Dynamics of Biopolymers and Their Hydration Water Studied by
Neutron and X-ray Scattering
by
MASSA CHUSETTS INSTITUTE
0 F TECHNOLOGY
Xiang-qiang Chu
EC 0 9 2010
B.S., Nuclear Physics (2002)
Peking University
L IBRARIES
M.S., Nuclear Technology and Applications (2005)
Peking University
ARCHIVES
Submitted to the Department of Nuclear Science and Engineering
in Partial Fulfillment of the Requirements for the Degree of
Doctor of Philosophy in Nuclear Science and Engineering
at the
Massachusetts Institute of Technology
May 2010
( 2010 Massachusetts Institute of Technology
All rights reserved
Signature of Author.......
Department of Nuclear Science and Engineering
May 18, 2010
Certified by ........
...........
.........................................
Sow-Hsin Chen
Professor
Thesis Supervisor
Read by ........................................
..................................
Sidney Yip
Professor
A/esis Reader
A ccepted by ................................................
./ .
.....
Jacquelyn C. Yanch
Chairman, Department Committee on Graduate Students
2
Dynamics of Biopolymers and Their Hydration Water Studied by
Neutron and X-ray Scattering
by
Xiang-qiang Chu
Submitted to the Department of Nuclear Science and Engineering
on May 10, 2010, in Partial Fulfillment of the
Requirements for the Degree of
Doctor of Philosophy in Nuclear Science and Engineering
ABSTRACT
Protein functions are intimately related to their dynamics. Moreover, protein hydration
water is believed to have significant influence on the dynamics of proteins. One of the
evidence is that both protein and its hydration water have the same dynamic transition
temperature at around 220 K. This thesis intends to understand the dynamic coupling of
biopolymers (mainly proteins) and their hydration water by means of neutron and X-ray
scattering.
We first approach this problem by studying the dynamics of hydration water and the
dynamics of hydrated proteins respectively.
We study the hydration water dynamics by using elastic neutron scattering (ENS) and
quasielastic
neutron
scattering
(QENS).
We
observe
a
fragile-to-strong
crossover
phenomenon at the temperature TL in supercooled water confined in substrates with
different hydrophilicity and geometry. We find that water confined in hydrophobic double
wall carbon nanotubes (DWNT) has a slightly lower TL than that confined in hydrophilic
MCM-41-S (a porous silica material). We then observe an interesting phenomenon that TL of
water confined in a hydrophobic mesoporous material CMK-1 occurs in-between the above
two. Our results indicate that besides the obvious surface effect brought about by the
hydrophobic confinements, the value of the crossover temperature is also dependent on the
dimensionality of the confinement. This result provides a possible way of understanding the
effect of pressure on protein-hydration-water system. The crossover temperature TL can be
used as an indicator of the hydrophilicity of the protein surface.
Meanwhile, we use three different methods to study the protein dynamics in the full
time range. We study the protein softness in the long-time a-relaxation region by measuring
the mean squared displacement (MSD) using ENS. We then use QENS to study the
logarithmic decay of protein dynamics in the mid-time p-relaxation range. In addition,
Inelastic X-ray scattering (IXS) is used to study the phonon dispersion relation (short-time
dynamics) inside the protein molecules and thus help us to understand the intra-protein
collective dynamics.
Finally, the coupled dynamics of the hydration water and the protein is studied. A series
of ENS and QENS experiments are performed at different temperatures and pressures in
order to investigate this problem. We find that the dynamics of protein follows that of its
hydration water and proteins remain soft at lower temperatures under pressure. We also
relate this phenomenon to the existence of the second critical point in the hydration water.
The comparison of experimental data with computer simulations (MC and MD) elucidates
the physical origin of the coupling between the dynamics of protein and its hydration water.
Thesis Supervisor: Sow-Hsin Chen
Title: Professor
Acknowledgements
My first and sincere thanks go to my supervisor, Professor Sow-Hsin Chen. Without
his insightful and patient guidance, it is not possible for me to finish any part of the thesis. I
am lucky to have such a great PhD supervisor during my five years at MIT. Many thanks go
to Professor Sidney Yip and Professor H. Eugene Stanley for their thoughtful advice and
wise suggestions during my PhD life. Special thanks to Dr. Eugene Mamontov, for his many
help in both experiments and career. I would also like to thank Professor Bilge Yildiz for
participating in my thesis committee.
Many thanks to all my collaborators, Professor Piero Baglioni and Dr. Emiliano Fratini
at University of Florence, Professor Chung-Yuan Mou and Kao-Hsiang Liu at National
Taiwan University, Dr. Alexander Kolesnikov at ORNL, and Professor Giancarlo Franzese at
University of Barcelona. I really appreciate them for their contributions to my researches.
I wish to thank Dr. Madhu Sudan Tyagi, Dr. Timothy Jenkins, and Dr. Juscelino B. Leio
at NIST, Dr. Ahmet Alatas, Dr. Ayman Said, Dr. Bogdan M. Leu and Dr. Ercan Alp at
Argonne National Laboratory, for their tireless support during my experiments.
Thanks for all my group members, Prof. Li Liu, Dr. Antonio Faraone, Dr. Yun Liu, Dr.
Wei-Ren Chen, Dr. Marco Lagi, Dr. Dazhi Liu, Yang Zhang, Chansoo Kim, Wei-Shan
Chiang, Mingda Li, Dr. Matteo Broccio, Dr. Jianlan Wu, Prof. Hua Li, and Dr. Cheng-Si Tsao.
They are both my collaborators in research and friends in life. They made my life at MIT
enjoyable and unforgettable.
Last but formost, my special thanks go to my family, my husband Tiejun Meng, my
parents Hezhen Zhou and Weiguo Chu. I will never finish this thesis without their constant
support and love.
This thesis is dedicated to my son, Lincoln Meng, the sweetest gift from god during my
PhD life.
6
Contents
3
ABSTRACT ............................................................................................................................................
Acknowledgem ents................................................................................................................................5
Chapter 1 Introduction.....................................................................................................................10
10
1.1 Biological Roles of Hydration Water .....................................................................................
1.2 Neutron and X-ray Scattering for Studying Dynamics .........
........
..........
...... 11
13
1.3 Survey of the Thesis .................................................................................................................
Chapter 2
15
Low Tem perature Dynam ics of Confined Water ..........................................................
2.1 Introduction..............................................................................................................................15
2.2 1-D Hydrophobic Confinement: double-wall carbon nanotubes (DWNT)...............18
24
2.3 2-D Biological Confinem ent: DNA, RNA and Proteins ............................................................
2.4 3-D Hydrophobic Confinement: Mesoporous Carbon Material CMK-1
.............................
27
2.5 Conclusion................................................................................................................................33
Chapter 3
36
Study of Protein Dynam ics.........................................................................................
3.1 Introduction..............................................................................................................................36
3.2 Long Time ct-D ecay: M easure of M SD and Protein Softness.....................................................38
38
3.2.1 The Concept of Protein Softness ...............................................................................
3.2.2 The Elastic Scan and the M SD of Hydrogen Atom s in Proteins.....................................39
3.3 Mid-Time @-Decay: Logarithmic Decay Studied by QENS.......................
...... 43
3.3.1 Introduction...................................................................................................................43
3.3.2 Experiments and D ata Analysis ...................................................................................
44
3.3.3 Results and Discussions...............................................................................................49
3.4 Short Time Dynamics: Phonon Dispersion Relation Studied by High Resolution Inelastic X-ray
Scattering (IXS) ..............................................................................................................................
52
3.4.1 Introduction...................................................................................................................52
3.4.2 Protein Samples and IXS Experim ents .......................................................................
53
3.4.3 M odel and D ata Analysis .............................................................................................
55
3.4.4 Results and Discussion ...............................................................................................
59
3.5 Conclusion................................................................................................................................62
Chapter 4
Coupling of Protein and its H ydration Water ..........................................................
4.1 Introduction..............................................................................................................................64
64
65
4.2 The MSD of Hydrogen Atoms in Protein and its Hydration Water ......................................
..... 67
4.3 Dynamics of Protein Hydration Water Analyzed by RCM....................................
4.3.1 RCM Analysis of Incoherent Quasi-elastic Scattering Data.............................................67
4.3.2 Relaxation time measurements of hydration water in biopolymers by QENS..............74
4.3.3 The relation between dynamic crossover FSC and the crossover in MSD...................77
4.4 The Pressure Dependence of Dynamic Crossover in Protein Hydration Water and the Pressure
effects on Protein D ynamics ...........................................................................................
............
78
4.5 Comparison with Computer Simulation Results......................................................................84
4.5.1 Com parison with a 2D M odel of Water..........................................................................84
4.5.2 Comparison with MD Simulation Results ...................................................................
4 .6 Co nclu sio n...........................................................................................................................---
Chapter 5
Appendix A
Summ ary ....................................................................................
87
.9 1
. ----------------------.............. 94
Incoherent Neutron Scattering for Studying Dynamics of Water.............96
A.1 Incoherent Elastic Scattering (E = 0 )
............................
A .2 Inelastic Scattering (E = hco # 0).........................................................................................
A.3 Incoherent quasielastic scattering (E
0 )..........................................................................
97
98
99
Appendix B
Relaxing-Cage Model (RCM) for the Single-Particle Dynamics of Water............100
Appendix C
A list of publications..................................................................................................104
C.1 Experimental evidence of fragile-to-strong dynamic crossover in DNA hydration water ........ 104
C.2 Observation of a dynamic crossover in water confined in double-wall carbon nanotubes ....... 105
C.3 Observation of a dynamic crossover in RNA hydration water which triggers a dynamic transition
in the biop olymer..........................................................................................................................106
C.4 The low-temperature dynamic crossover phenomenon in protein hydration water: Simulations vs
exp erim en ts ..................................................................................................................................
10 7
C.5 Dynamic crossover phenomenon in confined supercooled water and its relation to the existence
of a liquid-liquid critical point in water .........................................................................................
108
C.6 Studies of Phononlike Low-Energy Excitations of Protein Molecules by Inelastic X-Ray
S catterin g ......................................................................................................................................
10 9
C.7 Pressure effects in supercooled water: comparison between a 2D model of water and
experim ents for surface water on a protein ...................................................................................
110
C.8 Proteins Remain Soft at Lower Temperatures under Pressure ........................................
I11
C.9 Dynamical Coupling between a Globular Protein and its Hydration Water Studied by Neutron
Scattering and M D Simulation ......................................................................................................
112
C.10 Neutron Scattering Studies of Dynamic Crossover Phenomena in a Coupled System of
Biopolym er and Its H ydration Water.............................................................................................113
C.11 The Dynamic Response FunctionxT(Q,t) of Confined Supercooled Water and its Relation to
the D ynam ic Crossover Phenom enon...........................................................................................
114
C.12 Experimental Evidence of Logarithmic Relaxation in Single-particle Dynamics of Hydrated
P ro tein Molecules .........................................................................................................................
115
C.13 Low Temperature Dynamics of Water Confined in a Hydrophobic Mesoporous Material
CM K -1 .........................................................................................................................................
