SPECIAL SECTION:
Dynamic and thermodynamic anomalies of
water at low temperatures: from bulk water to
reverse micelles and DNA hydration layer
Biman Jana, Rakesh S. Singh, Rajib Biswas and Biman Bagchi*
Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore 560 012, India
Liquid water is known to exhibit remarkable thermodynamic and dynamic anomalies, ranging from solvation properties in supercritical state to an apparent
divergence of the linear response functions at a low
temperature. Anomalies in various dynamic properties of water have also been observed in the hydration
layer of proteins, DNA grooves and inside the nanocavity, such as reverse micelles and nanotubes. Here
we report studies on the molecular origin of these
anomalies in supercooled water, in the grooves of
DNA double helix and reverse micelles. The anomalies
have been discussed in terms of growing correlation
length and intermittent population fluctuation of 4and 5-coordinated species. We establish correlation
between thermodynamic response functions and mean
squared species number fluctuation. Lifetime analysis
of 4- and 5-coordinated species reveals interesting
differences between the role of the two species in
supercooled and constrained water. The nature and
manifestations of the apparent and much discussed
liquid–liquid transition under confinement are found
to be markedly different from that in the bulk. We
find an interesting ‘faster than bulk’ relaxation in reverse micelles which we attribute to frustration effects
created by competition between the correlations imposed by surface interactions and that imposed by hydrogen bond network of water.
Keywords: Dynamic and thermodynamic anomalies,
DNA hydration layer, reverse micelles.
Introduction
LIQUID water continues to draw immense attention from
scientists working in all branches of natural sciences. Different groups remain interested in different aspects of this
liquid. Although some study ‘structured water’ in
micelles and reverse micelles1–3, some study its properties
in protein and DNA hydration layers1,5–14, there are still
others who study it in carbon nanotubes15, while for some
attention remains focused on electrolyte solutions16, and
for many bulk water itself poses unlimited puzzles to
*For correspondence. (e-mail: bbagchi@sscu.iisc.ernet.in)
900
keep them engaged over a lifetime. Many books and
reviews have been devoted to water and their number
seems to be increasing every year17–21.
One can list the large number of anomalies that water
exhibits in different environments. The list continues to
grow. More recently a considerable amount of attention
has been devoted to water at temperatures below the
freezing temperature of 273 K22,23. Not only does water at
such a low temperature exhibit certain amazing anomalies, it is also hoped that this can serve as a key to understand properties at higher temperatures. Notable anomalies
are the divergent-like growth of the linear response functions (heat capacity, isothermal compressibility, etc.)22,23.
Several explanations of these anomalies have been put
forward. The explanations in terms of the re-crossing of
the gas–liquid spinodal at lower temperature (spinodal
retracing)24 and in terms of the negative slope of the temperature maximum density line in the (P, T) plane (singularity-free scenario)25 are only partly successful in
explaining the experimental results. The most recent and
promising approach in this area is in terms of liquid–
liquid phase transition26–29. In this scenario, water is
hypothesized to exhibit a phase transition in the region of
deeply supercooled water, at higher than ambient pressure, from high-density liquid (HDL) to low-density
liquid (LDL). This liquid–liquid critical point in water is
estimated to be located at a pressure P ≈ 100 MPa and
temperature T ≈ 220 K28. Beyond this critical point, one
can draw a line of the maximum density fluctuation in
(P, T) plane owing to the remnant effect of the criticality
and such a line is termed as Widom line27,29. The anomalous increase in the response functions upon cooling at
the ambient pressure can be a manifestation of the crossing of the Widom line29. This hypothesis not only
explains the response functions anomalies of water but
also explains the polymorphism of glassy water and seems
at present to be the most consistent with experiments30–32.
Moreover, liquid–liquid (L–L) phase transition scenario
is also consistent with the presence of a crossover in the
dynamics found in recent experiments in the nanoconfined water33,34.
The molecular origin of anomalous behaviour near the
Widom line is well-understood in several cases. For
example, in the gas–liquid case, it is the correlated denCURRENT SCIENCE, VOL. 101, NO. 7, 10 OCTOBER 2011
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sity fluctuation. In the case of supercooled water, as the
critical point is between LDL and HDL, the order parameter should again be the density, but as the LDL phase
is predominantly 4-coordinated and the HDL phase is a
mixture of 4- and 5-coordinated species, additional relevant order parameters should be the occupation numbers
of 4- and 5-coordinated water molecules.
Among many anomalies of water, the dominance of
single Debye spectrum with relaxation time τD = 8.3 ps
has remained an enigma. Bagchi and Chandra35 proposed
that the absence of non-Debye behaviour can be attributed to the translation–rotational coupling. In an interesting series of papers, Laage and Hynes36,37 showed that the
single exponential relaxation of central water molecule is
promoted by jump motions induced by migrations of a
water molecule from the first hydration shell water to the
second and vice versa and it happens through large amplitude jump motion.
We have carried out extensive molecular dynamics
simulation of TIP5P38,39 water model to explore the
microscopic processes associated with the crossing of the
proposed Widom line and also to understand the detailed
implications of these processes on the anomalous behaviour of supercooled water. As the non-linear four-point
susceptibility (χ4(t)) captures the presence of a growing
length scale and the concomitant emergence of dynamical
heterogeneity in density fluctuations, we have calculated
the same as a function of temperature. We have studied
the origin of the enhancement of correlated density fluctuations near Widom line in terms of time evolution of
the 4- and 5-coordinated species and calculated the relevant properties to demonstrate the microscopic origin of
response function anomalies in supercooled water. A
two-state model has been presented which can explain the
intermittency in the number fluctuations observed in
simulations. We have also calculated the lifetime correlation function and lifetime distribution function of 4- and
5-coordinated species. The theoretical and simulations
results seem to suggest that the anomalies are a consequence of an avoided criticality owing to the presence of
the 5-coordinated water molecules.
Water in the natural world is often found under constrained and/or restricted environments, in the hydration
layer of proteins and micelles, within reverse micelles
and microemulsions, in the grooves of DNA duplex and
within biological cells, to name a few1–3. Properties of
water under such constrained conditions can be quite
different from those of bulk, neat water. However, it is
likely that even under such restricted conditions water retains some of its unique properties. Study of these unique
properties of water, especially in the hydration layer of
biomolecules, particularly of proteins and DNA, has been
a subject of great interest in recent times. Hydration layer
not only provides the stability of the structure of the biomolecules, but also plays a critical role in the dynamic
control of biological activity. The intercalation of antiCURRENT SCIENCE, VOL. 101, NO. 7, 10 OCTOBER 2011
tumour drugs, such as daunomycin, into DNA involves
active participation of water molecules in the grooves40.
The low-temperature (near 200 K) ‘glass-like’ transition
of hydrated protein has drawn a great deal of attention in
both experimental and computer simulation studies41–45.
Above this transition temperature, proteins exhibit diffusive motion and below this temperature the proteins are
trapped in localized harmonic modes. An important issue
in recent times is to determine the effects of hydration
water on this dynamical transition46–50. Recent studies
have shown that dynamics of water in the hydration layer
of a protein also exhibits strong temperature dependence
around the same temperature and it seems to undergo a
fragile-to-strong transition which preempts an otherwise
expected glass transition at a lower temperature50–53.
Study of DNA hydration layer has recently indicated
interesting dynamical behaviour of water in the grooves10,11.
Several recent studies have discussed the origin of the
slow component of the solvation dynamics in DNA
hydration layer54. A recent computer simulation study by
Stanley and co-workers has shown that the L–L transition
in water induces a dynamic transition in DNA which has
striking resemblance to that of liquid to glass transition55.
This study, however, did not explore the dynamics of
water in the grooves of DNA.
There are many questions that have remained unanswered regarding dynamics of groove water at low temperature. For example, is there a dynamic transition in the
grooves of DNA near the L–L transition of bulk water?
Does it in any way resemble the one in protein hydration
layer? Note that the remarkable properties of bulk water
have recently been attributed to a highly interesting L–L
transition at around TL ≈ 247 K (refs 56–58). The effects
of the bulk water L–L transition on groove water dynamics have not yet been studied.
In this article, we report our finding that water in the
grooves of a DNA duplex shows a dynamical transition at
a temperature (TGL) slightly higher than the temperature
(TL), where the bulk water undergoes the L–L transition.
The nature and manifestation of the transition in the
grooves are stronger than those in the bulk for the same
TIP5P potential.
There are several effects of confinement on the properties of liquid water. First, fluctuations with wavelength
larger than that of the confining region are suppressed.
Second, the surface can induce changes within water. For
example, a hydrophobic surface can induce enhanced
local order among the water molecules. A hydrophilic
surface (such as a micelle or a reverse micelle) can
induce frustration among water molecules in the second
or third layer1,59–61. Both the surfaces are expected to
lower the entropy of hydration layer.
An interesting aspect of water molecules in the DNA
grooves is that they are free to exchange with the bulk.
Therefore, the entropy–energy balance needs to be maintained. As entropy of water in the hydration layer is signi901
SPECIAL SECTION:
ficantly less than that in the bulk, these water molecules
must be energetically stabilized by interactions among
themselves and also with DNA atoms.
Arrangement of water molecules in the grooves of
DNA are partly dictated by the gain in the stabilization
energy owing to the interaction with the charged groups
of DNA and partly by the loss of entropy because of confinement. These two factors lead to a change in the preference of arrangement to lower energy states which is
the 4-coordinated low-density state. Thus, the dynamical
(L–L) transition is expected to occur at higher temperature which is also found by computer simulations
presented here.
Models and simulation details
Bulk water
A series of 11 simulations at different temperatures starting from 300 K to 230 K has been carried out in isobaric–
isothermal ensembles (NPT). The TIP5P water model is
used, which has been examined to reproduce the low
temperature properties of water excellently. A system of
512 water molecules is first equilibrated for ~ 1 nanoseconds at 300 K and ~ 15 ns at 230 K and then the trajectory is saved for several nanoseconds for the analysis.
Both equilibration and the subsequent run have been
carried out in NPT ensemble. The long range electrostatic
interactions are calculated using Ewald summation. The
density profile of water has also been reproduced successfully.
DNA hydration layer
The system we studied consists of a Dickerson dodecamer DNA duplex (CGCGAATTCGCG)62 solvated
using the LEAP module of the AMBER63 software in a
TIP5P water box. The box dimensions were chosen in
order to ensure a 10 Å thick solvation shell around the
DNA structure. In addition, some water molecules were
replaced by Na+ counterions to neutralize the negative
charge on the phosphate groups of the backbone of the
DNA. These procedures resulted in a solvated structure,
containing around 8605 atoms which include 758 DNA
atoms, 22 counterions, and ~ 1565 water molecules. The
solvated structure is then subjected to 1000 steps of
steepest descent minimization of the potential energy,
followed by 2000 steps of conjugate gradient minimization. During this minimization, the DNA molecule was
kept fixed in its starting conformations using harmonic
constraints. This allows the water molecules to reorganize
to eliminate bad contacts with the DNA molecule. The
minimized structure was then subjected to 500 ps of
molecular dynamics (MD), using a 2 fs time step for
integration. Subsequently, MD was performed under con902
stant pressure–constant temperature conditions (NPT)
with temperature regulation achieved using the Berendsen weak coupling method (0.5 ps time constant for heat
bath coupling and 0.2 ps pressure relaxation time). This
was followed by another 5000 steps of conjugate gradient. The DNA–water system is then simulated at constant
pressure P = 1 atm, at several constant temperatures
(T = 300, 290, 280, 270, 260, 250, 240, 230 and 220 K)
with periodic boundary condition for 10 ns (for T =
300 K) to 30 ns (for T = 220 K). This ensures the equilibration of DNA system which has been checked by root
mean square displacement (RMSD) of DNA and other
relevant properties. Finally for the analysis, we have
carried out 30 ns of NPT simulation for each case with
2 fs time step. Statistical errors have been calculated
using four independent trajectories.
