The Dynamical Transition of Protein Hydration Water - E13 - TUM

The Dynamical Transition of Protein Hydration Water
W. Doster, S. Busch and A. Gaspar
Physics Department E 13 and ZWE FRM II, Technische Universität München, 85747 Garching, Germany ∗
M. S. Appavou, and J. Wuttke
Institut für Festkörperforschung, Forschungszentrum Jülich GmbH,
Jülich Center for Neutron Science At FRM II, Lichtenbergstr. 1, 85747 Garching, Germany
(Dated: July 22, 2009)
Thermodynamic anomalies and computer simulations of bulk water suggest a hidden critical
point in the deeply super-cooled regime, which is not accessible to experiment [1]. To suppress
crystallization, thin layers of water adsorbed to biomolecular surfaces were investigated with dynamic
neutron scattering and simulation [2, 3]. Enhanced molecular displacements of lysozyme hydration
water and a cross-over in the temperature dependence of the structural relaxation time at 220 K
were assigned to a liquid-liquid phase transition in support of the critical scenario. We present
more detailed neutron scattering experiments of water adsorbed to perdeuterated phycocyanin,
suggesting instead a widening of the relaxation time spectrum. It is shown that the protein surface
acts as a patch-breaker, suppressing critical fluctuations and the density maximum. This suggest a
conventional glass-transition at 170 K rather than a critical scenario.
PACS numbers: 61.20Ja,61.20Gy
The ’protein dynamical transition’ was introduced 20
years ago to denote an abrupt onset of structural displacements
observed at 240 K with hydrated myoglobin
and lysozyme [4]. The onset reflects a generic lowtemperature
property of hydrated proteins, which is absent
in dehydrated systems. The dynamical transition
was thus interpreted as the water-coupled freezing-in of
structural relaxation. Protein hydration water, about 0.4
g /g protein, can be super-cooled until the glass transition
interferes at TG ≈ 170 K. The respective arrest of
translational degrees of freedom induces discontinuities
in the specific heat and the thermal expansion coefficient
of hydration water [5–9]. The dynamic onset was deduced
originally from an anomalous loss in elastic intensity,
observed with energy-resolved neutron scattering experiments.
The spectral analysis showed, that the loss in
elastic intensity is compensated by enhanced quasi-elastic
scattering, where the respective protein-water relaxation
time crosses the instrumental time window [4, 10]. The
onset temperature thus varies with the probe frequency
and, more generally, the viscosity of the solvent near the
protein surface [4, 11–13]: A viscous liquid appears solid
on a scale shorter than the structural relaxation time.
The onset at Ton = 240 K is located 60 degrees above
the calorimetric glass temperature, since neutron scattering
probes the structural relaxation at 100 ps, while
the calorimetric glass temperature refers to a time-scale
of 100 s.
Recently, a structural transition, which would not display
a time-scale effect, was proposed as an alternative
explanation: High resolution neutron scattering ex-
∗ Electronic address: wdoster@ph.tum.de
APS/123-QED
FIG. 1: Neutron scattering spectra of H2O-hydrated C-PC
(red) versus energy exchange ∆E and fits to equ.(1) convolved
with the instrumental resolution function at Q = 1.6 ˚A −1
(black). Analysis with two spectral components, a narrow
elastic line due to the rigid protein structure (dashed-double
dotted) and (2) a ’stretched’ broad line (long dash) with β
= 0.5, reflecting the motion of protein- adsorbed water. A
Lorentzian spectrum with β = 1, (dotted) does not fit the
data. Dashed-dotted: Averaged experimental resolution function
R(ω), which also coincides with averaged data taken at
150 K.
periments (on the high-flux backscattering spectrometer
HFBS of NIST) on hydrated lysozyme, DNA and RNA
display an apparent cross-over between high-temperature
super-Arrhenius and low-temperature Arrhenius behavior
of the α-relaxation time [2, 3, 14, 15]. The authors
interpret this ’fragile to strong’ cross-over’ at 220 K as

the transition from the high density to the low density
phase of supercooled water [1, 3]. In this view,
a qualitative change in the dynamics occurs, when the
so-called Widom line is crossed, which extrapolates the
phase boundary beyond the conjectured critical point
[16, 17]. QENS measurements performed with the same
HFBS spectrometer reveal a similar cross-over with confined
water in various non-biological environments, such
as carbon-nanotubes and rutile [18]. These new results
also admit a ’dynamical’ interpretation: Tfst = 220 K
is located between TG and Ton: Due to the high energy
resolution of HFBS, the onset of quasielastic scattering is
observed on a time scale, which is intermediate between
calorimetry and previous neutron scattering experiments.