Bibliography ............................................................................................................................-
1 16
...--- 117
Chapter 1
Introduction
1.1 Biological Roles of Hydration Water
To quote a famous American natural science writer Loren Eiseley, "If there is magic on this
planet, it is contained in water" [1]. Considering the numerous physicochemical anomalies of
water and the fundamental role they play in controlling the structure and dynamics of
biopolymers, even if the property of water is not magical it is surely a fascinating subject. While
water has been considered as "life's solvent" (in a passive sense) for a long time, only in the past
20 years has it become an active constituent of cell biochemistry and not just a uniform
background [2].
One of the most striking examples of the importance of water in biosystems is that proteins
cannot perform their functions if they are not covered by a minimum amount of hydration water.
Hydration can be considered as a process, that adding water incrementally to dry protein, until a
level of hydration is reached, beyond which further addition of water produces no change of the
essential properties of the protein but only dilutes the protein [3]. The hydration shell can be
defined as the water associated with the protein at the hydration end point. This shell represents
monolayer coverage of the protein surface. Water outside the monolayer is perturbed to a
significantly small extent, which is typically not detectable by measuring the properties such as
heat capacity, volume or heat content.
Rupley et al. [4] measured the reaction of lysozyme with the hexasaccharide of
N-acetylglucosamine over the full hydration range.
The threshold hydration level was h = 0.2,
where h is the mass ratio of water to dry protein. They showed that the enzymatic activity closely
parallels to the development of surface motion, which is thus responsible for the functionality of
the protein.
Around 220 K, the protein has a transition that could be described as a dynamic transition or
a so-called glass transition [5, 6]. An analogous transition can also be detected in the protein
hydration water at the same temperature. Some IR data collected by Doster et al.[7] suggested
that the transition in the hydration water could be described as the melting of amorphous ice and
this solvent network is composed of water clusters with relatively strong internal bonding. They
used this information to address the problem of dynamic coupling of solvent motions with
internal protein motions, suggesting that the cooperativity of the solvent network provides the
coupling mechanism. However, our recent Quasi-Elastic Neutron Scattering experiments [8]
show that this dynamic crossover in hydration water is the result of a transition from a
predominantly low density form of water at lower temperature (low density liquids, or LDL), a
less fluid state, to a predominantly high density form at higher temperature (high density liquids,
or HDL), a more fluid state, derived from the existence of a second (liquid-liquid) critical point at
an elevated pressure [9].
1.2 Neutron and X-ray Scattering for Studying Dynamics
Neutron scattering offers many advantages for the study of the hydrogen atom dynamics in a
protein and its hydration water. The main reason is that the scattering cross section of hydrogen is
about 80 barns, which is much larger (at least 20 times) than that of other atoms in the
protein-hydration-water system, composed of oxygen, carbon, nitrogen and sulfur atoms.
Furthermore, the neutron scattering cross section of a hydrogen atom is mostly incoherent so that
the neutron scattering spectra reflect, essentially, the self-dynamics of the hydrogen atoms in the
protein or water. The fact that the neutron wave-length (- A) and energy (-
geV to meV)
correspond to the inter-atomic distances and the energy of thermal excitations makes it possible to
monitor protein motions at atomic and molecular levels without any damage to the samples.
.....
......
.. .
..................
......
..........................
......................
. .......
...................................
............
.
Therefore, various dynamic processes from vibration to the structural relaxation of protein
molecules and its hydration water can be characterized. Vibration modes appear as distinct
inelastic peaks, whereas relaxation processes are represented by a broadened elastic part, the so
called "quasielastic scattering". A detailed description of Incoherent Elastic Neutron Scattering
(ENS), Quasielastic Neutron Scattering (QENS) and Inelastic Neutron Scattering (INS) methods
are presented in Appendix A. Figure 1.1 shows a typical series of spectra of QENS and their
Fourier transform in the time domain, which is called the intermediate scattering function (ISF).
We can clearly observe a two-step relaxation process in the ISF. Thus QENS provides a possible
way to study the slow relaxational dynamics both in protein and its hydration water.
30
.270K
170K
35 .
Lysozyme Hydration Water
p = 1500 bar
Q=0.75A'
---
180K
190K
-
200K
>
20
250K
220K
205K
210K
220K
25
-- 260K
210K
0.6
200K
190K
I
230K
240K
15
0.4
Hydrated Lsozyme
10
0.2
0
-60.0
-7
-6-5-4
-3
-2
-10
1
E(peV)
2
3
4
5
6
7
10
10,
101
101
101
101
101
t (PS)
101
10,
101
10,
Figure 1.1 A typical series of quasielastic neutron scattering spectra (left) and their Fourier transform
in the time domainl intermediate scattering function (1SF) (right). The spectra are taken from a
backscattering spectrometer HFBS.
The high resolution inelastic X-ray scattering (IXS) is a relatively new scattering technique.
From some point of view, IXS has'some properties in common with QENS. The scattering peaks
look similar. In both methods, we study the dynamic process by analyzing the broadened part of
the peak. The difference is that, IXS is used to study the collective motions of atoms, such as the
phonon dispersion relation, due to the excellent coherence of X-rays. In addition, X-ray is totally
not sensitive to hydrogen atoms. Thus in this thesis, we combine both methods to study the
dynamic properties of protein and its hydration water.
1.3 Survey of the Thesis
This thesis summarizes my research work during the past five years at MIT. The goal of my
research is to understand the coupling of biopolymers (mainly proteins) and their hydration water
in the aspect of dynamics. I first approach this problem by studying the dynamics of confined
water (Chapter 2) and the dynamics of hydrated proteins (Chapter 3) respectively. In Chapter 4,
the coupled dynamics of water and biopolymers is studied. In order to investigate this problem,
we perform a series of neutron scattering experiments as a function of temperature at different
pressures. The comparison of experimental data with computer simulations (MC and MD) is also
presented at the end of Chapter 4.
14
Chapter 2
Low Temperature Dynamics
of
Confined
Water
2.1 Introduction
Bulk water shows many anomalous behaviors, especially in the supercooled temperature range
(below 0 'C): an anomalous increase of thermodynamic response functions and an apparent
divergent behavior of transport coefficients, towards a singular temperature T,= 228 K[10]. With
an increasing super-cooling the structural relaxation time of water shows a steeper temperature
dependence compared to the Arrhenius law. This behavior is known as a characteristic of a fragile
liquid. It is known that many glass forming liquids exhibit the fragile behavior at moderately
supercooled temperatures and then at sufficiently low temperature make a crossover transition to
a strong (Arrhenius) liquid [11]. Water is supposed to have a glass transition temperature at Tg=
165 K [12]. Unfortunately for bulk water, the observation of the fragile to strong dynamic
crossover transition, as well as the experimental study of the water behavior around the possible
second critical point are impossible due to the intervention of the homogeneous nucleation
phenomenon. It starts at TH = 235 K, resulting in crystallization to form a hexagonal ice before it
reaches the supercooled range of interest. It was predicted[13] that water should also show the
transition to a strong liquid in this inaccessible temperature range, around TL = 228 K.
To produce supercooled water, people reduced the nucleating impurities and reduced the size
of the water droplet to avoid the so-called "heterogeneous nucleation" [14]. However, even the
smallest and purest water droplet still crystallizes at a low enough temperature due to the entropy
fluctuation. This is called the "homogeneous nucleation". Homogenous nucleation temperature
depends on the size of the water droplet. The low limit people ever reached was about 230 K with
the smallest droplet diameter of 1 micron [15]. To suppress this limit, we use confining materials
to confine water in nano-geometry to avoid crystallization. In the next part of this chapter,
supercooled water confined in different geometries is studied by QENS.
The QENS measurement gives the self-dynamic structure factor SH(Q, co) of the hydrogen atom
in a typical water molecule convolved with the energy resolution function of the instrument (See
Appendix A for details). The SH(Q, co) is a Fourier transform of the Intermediate Scattering
Function (ISF) FH(Qt) of the hydrogen atom of the confined water molecule. The Q-independent
average translational relaxation time <rT> is obtained from the QENS data by fitting them with
the Relaxing Cage Model (RCM)[16].
H42
04
0.
H41
Figure 2.1 A schematic diagram of RCM. A water
molecule is trapped inside the cage formed by its
S-
- - ---- o0
------- ~
Hol
neighbor molecules.
Hi2
H3i
01
03
Hv2
The RCM was developed by our group to describe the translational and rotational dynamics of
a typical water molecule at supercooled temperature. On lowering the temperature below the
freezing point, around a given water molecule, there is a tendency to form a hydrogen-bonded,
tetrahedrally coordinated first and second neighbor shells (cage, see Figure 2.1). At short times,
less than 0.05 ps, the center of mass of a water molecule performs vibrations inside the cage. At
long times, longer than 1.0 ps, the cage eventually relaxes and the trapped particle can migrate
through the rearrangement of a large number of particles surrounding it. Therefore, there is a
strong coupling between the single particle motion and the density fluctuations of the fluid. The
mathematical expression of this physical picture is the so-called RCM. It assumes that the
short-time translational dynamics of the tagged (or the trapped) water molecule can be treated
approximately as the motion of the center of mass in an isotropic harmonic potential well,
provided by the mean field generated by its neighbors (See Appendix B for details).
By analyzing the QENS spectra using RCM, we are able to calculate the self-intermediate
scattering function FH(Qt) (ISF) of the typical hydrogen atom in water molecules. From the
ISF we then construct the so-called dynamic responsefunction XT(Qt). The dynamic response
function
%T(Q,t),
or sometimes called the dynamic susceptibility, is defined in analogy with
the thermodynamic response functions such as the specific heat and thermal expansion
coefficient, which are the temperature derivatives of the thermodynamic state functions, such
as the entropy S or specific volume v. In order to describe the dynamic response of a system
to an external perturbation AT, we can take the derivates of the time-dependent state functions,
such as the single-particle density correlation function FH(Q,t) which is called ISF in this
thesis. XT(Q,t) is one of the family of dynamic response functions and it is defined as the
derivative of FH(Q,t) with respect to temperature Tat constant pressure, namely,
XT(Q,t) = -(
%T(Q,t) is
07
(2.1)
)P
the linear response of the system to a small perturbing external field, in this case the
temperature change AT. The
of time at constant
Q.
%T(Q,t)
generally shows a single peak when plotted as a function
The peak position occurs at around the Q-dependent translational
relaxation time T(Q,T)[17] containing in the exponent of ISF. The height of the peak is
proportional to the dynamic correlation length [18]. Experimentally, XT(Q,t) is a quantity
which is much easier to measure, compared with the genuine multipoint correlator, the
four-point dynamic susceptibility X4(Q,t), which is commonly used to quantify the dynamic
heterogeneity [18]. However, the two susceptibilities are related to each other by the
fluctuation-dissipation theorem, since x 4(Q,t) measures the spontaneous fluctuations and
XT(Q,t) measures the temperature-induced fluctuations [18-2
1].
2.2
1-D
Hydrophobic
Confinement:
double-wall
carbon
nanotubes (DWNT)
Carbon nanotubes (CN) of nanometer diameter and micrometer length, besides many other
interesting properties, can serve as a quasi-one-dimensional confinement for other materials. Due
to hydrophobic interaction of water with carbon atoms, CN can play a very important role in
studying the properties of confined water. Owing to very weak van der Waals type interaction of
water molecules with carbon [22] compared to a hydrogen bond interaction between water
molecules, water confined in small diameter CN can be considered as quasi-one-dimensional
water cluster.