We have identified the groove water by using the following procedure. We have calculated the radial distribution function (g(r)) of water molecules in the system from
the major and minor groove atoms. On the basis of this
g(r), a cut-off distance of 3.5 Å (the first minima of g(r))
from the groove atoms is used for the selection. For bulk
water analysis, we have considered those water molecules
which are beyond 10 Å from any DNA atoms. We have
checked that at 10 Å distance, water indeed regains bulklike behaviour.
Bulk water: results and discussions
Signatures of dynamic transition
There are several signatures of the presence of a dynamical transition in supercooled liquid water. Here we present two dynamical features, namely average translational
relaxation time (⟨τT⟩) and average orientational relaxation
time (⟨τR⟩), which show the presence of a dynamical transition in our system. Average translational relaxation
time, (⟨τT⟩), can be obtained from the fitting of the
long-time intermediate scattering function (FS(k, t)) to a
stretched exponential function. The self-intermediate
scattering function is defined as:
FS (k , t ) = ⟨ exp[−ik.(r (t ) − r (0))]⟩
=
sin(|k| |r (t ) − r (0)|)
,
| k| | r (t ) − r (0)|
(1)
where k is the wave vector and r(t) is the position of the
oxygen atom of the water molecules. The |k| value taken
here is 2.5 Å–1.
In Figure 1 a, we have presented the ⟨τT⟩ at different
temperatures. While in the high temperature region it follows Vogel–Fulcher–Tammann (VFT) law, τT = τ0exp[DT0/
(T – T0)], where D is a constant measuring fragility
and T0 is ideal glass transition temperature at which
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Figure 1. Anomalous temperature dependence of a, translational and b, orientational relaxation times. Note that both translational and rotation relaxation time change the functional dependence on temperature around T = 250 K. This is the signature of the
presence of dynamical transition.
relaxation time diverges, it follows Arrhenius dependence
in the low temperature region. The crossover between
these two temperature dependence of ⟨τT⟩ around
T = 250 K marks the presence of a dynamical transition.
We have also calculated average orientational relaxation
time, ⟨τR⟩, by fitting the long-time part of the dipole–
dipole time correlation function (TCF) to a stretched
exponential. Dipole–dipole TCF calculated is defined as
Cμ (t ) =
⟨ μ (0)i μ (t )⟩
,
⟨ μ (0)i μ (0)⟩
(2)
where μ(t) is the dipole moment unit vector of the water
molecule at time t and the angular bracket corresponds to
the ensemble averaging. In Figure 1 b, we have presented
the ⟨τR⟩ at different temperatures. The temperature dependence of ⟨τR⟩ is found to be similar to what is observed
for translational dynamics with a crossover around similar temperature. These dynamical signatures confirm the
presence of a dynamical transition in the system around
T = 250 K.
Growth in non-linear response function
Appearance of correlated density fluctuations in the system gives rise to transient heterogeneity in the system
which can be detected by calculating the non-linear
response function, χ4(t). The latter is related to the fourpoint density correlation function G4 by the following relation64–67,
χ 4 (t ) =
βV
N2
∫ dr1 dr2 dr3 dr4 w(|r1 − r2 |)w(|r3 − r4 |)
× G4 (r1 , r2 , r3 , r4 , t ),
CURRENT SCIENCE, VOL. 101, NO. 7, 10 OCTOBER 2011
(3)
where four-point density correlation function G4 can be
written as:
G4(r1, r2, r3, r4, t) = ⟨ρ (r1, 0)ρ (r2, t)ρ (r3, 0)ρ (r4, t)⟩
– ⟨ρ (r1, 0)ρ (r2, t)⟩ × ⟨ρ (r3, 0)ρ (r4, t)⟩.
(4)
Thus, χ4(t) is dominated by the range of spatial correlation between the localized particles in the fluid. It can be
shown that definition of χ4(t) as given by eq. (3) is
equivalent to the following expression.
χ 4 (t ) =
βV
N2
[⟨Q 2 (t )⟩ − ⟨Q(t )⟩ 2 ],
(5)
where Q(t) is the time-dependent order parameter which
measures the localization of particles around a central
molecule through a overlap function which is unity inside
a region a and zero otherwise. Figure 2 a, displays the
non-linear response function, χ4(t), of water molecules
(computed with the oxygen atom displacement) for temperatures ranging from 300 K to 230 K (ref. 58). At
ambient pressure, the Widom line is located at TWL ≈ 250 K
for TIP5P water model. For every temperature, the χ4(t)
is nearly zero for very short and long time with a maximum value at some intermediate time t*. Both t* and the
amplitude of the peak, χ4(t*), increase sharply while
approaching the Widom line. After crossing the Widom
line, the value of χ4(t*) decreases with further decrease in
temperature. This suggests that both the spatial correlation between slow moving water molecules and the time
at which that correlation is maximum, increase as we
approach the Widom line from both the sides. This spatial
correlation and t* seem to attain the maximum values
at the Widom line. We have also calculated another
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Figure 2. Time dependence of the non-linear response functions, a, χ4(t), b, α T2 (t), at various temperatures, starting from 300 K
down to 230 K. Note the huge growth of the peak of response functions around the Widom line (T ≈ 250 K).
Figure 3. Nearest neighbour distribution of a tagged water molecule. a, Distribution of the distances calculated between the central water molecule and its fifth neighbour at various temperatures starting from 300 K down to 230 K. b, Temperature dependence of average fifth neighbour distances. Note the rapid change near T = 250 K. c, Distribution of the distances calculated between the central water molecule and its first four
neighbours at various temperatures starting from 300 K down to 230 K. Note the gradual squeezing of the distribution towards lower distances with
decreasing temperature.
non-linear response function, the non-Gaussian parameter
(αT2(t)), for the supercooled water and the results are presented in Figure 2 b. Both the peak height (αT2(t*)), and
the time at which the parameter attains, maximum value
(t*) increases as Widom line approaches from above
similar to χ4(t). After crossing the Widom line, αT2(t*) and
t* continue to increase rapidly further unlike χ4(t). This
surprising difference in the behaviour of these two
response functions after crossing the Widom line has not
been understood clearly.
Cross-over in fifth neighbour distance distribution:
a molecular marker
To understand the molecular origin of the anomalies, we
need to identify a microscopic order parameter that shows
significant change across the anomalous (T = 250 K at
ambient pressure) region. The microscopic quantity that
undergoes significant change is the coordination number
because as water is cooled towards 250 K, 5-coordinated
904
water molecules get replaced by 4-coordinated water to
this end, we calculated the distribution and the average of
the distances between a central water molecule and its
five nearest neighbours, previously also calculated by
Chandra and Chowdhuri68 in the context of correlation of
pressure-induced dynamical changes with the changes in
hydrogen bond properties of the aqueous solutions. The
distribution for the fifth neighbour (the furthest among
the five neighbours and the one that leaves the first coordination shell to join the coordination shell of a molecule
in the second neighbour list of the central molecule) distance is shown in Figure 3 a at different temperatures.
The distribution and the average fifth neighbour distance
(shown in Figure 3 b) show sharp change between 250
and 260 K. Above 260 K, the distribution has a peak
around 3.25 Å. Below 240 K, the peak of the distribution
shifts to 3.85 Å. The distribution becomes surprisingly
flat around 260 K, with a mean value now located at
around 3.5 Å. We have also calculated the distribution of
the distances of first four neighbours (as shown in Figure
3 c) which shows only a gradual squeezing towards a
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lower distance with decreasing temperature. These distributions indicate that upon lowering temperature, while
the first four neighbours (essential to maintain a tetrahedral geometry) of a water molecule come progressively
closer, it is the fifth neighbour that goes out of the first
coordination shell (3.5 Å). The temperature at which the
peak position of the fifth neighbour distance distribution
changes sharply coincides with the region where response
functions show anomalous rise (as discussed below). The
corresponding free energy surface (with the fifth neighbour
distance as an order parameter) is flat, as in a critical
phenomenon. Therefore, the number of 5-coordinated
water molecules (N5C) can serve as a suitable order
parameter to study the anomalous behaviour of supercooled water.
Average coordination number and number of
hydrogen bonds
In search of structural changes associated with observed
anomalies, we have studied both the average coordination
number and the number of hydrogen bonds formed by
water molecules. These two quantities satisfy different
criteria. We have taken a cut-off distance of 3.5 Å for coordination number analysis and a cut-off ∠HOO of 30°
for the hydrogen bond analysis. In Figure 4, we have presented the results of the analysis. At higher temperature
while the average coordination number is high, average
number of hydrogen bonds is less. With decreasing
temperature, average coordination number decreases and
becomes ~ 4.0 in low temperature region. However, average number of hydrogen bonds increases with decreasing
temperature and becomes ~ 4.0 in the low temperature
region. We also observe that both the quantities change
Figure 4. Temperature dependence of the average coordination number and the number of hydrogen bonds. Note the decrease in coordination number and increase in number of hydrogen bonds with decreasing
temperature. Note also the rapid change of both the quantities near
T = 250 K.
CURRENT SCIENCE, VOL. 101, NO. 7, 10 OCTOBER 2011
rapidly near T = 250 K. The results of this analysis infer
that although the number of water molecules decreases
progressively from the first coordination shell with
decrease in temperature, the arrangement becomes progressively rich towards the tetrahedral geometry. The
rates of these structural changes are maximum near the
Widom line (T = 250 K).
Intermittency and 1/f noise
We find that water molecules with coordination numbers
4 and 5 are abundantly present at all temperatures. It was
shown by Stanley and co-workers69,70 through inherent
structure analysis that, in the extended network of
liquid water dominated by 4-coordinated species, the 5coordinated species present should be regarded as normal
(i.e. not as an excitation) constituent of water. Additionally, the isochoric differential X-ray experiments have
demonstrated that the water molecules can exist in a distinct configuration with five neighbours in the first coordination shell (within 3.5 Å)71. 3- and 6-coordinated
species present in the system should be regarded as excitations (not as normal species) of the system as they do
not retain their identity in the inherent structure. Simultaneous presence of both 4- and 5-coordinated water molecules in the system suggests the possibility of an exchange
between them as a cooperative mechanism of relaxation.
Figure 5 a–c display the temporal variation of the number density of the 4- and 5-coordinated species (N4C(t)
and N5C(t)) in the system at three different temperatures
T = 280 K, 250 K and 230 K, respectively. Both in the
high (T = 280 K) and low (T = 230 K) temperature region
(away from Widom line), the fluctuations of N4C(t) and
N5C(t) are random and not correlated, as shown in Figure
5 a and c. However, near the Widom line, T = 250 K,
however, the fluctuations of N4C(t) and N5C(t) are slow
and surprisingly strongly anti-correlated. This suggests
that the anomalies near the Widom line and the divergence-like growth of the response function in supercooled
water may originate from the strongly anti-correlated
number density fluctuations of 4- and 5-coordinated species.