To address the question of ’structural’ versus ’dynamical’
transition, we measured the motion of protein hydration
water with enhanced sensitivity, employing an improved
neutron scattering set-up with a per-deuterated
protein sample, C-phycocyanin (C-PC). In this protein
99% of the non-exchangeable hydrogens were replaced
by D [19]. This emphazises the contribution of H2O to
the scattering function with respect to the protein, since
the proton has a ten times larger total cross-section compared
to the deuteron [20]. The per-deuterated protein
contributes essentially an elastic component to the spectrum,
from which the relevant quasi-elastic part of H2O
can be easily separated. The degree of hydration with
H2O was adjusted to 0.3 g/g, the same hydration was
used in the experiments performed with lysozyme [2]. C-
PC is a blue copper protein and water-soluble, which acts
as an antenna to collect light in bacteria. It consists of six
protein chains, each containing a chromophore, which are
organized as a ring structure surrounding a solvent channel
in the center [21]. Water on C-PC was investigated
with neutron back-scattering before, yielding an oscillating
spectral width depending on the wave-vector [22, 23].
Quasi-elastic neutron scattering data were collected with
the new high-flux, high-resolution back-scattering spectrometer
SPHERES at FRM II in Munich [24]. The
standard setup with 0.65 µeV (FWHM) resolution is
slightly better than HFBS (0.85 µeV). The spectrometer
was equipped with a temperature-controlled cryostat
and spectra between 150 and 320 K were measured typically
for 12 h each.
Fig. 1 displays selected spectra of H2O-hydrated C-
PC in the relevant temperature range. The log-intensity
scale emphasizes the wings of the spectra in contrast
to previous work [2]. A two-component analysis of the
data was performed: (1) a narrow elastic spectrum assuming
the shape of the instrumental resolution function
R(ω), which is present also in the absence of water. It
reflects the mainly coherent scattering from the rigid protein
structure [20], (2) a broader quasi-elastic component,
which is assigned to motions of adsorbed H2O molecules.
No further component (background) was assumed. As
fig. 1 illustrates, a Lorentzian line-shape (dotted) does
not account for the broad line at this wave-vector. A
stretched exponential relaxation defined by the stretch-
FIG. 2: Average relaxation rates at large Q, derived from the
fits of the spectra in fig. 1 with equ. 1 at 300 K (full red circles)
and at 270 K (open circles). Full circles (blue): stretching
exponents β. Dashed line: rate of continuous translational
diffusion with ˙ τ −1¸ = Q 2 Dhyd
ing exponent β ≤1 had to be introduced. Transformation
to the frequency domain and convolution with the resolution
function R(ω) yields:
SQ(ω) = AprotR (ω)+Ahyd·R(ω)∗FT exp(−t/τ) β (1)
The fits were constrained by fixing the protein- and water
spectral fractions, Aprot and Ahyd. The average relaxation
time 〈τ〉 of a Kohlrausch function is given by:
〈τ〉 = τ ·Γ (β)/β. Excellent fits of the spectra with equ. 1
were achieved for the entire temperature and Q-range, as
illustrated in fig. 1 on a log-intensity scale.
The correlation time τ and the stretching parameter
β were adjusted. Both parameters depend on the wavevector:
Below Q = 1 ˚A −1 , a Lorentzian line-shape, β = 1,
is compatible with data. The resulting spectral width increases
with Q as shown in fig. 2. The observed Q 2
dependence of the width is the signature of translational
diffusion and excludes any interpretation in terms of localized
motion (β-process) of protein residues or water
molecules. From 1/〈τ〉 = Q 2 Dhyd one estimates an effective
diffusion coefficient of Dhyd ≈ 0.2 Dbulk, consistent
with previous results [25]. Above Q = 1 ˚A −1 , the relaxation
rate tends to a Q-independent plateau. In this Q
regime, one records motions on a spatial scale comparable
to the intermolecular distance. The cage of nearest
neighbours forces the molecules to perform discrete
displacements. The respective displacement distribution
thus deviates from a Gaussian random process [12]. The
inter-cage motion restores the spatial symmetry and can
thus be interpreted as the main structural process, the
2

FIG. 3: Arrhenius plot of 〈τ〉 of H2O adsorbed to C-PC with
β = 0.5 (full red circles) and β = 0.35 (open circles). Full
red line: VFT-fit with equ.(2), parameters: τ0 = 1 (±0.5)
ps, A = 790 (±50) K and T0 = 145 (±10) K. Filled triangles:
H2O of hydrated myoglobin [12] and hydrated lysozyme
(black squares) [2], open square: water-coupled protein relaxation
of myoglobin [12, 27].
α-relaxation [26]. In this regime a Lorentzian fails to account
for the wings of the spectra (fig. 1). The constraint
of constant relative amplitudes (equ. 1) allows to confine
the stretching parameter to a narrow range of β = 0.5 ±
0.05.