MD simulations [23-33] and recent experimental studies [27, 34-38] were dedicated to
understand the structure and dynamics of water in single wall carbon nanotubes (SWNT). The
behavior of water in small diameter SWNT cannot be continuously scaled by the nanotube
diameters. Water cannot enter SWNT at all for nanotubes of diameter smaller than 8 A. Water in
(6,6) SWNT (8 A diameter) can enter the nanotube as a small file (or chain) of water molecules
and fast transfer through the nanotubes, as was shown by MD simulations [23]. Neutron
scattering study of water in (10,10) SWNT (-14 A diameter) revealed an anomalously soft
dynamics [27]. MD simulations [27, 28] proposed the structure of the nanotube water at low
temperatures as a square-ice sheet wrapped into a cylinder inside the SWNT and the interior
water molecules in a chainlike configuration. A drastic decrease in hydrogen-bond connectivity of
the central water-chain (<2) gives rise to anomalously enhanced thermal motions of water protons.
For (9,9) SWNT with smaller diameter (-12 A) there should be only the cylinder of water
molecules inside nanotube [28], while for (12,12) SWNT of larger diameter (-16 A) water at low
temperatures assembles two interconnected cylinders (one into another) with continuous
hydrogen bonded structure [29, 30]. Thus water in nanotubes of 16 A and larger diameter exhibits
more uniform structure.
Recent QENS experiments on water in SWNT of 14 A diameter and in double wall carbon
nanotubes (DWNT) of 16 A inner diameter showed a fragile to strong liquid transition for water
in SWNT at TL= 218 K, while only fragile behavior for water in DWNT in the temperature range
studied down to 190 K [34]. Here we extend QENS measurements on water in DWNT of 16 A
inner diameter to lower temperatures and show that water in this confinement exhibits the fragile
to strong dynamic crossover at even lower temperature, 190 K.
The DWNT material was synthesized by chemical vapor deposition technique. The
subsequent purification with hydrochloric acid was followed by the oxidation of non-tube carbon
components in air at 300-600*C.
These preparation and purification
steps produced
micrometer-long nanotubes of a high purity, that is, with low metal catalyst content and low
non-tube carbon content. The nanotube ends were opened by exposing the purified material to air
at 420'C for about 30 min. The samples were characterized by transmission electron microscopy
(TEM) and small-angle neutron diffraction. The (0,1) reflection of the two-dimensional
hexagonal lattice of the bundle was evident in the diffraction data. The mean inner and outer
diameters of the DWNT were 16 : 3 and 23 ± 3 A, respectively. The water absorption was
controlled by the following procedure: a mixture of de-ionized water and the DWNT was
equilibrated for 2 h in an enclosed volume at 110 C; excess water was then evaporated at 35'C
until reaching the targeted water mass fraction. In the present work 3.2 g of DWNT sample was
loaded with 12 wt.% of water. Hydrated nanotubes were placed in vacuum sealed thin annular
aluminum sample holder chosen to ensure greater than 90% neutron beam transmission through
the samples in order to minimize the effects due to multiple scattering. The sample was mounted
onto the cold stage of a closed-cycle refrigerator, with the temperature being controlled within
±0.1 K. QENS experiments were performed using the high flux backscattering spectrometer [39]
(HFBS) at the National Institute of Standards and Technology. The instrument was operated with
a dynamic range of ±11 pteV, providing an energy resolution of 0.8 geV, full width at half
maximum. The measurements were performed between 150 and 250 K in 10 degrees steps and at
5 K. The spectra obtained at 5 K were used as the resolution functions.
Figure 2.2 shows qualitatively that there is some kind of crossover temperature at around 190
.
..................................
............
......
K, visible from the inspection of temperature variation of the quasielastic peak height and width.
However, a much sharper definition of this dynamic crossover temperature TL can be obtained
from the RCM analysis of the normalized quasielastic peak.
6
5-250K
S240K - "240K
(A)
250
H /WN
200-
QENS Full Pe
Q=0.75A~'
20K
-
HH2/0/
WN
*,QENS
it
T 190K:
210K
--
(B3)
200K
190K
-B/
180K
190K
50
-1200K2
160K
150K
C.
100
.104 4 -4 -2 0 2 4 4 i10
E(peV)
U*fI 1
I
I
Resolution
2
6'
L
1
--
50 -
(C)
H2 0/DWNT
m
QENS Peak Height
-4
-2
150
4
2
0
170
190
210
230
250
T(K)
E(pteV)
Figure 2.2 Measured QENS spectra of water confined in DWNT at various temperatures T.
(A) Normalized QENS spectra at Q = 0.75 A'. (B) Wings of the peaks, from which we extract the
average relaxation time <rr> by fitting with RCM. (C) T dependence of the peak heights, which is
related to the MSD of the H atoms of the confined water through the Debye-Waller factor. Both peak
widths and peak heights indicate qualitatively the existence of a crossover temperature TL for the
confined water.
Figure 2.3 compares the log< rT> vs. 1/T plots of water confined in two different materials,
DWNT and MCM-41 [40]. The MCM-41 is a hydrophilic silica material with nano-sized
cylindrical
pores.
In panel
Vogel-Fulcher-Tammann
(VFT)
(A),
at
temperatures
law, namely,
(rT)
above
190
K,
<T>
= To exp[DT /(T - To)] , where
obeys
D
a
is a
dimensionless parameter providing the measure of fragility and To is the ideal glass transition
temperature. Below 190 K, the < rT> switches over to an Arrhenius behavior, which
is (rT) = ro exp(EA / RT), where EA, is the activation energy for the relaxation process and R is the
.....
.......
.......
gas constant. This dynamic crossover from the super-Arrhenius (the VFT law) to the Arrhenius
behaviors sharply defines the crossover temperature to be TL = 190 K, much more accurately than
that indicated by temperature variation of the peak heights and peak widths, shown in Figure 2.2.
In panels B 1 and B2 we show the same analyses of water confined in MCM-41 with two different
pore sizes studied by Fraone et al. [40] for comparison. Note that the crossover temperature in the
case of MCM-41 is 224 ± 2 K. From the results shown in the upper and lower panels, we estimate
that the water confined in a hydrophobic substrate (DWNT) has a lower dynamic crossover
temperature by ATL ~ 35K, as compare to that in a hydrophilic substrate (MCM-41-S).
220
230
240
T(K) 250
(A)
170
180
190
200
210
K
TL
2.3
Figure
of
O'kcal/mol
E=2.63
^
Hydrated
DWNT
1
Exp. resuit
- - - - Arhenaus law
--
VFT
water
law
0,65
0.80
T 0 FT, T,=146
T (KJ
2W
33o
T..225
0.80
075
0.70
K 200
01
K
DWNT
(inner
IT.
/T.sizes,
.
Arrhenius
Arrhenis
0.8
0.7
0.9
T/T, TOw200 K
0.
10
0.8
OA
0.7
T/T, T
170 K
in
confined
a log
16
A)
by
against
scale
supercooled
water
porous silica material
with
which
two
temperature
insensitive
to
pore
different
show
crossover
sizes.
0.5
of
-S
quasielastic
1) and (B2) show the
Panels (B
MCM-41
and
<T>
diameter
in
in
FSC
DWNT
the
water
plotted
confinedw a2t
14 A pore size
0 1 a - A pore size
of
of
results
5o
300
(A)
spectra
the
Extracted
fitting
RCM
in
confined
MCM-41.
from
of
Comparison
confinement
that
the
TL
is
pore
.............
......
...
..
....
......
.
.......
........................
..
...
.......
...........
One can also detect a dynamic crossover phenomenon in terms of the sudden change of the
slope in the plot of mean-squared atomic displacement (MSD) of the confined water
molecule, (x1 20 ), as a function of temperature. The calculation of MSD will be described in
details in Chapter 3. In Figure 2.4, we show the MSD measured in the observation time interval
of about 2 ns (corresponding to the energy resolution of 0.8 geV). The slope changes at around
190 K, in agreement with the Arrhenius plot of the u-relaxation time in Figure 2.3 (A).
8
6
4
10
A
.'
Hydrated DWNT
M QENS result
A
V
Arrhenius law
---- VFTlaw
103~RO
60
80
xH
100
-
120
140
160
180
200
220
240
260
0
280
T(K)
Figure 2.4 Comparison of the thermal dynamic crossover shown by MSD and the FSC shown by
relaxation time <rT>for water confined in DWNT.
In Figures 2.5 and 2.6, we re-examine the previously obtained ISF at
Q = 0.87 A' (Upper panel
of Figure 2.5) and construct the temperature dependence of XT(Q, t) (Lower panel of Figure 2.5).
In this way, we determine the crossover temperature TL to occur at 205 ± 5K (black dotted curve).
In Figure 2.6, we show the Arrhenius plot of log(T) vs. l/T extracted from RCM analysis. In the
same figure, we also show the maximum of the slope occurring at 205 ± 5K. This model
independent determination of the crossover temperature TL seems to give a higher value than the
previous analysis shown in Figures 2.3 and 2.4. But it is closer to the case we obtained in SWNT
.......
..........................
(218K) [34]. In section 2.4, we will further compare this result with water confined in other
substrates.
1.0
0.8
0.6
0.2
0.0
-
10~3
10-4
0.020
0.015 -
0.010 -
10-
10-1
101
100
102
103
104
105
106
105
10*
24UK----230K220K-
-Z
~* ~21OK-,
---
--
200K-
- -190K180K+-.
...--
+-.-
170K-
160K- -150K0.005 -
0.000
10~3
10-2
10-,
10"
102
10'
103
104
t (ps)
Figure 2.5 Upper Panel: Intermediate Scattering Functions of water confined in DWNT, extracted
from analysis of QENS data using the relaxing cage model. We show here the specific case at Q =
0.87
A for 11 temperatures, ranging from 150 K to 250 K. Lower Panel: Dynamic response function
XT(Q, t), computed from the ISF shown in the upper panel of this figure. The peak height of this
quantity increases as temperature is lowered toward TL = 205 ± 5K (black dashed line), and decreases
when T is further decreased.
..
210
T(K) 250 240 230 220
-
- - ....
..........
- ..
..........................
........
..
...
... ........
......
.......................
200
190
170
180
II.|"I."I.'I*'I*'I*
I
'
I
'
-14
4.5 -I
-12
-'
0.
10 'L
4.0
A
A
v
0)
_o
8
3.5
6
,-.-.6
3.0 -*
,-'
Hydrated DWNT
-
Sigmoidal fitting
2.5 -
4.0
2
Experimental data
d(log<,r>)/d(1/T)
4.2
4.4
4.6
4.8
5.0
5.2
5.4
- 0
5.6
5.8
6.0
1000/T (K1 )
Figure 2.6 Arrhenius Plot of the average translational relaxation time <rT> of water confined in
DWNT, extracted from analysis of QENS spectra with the relaxing cage model. The pink line is the
derivative of this curve, dlog(<rT>)/d(1/T). It shows a peak at the dynamic crossover temperature TL
205 ± 5K, agreeing with the estimate based on ,;{Q, t), namely, between 200 and 210 K.