The plots of the temporal variation of the number density of 4- and 5-coordinated species (Figure 5) also indicate that near the Widom line, the number density of the
individual species (4- and 5-coordinated species) fluctuates intermittently in time. The signature of intermittent
behaviour can be confirmed by calculating the power
spectrum of the fluctuation time correlation function. The
power spectrum of the fluctuation of the 5-coordinated
species (similarly for the 4-coordinated species) is presented in Figure 6 both for T = 300 K and 250 K. The
linear dependence of the power spectrum for a wide range
of frequency region with slope ≈ –1 (in log–log plot) at
T = 250 K confirmed the strong intermittency present in
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the fluctuation. Linear dependence of the power spectrum
in the low frequency range also indicates the large timescale intermittency in the fluctuations. At T = 300 K, the
power spectrum shows a linear dependence only at the
higher frequency region indicating the presence of small
timescale intermittency in the fluctuations. The large
timescale intermittency in the fluctuation concurrently
induces spatial heterogeneity (as calculated by αT2(t), Figure 2 b) as well as dynamical heterogeneity (calculated by
the function χ4(t) as shown in Figure 2 a). This intermittency in the fluctuation of the number of species in the
system further substantiates the microscopic origin of the
Widom line in terms of space and time correlated fluctuations of N5C(t). When one analyses the snapshots of the
trajectory visually, the intermittent dynamics is seen as a
region where a cluster of 5-coordinated water molecules
get converted into 4-coordinated water, whereas the
reverse transformation occurs in a nearby region. Such
intermittent dynamics has also been observed in the case
of hydrogen bond network rearrangement at room temperature and effect of such rearrangement on the dynamical properties of water has been studied extensively72.
Two-state model for intermittent population
fluctuation
Next, we explain the intermittency by borrowing a model
well known in the area of stochastic resonance73. We
consider the motion of a Brownian particle in a bistable
potential where the two minima are HDL and LDL states.
1
1
V ( x) = − x 2 + x 4 .
2
4
(6)
Particle is acted upon by a periodic forcing, A0cos(ω t),
and a random force η(t). Periodic forcing term appears
owing to fluctuation of the total volume of the system
as the two states have different specific volumes
Figure 5. Temporal variation of the numbers of 4- and 5-coordinated
species in the supercooled water at a, T = 300 K; b, T = 250 K and
c, T = 230 K. Note the strong anti-correlated fluctuations between
N4C(t) and N5C(t) and intermittency in the fluctuations of both the species at T = 250 K58.
906
Figure 6. Power spectrum of the time correlation function of the fluctuations of 5-coordinated species in log–log plot at T = 300 K and
250 K. Note the linear dependence over a wide range of frequency with
slope ≈ –1 (1/f noise) at T = 250 K which confirms the intermittency in
the fluctuations. The dotted line represent a line with slope = –1 for
comparison58.
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Figure 7. Temporal variation of the number of 4- and 5-coordinated species in supercooled water as derived from the model at T = 250 K. a, The
volume fluctuation from simulation at T = 250 K. b, N4C(t) and N5C(t) are calculated using volume fluctuation.
(VLDL > VHDL). In the presence of periodic forcing, the
effective potential V′(x) = V(x) + A0x cos(ω t) will be tilted
back and forth, thereby raising and lowering successively
the potential barriers for the HDL and LDL states, respectively. Now, we can write total volume of the system as,
– + δ V(t) and then clearly A ∝ ⟨ (δ V ) 2 ⟩ . The
V(t) = V
0
random force, η(t), has zero mean and obeys the fluctuation–dissipation theorem.
⟨η(0)η(t)⟩ = 2kBTζδ (t).
(7)
Here ζ is the dissipation coefficient. In the absence of the
– ) the system will
periodic forcing (i.e. at fixed volume V
fluctuate around its local minima (LDL and HDL) with
the noise induced hopping between the local minima
which can be described by Kramer’s theory.
rK =
1
2πζ
exp(− β Eact ) =
⎛ β⎞
exp ⎜ − ⎟ .
2πζ
⎝ 4⎠
1
(8)
Here, β = 1/kBT and Eact = 1/4. Next, we define the probabilities that the system is in either of the local minima as
nH/L = prob(state = HDL/LDL) and they obey the simple
relation nH = 1 – nL between them. Now the governing
rate equation of the above system is58 as follows.
dnH
dn
= − L = WL (δ V (t ))nL − WH (δ V (t ))nH
dt
dt
= WL (δ V (t )) − [WH (δ V (t )) + WL (δ V (t ))]nH ,
(9)
where WH/L(δV(t)) is the volume-dependent transition rate
out of HDL or LDL local minima in the presence of periodic forcing. Now the rate equation can be solved to
obtain58,
CURRENT SCIENCE, VOL. 101, NO. 7, 10 OCTOBER 2011
nH (t ) =
t
⎤
1 ⎡
⎢ nH (t = 0) g (t = 0) + ∫ WL (δ V (t ′)) g (t ′)dt ′⎥ ,
g (t ) ⎣⎢
0
⎦⎥
(10)
with
⎡t
⎤
g (t ) = exp ⎢ ∫ (WH (δ V (t ′)) + WL (δ V (t ′)))dt ′⎥ .
⎣⎢ 0
⎦⎥
(11)
For simplicity, we now assume that the rate constant
(WH/L(δ V(t))) can be obtained under the periodic volume
fluctuation as WH/L(δV(t)) = rKexp[± βA0cos(ω t)]. Analytical and numerical studies reveal that at higher and
lower temperature regions, far away from T = 250 K, the
magnitude of total volume fluctuation is less (A0 is less)
and also very fast (ω is high). In this condition, nH(t)
oscillates around 0.5 showing the local equilibrium in
both the wells. The fluctuation in the number of 4- and 5coordinated species in the system also fluctuates near
their respective equilibrium values in the temperature
region away from T = 250 K.
However, as we approach T = 250 K, the volume fluctuation becomes larger (A0 becomes larger) and slow (ω
becomes lower). In this condition, nH(t) oscillates intermittently between 0 and 1 (between the two states).
Simulation also shows long-lived periodic fluctuation in
total volume. As the free energy surface and hence the
rate of transition between LDL and HDL forms depends
on volume, the present model can explain the intermittency in the number fluctuation of 4- and 5-coordinated
species near T = 250 K (Figure 5 b).
We have calculated the temporal fluctuations of N4C
and N5C using the volume fluctuation (as shown in Figure
7 a) as obtained from the simulation at T = 250 K. In this
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SPECIAL SECTION:
case, we have assumed a linear dependence of the rate on
volume fluctuation as
⎛ ∂W
0
+ ⎜ L/H
WL/H (δ V (t )) = WL/H
⎝ ∂V
⎞
⎟ δ V (t ).
⎠
0
WL/H
is obtained as the inverse of the corresponding lifetime at T = 250 K and (∂WL/H/∂V) is obtained numerically
0
with variation of the total volfrom the slope of the WL/H
ume of the system. We find that the calculated temporal
fluctuation of N4C and N5C (as shown in Figure 7 b) essentially capture the behaviour of the fluctuation calculated
from simulation (Figure 5 b). The remaining difference
observed between the fluctuations derived from the
model and simulation might be because of non-linear
dependence of the rate on volume fluctuation.
Species number fluctuations and growth in linear
response functions
To further confirm the correlation between the fluctuations in N5C(t) and the anomalies in linear response functions, in Figure 8, we compare the temperature dependence
of ⟨(δN5C)2⟩ with the isothermal compressibility, κT, the
latter is related to the mean-squared volume fluctuation,
⟨(δV)2⟩, (κT ∝ ⟨(δV)2⟩/VkBT) (refs 22, 23). The calculated
κT exhibits a maximum precisely at the same temperature
where ⟨(δN5C)2⟩ exhibits a sharp maximum, at T = 250 K.
Moreover, with proper scaling, the values of the two
overlap (within the standard deviations) with each other
at each temperature over the entire temperature range. In
the same figure, we have plotted the experimental values
Figure 8. Observed similarities between the mean-squared number
fluctuation of the 5-coordinated species (N5C) and the thermodynamic
response function in supercooled water. Temperature dependence of
mean-square fluctuation ⟨(δN5C)2⟩, κT from simulation and from
experiment. The data has been normalized at T = 250 K. Note the striking similarity in the temperature dependence of both the quantities.
Note also that the quantities plotted in the figure overlap (within the
standard deviation of experiment and simulation) with each other over
the entire temperature range. For experimental κT values, the temperature has also been shifted by 18 K for the comparison (κT diverges at
T = 228 K experimental system and at T = 246 K for model system)58.
908
of the κT which shows that the present hypothesis
⟨(δN5C)2⟩ is responsible for the anomalous rise is in
agreement with all the data.
Anomalous lifetime dynamics
We next discuss the lifetime dynamics of the different
species. The lifetime correlation function SLi(t) (i = 4, 5)
of 4- and 5-coordinated water molecules is defined as follows.
SLi (t ) =
⟨ ni (0)ni (t )⟩
,
⟨ ni (0)⟩
(12)
where ni(t) is considered to be unity if a water molecule
is continuously found in a state of coordination number i
for the time interval 0 to t, and otherwise zero. This function provides information about the probability that a particular water molecule remains in a particular state of
coordination for a time interval 0 to t. Figure 9 a and b
displays the decay of the correlation function of 4- and
5-coordinated species, respectively, at different temperatures. For the 4-coordinated species, the decay of the lifetime correlation function SL4(t) slows down upon cooling
across the Widom line. This is similar to features observed in the dynamics (such as FS(k, t)) of supercooled
water. On the other hand, the decay of SL5(t) remains fast
over the entire temperature range and shows no dramatic
change on crossing the Widom line. We have also calculated the average lifetime by fitting of the correlation
functions. The result is displayed in Figure 10. This indicates that the barrier height for the 4-coordinated species
becomes higher after crossing the Widom line, but the
same for 5-coordinated species continues to remain low
even after crossing the line. This behaviour suggests the
important role of 5-coordinated species in the dynamics
of supercooled water.
We have also calculated the distribution of lifetimes of
the 4- and 5-coordinated species at T = 250 K. Figure
11 a and b displays the distributions for 5- and 4coordinated species, respectively. Lifetime distribution
for 5-coordinated species is an exponential distribution
starting at t0 = 0.2 ps with a time constant of 0.08 ps.
However, the distribution for 4-coordinated species starts
from a value of 0.37 at 0.1 ps and then continues to
decrease up to 1.4 ps. After 1.4 ps, the distribution starts
increasing up to 2.1 ps and finally decays to zero with a
long time tail. We have decomposed the distribution as
the sum of two different distributions and shown in Figure 11 c. The decomposed short-time distribution takes
care of the initial decay of the total distribution. This part
describes the lifetime distribution of the relatively shortlived 4-coordinated species which are present as immediate neighbours to a 5-coordinated species making the
inter-conversion between 4- and 5-coordinated species
CURRENT SCIENCE, VOL. 101, NO. 7, 10 OCTOBER 2011
CHEMISTRY – STRUCTURE, SYNTHESIS AND DYNAMICS
Figure 9. Decay of the lifetime correlation function, SLi(t), in log–log plot for a, 4-coordinated (SL4(t)) and b, 5-coordinated
(SL5(t)) water molecules. Note the slowdown of the decay for SL4(t) after crossing the Widom line and relatively unchanged decay
pattern for SL5(t) over the entire temperature range.
diagram between 4- and 5-coordinated species is
governed by the following equation.
ΔG = a(T – TC)x2 + Bx3 + Cx4.
(14)
Here x = ⟨N4C⟩ – ⟨N5C⟩. However, the activation energy
for the transformation from 5- to 4-coordinated species
remains almost the same in the whole temperature range
as lifetime distribution does not change significantly.
Time correlation functions of number density
fluctuations: emergence of slow decay
Figure 10. Temperature dependence of the lifetimes of 4- and 5coordinated species. Lifetime has been obtained from the fitting of the
corresponding lifetime correlation function (as shown in Figure 9).