At lower temperatures (270 K) the same scenario persists
though with lower rates. The reported oscillatory
behavior of the line-width [22] is not reproduced. It results
in our view from neglecting the elastic component,
which varies with Q [20]. In the following, we focus on
the initial step of diffusion, the α-process, by averaging
the weakly Q-dependent spectra above 1.4 ˚A −1 . The
Arrhenius plot of the average relaxation time in fig. 3
displays the expected super-Arrhenius behaviour, as observed
previously with hydrated lyoszyme [2] and myoglobin
[12]. The data were adjusted to a Vogel-Fulcher-
Tamman (VFT) law, shown in fig. 3:
A/(T −T0)
〈τ〉 = τ0e
(2)
The extrapolated glass temperature TG(τ = 100 s) ≈
170 K, coincides with previous estimates, as shown in fig.
4. The VFT fit becomes less satisfactory below 220 K.
The respective ’fragile to strong’ cross-over is however
less pronounced than with lysozyme [2]. An alternative
explanation involves the widening of the relaxation
FIG. 4: Apparent elastic fraction fapp of H2O-C-PC neutron
scattering spectra at Q = 1.6 ˚A −1 (open circles) and the prediction
based on the dynamic analysis of equ. 3 at 0.65 µeV
resolution (full line, red). Dashed-dotted line (blue): normalized
elastic intensity (HFBS, NIST) of water on hydrated
lysozyme by Chen et al. [2]. Dashed line: prediction of fapp at
7 µeV resolution, full circles: hydrated lysozme (IN13, ILL).
Full triangles: Spectroscopic thermal expansion coefficient, α,
of water in hydrated lysozyme powder, open triangles: Densitometric
thermal expansion coefficient of hydration water
(lysozyme in solution), dashed line: expansion coefficient of
bulk water [9, 30].
time spectrum: By adjusting the stretching parameter
β from 0.5 above to 0.35 below 220 K, one can recover
the VFT-behavior (fig. 3). It is known from dielectric
and NMR experiments that a slow β-relaxation decouples
from the main α-relaxation in this temperature range
[28, 29], which may increase the apparent width of the
distribution.
Simulations, supporting the critical scenario, interpret
the anharmonic onset in the displacements at Tfst by an
abrupt loosening of the water structure [3]. The analogous
explanation was given by Chen et al. [2] for the
step-like decrease of the elastic intensity observed with
hydrated lysozyme (dashed-dotted line in fig. 4) . With
C-PC water a similar transition is found at about the
same temperature. Since the elastic intensity responds
to structural as well as to dynamic changes, we introduce
the apparent elastic fraction, defined as the relative area
covered by the elastic spectral component. According to
equ. 1 it can be written as [27]:
dωR(ω, ∆ω)L(ω, 〈τ〉) (3)
fapp = Aprot + Ahyd
The second term, where the spectrum is approximated by
a Lorentzian, exhibits a step-like decrease, when the average
relaxation time 〈τ〉 becomes comparable to 1/∆ω,
the instrumental resolution. The calculated fapp with ∆ω
3

= 0.65 µeV explains the observed elastic fraction of the
C-PC water spectrum rather well (fig. 4). Also shown is
the prediction for ∆ω = 7 µeV and the respective measurements
of lysozyme-adsorbed water performed at the
same resolution with the back-scattering spectrometer
IN13 (ILL). The shift in the onset temperatures from
220 K to 240 K with decreasing spectral resolution is a
typical feature expected of a dynamical transition. In
previous work with hydrated myoglobin and lysozyme
using IN13, the same onset Ton ≈ 240 K was derived
[4, 12]. These findings point to a dynamical rather than
to a structural transition.
To date, mainly neutron scattering experiments performed
with HFBS provide support for a ’fragile to
strong’ cross-over in protein hydration water. In contrast,
dielectric and NMR relaxation experiments did not
show a cusp in the temperature dependence of the respective
structural relaxation time [28, 29, 31]. This
discrepancy could indicate that the anomalous density
fluctuations, present in bulk water, are suppressed in adsorbed
water by interactions with the protein surface.
This raises the question, whether hydration water ex-
[1] P. Poole, F. Sciortino, U. Essmann, and H. Stanley, Nature
360, 324 (1992).
[2] S.-H. Chen, L. Liu, E. Fratini, P. Baglioni, A. Faraone,
and A. Mamontov, Proc. Natl. Acad. Sci. USA 103,
9012 (2006).
[3] P. Kumar, Z. Yan, L. Xu, M. Mazza, S. Buldyrev,
S. Chen, and H. E. Stanley, Phys. Rev. Lett. 97, 177802
(2006).