2.3 2-D Biological Confinement: DNA, RNA and Proteins
The surfaces of biopolymers provide a 2-D confinement of water. The surface water, which is
usually called the hydration water, is approximately the first layer of water molecules that
interacts with the solvent-exposed protein atoms of different chemical character, feels the
topology and roughness of the protein surface, and exhibits slow dynamics. We perform a series
of experiments on different hydrated biopolymers at ambient pressure during the past several
years. We measured the average translational a-relaxation time (rT) of the hydration water
molecules by QENS and found that this dynamic crossover in hydration water occurs at a
universal temperature TL = 225±5 K in three bio-molecules -
lysozyme protein [8], B-DNA
[41] and RNA [42], and can be described as a fragile-to-strong dynamic crossover (FSC) [13].
Thus we have shown that TD ~ TL at ambient pressure. Figure 2.7 shows the MSD of the three
biopolymers and their hydration water in the form of scaled plots. From these plots we can see
7,
.. ............
- .......
.......
..
........................
......
.......
....
. . .......
nicely the synchronization of TD(the glass transition temperature of the biopolymer) and TL (the
dynamic crossover temperature of the hydration water).
Figure 2.8 shows the determination of
the dynamic crossover temperatures in the hydration water of the three biopolymers using the
Arrhenius plots of average translational relaxation time <rT>vs. 1/T.
10
(A)
<X
6<
A6
SH20
temperature dependence of the
MSD of hydrogen atoms in both
the biopolymer and its hydration
2
A
>
x
L
L-
XT
4 -
v
Figure 2.7 Each panel shows the
Lysozyme
.
0
2
water,
2 TD0
D
0
1water,
(B)
6
15-
<X2
H20
A
4 A
2
-
0
X
T
VL
V
2
T -the
0
3
>
A
0
<X 2>
RNA
-2
4-1-4T
>
LV
0-
0
-0
60
80 100 120 140 160 180 200 220 240 260 280
T(K)
A
It
shows
evidence that the crossover
temperatures of the two systems,
the biopolymer and its hydration
are closely synchronized.
(A): MSD of hydrated lysozyme;
(B): MSD of the hydrated B-DNA;
(C): MSD of the hydrated RNA.
The arrow signs indicate the
approximate positions of the
crossover temperature in both the
biopolymer (TD) and its hydration
water (TL). Note that the scale on
left hand side is for MSD of
the hydration water and that on the
right hand side is for the
biopolymer.
2H<X
6'
respectively.
.
.......
......................
...
..........
.....
.
. .......
.....
........
U)
V
2
10
0.6
T(K) 280 270
105
260
TO/T, To=176 K
230
240
250
220
210
(B)DNA
T =222 K
104
A
E =3.48 kcal/mol
V
65
0.70
0.80
0.75
T0/T, To=186 K
0.90
0.85
0.80
TJ/T, T,=183.3 K
0.85
0.95
0.90
1.00
Figure 2.8 The extracted <ry >
from fitting of QENS spectra by
RCM plotted in the log scale vs. I/T.
Panels (A), (B), and (C) show
clearly well defined cusp-like
dynamic crossover behavior in each
case. The dashed line represents
fitted curves using the VFT law,
while the solid line is the fitting
according to the Arrhenius law. FSC
temperatures are respectively, (A)
220 K, hydration water in lysozyme;
(B) 222 K, hydration water in DNA;
and (C) 220 K, hydration water in
RNA.
All three temperatures are essentially
the same within the experimental
error of 5 K suggesting universality
of TL in hydration water of all
biopolymers.
2.4
3-D
Hydrophobic
Confinement:
Mesoporous
Carbon
Material CMK-1
QENS experiments on water in single-wall carbon nanotubes (SWNT)[34] and double-wall
carbon nanotubes (DWNT)[43] showed TL = 218 K and 190 K respectively. In order to
investigate further into this difference in the dynamic crossover temperature, we study the
dynamics of water confined in a hydrophobic mesoporous material CMK-1 by a direct
analysis of the incoherent neutron scattering (QENS) spectra using RCM. Although a recent
literature[44] provides evidence that there might be a hydrophobic-hydrophilic transition
under some specific temperature, the hydrophilicity of the sample does not change in our
measurement range.We analyze the ISF FH(Q,t) of hydrogen atoms in the confined water and
observe that the peak height of Xr(Q,t) for supercooled water increases as T approaches the
dynamic crossover temperature TL, indicating the growth of the dynamic correlation length.
But below TL the peak height decreases due to the onset of the dynamic crossover [19]. In
addition, we compare the crossover temperature of water confined in CMK-1 with the water
confined in DWNT and MCM-41 by using a model-independent analysis method. This
method is an unbiased and a more reliable determination of the crossover temperature, by
taking the slope of the average translational relaxation time <TT> in its Arrhenius plot. We
numerically calculate the quantity d(log<rT>)/d(1/T) from the Arrhenius plot and determine
the crossover temperature TL from the position of the maximum slope[19]. Our result
provides the evidence that besides the obvious surface effect brought about by the
hydrophobic confinements, the value of the crossover temperature is also dependent on the
geometry of the confinement.
The ordered mesoporous carbon CMK-1[45] was synthesized according to the method of
Ryoo et al. In brief, it was made by sulfuric acid dehydration of loaded sucrose inside the
pores of MCM-48 mesoporous silica (cubic, Ia3d symmetry, consisting of two disconnected
interwoven three-dimensional pore systems). Then silica was dissolved by hydrogen fluoride.
..
......
....
....
- .. ..
:..............
m-n...........................
-
. ...
.....
The only difference is that the MCM-48-S was used as template [46]; so that a much smaller
pore size (BJH pore size 14 A, compared to regular CMK-1, which has a pore size around 30
A) can be made. Since CMK-1-14 is composed of amorphous carbon, its surface is uniformly
hydrophobic, but not too hydrophobic to be hydrated.
,800
(A)
Adsorption
*
700
Desorption
600
0.08
c)500
0-07
006
-
0
-
E 0.05
-~400
a)
0.04'0
003
E 300
o2
> 200
10
15
100
0.2
0.0
20
25
0.6
0.4
30
Pore diameter (A)
Relative Pressure (P/P0 )
(B)
0.8
40
35
1.0
CMK-1-14
CMK-3-28
2.5 l
-2.5
-5.0
-150
*
I
*
I
'
I
i
-100
-50
Temperature (0C)
Figure 2.9 (A)The nitrogen adsorption/desorption isotherm of CMK-1-14. (inset: pore size
distribution plot) (B) The Differential scanning calorimetry (DSC) results of CMK-1-14 and
CMK-3-28, which are taken from 123 K to 323 K with the heating rate of 10 K/min.
Figure 2.9 (A) shows the nitrogen adsorption/desorption isotherm of CMK-1-14. With the
Barret-Joyner-Halenda (BJH) analysis, one can obtain the pore volume and the pore diameter as
0.84 cm 3/g and 14 A, respectively. Thermogravimetry analysis (TGA) of hydrated CMK-1-14
shows a 45% weight loss, which means the hydration level is at about 98%. Figure 2.9(B) shows
the comparison of the differential scanning calorimetry (DSC) result of CMK-1-14 with another
mesoporous carbon material CMK-3-28. The template of CMK-3-28 is SBA-15, instead of
MCM-48 for CMK-1-14, so the pore structure is 2D hexagonal and the pore size is 28 A. One can
see that there are two melting peaks in CMK-3-28, which shows the freezing of water in larger
pores. Since there is no obvious melting peak down to 150 K, we believe that the water inside
CMK-1-14 does not freeze.
In Figure 2.10 (A) and (B), we plot a set of raw data directly taken from QENS
measurements as a function of temperature. Panel (B) shows an enlarged view of the peak
wing part in panel (A). It is visible from the inspection of temperature variation of the
quasielastic peak height and width that there is some kind of crossover at around 200~220 K.
In panel (C) we show the mean-squared atomic displacement (MSD) of the confined water
molecule,
(x1 2)
in the observational time interval about 2 ns (corresponding to the energy
resolution of 0.8 geV). One can observe a sudden change of the slope at around 200 K. This
temperature is about 25 K lower than the one we recently observed from the MSD of
Lysozyme hydration water [47] and the one we obtained from the MSD of water confined in
MCM-41-S [48]. On the other hand, it is 10 K higher than what we observed in the MSD of
water confined in DWNT[43]. All these raw data sets without any fitting at different
temperatures show clearly that a crossover takes place at about 200~220K. However, a much
sharper definition of this dynamic crossover temperature TL can be obtained from the RCM
analysis of the normalized quasielastic peak.
...........
................
...
(A)
1.0 Water confined in CMK
0.9 Q=0.87A'
1.1
250K
240K
230K
0.8
0.7
0.6 -
.
Z 0-6
CI' 0.4
/
> 0.0
210K
-0.2
160
200K-190K()
180K
n0.4
0.3 -
-
S 0.2
220K
0.5 -
*
Peak Height
0.8
0.2
170K
0.1
resolution
180
2
2
240
0.0
6
4
2
0
-2
-4
-6
8
E(pteV)
0.10
,10
9 (C)
(D
0.08 Peak Width
7
S0.06-
MSD<X 2
>
-
6
T - 220K
}{ 50-
0.04-
4
0.02
2
0.00
2
80 100 120 140 160 180 200220240
-6
-4
-2
0
E(peV)
2
4
6
T(K)
1
Figure 2.10 (A) Normalized QENS spectra at a series of temperatures at Q = 0.75A~ . Inset
represents the T dependence of the peak heights. We took the logarithm of the peak heights so that it is
linearly related to the MSD of the H atoms. (B) The wings of the peaks, from which we extract the
average translational relaxation time <-rT> by fitting with RCM. (C) MSD of the hydrogen atoms,
(xh2 ), extracted from the Debye-Waller factor measured by elastic neutron scattering.
...................
.....
.........................
.
.
.
.....
..
. ....
.....
. .........
....
.......
.. .. .......................
0.6
0
Exp. Data
Quasiclastic comp.
0.5
--
Elastic Comp.
Fitting Curve
- --
Resolution
- -
0.4
0
75K'
4
6
0.3
0.2
>
0.1
0.0
-6
-4
-2
0
2
4
6
8 -6
-4
-2
0
2
E (peV)
Figure 2.11 RCM analysis of QENS spectra taken at two typical temperatures T 210K (A,C),
230K (B,D) at Q = 0.75A and 0.365A-'. The circles are the measured neutron intensity as a
function of the energy transfer E. Panels (A) and (B) are plotted in linear scale and panels (C) and
(D) are plotted in logarithm scale. The red line represents the fitted curve using the RCM model.
The green dashed line is the Q-dependent instrumental resolution function. The blue line is the
quasi-elastic scattering component. Error bars throughout the paper represent standard deviation.
These figures show that the quality of fitting is good enough for our purpose.