Next, we have studied the self- and cross-correlation of
the number fluctuation of the 4- and 5-coordinated species in time. The self-correlation function Ci(t) (i = 4, 5) is
defined as follows.
Ci (t ) =
faster. However, another part of the distribution which
has the long time tail describes the lifetime distribution of
the 4-coordinated species which are not immediate
neighbours to a 5-coordinated species.
Now, one can consider the following equation for 4and 5-coordinated species as the system is in equilibrium.
⎛ ΔG ⎞
⟨ N5C (t )⟩ k4→5
=
= exp ⎜ −
⎟.
⟨ N 4C (t )⟩ k5→4
⎝ kBT ⎠
(13)
Here kA → B represents the rate at which species A transforms to species B and ΔG is the free energy difference
between species A and species B. Now as we lower the
temperature k5→4 remains same but k4→5 slows down.
According to the above relation, ΔG also increases with
lowering of temperature. This infers that the free energy
CURRENT SCIENCE, VOL. 101, NO. 7, 10 OCTOBER 2011
⟨δ Ni (0)δ N i (t )⟩
.
⟨δ Ni (0)δ N i (0)⟩
(15)
Similarly, we define the cross-correlation function C4,5(t)
as follows.
C4,5 (t ) =
⟨δ N 4C (0)δ N5C (t )⟩
.
|⟨δ N 4C (0)δ N5C (0)⟩|
(16)
Figure 12 a–c displays the decay of the number fluctuation of the time correlation function in the log–log plot
for 4-coordinated species, 5-coordinated species and
between both of them. The decay of the self-fluctuation
time correlation function of both the species (as shown in
Figures 12 a and b) becomes slowest at T = 250 K
(Widom line). A step-like feature also develops (such as
glassy relaxation) in the relaxation pattern as the Widom
line is approached from above and continues to be present
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SPECIAL SECTION:
Figure 11. Distribution of the lifetimes of a, 5-coordinated and b, 4-coordinated species in supercooled water at T = 250 K. Note the maximum at
intermediate time and long time tail in the latter. c, Decomposition of the 4-coordinated lifetime distribution to short and long time part.
Figure 12. Decay of fluctuation time correlation function. a, C4(t); b, C5(t) and c, C4,5(t) in log–log plot. Note the negative cross-correlation
(C4,5(t)) between the fluctuations of 4- and 5-coordinated water molecules. Note also the slowest decay of all the correlation functions at T = 250 K
and also the emergence of step-like feature near the Widom line.
after crossing. The cross-fluctuation time correlation
function (Figure 12 c) between 4- and 5-coordinated
species is negative and the decay pattern is similar to the
self-fluctuation time correlation function. This negative
cross-correlation indicates the anticorrelation between the
numbers of 4- and 5-coordinated species, as discussed
earlier. The slowest decay near the Widom line (T = 250 K)
suggests the appearance of strong anticorrelation which is
correlated over a long time. The appearance of step-like
feature in the relaxation pattern of self- and crossfluctuation time correlation function of the species is an
indication of the crossing of Widom line for the supercooled water.
DNA hydration layer: results and discussions
Left panel of Figure 13 displays the same. We find that
the mean-square fluctuation (MSF) of DNA slows down
dramatically around 247 K and continues to remain slow
for the lower temperatures. The onset of the change in
slope (near TDNA ≈ 247 K) of MSF indicates a macromolecular dynamic transition. Right panel of Figure 13
shows temperature dependence of the diffusivity (obtained from the slope of the mean-square displacement of
water molecules at long time) for all the water molecules
in the system. It shows a cross-over around the same
temperature (TL ≈ 247 K) from a high-temperature power
law form to a low-temperature Arrhenius form75. From
the power law fit to the high-temperature region, we get a
glass transition temperature of 231 K which is in agreement with the earlier simulation study by Stanley and
co-workers55.
Mean-square fluctuation of DNA and translational
diffusivity of water
Intermediate scattering function
We first report the calculated mean-square atomic fluctuation (which measures the variance of the position of
atoms at equilibrium) ⟨X2⟩ of the DNA atoms starting
from 300 K down to 220 K in order to characterize the
macromolecular ‘glass’ transition temperature (TDNA).
We next discuss the self-intermediate scattering function
(ISF) of the oxygen atoms of the water molecules in the
grooves of DNA for a set of temperatures starting from
300 to 220 K. The self intermediate scattering function is
defined by eq. (1). The translational relaxation time (τT)
910
CURRENT SCIENCE, VOL. 101, NO. 7, 10 OCTOBER 2011
CHEMISTRY – STRUCTURE, SYNTHESIS AND DYNAMICS
Figure 13. Mean-square fluctuation of DNA duplex (left panel) and diffusivity (right panel) of the oxygen atoms of all the water
in the system. In the left (DNA) panel, MSF of DNA shows a dynamic transition at T ≈ 247 K. We have fitted two straight lines
(one using T = 300–250 K data and other using T = 240–220 K data) to show the transition. In the right (water) panel, water shows
dynamical cross-over around same temperature from a high-temperature power law (fitted using T = 300–250 K data) behaviour
(cyan) to a low-temperature Arrhenius (fitted using T = 240–220 K data) behaviour (red)75.
is obtained by fitting the two-step relaxation of ISF at different temperatures using relaxing cage model (RCM)76.
The fitting equation used here is given by
⎡ ⎛ t ⎞2 ⎤
⎡ ⎛ t ⎞β ⎤
FS (k , t ) = (1 − A(k )) exp ⎢ − ⎜ ⎟ ⎥ + A(k ) exp ⎢ − ⎜ ⎟ ⎥ .
⎢ ⎝ τS ⎠ ⎥
⎢ ⎝τT ⎠ ⎥
⎣
⎦
⎣
⎦
(17)
Here A(k) is the Debye–Waller factor and β is the
stretched exponent.
Figure 14 a shows ISF of oxygen atom for the water
molecules in bulk, major groove and minor groove at 300
and 260 K. It is evident from both the figures that water
molecules in the major and the minor grooves tend to behave like a liquid at a temperature lower than the bulk.
The behaviour is more prominent for water molecules in
the minor groove. This can be ascribed to the fact that
translational motion of water molecules in the minor
groove is more constrained owing to the more ordered
structure in the minor groove than water molecules in the
major groove of DNA. Water molecules in the major
groove are, in turn, translationally more constrained than
bulk water. Figure 14 b shows the temperature dependence of τT for water molecules in bulk, major and minor
grooves. For both bulk and major groove water, the temperature dependence at high-temperature region can be
fitted to the VFT law. In reality, however, the divergence
is avoided as below a certain characteristic temperature,
the functional dependence of relaxation time switches
over to an Arrhenius form which indicates a strong liquid.
CURRENT SCIENCE, VOL. 101, NO. 7, 10 OCTOBER 2011
The cross-over temperatures for bulk water and major
groove water are found to be T ≈ 247 K and TGL ≈ 255 K,
respectively. The dynamical transitions are of fragile-tostrong type, although the fragility of major groove water
is smaller of the two.
The minor groove water molecules however show a
remarkably different translational dynamics. Minor groove
water does not show any signature of a fragile liquid
in the studied temperature range. Instead, temperature
dependence of translational relaxation time for minor
groove water fits well into two Arrhenius forms of different
slopes with a cross-over temperature around TGL ≈ 255 K
(same as major groove water). This can be understood in
the context of difference in the structure of hydration
layer in the grooves of DNA. Hydration in the minor
groove is more extensive, regular with a zig–zag spine of
the first and second shells of hydration whereas hydration
in major groove is restricted to a single layer of water
molecules77. Water molecules in minor groove are thus
more structured in comparison with major groove water
which results in a strong liquid type of behaviour for
water molecules in minor groove even in the hightemperature region. This explains why in contrast to bulk
and major groove water, minor groove water shows a
strong-to-strong type of dynamical transition.
Orientational dynamics
We next analyse orientational (dipole–dipole) time correlation function (TCF) (defined by eq. (2)) of water molecules in different regions of aqueous DNA. Figure 15 a
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SPECIAL SECTION:
Figure 14. a, Intermediate scattering functions (FS(k, t)) of the oxygen atoms of water molecules in bulk, major and minor
grooves of DNA duplex at two different temperatures, T = 300 K (left panel) and T = 260 K (right panel) for |k| = 2.5 Å–1.
b, Translational relaxation time (τT) for bulk (left panel), major groove (middle panel) and minor groove (right panel) water. Bulk
and major groove water show dynamical cross-over between high-temperature VFT behaviour (cyan) and low-temperature
Arrhenius behaviour (red). Minor groove water shows a transition between two Arrhenius behaviours. For bulk water, VFT fitting
has been done using T = 300–250 K data, and Arrhenius fitting has been done using T = 240–220 K data. For major groove water,
VFT fitting has been done using T = 300–260 K data, and Arrhenius fitting has been done using T = 250–220 K data. For minor
groove water, two Arrhenius fittings have been done using T = 300–260 K data and T = 250–220 K data75.
displays Cμ(t) for water molecules in bulk, major and minor grooves at 300 and 260 K, respectively. Similar to the
translational motion, rotation of the minor groove water
molecules is found to be the most constrained. Figure
15 b shows the temperature dependence of orientational
relaxation time (τR) as obtained from stretched exponential fitting at long time of dipole–dipole TCF for bulk,
major and minor groove water. Bulk water shows a fragile-to-strong transition around the same temperature
(TL ≈ 247 K) as observed for translational relaxation
912
time. However, unlike translational relaxation, orientational relaxation shows a transition between two Arrhenius
forms of different slopes with a cross-over temperature
TGL ≈ 255 K for both major and minor groove water.
Strong-to-strong transition observed in the minor groove
(both translational and orientational dynamics) can be attributed to the effect of confinement in the minor groove
(higher depth and lower width). It is known that a confined liquid is comparatively less fragile than in the bulk
and this eventually gives rise to Arrhenius temperature
CURRENT SCIENCE, VOL. 101, NO. 7, 10 OCTOBER 2011
CHEMISTRY – STRUCTURE, SYNTHESIS AND DYNAMICS
Figure 15. a, Dipole–dipole time correlation functions (Cμ(t)) of water molecules in bulk, major groove and minor groove of
DNA duplex at two different temperatures, T = 300 K (left panel) and T = 260 K (right panel). b, Rotational relaxation time (τR)
for bulk (left panel), major groove (middle panel), and minor groove (right panel) water. Bulk water shows a cross-over between
high temperature VFT behaviour (cyan) and low temperature Arrhenius behaviour (red). Major groove and minor groove water
show transition between two Arrhenius behaviours. For bulk water, VFT fitting has been done using T = 300–250 K data, and
Arrhenius fitting has been done using T = 240–220 K data. For major and minor groove waters, two Arrhenius fittings have been
done using T = 300–260 K data and T = 250–220 K data in each case75.
dependence of the relaxation times (signature of strong
liquids) even at the higher temperature region. The reason
for the different behaviour of major groove water is thus
probably because rotation probes local environment more
faithfully than translation.
Microscopic characterization: O–O–O angle
distribution
To understand how the structure of groove water changes
across the dynamical transition, we have calculated the
CURRENT SCIENCE, VOL. 101, NO. 7, 10 OCTOBER 2011
O–O–O angle distribution inside the first coordination
shell of a water molecule. Angle distributions at three
different temperatures (300, 250 and 230 K) for groove
water molecules are displayed in Figure 16. At all the
temperatures, the distribution has a two-peak character.
While the peak at lower angle is the signature of the presence of interstitial water molecules inside the first coordination shell, higher angle peak characterizes the degree
of tetrahedrality present. As it is evident from Figure 16,
with decreasing temperature the degree of tetrahedrality
increases (at higher angle peak, height increases) with the
removal of interstitial water molecules (at lower angle
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SPECIAL SECTION:
peak, height decreases) from the first coordination shell.
