramolecular hydrogen bonds in gas phase. On the other hand, in aqueous solution, a competition
can occur between the neighboring water molecules and intramolecular hydroxyl groups when a
D-glucose molecule forms hydrogen bonds. The behavior of the intramolecular electrostatic contri-
bution observed in table 2 may be interpreted as the evidence that the β anomer interacts with
water molecules through hydrogen bonds more preferably than α in solution, which is regarded as a
Table 2. Differences in averaged energy components [kcal/mol] between α-D-glucose and β-D-
glucose. The values are in the form of a corresponding energy change when an α-D-glucose is
transformed into a β-D-glucose.
EC,α→β Evdw,α→β Eelec,α→β Etors,α→β ∆µS,α→β
gas phase –0.84 –3.46 –0.37 2.99
XRISM/HNC (water) 0.84 –2.75 1.29 2.30 –2.45
XRISM/KH (water) 0.84 –2.75 1.30 2.29 –2.51
consequence of the above competition. This interpretation is consistent with the above-mentioned
fact that the solvation free energy stabilizes the β anomer better than α. Also, our results and
interpretation qualitatively agree with the data of each energy component reported by Ha et al. [3].
437
T.Miyata
4. Conclusion
The anomeric equilibrium of D-glucose was studied using the XRISM/HNC and XRISM/KH
theories. All 729 possible torsional stereoisomers of the 4C1 chair form were taken into consideration
in this study for each anomer. The free energy difference between the α and β anomers was
calculated from partition functions, and a relative stability of each anomer was discussed on the
basis of the free energy difference. Both the XRISM/HNC and XRISM/KH theories predicted
that β-D-glucose was more stable in aqueous solution than α-D-glucose, which agreed with an
experimental result qualitatively. It was found that the principal factor to stabilize the β anomer
in solution compared with the α was the solvation free energy, which was revealed by the analysis
of each component of the potential of mean force. Correspondingly, the intramolecular electrostatic
energy of the β anomer was remarkably higher than that of α in solution. These findings imply that
in aqueous solution, the β anomer favors an interaction with water molecules through hydrogen
bonds, compared to α. Although our method succeeded in reproducing experimental data in a
qualitative sense, it overestimated the relative stability of the β anomer significantly. This is still
left as an open problem to be overcome, probably by introducing a better sampling algorithm in
a conformational space.
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RISM study on anomeric equilibrium of glucose
Вивчення методом RISM аномеричної рiвноваги D-глюкози у
водних розчинах
Т.Мiята
Iнститут молекулярних наук, 38 Нiшiго-Нока Мiодаiї, Оказакi, Аiчi, Японiя
Отримано 30 травня 2007 р., в остаточному виглядi – 3 липня 2007 р.
В рамках розширеної теорiї базисних силових центрiв (XRISM) вивчається аномерична рiвновага
D-глюкози у водних розчинах. В цих дослiдженнях всi обертовi ступенi вiльностi розглядаються для
ексоциклiчних гiдроксильних та гiдроксометильних груп, зокрема 729 стереоiзомерiв для кожно-
го аномера. Рiзницi вiльних енергiй α та β аномерiв розраховуються на основi функцiй розподiлу.
XRISM теорiя передбачає, що β-D-глюкоза є стабiльнiшою у водному розчинi нiж α-D-глюкоза, що якi-
сно узгоджується з експериментальними даними. Встановлено, що вiльна енергiя сольватацiї кра-
ще стабiлiзує β-аномер нiж α-аномер та що внутрiмолекулярна електростатична енергiя β-аномеру
в розчинi значно вища нiж у випадку α-аномеру. β-аномер у водному розчинi є бiльш схильним до
взаємодiї з молекулами води через водневi зв’язки, порiвняно з α-аномером.
Ключовi слова: XRISM теорiя, D-глюкоза, аномерична рiвновага, водний розчин, вiльна енергiя
PACS: 82.60.-s, 82.60.Lf, 05.20.-y
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