Figure 2.11 illustrates the process of the RCM analysis. It is shown that the RCM analysis
agrees with the measured QENS data satisfactorily. The comparison was made of the data
taken from temperatures just above and below the crossover temperature TLIn Figure 2.12 (A) we show the ISF calculated by Eqs. (B.6) and (B.7) from the fitting
parameters
/Jro and
yat several temperatures of the water confined in CMK-1 as a function of
time. Figure 2.12 (B) shows a series of dynamic response functions calculated from the ISF
shown in (A). The peak height of
TrQt),
XT*(Q), grows as T is lowered and reaches a
8
.
- ......
.....
. .......
-
.....
.........
maximum at TL = 230 ± 5 K, but this growth is interrupted when the dynamic crossover sets
in. The only parameter in FH(Q,t) that has to be differentiated with respect to T is r 7(Q, 7),
since # remains almost constant and close to 0.5 ± 0.1 as T is lowered[19, 49].
%T*(Q)
is
therefore directly proportional to the change of slope of the Arrhenius plot of rT(Q, T) (Figure
2.12 (C)). Therefore, this change of slope in the Arrhenius plot of rT(Q,T) is in our opinion
the most unbiased way of defining the crossover temperature.
T(K) 250 240 230
L 11
4.5
1.0
220
210
200
190
180
170
T
0.8
LIUN
-
200K
+-
190K
180K
-
0.6
00
a 3 .5
'
3.0
2.
*H170K
LL
iCMKIH2
0.4 -
A-
2.5
0.56AX
.4 Q
2.0
0.2
1.5
0.0
x
10-
102
103
,..1
1
..
---
-
10-
L
H
102
10 310
10
10"
T(K)
,,1
6
180K-190K
--
6'
10
170K-180K
-*-
15
,
10
-
t
/5
190K-200K
200K-210K
34-
210K-220K
220K-230K
-+230K-240K
-+-
A
3
240K-250K
101
-
0 -
0
103
2
102
101
10"
10
102
t (ps)
103
104
101
101
4.0
4.5
5.0
5.5
6.0
1000rr
Figure 2.12 (A) The self-intermediate scattering functions (ISF) of hydrogen atoms in water
confined in CMK, extracted from analysis of QENS data. We show here the specific case at Q =
0.56 ~'for 9 temperatures, ranging from 250 K to 170 K. (B) Dynamic response function XT(Q,
t), computed from the ISF shown in the upper panel of this figure. The peak height of this quantity
increases as temperature is lowered toward T L= 230 ± 5K (brown solid line), and decreases when
the temperature goes below TL. (C) Comparison of the experimentally extracted average
translational relaxation time <rT> of water confined in CMK with those of water in MCM-41-S
and DWNT. (D) Derivative of the Arrhenius plot of the o-relaxation time, d(log<zT>)/d(1/T), for
the three cases in panel (C). The peak positions in panel (D) is a suitable indicator of the crossover
temperature T Lin each case.
Thus here we use the model -independent determination of the crossover temperature to
determine TL. It is by taking the slope of the translational relaxation time <Tr> in its
Arrhenius plot, i.e. d(log<rT>)/d(1/T). The peak position in the d(log<TrT>)/d(1/T) vs. l/T plot
represents the temperature where the largest slope in the Arrhenius plot occurs and is a
suitable indicator of the crossover temperature TL. The TL determined by this method is
usually 10~20K higher than the one determined by the traditional method (fitting the
Arrhenius plot with the Arrhenius law at low temperatures and with the VFT law at high
temperatures respectively) [17, 40, 43, 50]. In Figure 2.12 (C) and (D) we compare the
log<rT> vs. 1IT plots of water confined in three different materials, CMK-1, DWNT[43] and
MCM-41-S[40] and can find from the peak position in panel (D) that the maximum slope in
the Arrhenius plot of <r> for CMK-1 appears at a temperature about TL = 225 ± 5K. This
temperature agrees within the error bar with the temperature TL = 230 ± 5K shown in panels
(A) and (B), at which the maximum in the peak height of the calculated dynamic response
function XT(Q,t) appears. In addition, we can clearly see that the crossover temperature TL of
the CMK-1 is slightly lower than that of the MCM-41-S, TL= 235 ± 5K, but higher than that
of the DWNT, TL = 205 ± 5K.
2.5 Conclusion
In this chapter, we bring up interesting observations that the crossover temperature depends
on the degree of hydrophilisity of the interface between the water and the confining substrate.
DWNT has an obvious hydrophobic interface between water and the substrate. As one can
observe, the crossover temperature for water confined in a hydrophilic substrate (MCM-41) is
higher than that confined in a hydrophobic substrate (DWNT) by about 35 K. Meanwhile, we
determine the crossover temperature by the model-independent analysis of the average
translational relaxation time <rT> by computing d(log< T>)/d(1/T) as a function of T. The
crossover temperature TL is 225 ± 5 K for water confined in CMK-1 hydrophobic substrate. It
decreases by ATL of about 10 K as compare to water confined in hydrophilic substrate MCM-4 1-S.
While for DWNT case, ZTL is about 30 K instead. From this result, CMK-1 is seen to be not a
completely hydrophobic material and its hydrophilisity is in-between MCM-41 and DWNT cases.
The value of ATL may also be dependent on the geometry of the confinement (3-D in the case of
CMK-1 as compare to 1-D in the case of DWNT). In the temperature range, from 250 K to 170 K,
the hydrophilisity of CMK- 1 does not change judging from our experimental result [44].
The peak height of the dynamic response function XT(Q,t) as a function of temperature is
another way of determining the crossover temperature. However, this method suffers from the
inaccuracy due to the large temperature interval between different measurement points and thus
has big error bars. Our results show that the dynamics of water under temperatures below 170 K
is so slow that it runs to the limit of the instrumental resolution. However, our previous
experiments [47, 50] indicate that the relaxation time of water molecules are shorter under
pressure. Thus studying the pressure effects on water dynamics under hydrophobic confinement
should be another interesting topic to be investigated in the future.
Previously we detect the crossover temperatures in hydrated DNA to be 222 K [41], vs in the
case of protein lysozyme to be 220 K [8], showing that DNA has more hydrophilic interface
presumably due to the presence of the phosphate groups. Thus it can be conjecture that the
magnitude of the crossover temperature TL can be used as an indicator of the hydrophilisity of the
substrate. A good test of this idea may be to measure the crossover temperatures of protein
hydration water with proteins of different hydrophilic and hydrophobic interfacial exposure.
On the other hand, it is shown in the literature that applying pressure can also increase
protein-water interactions and improve water accessibility to the hydrophobic core of the protein
[51]. From the above interpretation, this effect of pressure on protein-hydration-water system may
contribute to the phenomenon that the crossover temperature of protein hydration water decreases
with pressure.
35
Chapter 3
Study of Protein Dynamics
3.1 Introduction
Globular proteins are hetero-polymers consisting of densely packed amino acid chains.
Although crystallographic structures are known for many of them, these static structures alone are
not sufficient to understand their biological behavior. Their function is in fact eventually governed
by their slow conformational dynamics [52, 53]. Protein dynamics, triggered by thermal energy
(kBT per atom), allows the biomolecule to sample many conformations around the average
structure, the so-called conformational substates (CS). A complete description of proteins requires
therefore a multidimensional potential energy landscape (EL), a concept proposed for proteins by
Frauenfelder and co-workers in the 1970s [54-56]. The EL defines the relative probabilities of the
CS (the minima) and the energy barriers between them (the maxima). In particular, the EL of a
complex system that contains N atoms is described by the potential energy surface in a space of
3N dimensions, where each axis gives one coordinate of a specific atom.
As a first approximation, protein dynamics can be divided into two main groups according to
their timescale or, equivalently, to the region of the EL sampled [52]: (a) Slow timescale
dynamics (ps-ms, or the a.-relaxation) define fluctuations between states separated by energy
barriers of EA >> kBT, i.e. large-amplitude collective motions. Biological processes like enzyme
catalysis and protein-protein interactions occur on this timescale. (b) Fast timescale dynamics
(1ps-lOns, or n-relaxation) define fluctuations between structurally similar states that are
separated by EA < kBT They are more local, small-amplitude fluctuations at physiological
temperature like loop motions and side-chain rotations.
Slow and fast dynamics are somehow linked to each other. The correlation between
dynamics and biological activity has been demonstrated on the ps-ms timescale, but fluctuations
at atomic level are much faster than this, leading to the more complex idea of a hierarchy of
substates [54-56]. The EL is organized in a fractal-like hierarchy of a number of tiers; there are
valleys within valleys within valleys. Some aspects of protein dynamics are also 'slaved' to the
solvent fluctuations, with the protein component dictating the relative rates [5, 57].
Proteins and glasses are stochastic complex systems, and one of the distinctive features of
complex systems is a slow non-exponential relaxation of the density and single-particle
correlation functions
#q(t)
observed in a wide range of time scales. The time dependence of the
relaxation scenario usually follows these three steps: it begins with (a) a short-time gaussian-like
ballistic region, followed by (b) the fp-relaxation region which is governed by either two
power-law decays #(t) ~
(t/TqO)-a
and
#q(t)
~ (-t/Tq
)b
or a logarithmic decay #q(t) ~ Aq - Bq
ln(t/TO), which then evolves into (c) an a-relaxation region that is governed by a stretched
exponential decay (or Kohlrausch-Williams-Watts law), q(t) ~ exp(-t/Tq") . These types of
relaxation are characteristic of complex systems[58], just as the simple exponential relaxation (or
Debye law) q(t) ~ exp(-t/Tq) is typical for gases and liquids. Proteins and glasses have also
important differences: both systems are aperiodic, but the organization of protein EL is far more
sophisticated than the glass one.
Figure 3.1 shows the complete time-dependence of a typical ISF for hydrated protein powder
[59]. In this chapter, we are going to study the whole curve, dividing protein dynamics into 3
sections by different time range:
(1) Long-time dynamics, i.e. a-relaxation, a stretched exponential decay, studied in section 3.2;
(2) Mid-time dynamics, i.e. p-relaxation, the logarithmic-like decay, studied in section 3.3;
(3) Short-time dynamics, i.e. phonons in proteins, studied in section 3.4.
Mid time:
Log / -Decay
0.8-'0.6
Figure 3.1 Complete time dependence
of protein relaxation. Results from MD
simulations of the hydrated protein
powder model at T= 310 K.
Long time:
Short time:
a -relaxation
Phonons
0.4-
-
0.2-
-
0.0
10-2
10~
100
10
t (ps)
102
103
105
104
3.2 Long Time o-Decay: Measure of MSD and Protein Softness
3.2.1 The Concept of Protein Softness
Protein flexibility is generally known to be essential for their enzymatic catalysis and for their
other biological activities. It has been described qualitatively as a consequence of protein's
conformational disorder. But the description from the concept of dynamics can be more precise
it pertains to response to applied forces, which are known to maintain biological structure and
govern atomic motions in macromolecules [60]. At room temperature a biological matter can be
looked upon as being "soft". This "softness" can be estimated from the displacement x of a given
atom in response to a given applied force F. Assuming the atom is bound to the protein by a
spring with a spring constant K, then x is given by the ratio F/K (Hook's law). Thus for a given F,
the smaller the spring constant K, the larger the displacement x, meaning the softer is the
biological material. One way of calculating the magnitude of K in protein is to use the
equi-partition theorem, which states that the average potential energy of the harmonically bound
atom is equal to one half kBT,
1
1
(V)=-K(x2)=
- kBT
2
2
(3.1)
at a given temperature T, where kB is the Boltzman constant. Therefore K is proportional to the
inverse of the derivative of the MSD (x2) with respect to T, namely,
K = kB
(3.2)
-)j2
d-T
3.2.2 The Elastic Scan and the MSD of Hydrogen Atoms in
Proteins
To obtain the MSD (x2) of hydrogen atoms, we perform fixed window scan (an elastic
scattering measurement with a fixed resolution window of FWHM of
±
0.8 geV for HFBS
spectrometer) [61] in the temperature range from 40 K to 290 K, covering completely the
supposed crossover temperature TL. Since the system is in a stationary metastable state at
temperature below and above TL, we make measurements by heating and cooling respectively at a
heating/cooling rate of 0.75 K/min and observe exactly the same results.