Structural change of this kind (increase in order with
decrease in temperature) is responsible for the dynamical
transition for groove water molecules.
Bulk water also exhibits a dynamical transition near
250 K. The signatures are, however, weaker in the case of
bulk water than what are observed in the grooves. The
role of confinement in fostering the transition of tetrahedral water can be understood in the following fashion. In
the confined state, water molecules gain in energy but
lose entropy (see next section). The tetrahedrally coordinated water is a low entropy state of the system. Confinement thus favours the cross-over/transition to the
tetrahedral state.
Entropy of layer water and Adam–Gibbs correlation
To understand the origin of the large observed differences
between the dynamics of water molecules in the minor
groove and in the bulk, we have calculated the entropy of
water molecules in the respective regions at two different
temperatures (300 and 280 K). We have used 2PT
method11,78 to calculate the entropy. In this scheme, the total
entropy is decomposed in four parts as S = Svib + SConf +
Srot + Sb–vib. Sb–vib is negligible compared to other parts
and Srot has been considered to be constant for each
region. To calculate the other two parts of the total
entropy, the method requires the translational velocity
autocorrelation (VAC) function as input. We have
obtained the total density of states (DOS) by taking the
Fourier transform of the translational VAC function.
Now, one can decompose the total DOS into a solid-like
nondiffusive DOS (gS(ω)) and a gas-like diffusive DOS
(gg(ω)) using 2PT method. Under the harmonic approximation, the vibrational entropy (Svib) can be written as
follows.
∞
S vib = ∫ dω g S (ω )WSHO (ω ).
(18)
0
Here WHSO(ω) is the well-known weight function for the
entropy of a harmonic oscillator. Now, the configurational
entropy (SConf) can be written as follows.
∞
Figure 16. O–O–O angle distribution of the groove water molecules
inside the first coordination shell at 300, 250, and 230 K. Note the
decrease of lower angle (interstitial) peak and increase of higher angle
(degree of tetrahedrality) peak height with decreasing temperature75.
Figure 17. Adam–Gibbs plot of translational diffusivity (ln(DT)) versus 1/TSConf for water molecules in the different regions of DNA duplex
(major groove, minor groove and bulk) at two different temperatures,
T = 300 K and T = 280 K. At a particular temperature, the points representing the bulk, major groove and minor groove are in the downward
direction of the y-axis75.
914
SConf = ∫ dω g g (ω )WSHS (ω ).
(19)
0
Here WHSS(ω) is the weight function for the entropy of the
hard sphere gas. In both the temperatures, minor groove
water molecules have substantially lower entropy than
bulk. At 300 K, the difference is ~ 60% of the latent heat
of fusion of bulk water. Entropy is usually found to be
closely correlated with diffusion coefficient and structural relaxation time, in Figure 17, we show the correlation between TSConf and translational diffusivity and show
that the Adam–Gibbs relation remains valid for the different regions of DNA. Interestingly, we find that the
Adams–Gibbs plot for the two different temperatures collapse on a single curve which can be fitted to a straight
line. This seems to indicate that the activation energies
for the transfer of water molecules between different
regions of aqueous DNA are utmost weakly dependent on
temperature above the L–L transition. Dynamics below
the L–L transition is too slow to allow a comprehensive
study. The present calculation of entropy is semiquantitatively reliable as the entropy of bulk water is
correctly (within 5%) reproduced and also the chemical
potential of bulk water and groove water is found to be
the same, as expected for systems in equilibrium.
CURRENT SCIENCE, VOL. 101, NO. 7, 10 OCTOBER 2011
CHEMISTRY – STRUCTURE, SYNTHESIS AND DYNAMICS
In a thermodynamic coexistence between two phases, a
discontinuous change in entropy signals the presence of
latent heat and a first-order phase transition. However, in
this study, the large difference in entropy between bulk
and minor groove water molecules should be regarded as
a signature in the difference in structure between the two
phases. Owing to the small number (~ 120 for major
groove and ~ 80 for minor groove) of water molecules
present in the groove region, a detailed quantification of
microscopic structural arrangement is difficult to perform.
Correlation between tetrahedral ordering and
configurational entropy
We have studied the structure, dynamics and thermodynamics of water molecules in different grooves of polyAT and poly-GC DNA79. We have calculated the O–O–O
angle distribution for water molecules in different
grooves and quantified the average tetrahedral order parameter, ⟨th⟩, for water molecules in the different region
using the relation80
⟨th ⟩ = 1 −
9 ⎛
1⎞
⎜ cos(θ OOO ) + ⎟
4 ⎝
3⎠
π
= 1−
9
4 ∫0
2
2
1⎞
⎛
⎜ cos(θ OOO ) + ⎟ P (θ OOO )dθ OOO .
3⎠
⎝
(20)
Here θOOO is the O–O–O angle and P(θOOO) is the distribution. We find the values of ⟨th⟩ are 0.41, 0.47, 0.48,
0.52 and 0.57 for bulk water, major groove water of polyGC, major groove water of poly-AT, minor groove water
of poly-G and minor groove water for poly-AT, respectively. Thus tetrahedral ordering in the groove of DNA
increases with increasing confinement. We have also calculated entropy and diffusivity of water molecules in the
different regions and the Adam–Gibbs relation is found to
be valid as shown by the linear fit of the data in Figure
18. We found a correlation between ⟨th⟩ and configurational entropy of water in different regions as indicated
by the dashed curve in Figure 18. It is clear from the
figure that ⟨th⟩ increases with decreasing configurational
entropy.
existence of a weak first-order phase transition. Across
this apparent transition, the number of 5-coordinated
water molecules change sharply. A separate calculation
with SPC/E water shows that the transition of a 4coordinated water molecule to a 5-coordinated water
molecule and vice versa becomes increasingly correlated
as temperature is lowered. It is shown in Figure 19 that
such an event takes the form of a connected string at low
temperatures and 3-coordinated H-bonded water molecules behave as a sink74.
Propagating jump events can have an interesting resemblance with the excitation energy transfer between
molecules observed in many chemical and biological systems. If we consider 5-coordinated species as excitations
then it can relax either by transferring the extra water
molecule to the 4-coordinated water molecule in the 2nd
hydration layer and making it 5-coordinated (this step is
similar to the jump of excitation to other molecule by
Förster mechanism) or by transferring to 3-coordinated
species (traps) from which further excitation transfer is
not possible (this step is similar to the fluorescence
quenching). Unlike the molecular relaxation, the 5coordinated species cannot relax by a mechanism similar
to fluorescence (radiative decay), particularly at low temperature. The quenching of propagating jump event can be
described as (shown in Figure 19 a).
N5 + N3 + N4 → (N5 – 1) + (N3 – 1) + (N4 + 2).
(21)
We simplify the description further by treating N4 as bulk
matter. Then the corresponding rate equation is as follows.
N
dN 4
= kN3 5 .
dt
V
(22)
What is the nature of the phase transition at 247 K?
The divergent-like growth of the response functions, such
as specific heat and isothermal compressibility certainly
appears to support the conjecture of a phase transition at
247 K at ambient pressure. Owing to the finite size of the
system, we cannot truly address the nature of the transition. However, we can still attempt to answer a few questions. First, the presence of intermittency suggests the
CURRENT SCIENCE, VOL. 101, NO. 7, 10 OCTOBER 2011
Figure 18. Correlations between diffusion coefficient, configurational entropy and tetrahedral order parameter (⟨th⟩). Note that left
side of the y-axis represents logarithm of diffusivity and right side of
the y-axis represents ⟨th⟩. The straight line fitting of the data validates
the Adam–Gibbs relation79.
915
SPECIAL SECTION:
of quenching can be given by the well-known Smoluchowski relation.
⎛
R0
k = 4π D35 R0C ⎜ 1 +
⎜ (π D t )1/2
35
⎝
⎞
⎟⎟ ,
⎠
(23)
where D35 is the mutual diffusion constant given by
D3 + D5. C is the concentration of 5-coordinated water
molecules. Note that the above rate expression for
quenching is for a single sink (3-coordinated water molecule) only.
As the temperature T of the system is lowered, the concentration of 3-coordinated water molecules decreases
(sharply). At the same time, the rigidity of the H-bond
network increases and D35 decreases. Both the factors
lead to the decrease in the rate of annihilation of excitations or increase in the survival time of a 5-coordinated
water molecule, leading to the prediction of a strong temperature dependence of the relaxation time of deeply
supercooled water.
In the above discussion, we have neglected the interaction between the 5-coordinated and 3-coordinated species. At low T, when the H-bonded network is rigid, the
defects can interact with each other. If we assume that
there is a long range (such as Coulombic) interaction between diffusing 3-coordinated and 5-coordinated species
(defects), then the probability of finding the 3-coordinated
and 5-coordinated species at a separation R at any time t
can be described by the Smoluchowski equation.
Figure 19. a, Schematic representation of the mechanism of propagation and death of the string-like motion in supercooled liquid water.
The numbers indicated here are the coordination states of the water
molecules. The arrow indicates the transfer of water molecules during
the H-bond breaking events. For clarity, we have not shown all other
water molecules inside the coordination sphere. b, Histogram of the
distribution of correlation lengths in terms of number of water molecules (n) involved in sequential H-bond breaking events at three different temperatures (300, 273 and 250 K)74.
The relaxation of 5-coordinated water molecules can be
modelled as reaction–diffusion phenomena, usually used
to study the dynamics of fluorescence quenching and diffusion controlled charge transfer reactions in solution81.
At low temperature, concentrations of 5- and 3-coordinated
species are quite low compared to the 4-coordinated species, so one can neglect the self-interaction between 5–5
and 3–3-coordinated species. We consider that the two
particles (3-coordinated and 5-coordinated) execute
Brownian motion independently of each other with diffusion coefficients D3 and D5. Following Smoluchowski
approach to the diffusion controlled reactions, we consider a sink at the centre of a sphere of radius R0 = 3.5 Å
(1st peak of g(r) of water) and an absorbing boundary at
the surface of the sphere (reaction surface), then the rate
916
∂P( R, t )
= D35 ∇[∇ + β ∇V ( R)]P,
∂t
(24)
where V(R) is the interaction potential between 3coordinated and 5-coordinated defects. We assume that it
can be approximated as –A/R. To get the time-dependent
survival probability, one can solve the above equation
with appropriate initial and boundary conditions. The
interaction between defects can play an important role for
relaxation, however, the exact nature of the interaction or
the form of potential is still not known.
Note that 4-coordinated water molecules in an ice-like
structure is the lowest energy configuration at temperatures below the freezing/melting temperature of 273 K at
ambient pressure. However, this ideal structure is separated from disordered water by a large barrier. What we
observe here is a muted transition between low density
water which comprises mostly 4-coordinated water molecules and high density water which has a significant
number of 5-coordinated water molecules. This L–L transition is believed to have a critical temperature (for
TIP5P water model) at a higher than ambient pressure. It
has been conjectured that the effects we observe is a consequence of crossing the Widom line. A physical explanation, not too different from this is forwarded here in terms
CURRENT SCIENCE, VOL. 101, NO. 7, 10 OCTOBER 2011
CHEMISTRY – STRUCTURE, SYNTHESIS AND DYNAMICS
of frustration, discussed by Kivelson and coworkers82 to
explain rapidly growing timescales in supercooled liquids
as temperature is lowered. Here, the cause of frustration
is the existence of 5-coordinated water molecules which
are difficult to destroy as they are locally conserved.