[4] W. Doster, S. Cusack, and W. Petry, Nature 337, 754
(1989).
[5] W. Doster, T. Bachleitner, M. Hiebl, E. Luescher, and
A. Dunau, Biophys. J. 50, 213 (1986).
[6] Y. Miyazaki, T. Matsuo, and H. Suga, Chem. Phys.
Lett. 213, 303 (1993).
[7] G. Sartor, E. Mayer, and G. Johari, Biophys. J. 66, 249
(1994).
[8] Y. Miyazaki, T. Matsuo, and H. Suga, J. Phys. Chem.
B 104, 8044 (2000).
[9] F. Demmel, W. Doster, W. Petry, and A. Schulte, Europ.
Biophys. J. 26, 327 (1997).
[10] W. Doster, S. Cusack, and W. Petry, Phys. Rev. Lett.
65, 1080 (1990).
[11] H. Lichtenegger, W. Doster, T. Kleinert, B. Sepiol, and
G. Vogl, Biophys. J. 76, 414 (1999).
[12] W. Doster and M. Settles, Biochim. Biophys. Act. 1749,
173 (2005).
[13] W. Doster, Eur. Biophys. J. 37, 591 (2008).
[14] S.-H. Chen, L. Liu, and Y. Zhang, J. Chem.. Phys. 125,
171103 (2006).
[15] M. Lagi, X. Chu, Ch.Kim, F. Mallamace, P. Baglioni,
and S. Chen, J. Phys. Chem. B 112, 1571 (2008).
[16] L. Xu, P. Kumar, S. Buldyrev, S. Chen, P. Poole,
F. Sciortino, and H. Stanley, Proc. Natl. Acad. Sci.
hibits a density maximum required for critical behavior.
The answer is provided by measurements of the
thermal expansion coefficient of water near the surface
of lysozyme: With densitometry, employing a vibrating
densitometer (Parr), the combined expansion of protein
and hydration shell in concentrated protein solution is determined.
The bulk component is subtracted [30]. The
resulting expansion coefficient is nearly temperature independent
and larger than the bulk value as shown in
fig. 4. In the hydrated powder the expansion coefficient
is derived from the O-H stretching frequency of water,
depending on the average hydrogen bond length O-H–
H [9]. The expansion exhibits a striking discontinuity
at TG =170 K, induced by the softening of the O-H–O
hydrogen bond network [5, 9]. Both methods yield overlapping
values in the intermediate temperature range.
No anomaly is observed at Tfst = 220 K. These results
are hardly compatible with a density maximum or critical
entropy-volume fluctuations. All observations agree,
however, with a glass transition scenario of the hydration
shell and a dynamic onset temperature, which varies with
the probe frequency.
USA 102, 16558 (2005).
[17] K. Ito, C. Moynihan, and C. A. Angell, Nature 398, 492
(1999).
[18] E. Mamontov, L. Vlcek, D. Wesolowski, P. Cummins,
J. Rosenqvist, W. Wang, D. Cole, L. Anovitz, and
G. Gasparovic, Phys. Rev. E. 79, 051504 (2009).
[19] H. Crespi, in: Stable isotopes in the life sciences IAEA,
Vienna, 111 (1977).
[20] A. Gaspar, S. Busch, M. Appavou, W. Haeussler,
R. Georgiee, Y. Su, and W. Doster, Bioch.
Biophys. Act. Protein and Proteomics doi:
10.1016/j.bbapap.2009.024 (2009).
[21] T. Schirmer, W. Bode, and R. Huber, J. Mol. Biol. 196,
677 (1987).
[22] H. Middendorf and S. J. Randall, Phil. Trans. R. Soc.
London B 290, 639 (1980).
[23] K. Bradley, S. Chen, M. Bellissent-Funel, and H. Crespi,
Biophys. Chem. 53, 37 (1994).
[24] J. Wuttke and al., Z. Phys. Chem. submitted (2009).
[25] M. Settles and W. Doster, Faraday Discussion 103, 269
(1996).
[26] W. Goetze and L. Sjoegren, Rep. Prog. Phys. 55, 241
(1992).
[27] W. Doster, M. Diehl, R. Gebhardt, R. Lechner, and
J. Pieper, Physica B 301, 65 (2003).
[28] J. Swenson, H. Jansson, and R. Bergman, Phys. Rev.
Lett. 96, 247802 (2006).
[29] M. Vogel, Phys. Rev. Lett. 101, 225701 (2008).
[30] M. Hiebl and R. Maksymiw, Biopol. 31, 161 (1991).
[31] S. Pawlus, S. Khodadadi, and A. Sokolov, Phys. Rev.
Lett. 100, 108103 (2008).
4