In Figure 3.2(A) we show the elastic scattering intensity as a function of temperature at a
specific
Q value
(0.469k-'). We can see from the figure a sudden decrease in the elastic scattering
intensity above about 220K, which implies a sudden increase in the MSD of hydration water. We
can calculate (x2) from the Debye-Waller factor, SH (Q,w=0)=Xp[Q2(X2)],
of the logarithm of SH (Q,&= 0)vs.
Q2 plot.
SH (Q,a
ratio of the temperature dependent elastic
=
by a linear fitting
0) can be easily calculated by taking the
scattering intensity
e(Q,T,
a
=
0) and its low
temperature limit,
Sn (Q, o =0) = I,, (Q, T, o =0) / I,(Q, T =0, o =0)
(3.3)
Figure 3.2(B) shows this fitting procedure for three different temperatures (below, at and
above the crossover temperature).
of
Q2 . Since the
Q2 dependence
0)/Iet (Q,T =0,0
We plot - In[Ie (Q,T,m=
exponential form of the Debye-Waller factor is a low
is not linear for high Qs, we only use the lowest
=
0)] as a function
Q approximation,
Q points
and the
in the fitting to obtain
the MSD. The dashed lines in figure 3.2(B) show the linear fitting of the lowest five
Q values
and
................................................................
..................
..
..
............
. ................
..
. ....
..
.
figure 3.2(C) shows the temperature dependence of thus extracted (x2) from the fitting.
0.22
0.20
0.18
c 0.16
0.14
0.12
0.10
T(K)
.0
2.5 - (B)
2.0
0
-
1.5
223
- e
E~1 .0
A
-0
AL
0.0
0. 0
15
1
/
AA
1.5
1.0
0.5
A
2.0
U- 2 2 K
A
3.0
2.5
Q2(A2)
-Ile
(C)
T
-
e
-
Se
10
V
A
o
-
5
0
50
100
150
200
250
300
T(K)
Figure 3.2 Method of data analysis to obtain
(xo).
Panel (A) shows the intensity of elastic
scattering within the resolution window of ± 0.8peV as a function of temperature (the so-called elastic
scan). The intensity plotted in the figure is taken from the difference between the H20 hydrated and
D2 0 hydrated samples. Panel (B) shows plots of logarithm of intensity vs. Q2 at three temperatures.
The slope of the linear fit to the first five points (low Q points) is used to extract the MSD from the
data. Panel (C) shows the extracted MSD of the hydration water as a function of temperature.
1.
*
..
I.
M.
-
-
........
---
-
-
-
t
10
92.0
8
7
-. -2
2e
<x
2
0
<X
>
1.5
LysozymeA
T
L
6
o,,, 5 -
v
1.0
43-
0.5
2-
0.
0
60
80
100
120
TC
140
160
180
200
220
240
- 0.0
260
280
T(K)
Figure 3.3 Comparison of MSDs measured for the protein and its hydration water. Note that the MSD
for hydration water is plotted using the scale on the left hand side and MSD for the protein is using the
scale on the right hand side (the multiplication factor of the left and right scales is 4.2). MSD for the
protein is taken from the elastic scan of D2 0 hydrated sample. Note the crossover temperature of the
hydration water (TL) and the crossover temperature of the protein (Tc) agree with each other.
In Figure 3.3 we show an example of the data taken from the D20 and H20 hydrated
lysozyme samples, from which we can extract both MSDs from lysozyme and its hydration water.
In order to show the synchronization of the temperature dependence of the two MSDs thus
extracted, we multiply the (xLsome) by a factor 4.2, so both curves superpose onto each other.
This figure nicely illustrates that the crossover temperatures for both protein and its hydration
water defined by a sudden change of slope of MSD from a low temperature behavior to a high
temperature behavior is coincident within the experimental errors [47].
We have shown that the MSD as a function of temperature can be directly measured by an
incoherent elastic neutron scattering. Therefore, if we plot MSD as a function of T, the steeper the
curve, the softer is the biological material at a given temperature.
.
. .
........
....
..............
...............
........
.........
.
.. .....
.............
....
........
......
Figure 3.4 shows the change of softness below and above the crossover temperature in both the
RNA and its hydration water [42]. The straight lines going through the low temperature points
and high temperature points allow us to compute
d)
dT
from which we can estimate the softness
of hydration water and RNA. It is striking to see that by crossing the crossover temperature TL,
the softness of RNA and its hydration water increase by a factor of 15 and 20 respectively.
0
20
40
60
80 100 120 140 160 180 200 220 240 260 280 300 320
T(K)
Figure 3.4 It has been shown in the text that the slope of the MSD vs T curve can be used qualitatively
as a measure of how soft a material is.
This figure shows the case of RNA and its hydration water.
As one can see, above the crossover temperature (Tc), the RNA becomes 15 times softer than its
glassy state, while the hydration water becomes 20 times softer when crossing the temperature TL.
3.3 Mid-Time
P-Decay: Logarithmic Decay Studied by QENS
3.3.1 Introduction
We have shown in a previous paper [62] by means of MD how the fast dynamics of hydrated
lysozyme powder follows a logarithmic relaxation in the time domain. In particular, we were able
to fit the protein single-particle intermediate scattering function between 2 ps and 5 ns with the
predictions of the mode coupling theory (MCT) for systems close to a high-order singularity. So
the relaxation dynamics of globular proteins may also be described by the MCT [63].
The fact that the most popular glass transition theory, i.e. the MCT[64], can be used to
explain glassy dynamics of proteins should not be surprising. It is well-known, in fact, that the
dynamics of native globular proteins has much in common with the dynamics of glass-forming
liquids [6, 65-70]. They both consist of non-crystalline packing in which their constituents
(molecules or amino acid residues) assemble. They also have a complex EL, composed of a large
number of alternative conformations at similar energies [65]. Other similarities are the so-called
glass transition [6, 66] (sudden change of slope in their hydrogen atoms mean square
displacement as a function of T), the boson peak [67] (typical of strong glass formers), and the
two types of equilibrium fluctuations, the cooperative a (involving large domains of the
biomolecule) and the local
p (involving
side-chains), typical of glass-formers [69].
It is in principle possible to study the relaxation dynamics of protein in the time range of
several picoseconds to several nanoseconds through the measurement of the intermediate
scattering function (ISF) FH(Qt), which is equivalent to the
#q(t)
in the theory, with new
generation of backscattering instruments [71]. In this thesis, we perform two separate experiments
on two different backscattering instruments [39, 71] and demonstrate the possibility of studying
the protein dynamics in the p-relaxation region by both spectrometers. After thoroughly
correcting for the background from the experimental data signal, we first show the
logarithmic-like decay in the ISF in time domain obtained from Fourier transformation of the
background corrected QENS spectra. We then analyze the ISF by the asymptotic formula
developed by MCT and compare the fitting parameters in both experiments. It is striking that the
two separate experiments involving two batches of samples give consistent sets of results,
supporting the logarithmic relaxation scenario.
3.3.2 Experiments and Data Analysis
We use D2 0 hydrated protein sample in order to obtain signals which is dominated by
contribution of the incoherent scattering from hydrogen atoms of the protein molecules. In
this study we choose hen egg white lysozyme (L7651, three times crystallized, dialysed and
lyophilized) which has a molecular weight of 14.4 kDa. The protein powder, as was
purchased from Fluka, was used without further purification, except an extensive
lyophilization to remove any water left. The dried protein powder was then hydrated
isopiestically at 5*C by exposing it to D20 vapor in a closed chamber (r.h. = 100%) until h =
0.34 is reached (i.e. 0.34 g D20 per g dry lysozyme). The hydration level was determined by
thermo-gravimetric analysis and also confirmed by directly measuring the weight of absorbed
D20. This hydration level was chosen to have almost a monolayer of heavy water covering
the protein surface[72]. Differential scanning calorimetry (DSC) analysis was performed in
order to detect the absence of any feature that could be associated with the presence of
bulk-like water.
Two separate experiments were performed using two backscattering spectrometers with
different resolutions and dynamic ranges, in order to be able to obtain the broad range of
relaxation time from 10 ps to 1 ns. One is a near-backscattering spectrometer BASIS at the
Spallation Neutron Source (SNS) in Oak Ridge National Laboratory (ORNL), and the other is
the High-Flux Backscattering Spectrometer (HFBS) in NIST Center for Neutron Research
(NCNR). For the chosen experimental setup, the BASIS has an energy resolution of 3.4 peV
(full-width at half-maximum, for the Q-averaged resolution value) and a dynamic range of ±
100teV; the HFBS spectrometer has an energy resolution of 0.8
half-maximum) and a dynamic range of ±36 teV[39].
teV (full width at
of the
The QENS measurement essentially gives the self-dynamic structure factor SH(Q, CO)
hydrogen atom in a typical protein molecule convolved with the energy resolution function
R(Q, co) of the instrument.
The SH(Q, co) can be presented as the Fourier transform of the ISF
FH(Q,t) of the hydrogen atom of the protein molecule, i.e.,
(3.4)
SH(Q, c) =FTFH(Q, t) R (Q, t)]
Then the ISF FH(Qt) can be easily calculated by dividing the Fourier transform of the
measured data (after subtracting the background) Fm(Qt)=FTjSH(Q, c)], with the Fourier
transform of the resolution function R(Qt):
(3.5 )
F H(Q,t) = Fm (Q, t) /R (Q, t).
In this thesis, we use an asymptotic expression derived from mode coupling theory (MCT)
to fit the ISF FH(Q,)[73, 74]:
FH(Q,t) ~ [f(Q, T)-H, (Q, T)ln(t/rp(T)) +H2 (Q, T)ln 2('t/r(T))] ex p(t/ra(Q, T))
Where rp(T)and ra(Q,T) are the characteristic
#- and
(3.6)
a-relaxation time respectively, and f(Q, T)
is the Q-dependent prefactor which can be written as a function of temperature, proportional
to the Debye-Waller factor for small
H2(Q,T) can be written as Hz(QT)
=
Q, f(Q, T)
= exp[-A(T)Q2 ]. The parameters H(Q, T) and
hi(Q)BI(T) and H 2(Q,T)
dependence of h1 (Q) is a power law of
Q for
=
hI(Q)B 2(Q,T), where the
Q
small Q[62], and the temperature dependent
factor B1 (T) goes like IT/Tc-1 "2, where Tc is the MCT critical temperature[74].