However, we still do not have a quantitative theory for
the role of the 5-coordinated water molecules.
Reverse micelles: frustration effects owing to
surface interactions
In a reverse micelle (RM), water is confined within a
small, nearly spherical, cavity and walls are formed by
charged groups. The charged groups on the surface
undergo strong interactions with the nearest neighbouring
water molecules. A popular example is given by sodium
dodecyl sulphate (SDS), where the negatively charged
sulphonate groups in the surface form strong hydrogen
bonds with the water molecules. Dynamics in RMs has
drawn tremendous attention in recent times as it represents a nano-confined system where water dynamics gets
significantly modified1–3,79,83–96.
Water in confinement exhibits slow as well as fast dynamics. The slow dynamics has been reported to have
time constants 2–3 orders of magnitude larger than that in
the bulk. Paradoxically, the fast dynamics has been found
faster than the bulk, with time constants smaller by as
much as a factor of 3. The origin of both fast and slow
components are the subjects of significant interest.
Recently, we have proposed a simple analysis based on
the one-dimensional Ising model97 to illustrate the dynamical behaviour of water in confined systems. Our model is
especially applicable to RMs. We discuss here this modified finite length one-dimensional Ising model and use it
to study the propagation and the annihilation of dynamical correlations in finite systems and to understand the intriguing shortening of the orientational relaxation time
that has been reported for small-sized RMs. This model
has been designed to mimic the frustration scenario present in RMs, which arises owing to the strongly hydrogen-bonded surface water molecules.
The main motivation behind this model is that in confined systems, such as RMs, the water molecules that are
located diametrically opposite to each other are orientated
opposite to each other. Thus the opposite correlations
induced by spatially opposite surface groups propagate
inside and are expected to annihilate each other at the
centre.
Effects of correlations on orientational relaxation can
be modelled in a very simple way by using the ferromagnetic interaction in a one-dimensional Ising chain with
two terminal spins fixed in opposite directions, one as up
(i.e. ‘+1’) and the other at the opposite side as down (i.e.
‘–1’) (see Figure 20). The inhomogeneity created by the
fixed spins at surface will propagate through the nearest
CURRENT SCIENCE, VOL. 101, NO. 7, 10 OCTOBER 2011
neighbour interaction and naturally decrease as one
moves away from the terminal towards the centre. The
two opposite polarizations will cancel each other exactly
at the centre. So the central spin will behave similar to a
free spin and can relax faster than the bulk.
We have carried out both analytical and numerical calculations of our new model by using Glauber master
equation for various number of spin systems.
Theoretical formulation
The Glauber master equation98 for one-dimensional array
of spin is given by:
d
p (σ 1 , σ 2 ,..., σ N , t )
dt
= −∑ w j (σ j −1 , σ j , σ j +1 ) p (σ 1 , σ 2 ,..., σ j ,..., σ N , t )
j
+ ∑ w j (σ j −1 , − σ j , σ j +1 ) p(σ 1 , σ 2 ,..., − σ j ,..., σ N , t )
j
(25)
and the transition probability wj(σj–1, σj, σj+1) is given by
1 ⎡ 1
⎤
w j (σ j −1 , σ j , σ j +1 ) = α ⎢1 − γσ j (σ j −1 + σ j +1 ) ⎥ .
2 ⎣ 2
⎦
(26)
One can define a stochastic variable for average spin
value as
q j (t ) = ⟨σ j (t )⟩ = ∑ σ j (t ) p (σ 1 , σ 2 ,..., σ N , t ).
(27)
{σ }
By using the value of wj(σj–1, σj, σj+1) and qj(t), one can
find the following equation of motion for the k-th spin
dqk (t )
αγ
= −α qk (t ) +
{qk −1 (t ) + qk +1 (t )}.
dt
2
(28)
This equation of motion can be solved for short chains,
and numerically for large system size. We have obtained
the analytical solutions for N = 3, 4 and 5 spins systems.
The time dependence of various spins in these systems is
given as follows.
Figure 20. A schematic illustration of the proposed one-dimensional
Ising chain model with the spins at the boundary having fixed orientation in the opposite directions97.
917
SPECIAL SECTION:
For N = 3 system with terminal spin fixed, the central
spin will decay as
q2(t) = q2(0)exp(–α t).
(29)
Thus, the decay of the central spin follows the dynamics
in the non-interacting limit. This gives a nice and simple
example of the destructive interference owing to the interaction with the surface.
In case of N = 4 system, the same treatment leads to the
following solution.
q2 (t ) =
1 +
⎡1
⎤
q3 (t ) = ⎢ q3 (0) −
q24 (0) ⎥ exp(−αλ5+ t )
2 2
⎣2
⎦
1 +
⎡1
⎤
+ ⎢ q3 (0) +
q24 (0) ⎥ exp(−αλ5− t ),
2 2
⎣2
⎦
q4 (t ) = −
q3 (t ) = −
±
q24
(0) = q2 (0) ± q4 (0)
and
⎛
λ5± = ⎜1 ±
(32)
and
⎝
⎠
(33)
It is clear from eqs (30) and (31) that the decay pattern of
q2(t) and q3(t) have two time constants, one is smaller
(the decay is faster) and the other is larger (the decay is
slower) than the time constant for the non-interacting
limit.
At high temperature or low J, limit γ → 0, thus q2(t)
and q3(t) decay with only one time constant, i.e. 1/α.
However, the timescales differ by as much as a factor of
3 in the strong coupling limit (γ = 1).
We could also solve the system of equations of motion
for the N = 5 system and the solution is as follows.
q2 (t ) =
γ
2
(37)
(31)
⎝
⎛ γ⎞
λ4± = ⎜1 ± ⎟ .
2
(36)
where
where
±
q23
(0) = q2 (0) ± q3 (0)
−
+ [q24
(0) + γ ]exp(−α t )
1
⎡1 +
⎤
q3 (0) ⎥ exp(−αλ5− t ),
+ ⎢ q24
(0) +
2 2
⎣4
⎦
(30)
γ
1
+ q + (0) exp(−αλ4− t )
γ + 2 2 23
1⎡ −
2γ ⎤
− ⎢ q23
(0) −
exp(−αλ4+ t ),
γ + 2 ⎥⎦
2⎣
2
1
⎡1 +
⎤
+ ⎢ q24
(0) −
q3 (0) ⎥ exp(−αλ5+ t )
2 2
⎣4
⎦
γ
1
+ q + (0) exp(−αλ4− t )
γ + 2 2 23
1⎡ −
2γ ⎤
+ ⎢ q23
(0) −
exp(−αλ4+ t ),
2⎣
γ + 2 ⎥⎦
γ
(35)
γ ⎞
⎟.
2⎠
(38)
Numerical results and discussions
For larger number of spins, we have solved Glauber
equation of motion (eq. (28)) at temperature T = 1.0 J/
kBT, with time step dt = 1 × 10–3 (α = 1 sets the timescale), with the terminal spins fixed in the opposite directions for several system sizes.
The opposite polarizations created by the two-terminal
fixed spins propagate from surface to the centre and cancel each other at the centre (see Figure 21). Therefore, the
−
+ [q24
(0) − γ ]exp(−α t )
1
⎡1 +
⎤
+ ⎢ q24
(0) −
q3 (0) ⎥ exp(−αλ5+ t )
2 2
⎣4
⎦
1
⎡1 +
⎤
q3 (0) ⎥ exp(−αλ5− t ),
+ ⎢ q24
(0) +
2 2
⎣4
⎦
918
(34)
Figure 21. The calculated equilibrium average spin values for various
spins for N = 11 chain system along the chain. Note the zero average
value for the central spin (N = 6)97.
CURRENT SCIENCE, VOL. 101, NO. 7, 10 OCTOBER 2011
CHEMISTRY – STRUCTURE, SYNTHESIS AND DYNAMICS
central spin can exhibit a behaviour which is different
from the bulk which can be described either by imposing
periodic boundary condition, or by taking the central spin
in a very large system (N very large).
In the case of small size RMs, the central spin exhibits
an initial decay rate faster than the bulk generated with
periodic boundary condition. The central spin decay pattern also exhibits a cross-over from overall faster decay
to bulk-like behaviour with increase in system size, as
shown in Figure 22. For small chains (such as N = 5), we
Figure 22. The semi-log plot of qi(t) versus time for various spins
with following notations; the central spin (the middle one) for different
chain lengths (N = 5 (solid red line), 7 (solid blue line), 9 (solid cyan
line), 15 (solid magenta line), 19 (dashed orange line), 21 (dashed
green line), 31 (solid maroon line)), bulk (dashed blue line) and noninteracting (NINT) case (solid black line)97.
Figure 23. The proposed model consists of several concentric rings
having identical spin density. The spins in the outermost ring are kept
fixed in such a way that two-terminal spins along a diameter are oriented exactly opposite to each other. The spatial direction of every spin
is represented by blue arrow. The central spin is referred as zeroth ring,
first ring is labelled as ring-1 and then the numbering follows an outwards direction.
CURRENT SCIENCE, VOL. 101, NO. 7, 10 OCTOBER 2011
have found that the central spin indeed has two decay
constants (eq. (35)), and an overall faster decay rate than
the bulk, as shown in Figure 22.
Note that the decay of spins in the non-interacting limit
(given by rate α) is considerably faster than that of the
interacting limit. This is the reason for the faster decay of
the central spin for small chains.
The frustration behaviour in RMs can be explained in a
more general way, in terms of a quasi-two-dimensional
model. We have designed a new model by partly following Shore–Zwanzig99 model of interaction among spins.
Instead of working with a two-dimensional (2D) square
lattice, we have designed this new model that consists of
several concentric rings having unit inter-ring spacing
with constant spin density for every ring (see Figure 23).
The spins on the outermost ring (layer) are kept fixed in
such a way that the two-terminal spins along a diameter
are oriented exactly opposite to each other (see Figure
23). Other spins are free to move in an xy plane. These
fixed spins will create inhomogeneity (frustration) in the
system and thus the opposite polarization will propagate
from the terminal ring towards the centre.
We define a spin–spin time correlation function by
averaging over all the spins in a given ring by
Ci (t ) =
1
N
N
⟨σ j (0).σ j (t )⟩
,
.
j (0) σ j (0)⟩
∑ ⟨σ
j =1
(39)
where N is the total number of spins in ith ring.
The spin–spin orientational function defined as eq.
(39), shows an interesting behaviour especially in the
short-time window (Figure 24). As depicted in Figure 24,
the overall decay pattern for the ring adjacent to the fixed
one is slower than the other, and it becomes faster as one
moves towards the centre. The central region exhibits a
bit slower decay at shorter times but faster in the longer
times.
Figure 24. Semilog plot of spin–spin orientational autocorrelation
function, averaged overall spins in a given ring. Central spin (black),
ring-1 (red), ring-2 (blue), ring-3 (cyan) and ring-4 (magenta).
919
SPECIAL SECTION:
Therefore, this model also established the fact of annihilation of opposite polarizations propagated from surface
to the centre.
9.
Conclusions
10.
We have discussed the fascinating problem of anomalous
static and dynamic properties of water in the bulk, in
RMs and in the DNA hydration layer. Although, the
simulation results in bulk water are in close agreement
with experimental ones, we hardly have any experimental
result for the DNA hydration water except that the tetrahedral nature of water coordination in the ‘spine of
hydration’ along the AT minor grooves are well known
from X-ray studies. Water within RMs also pose several
intriguing problems.
Although a complete theoretical understanding of the
anomalous behaviour of low-temperature water is yet not
fully understood, we have demonstrated here a critical
role of 5-coordinated water molecules. It will be interesting to study the importance of this 5-coordinated water
molecule in confined water. We are yet to study this
problem in detail for water within RM or even when the
confining surface is structureless. In the minor groove of
DNA, relative importance of the 5-coordinated water
molecules decreases substantially, because of the interactions with the polar groups. In the entropy–enthalpy
balance, stabilization by interaction energy favours 4coordinated structures.
To study the effects of confinement, we have introduced two different lattice models that are shown to exhibit
interesting dynamics, some of which are in agreement
with experimental results.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
1. Bagchi, B., Water dynamics in the hydration layer around proteins
and micelles. Chem. Rev., 2005, 105(9), 3197–3219; Bagchi, B.
and Jana, B., Solvation dynamics in dipolar liquids. Chem. Soc.
Rev., 2010, 39(6), 1936–1954.
2. Nandi, N., Bhattacharyya, K. and Bagchi, B., Dielectric relaxation
and solvation dynamics of water in complex chemical and biological systems. Chem. Rev., 2000, 100(6), 2013–2046.
3. Bhattacharyya, K., Solvation dynamics and proton transfer
in supramolecular assemblies. Acc. Chem. Res., 2002, 36(2), 95–
101; Bhattacharyya, K., Nature of biological water: a femtosecond
study. Chem. Commun., 2008, 25, 2848–2857.
4. Senapati, S. and Chandra, A., Dielectric constant of water
confined in a nanocavity. J. Phys. Chem. B, 2001, 105(22), 5106–
5109.
5. Cheng, Y.-K. and Rossky, P. J., Surface topography dependence
of biomolecular hydrophobic hydration. Nature, 1998, 392(6677),
696–699.
6. Tarek, M. and Tobias, D. J., Role of protein–water hydrogen bond
dynamics in the protein dynamical transition. Phys. Rev. Lett.,
2002, 88(13), 138101.
7. Lehninger, A., Nelson, D. and Cox, M., Principles of Biochemistry
W. H. Freeman, 2008.
8. Tarek, M. and Tobias, D. J., The dynamics of protein hydration
water: A quantitative comparison of molecular dynamics simu920
22.
23.
24.
25.
26.
27.
lations and neutron-scattering experiments. Biophys. J., 2000,
79(6), 3244–3257.
Murarka, R. K. and Head-Gordon, T., Dielectric relaxation of
aqueous solutions of hydrophilic versus amphiphilic peptides. J.
Phys. Chem. B, 2007, 112(1), 179–186.
Pal, S., Maiti, P. K. and Bagchi, B., Exploring DNA groove water
dynamics through hydrogen bond lifetime and orientational
relaxation. J. Chem. Phys., 2006, 125(23).
Jana, B., Pal, S., Maiti, P. K., Lin, S. T., Hynes, J. T. and Bagchi,
B., Entropy of water in the hydration layer of major and minor
grooves of DNA. J. Phys. Chem. B, 2006, 110(39), 19611–19618.
Berg, M. A., Coleman, R. S. and Murphy, C. J., Nanoscale
structure and dynamics of DNA. Phys. Chem. Chem. Phys., 2008,
10(9), 1229–1242.
Andreatta, D., Sen, S., Perez Lustres, J. L., Kovalenko, S. A.,
Ernsting, N. P., Murphy, C. J., Coleman, R. S. and Berg, M. A.,
Ultrafast dynamics in DNA: ‘Fraying’ at the end of the helix. J.
Am. Chem. Soc., 2006, 128(21), 6885–6892.
Jayaram, B. and Beveridge, D. L., Modeling DNA in aqueous
solutions: Theoretical and computer simulation studies on the ion
atmosphere of DNA. Ann. Rev. Biophys. Biomol. Struct., 1996,
25(1), 367–394.
Kolesnikov, A. I., Zanotti, J. M., Loong, C. K. and Thiyagarajan,
P., Anomalously soft dynamics of water in a nanotube: A
revelation of nanoscale confinement. Phys. Rev. Lett., 2004, 93(3),
035503.
Chandra, A., Effects of ion atmosphere on hydrogen-bond
dynamics in aqueous electrolyte solutions. Phys. Rev. Lett., 2000,
85(4), 768.
Franks, F. (ed.), Water A Comprehensive Treatise, Plenum Press,
New York, 1971–1982.
Robinson, G. W., Zhu, S. B., Singh, S. and Evans, M. W., Water
in Biology, Chemistry and Physics: Experimental Overviews and
Computational Methodologies, World Scientific Series in
Contemporary Chemical Physics, World Scientific Publishing Co
Pte Ltd, Singapore, 1996.
Eisenberg, D. and Kauzmann, W., The Structure and Properties of
Water (Oxford Classic Texts in the Physical Sciences), Oxford
University Press, USA, 2005.
Hutchenson, K. W. and Foster, N. R. (eds), Innovations in Supercritical Fluids: Science and Technology, Acs Symposium Series,
An American Chemical Society Publication, 1995.
Clark, G. N. I., Cappa, C. D., Smith, J. D., Saykally, R. J. and
Head-Gordon, T., The structure of ambient water. Mol. Phys.,
2010, 108(11), 1415–1433.
Angell, C. A., Shuppert, J. and Tucker, J. C., Anomalous properties of supercooled water. Heat capacity, expansivity, and
proton magnetic resonance chemical shift from 0 to –38%. J.
Phys. Chem., 1973, 77(26), 3092–3099.
Speedy, R. J. and Angell, C. A., Isothermal compressibility of
supercooled water and evidence for a thermodynamic singularity
at –45°C. J. Chem. Phys., 1976, 65(3), 851–858.
Speedy, R. J., Stability-limit conjecture. An interpretation of the
properties of water. J. Phys. Chem., 1982, 86(6), 982–991.
Sastry, S., Debenedetti, P. G., Sciortino, F. and Stanley, H. E.,
Singularity-free interpretation of the thermodynamics of supercooled water. Phys. Rev. E, 1996, 53(6), 6144.
Poole, P. H., Sciortino, F., Essmann, U. and Stanley, H. E., Phase
behaviour of metastable water. Nature, 1992, 360(6402), 324–
328.
Stanley, H. E., Angell, C. A., Essmann, U., Hemmati, M., Poole,
P. H. and Sciortino, F., Is there a second critical point in liquid
water? Physica A, 1994, 205(1–3), 122–139; Stanley, H. E., Cruz,
L., Harrington, S. T., Poole, P. H., Sastry, S., Sciortino, F., Starr,
F. W. and Zhang, R., Cooperative molecular motions in water:
The liquid–liquid critical point hypothesis. Physica A, 1997,
236(1–2), 19–37.
CURRENT SCIENCE, VOL. 101, NO. 7, 10 OCTOBER 2011
CHEMISTRY – STRUCTURE, SYNTHESIS AND DYNAMICS
28. Mishima, O. and Stanley, H. E., Decompression-induced melting
of ice IV and the liquid–liquid transition in water. Nature, 1998,
392(6672), 164–168.
29. Franzese, G. and Stanley, H. E., The widom line of supercooled
water. J. Phys. Cond. Matter, 2007, 19(20).
30. Mishima, O., Calvert, L. D. and Whalley, E., An apparently firstorder transition between two amorphous phases of ice induced by
pressure. Nature, 1985, 314(6006), 76–78.
31. Mishima, O., Relationship between melting and amorphization of
ice. Nature, 1996, 384(6609), 546–549.
32. Giovambattista, N., Stanley, H. E. and Sciortino, F., Phase
diagram of amorphous solid water: Low-density, high-density, and
very-high-density amorphous ices. Phys. Rev. E, 2005, 72(3),
031510.
33. Liu, L., Chen, S. H., Faraone, A., Yen, C. W. and Mou, C. Y.,
Pressure dependence of fragile-to-strong transition and a possible
second critical point in supercooled confined water. Phys. Rev.
Lett., 2005, 95(11), 117802.
34. Chen, S.-H. et al., Observation of fragile-to-strong dynamic
crossover in protein hydration water. Proc. Natl. Acad. Sci. USA,
2006, 103(24), 9012–9016.
35. Bagchi, B. and Chandra, A., Dielectric relaxation in dipolar
liquids: Route to Debye behavior via translational diffusion. Phys.
Rev. Lett., 1990, 64(4), 455.
36. Laage, D. and Hynes, J. T., A molecular jump mechanism of water
reorientation. Science, 2006, 311(5762), 832–835.
37. Laage, D. and Hynes, J. T., On the molecular mechanism of water
reorientation. J. Phys. Chem. B, 2008, 112(45), 14230–14242.
38. Mahoney, M. W. and Jorgensen, W. L., A five-site model for
liquid water and the reproduction of the density anomaly by rigid,
nonpolarizable potential functions. J. Chem. Phys., 2000, 112(20),
8910–8922.
39. Mahoney, M. W. and Jorgensen, W. L., Diffusion constant of the
TIP5P model of liquid water. J. Chem. Phys., 2001, 114(1), 363–
366.
40. Mukherjee, A., Lavery, R., Bagchi, B. and Hynes, J. T., On the
molecular mechanism of drug intercalation into DNA: A
simulation study of the intercalation pathway, free energy, and
DNA structural changes. J. Am. Chem. Soc., 2008, 130(30), 9747–
9755.
41. Ringe, D. and Petsko, G. A., The ‘glass transition’ in protein
dynamics: what it is, why it occurs, and how to exploit it. Biophys.
Chem., 2003, 105(2–3), 667–680.
42. Hartmann, H., Parak, F., Steigemann, W., Petsko, G. A., Ponzi,
D. R. and Frauenfelder, H., Conformational substates in a protein:
structure and dynamics of metmyoglobin at 80 K. Proc. Natl.
Acad. Sci. USA, 1982, 79(16), 4967–4971.
43. Lee, A. L. and Wand, A. J., Microscopic origins of entropy, heat
capacity and the glass transition in proteins. Nature, 2001,
411(6836), 501–504.
44. Rasmussen, B. F., Stock, A. M., Ringe, D. and Petsko, G. A.,
Crystalline ribonuclease A loses function below the dynamical
transition at 220 K. Nature, 1992, 357(6377), 423–424.
45. Doster, W., Cusack, S. and Petry, W., Dynamical transition of
myoglobin revealed by inelastic neutron scattering. Nature, 1989,
337(6209), 754–756.
46. Vitkup, D., Ringe, D., Petsko, G. A. and Karplus, M., Solvent
mobility and the protein ‘glass’ transition. Nat. Struct. Mol. Biol.,
2000, 7(1), 34–38.
47. Tarek, M. and Tobias, D. J., The dynamics of protein hydration
water: A quantitative comparison of molecular dynamics simulations and neutron-scattering experiments. Biophys. J., 2000,
79(6), 3244–3257.
48. Zanotti, J.-M., Bellissent-Funel, M. C. and Parello, J., Hydrationcoupled dynamics in proteins studied by neutron scattering and
NMR: The case of the typical EF-hand calcium-binding parvalbumin. Biophys. J., 1999, 76(5), 2390–2411.
CURRENT SCIENCE, VOL. 101, NO. 7, 10 OCTOBER 2011
49. Sokolov, A. P., Grimm, H. and Kahn, R., Glassy dynamics in
DNA: Ruled by water of hydration? J. Chem. Phys., 1999,
110(14), 7053–7057.
50. Norberg, J. and Nilsson, L., Glass transition in DNA from
molecular dynamics simulations. Proc. Natl. Acad. Sci. USA,
1996, 93(19), 10173–10176.
51. Lagi, M., Chu, X., Kim, C., Mallamace, F., Baglioni, P. and Chen,
S. H., The low-temperature dynamic crossover phenomenon in
protein hydration water: Simulations vs experiments. J. Phys.