Since our experimental measured time range (10 ps to Ins) is much shorter than the
a-relaxation time range, i.e., t is much smaller than Ta, we can simply put the last exponential
factor to be unity and fit the measured ISF with a simpler expression:
FH(Q,t) ~ [f(Q, T)-Hz(Q, T)ln(t/rp(T))+H 2(Q,T)In 2 (t/rp(T))]
(3.7)
Before Fourier-transformation of the BASIS data from the energy into the time domain, we
have carefully subtracted background from the experimental spectra. Failure to perform
proper background subtraction would not significantly affect the so-obtained ISF at long
times, but would distort its behavior around t ~ 0 due to termination error of the Fourier
transformation. On the BASIS,
as well as on any other neutron spectrometer, the
measurement background includes sample-independent and sample- (and temperature)
dependent contributions. While the former is easy to subtract explicitly using the calibration
measurements of the empty sample holder, empty sample environment equipment, etc., the
latter has to be evaluated. In the past, it has been assumed that the sample-dependent
background is approximately constant as a function of the experimentally measured neutron
time-of-flight (TOF). In the energy space, this would yield a background term non-linear in
the energy transfer. Indeed, we have found that such a non-linear background adequately
describes the background in the data fits. In this work, we have taken a further step in the
background evaluation as follows. Since the background signal was found to be proportional
to the incident flux of the sample, in the course of the data reduction we subtracted from the
raw data (in TOF, or incident wavelength) not merely a constant, but rather the incident beam
spectrum measured at the incident beam monitor and properly offset in the TOF to account
for the distances between the monitor, sample, crystal analyzers and neutron detectors. Since
the incident intensity on the BASIS is somewhat wavelength-dependent, this approach to
background subtraction is more accurate than simply subtracting a constant in the TOF raw
data assuming a wavelength-independent background. Thus, the spectral shape of the
background to be subtracted from the raw data is determined from the monitor data. The
amount of the background to be subtracted is determined in the course of iterative procedure,
where progressively larger background spectrum (of the fixed spectral shape) is subtracted
from the raw data presented as a function of the incident wavelength until the resulting
spectrum in the energy transfer satisfies the temperature-dependent detailed balance condition,
S(Q,ao) = exp(E/kBT)S(Q,-co). Here kB is the Boltzmann constant, E is the energy transfer, and
Q is the scattering momentum
transfer.
Even after evaluation and subtraction of the background, the SH(Q, CO)spectra do not
necessarily decay to near-zero values at the extremes of the measured energy transfer. This is
because of the possible presence of the relaxation processes that are not instrument
background artifacts, but are simply too fast for the dynamic range of the experiment.
..........
......
... ......
....
........ ................
..............
_
_. .......
..........
Therefore, prior to Fourier-transformation, we have subtracted a constant from the SH(Q, C)
spectra already corrected for the background to suppress the termination error. The resulting
FH(Q,t) spectra represent the ISF that describes the processes reliably measurable in the
dynamic range of the experiment.
For the QENS data obtained from HFBS, the Fourier transformation and the
deconvolution procedures were performed using the FFT toolkit in DAVE software package
developed by NCNR[75].
0.8
0.6
' 1E-4
d
04
IE-5
0.2
1E-6
-100
-50
0
E (peV)
50
100
00 '10
1000
100
t (ps)
Figure 3.5 (A) Normalized QENS spectra at T = 300K and Q = 0.5A~', before (red circle) and
after (blue circle) background subtraction. (B) Intermediate scattering function (ISF) of the QENS
spectra at nine different Q values. (C) Resolution spectra taken at Q = 0.5A-, before and after
background subtraction. (D) Fourier transforms of the BASIS resolution functions at nine Q
values.
Figure 3.5 shows the above subtraction and deconvolution procedures in details. Panels (A)
....
.. ....
and (C) show the QENS spectra taken at 300K and resolution at 10 K at a specific
Q = 0.5k-
respectively. The figures are plotted on a log scale to show the difference of the data before and
after background subtraction. A small value of constant background (shown in the figure by the
green dotted lines) was also subtracted before Fourier transformation. All the QENS spectra were
normalized before applying Fourier transformation and deconvolution procedures. Panel (D)
shows the Fourier transforms of the resolution function R(Q,t) at nine different
Q values.
Panel (B)
shows the result of dividing the Fourier transformed data with R(Qt) (as shown by Eq. (3.5)) at
the above nine
Q values at 300K. From these
ISFs we can see that the measurement time scale is
approximately 10 ps to 1 ns, which is within the -relaxation range of the protein.
1.0
1.0
0.9
0.9
0.8 -
2
0
0.8-
0=013'
0=0.5A'
Aa=.7LL
0.7 - *
0.6-
4
0
*
*
0-7-
Q=1.1A
0.5
10
T =320K
100
=
I
10
V
Q=0.9Al
*
Q=1.1'
4
Q=1.3A
0
Q=15A'
*
*
1000
A.9
0
0=0.5Ak
A Q=0 7
Q =0.9A:
Q=1.3A:'
Q=1.5A
Q=17A
0=1 9K*
0 Q=0 3A
*
0.5
Q=17A
Q=1 9A
10
T
280K
100
1000
100
1000
0-.7A Q=.7
A=
V
O)=0.9A'
100
t(ps)
1000
10
Q=0.9Al
t(ps)
Figure 3.6 Analysis of the $-relaxation range of the ISF according to Eq. (3.7). The ISF is calculated
from the analysis of QENS spectra taken from BASIS at four different temperatures T = 320K, 300K,
280K and 260 K, at nine Q values.
. ....
meme! H ...
.........
.
.... ........
. .......
.................
...........
.
0.9
MQ=0.252A'
Q=0.252AA~
0 Q=0.365A
U-
C)
-
0.8
HFBS results
Q=0.469A
Q=0.558A1
Q=0.991A'
Q=1.11A 1
0.7..
U.
* Q=.35r
Q=0.252k'
A QO.469A'
V Q=0.558k,
* Q=0.991A'
0 Q=1.22A'
08
T=260K
1000
100
10
1 lo
a
*
1
A
y
*
*
'
T
1.
0.7
T=283K
100
10
1000
-1.0
(D)
(C)
0.9 --.
a
2
Q=0.252A
Q=0.365A
-Q0.8- A Q=0.469A
0.80.
y Q=0.558A:*
* Q=0.991A
4 Q=1.22A
L
0.7
10
.1
283K
260K
1
2A
100
T=302K.991A
0.7... ...
T
t(ps)
1000
10
..
1
....
100
1000
t(ps)
Figure 3.7 Analysis of the 1SF calculated from QENS spectra taken from HFBS at three different
temperatures T =300K, 280K and 260 K, at different Q values. Panel (D) represents the comparison
of the 1SF at three temperatures at the same Q value.
3.3.3 Results and Discussions
In Figures 3.6 and 3.7, we fit the 1SF FH(Qt) calculated from the analysis of QENS spectra
taken from BASIS and HIFBS respectively, according to Eq. (3.7). We essentially use four
parameters,A (T), ,#('T), H, (Q, T') and H2(Q, T). While A(T) and l(T) are Q-independent and A(T)
represents the prefactor f(Q, ) by the relation of the Debye-Waller factor. We analyze the curves
at all nine Q-values together to obtain the Q-independent parameters as well as the Q-dependent
parameters. The fitting results show that all the FH(Qt) values at all nine Qs merge to a value
f(Q,T) which is very close to 1 at a specific short time (ir,(T), usually around l~ps). It does not
directly go to 1 since our measured time range is not short enough for us to tell what happens in
-- M-..........
---
.......
. .
.......
. .. ....
the time range less than 10 ps. Note that there is an upturn in the data in large
3.6 and 3.7 and a downturn in the data in small
Q region in Figure
Q region
in Figure
3.6. This is due to the presence
of the second order term H2(Q, T)ln 2(t/r(T)) which gives the positive or negative curvatures to the
otherwise straight line. We thus obtain the values of H,(Q, T) and H2(Q, T) by fitting the curves
in the measured time range.
II
I
0.12 -
.
10.10
I.
(B) HFBS fitting result
(A) BASIS fitting result
0.10-
* 320K
A 300K
0.08
0.06
0 260K
220K
-
y
280K
A 260K
223K
0.06
Ki 0.04
T
0.04 -
'
0.02 --
2
.0
2
0.(
-
0.02
0.00
0.08
0.0 0.2 0.4 0.6
0.8
1.0
1
Q(A
MW02
1.2 1.4 1.6
1.8 2.0
)
0.00 0.0
0.1
0.6-(C) BASIS result2
:
T.0
12
0.086(T/Tc-1)
B(T)
0.5
0.4
0.7
0.8
MI
0,2
0.
04
10
06
-
0.04
0.02MFB
n
(D)HFBS result
H,(QT)
220.02
0.6
0.5
0.4
0.3
0.2
02
, Tc=210 ± 10OK
I(T-T0 )TI
0.7
=
B(T)Q
-'-
0.02
0.1
1.0
0.9
.0
0.06
e0.03 -
0.0
0.6
4
0.0.--1
0.04
0.3
W
H (T
(Q,T)
= 0=- .08,(T)Q'08
6(T T c
0.05 -
0.2
0.10
0.0
0.1
0.6
0.5
0.4
0.3
I(T-Tc)rr 0cl~ Tc=21 0 ± 10OK
0.2
0.7
Figure 3.8 Analysis of the fitting results from both BASIS (panels (A) and (C)) and HFBS (panels
(B) and (D)) instruments. Panels (A) and (B) show the fitted H, (Q, T) values as a function of Q for
both cases at different temperatures, which is found to obey a power law of Q, i.e. HQT)=B(T)Q.
T
Panels (C) and (D) show the fitted BI(T) values plotted as a function of I(T-Tc)/TcI 1/2, where c is the
2
critical MCT temperature and is chosen to make B,(T) linearly dependent on I(T-Tc)/TcV11 . The inset
of panels (C) and (D) show the fitted H2(Q, T) values as a function of Q for BASIS and HFBS
respectively.
Figure 3.8 shows the Q dependence of the fitting parameters obtained from both BASIS
and HFBS. We find that H1 (Q,T) obeys a power law in Q at small Q, i.e. H1 (QT)=Bg'T)r,
where the power 8 is a value between 1-2, B;(T) is a temperature dependent parameter. We
then plot the fitted BI(T) values as a function of |(T-Tc)/TcI' , where Tc is the MCT critical
temperature and is chosen to make BI(T) linearly dependent on |(T-Tc)/Tcj' . We found that
Tc is about 210±10 K, and is consistent in both experiments. This value is also very close to
the well-known dynamic transition temperature in protein TD- 220 K [6, 60, 66, 76].
Previous analyses[77] on QENS data obtained from proteins simply fit the data with a
single Kohlrausch-Williams-Watts (KWW) stretched exponential function, which simplifies
the protein relaxation process to only the c-relaxation. However, while in the QENS
measurement range proteins cannot relax completely, our analysis provides a reasonable way
of approaching the p-relaxation process. We demonstrated in the above analysis that the
logarithmic stretching of the p-relaxation range is consistent with that predicted by the MD
simulation [62], although we would not preclude different scenarios proposed by other
researchers [69, 78, 79] due to the large error bars in our measured ISF.