Chem. B, 2008, 112(6), 1571–1575.
52. Chen, S. H. et al., Experimental evidence of fragile-to-strong
dynamic crossover in DNA hydration water. J. Chem. Phys., 2006,
125(17).
53. Mallamace, F. et al., Role of the solvent in the dynamical
transitions of proteins: The case of the lysozyme-water system. J.
Chem. Phys., 2007, 127(4).
54. Sen, S., Andreatta, D., Ponomarev, S. Y., Beveridge, D. L. and
Berg, M. A., Dynamics of water and ions near DNA: Comparison
of simulation to time-resolved Stokes-shift experiments. J. Am.
Chem. Soc., 2009, 131(5), 1724–1735.
55. Kumar, P. et al., Glass transition in biomolecules and the liquid–
liquid critical point of water. Phys. Rev. Lett., 2006, 97(17),
177802.
56. Harrington, S., Zhang, R., Poole, P. H., Sciortino, F. and Stanley,
H. E., Liquid–liquid phase transition: Evidence from simulations.
Phys. Rev. Lett., 1997, 78(12), 2409.
57. Xu, L., Kumar, P., Buldyrev, S. V., Chen, S. H., Poole, P. H.,
Sciortino, F. and Stanley, H. E., Relation between the widom line
and the dynamic crossover in systems with a liquid–liquid phase
transition. Proc. Natl. Acad. Sci. USA, 2005, 102(46), 16558–
16562.
58. Jana, B. and Bagchi, B., Intermittent dynamics, stochastic resonance and dynamical heterogeneity in supercooled liquid water. J.
Phys. Chem. B, 2009, 113(8), 2221–2224.
59. Balasubramanian, S. and Bagchi, B., Slow orientational dynamics
of water molecules at a micellar surface. J. Phys. Chem. B, 2002,
106(14), 3668–3672.
60. Balasubramanian, S., Pal, S. and Bagchi, B., Hydrogen-bond
dynamics near a micellar surface: origin of the universal slow
relaxation at complex aqueous interfaces. Phys. Rev. Lett., 2002,
89(11), 115505.
61. Balasubramanian, S. and Bagchi, B., Slow solvation dynamics
near an aqueous micellar surface. J. Phys. Chem. B, 2001,
105(50), 12529–12533.
62. Drew, H. R., Wing, R. M., Takano, T., Broka, C., Tanaka, S., Itakura, K. and Dickerson, R. E., Structure of a B-DNA dodecamer:
conformation and dynamics. Proc. Natl. Acad. Sci. USA, 1981,
78(4), 2179–2183.
63. Case, D. A. et al., AMBER 8, University of California, San
francisco, 2004.
64. Donati, C., Franz, S., Glotzer, S. C. and Parisi, G., Theory of
nonlinear susceptibility and correlation length in glasses and
liquids. J. Non-Cryst. Solids, 2002, 307, 215–224.
65. Dasgupta, C., Indrani, A. V., Ramaswamy, S. and Phani, M. K.,
Is there a growing correlation length near the glass transition?
Europhys. Lett., 1991, 15(3), 307–312.
66. Glotzer, S. C., Novikov, V. N. and Schroder, T. B., Time-dependent, four-point density correlation function description of
dynamical heterogeneity and decoupling in supercooled liquids. J.
Chem. Phys., 2000, 112(2), 509–512.
67. Cardenas, M., Franz, S. and Parisi, G., Glass transition and
effective potential in the hypernetted chain approximation. J.
Phys. A, 1998, 31(9), L163–L169; Cardenas, M., Franz, S. and
Parisi, G., Constrained Boltzmann–Gibbs measures and effective
potential for glasses in hypernetted chain approximation
and numerical simulations. J. Chem. Phys., 1999, 110(3), 1726–
1734.
921
SPECIAL SECTION:
68. Chandra, A. and Chowdhuri, S., Pressure effects on the dynamics
and hydrogen bond properties of aqueous electrolyte solutions:
The role of ion screening. J. Phys. Chem. B, 2002, 106(26), 6779–
6783.
69. Sciortino, F., Geiger, A. and Stanley, H. E., Effect of defects on
molecular mobility in liquid water. Nature, 1991, 354(6350), 218–
221.
70. Sciortino, F., Geiger, A. and Stanley, A., Isochoric differential
scattering functions in liquid water: The fifth neighbor as a
network defect. Phys. Rev. Lett., 1990, 65(27), 3452.
71. Bosio, L., Chen, S. H. and Teixeira, J., Isochoric temperature
differential of the X-ray structure factor and structural rearrangements in low-temperature heavy water. Phys. Rev. A, 1983, 27(3),
1468.
72. Kumar, P., Yan, Z., Xu, L., Mazza, M. G., Buldyrev, S. V., Chen.
S. H., Sastry, S. and Stanley, H. E., Glass transition in
biomolecules and the liquid–liquid critical point of water. Phys.
Rev. Lett., 2006, 97(17), 177802.
73. Gammaitoni, L., Hanggi, P., Jung, P. and Marchesoni, F.,
Stochastic resonance. Rev. Mod. Phys., 1998, 70(1), 223.
74. Jana, B., Singh, R. S. and Bagchi, B., String-like propagation of
the 5-coordinated defect state in supercooled water: molecular
origin of dynamic and thermodynamic anomalies. Phys. Chem.
Chem. Phys., 2011 (DOI: 10.1039/C0CP02081H).
75. Biswal, D., Jana, B., Pal, S. and Bagchi, B., Dynamical transition
of water in the grooves of DNA duplex at low temperature. J.
Phys. Chem. B, 2009, 113(13), 4394–4399.
76. Chen, S. H., Liao, C., Sciortino, F., Gallo, P. and Tartaglia, P.,
Model for single-particle dynamics in supercooled water. Phys.
Rev. E, 1999, 59(6), 6708.
77. Subramanian, P. S., Ravishanker, G. and Beveridge, D. L., Theoretical considerations on the ‘spine of hydration’ in the minor
groove of d(CGCGAATTCGCG). d(GCGCTTAAGCGC): Monte
Carlo computer simulation. Proc. Natl. Acad. Sci. USA, 1988,
85(6), 1836–1840.
78. Lin, S. T., Blanco, M. and Goddard, W. A., The two-phase model
for calculating thermodynamic properties of liquids from molecular dynamics: Validation for the phase diagram of Lennard–
Jones fluids. J. Chem. Phys., 2003, 119(22), 11792–11805.
79. Jana, B., Pal, S. and Bagchi, B., Enhanced tetrahedral ordering of
water molecules in minor grooves of DNA: Relative role of DNA
rigidity, nanoconfinement, and surface specific interactions. J.
Phys. Chem. B, 2010, 114(10), 3633–3638.
80. Chau, P. L. and Hardwick, A. J., A new order parameter for
tetrahedral configurations. Mol. Phys., 1998, 93(3), 511–518.
81. Calef, D. F. and Deutch, J. M., Diffusion-controlled reactions.
Ann. Rev. Phys. Chem., 1983, 34(1), 493–524.
82. Tarjus, G., Alba-Simionesco, A., Grousson, M., Viot, P. and
Kivelson, D., Locally preferred structure and frustration in glassforming liquids: a clue to polyamorphism? J. Phys. Cond. Matter,
2003, 15(11), S1077–S1084.
83. Bhattacharyya, K. and Bagchi, B., Slow dynamics of constrained
water in complex geometries. J. Phys. Chem. A, 2000, 104(46),
10603–10613.
84. Levinger, N. E., Water in confinement. Science, 2002, 298(5599),
1722–1723.
85. Sarkar, N., Datta, A., Das, S. and Bhattacharyya, K., Solvation
dynamics of Coumarin 480 in micelles. J. Phys. Chem., 1996,
100(38), 15483–15486.
922
86. Telgmann, T. and Kaatze, U., On the kinetics of the formation of
small micelles. 1. Broadband ultrasonic absorption spectrometry.
J. Phys. Chem. B, 1997, 101(39), 7758–7765; Telgmann, T. and
Kaatze, U., On the kinetics of the formation of small micelles. 2.
Extension of the model of stepwise association. J. Phys. Chem. B,
1997, 101(39), 7766–7772.
87. Datta, A., Mandal, D., Pal, S. K. and Bhattacharyya, K., Solvation
dynamics in organized assemblies, 4-aminophthalimide in
micelles. J. Mol. Liq., 1998, 77(1–3), 121–129.
88. Sarkar, N., Das, K., Datta, A., Das, S. and Bhattacharyya, K.,
Solvation dynamics of coumarin 480 in reverse micelles. Slow
relaxation of water molecules. J. Phys. Chem., 1996, 100(25),
10523–10527.
89. Harpham, M. R., Ladanyi, B. M., Levinger, N. E. and Herwig,
K. W., Water motion in reverse micelles studied by quasielastic
neutron scattering and molecular dynamics simulations. J. Chem.
Phys., 2004, 121(16), 7855–7868.
90. Vajda, S., Jimenez, R., Rosenthal, S. J., Fidler, V., Fleming, G. R.
and Castner, E. W., Femtosecond to nanosecond solvation dynamics in pure water and inside the [gamma]-cyclodextrin cavity. J.
Chem. Soc., Faraday Trans., 1995, 91(5), 867–873.
91. Nandi, N. and Bagchi, B., Ultrafast solvation dynamics of an ion
in the γ-cyclodextrin cavity: The role of restricted environment.
J. Phys. Chem., 1996, 100(33), 13914–13919.
92. Willard, D. M., Riter, R. E. and Levinger, N. E., Dynamics of
polar solvation in lecithin/water/cyclohexane reverse micelles.
J. Am. Chem. Soc., 1998, 120(17), 4151–4160.
93. Piletic, I. R., Tan, H.-S. and Fayer, M. D. Dynamics of nanoscopic
water: Vibrational echo and infrared pump–probe studies of
reverse micelles. J. Phys. Chem. B, 2005, 109(45), 21273–
21284.
94. Tan, H.-S., Piletic, I. R., Riter, R. E., Levinger, N. E. and Fayer,
M. D., Dynamics of water confined on a nanometer length scale in
reverse micelles: ultrafast infrared vibrational echo spectroscopy.
Phys. Rev. Lett., 2005, 94(5), 057405.
95. Piletic, I. R., Moilanen, D. E., Spry, D. B., Levinger, N. E. and
Fayer, M. D., Testing the core/shell model of nanoconfined water
in reverse micelles using linear and nonlinear IR spectroscopy. J.
Phys. Chem. A, 2006, 110(15), 4985–4999.
96. Moilanen, D., Fenn, E. E., Wong, D. and Fayer, M. D., Water
dynamics in large and small reverse micelles: From two ensembles
to collective behavior. J. Chem. Phys., 2009. 131(1), 014704.
97. Biswas, R. and Bagchi, B., A kinetic Ising model study of
dynamical correlations in confined fluids: Emergence of both fast
and slow time scales. J. Chem. Phys., 2010, 133(8), 084509.
98. Glauber, R., Time-dependent statistics of the Ising model. J. Math.
Phys., 1963, 4(2), 294–307.
99. Shore, J. and Zwanzig, R., Dielectric relaxation and dynamic
susceptibility of a one-dimensional model for perpendicular-dipole
polymers. J. Chem. Phys., 1975, 63(12), 5445–5458.
ACKNOWLEDGEMENTS. We thank Mr M. Santra for helpful
discussions. This work has been supported partly by grants from DST
and CSIR. B.B. thanks DST for support through a J. C. Bose Fellowship. R.B. thanks CSIR for providing SRF.
CURRENT SCIENCE, VOL. 101, NO. 7, 10 OCTOBER 2011