Recent neutron scattering experiments[80] and MD simulations[81] have demonstrated that
the rotational and reorientational dynamics of methyl groups are the processes associated with
the
p-relaxations
and these fl-relaxation processes are solvent-independent. However, our
measured decay time in the
p-relaxation range
is both
Q and
T dependent, indicating that the
logarithmic-like relaxation process can include processes other than the methyl group
rotations. On the other hand, a unified model of protein dynamics has been recently proposed
by H. Frauenfelder and collaborators[69], which implies that the fluctuations in the hydration
water molecules also control protein internal motions. This scenario provides a possible way
to explain the origin of the relaxation process we observe here. It contains both
solvent-independent p-relaxation introduced by the rotational dynamics of methyl groups and
the solvent-induced relaxation. Also in our previous experiments[8, 47], we observe a
dynamic crossover temperature TL- 220 K in the protein hydration water, which is very close
to the critical temperature Tc shown in Figure 3.8. This result provides another evidence that
the intermediate time motion of proteins is partly controled by the hydration water.
3.4 Short time Dynamics: Phonon Dispersion Relation Studied
by High Resolution Inelastic X-ray Scattering (IXS)
3.4.1 Introduction
Hydrated proteins exhibit a dynamic transition, sometimes called a glass transition, at TD
220K. Above TD the protein shows conformational flexibility, characterized by collective slow
dynamics with large amplitude motions. Below TD proteins exist in a glassy state with solid-like
structures, executing harmonic vibrations. As the temperature increases above TD, atomic motions
evolve from harmonic solid to anharmonic liquid-like motions [82]. Experiments show that
biological functions of proteins decrease nearly to zero below TD [66]. This suggests that the
presence of large amplitude conformational flexibility in a protein molecule is essential to its
biological function such as enzymatic catalysis.
Molecular dynamics (MD) simulations [83, 84], elastic neutron scattering (ENS) experiments
[6, 63, 85] and quasi-elastic neutron scattering (QENS) [86]showed an abrupt change in slope of
the mean square displacement (MSD) of hydrogen atoms in proteins at the dynamic transition
temperature. In literature, the correlation between dynamic transition of proteins and their
hydration water has been extensively discussed [87]. A recent QENS experiment indicated that
the temperature dependent translational relaxation time of protein hydration water shows a
dynamic crossover phenomenon at TL = 225 L 5 K [8], which coincides with the protein dynamic
transition temperature TD. The above studies are dominated by the incoherent neutron scattering
because hydrogen has a huge incoherent neutron scattering cross section compared to other atoms
in bio-materials. The incoherent scattering always shows the motions of single particle. Different
from the incoherent neutron scattering, the x-ray scattering is coherent and is always used to
study the collective motion of molecules. In this section, we use inelastic x-ray scattering (IXS) to
investigate the collective atomic motions in two globular proteins, lysozyme (LYZ) and bovine
serum albumin (BSA) and a phosphoprotein, casein. We show that the
Q dependent
intra-protein
collective vibrational frequencies also exhibit a substantial softening above the transition
temperature TD.
Inelastic X-ray scattering (IXS) is a very powerful tool to study the collective motions of
atoms, such as phonon dispersion relation. Using this technique, we have studied the phonon
dispersion relations in biological assemblies such as lipid bilayers [88] (2-D system) and aligned
DNA [89] (1-D system). Recently, some researchers studied the inter-protein phonons in protein
crystals by MD simulations [70, 90, 91]. However, it is also relevant to study the intra-protein
collective atomic motions since it is intimately connected to the biological activities of the
macromolecule. In this section, we use IXS to study the intra-protein collective atomic motions
and identify well-defined Q-dependent phonon-like low energy excitations for the first time.
While the intra-protein low-Q phonon-like excitations show little visible temperature dependence
in the temperature range investigated, the intra-protein phonons above the major diffraction peak
show considerable temperature dependence above TD [92].
3.4.2 Protein Samples and IXS Experiments
We used two structurally different proteins, LYZ and BSA. LYZ is an enzyme consisting of 129
amino acid residues which folds into a compact globular structure having an ellipsoidal shape
with dimensions a x b x b = 2.25 x 1.5 xl.5 nm 3, having a molecular weight of 14.4 kDa [93].
LYZ has five helical regions and five beta sheet regions consisting of a large amount of random
coil and beta turns [94, 95]. BSA is a transport protein and the principal carrier of fatty acids that
are otherwise insoluble in circulating plasma. It is a prolate ellipsoid with a x b x b = 7 x 2 x 2
nm 3, having a molecular weight of about 66.7 kDa [96]. It consists of 607 amino acid residues
that give an all helix structure. Comparing to LYZ and BSA, casein has a relatively little
secondary structure or tertiary structure. The conformation of caseins is much like that of
denatured globular proteins. As well, the lack of tertiary structure accounts for the stability of
caseins against heat denaturation because there is very little structure to unfold. Without a tertiary
structure there is considerable exposure of hydrophobic residues. This results in strong
.
...................
...............
.. ..................
........
..
..
association reactions of the caseins and thus forms the quaternary structure. Hen egg white LYZ
(L765 1), three times crystallized, dialyzed and lyophilized, and BSA (A7638), were both obtained
from Fluka and used without further purification. The protein powder was extensively lyophilized
to remove any water left. The dried protein powder was then hydrated isopiestically at 5 'C by
exposing it to water vapor in a closed chamber until h = 0.3 is reached (i.e. 0.3 g H20 per g dry
protein). This hydration level was chosen to have almost a monolayer of water covering the
protein surface. In addition, we grow Lysozyme crystals to observe the phonon dispersion relation
in the crystal. Figure 3.9 show nice diffraction peaks in the structure factor measured by IXS.
The experiments were performed at the inelastic x-ray scattering beamline, 3-ID-XOR, and the
high energy resolution inelastic x-ray scattering (HERIX) beamline, 30-ID-XOR at the Advanced
Photon Source (APS), Argonne National Laboratory [97]. Both instruments can measure the
dynamic structure factor S(Q,E) of the sample, which contains information on collective motions
of atoms with an energy resolution of about 2 meV (for IXS) and 1.5 meV (for HERIX). The
measured
Q (magnitude
of wave vector transfer in the scattering process) range is from 0 to 35
nm and an energy window from -20 to 40 meV.
5
10
-
Lysozyme Crystal
20
101r
C
1
..
.
..
2
2
3
4
5
6
.
.
.
7
8
9
t.
2theta (degree)
Figure 3.9 Lysozyme crystal and its structure factor measured by IXS.
*
.
10 11 12 13 14
15 16
17
......
3.4.3 Model and Data Analysis
A measured IXS spectrum I(Q,E) can be expressed as I(Q,E)=S(Q,E)OR(Q,E),
where
S(Q,E) is the dynamic structure factor, R(Q,E) the resolution function, and 0 means numerical
convolution. In the past we used the Generalized Three Effective Eigenmode model (GTEE) [98]
for the analysis of IXS data. In this section we shall use a simplified model of GTEE, which is
called the damped harmonic-oscillator (DHO) model to analyze the normalized dynamic structure
factor given by [99]:
S(Q,E)
S(Q)
F(Q)Q(Q) 2
1
2 )2
2
g (E -(Q)
where the structure factor S(Q) = JS(Q, E)dE, Q(Q)
transfer
Q,
(3.8)
,
+(F(Q)E) 2
is the phonon energy at wave vector
and F(Q) is the phonon damping. In principal, the DHO model has no central
Rayleigh (elastic) peak, but has only the two Brillouin side peaks given by Eq. (3.8). But
experimentally we observe the presence of a large resolution limited central peak. Therefore, we
phenomenonlogically added a delta function central peak of a weight fraction fg(Q). In addition,
we also take into account the detailed balance factor, so that the extended DHO model is given as
[100]:
S(Q, E) = A E (n(E) +1)
kBT
ff(Q),(E)
+ (1-
f(Q))
r (E' -
where n(E)+1 is the detailed balance factor , n(E) = (e
2
F(Q)Q(Q)
+(Q))(Q)E)
T
-
(3.9)
1)-1 the Bose factor, A
a
normalization constant, and fg(Q) represents the fraction of the elastic peak. At the low Q
region fg(Q)> 0.95 and at the high Q region fg(Q)
0.6 ~ 0.8.
To verify the experimental S(Q) for LYZ, we calculated it from 1) the crystallographic structure
(lAKI.pdb), and 2) an MD simulation at 250 K using a hydrated LYZ powder model [101, 102].
It was calculated according to:
S(Q)
1Q
Z>N
N j
-
e iQR j
2
(3.10)
........
.
.......................
where N is the number of heavy atoms in the protein and R, their coordinates. The comparison is
shown in Figure 3.10. Only S(Q) calculated from MD shows the 4 expected peaks, centered at
Q
7, 14, 30 and 55 nm~' [70, 103], while peak A cannot be seen reproduced from the
crystallographic structure. Peak B arises from the order of the secondary structure (P-sheets
average distance and a-helix repeat and width), as displayed in Figure 3.10. Peak C is ascribed to
the intermediate range order between amino acidic residues, while peak D is attributed to the
covalent bonds between heavy atoms (like C-C, C-N etc.). Finally, the sharp increase at low
Q
indicates that, on average, a protein can be regarded as a fluctuating continuum.
I
I
10
I
C--
I
I
I
|
I
I
I
I
PDB
14.5 A
.5A
6'5
MD
B
4.
AD
CD
2-
5
10
15
20
25
30
35
40
45
50
55
60
4
Q (nm)
Figure 3.10 Lysozyme structure factor S(Q) calculated from the crystallographic structure (red) and
from the MD trajectories (blue). Arrows point at the main peaks in the S(Q) spectrum: A) 7 nm~, B)
14 nm', C) 30 nm~1, D) 55 nm- 1. Only the MD trajectories can reproduce the experimentally observed
shoulder Peak A. Peak B corresponds to typical distances of the protein secondary structure, peak C to
some medium range order between residues and peak D to the protein covalent bonds. The meaning of
the shoulder peak A is still uncertain.
In Figure 3.11, we compare the structure factor S(Q) measured by IXS for three different
proteins. We can see that peak A at ~ 7 nm-' exists for all three proteins and looks similar in three
cases. However, although peak B also exists for all three proteins, it looks different in casein case.
There is a shoulder on the high
Q side
of peak B, which might come from the rich quaternary
.
. ..............
structure in casein.
25
1.0
4
30
LYZ
0.8
C0.6
0.4
0.2
0.0
2.5k
|
|
I
|
|
I
Casein
2.0k
1.5k -
1.0k -
5
0
10
25
20
15
30
Q(nm')
Figure 3.11 Structure factor S(Q) measured by IXS for three different protein cases. From the top to
bottom: BSA, LYZ and Casein.
We show in Figure 3.12 and 3.13the analysis of measured IXS spectra S(Q,E) of BSA by the
DHO model at three different temperatures T = 170, 220 and 250 K. Figure 3.12 shows the results
of the model fit at
Q=
4.5, 5.6 and 6.7 nm-' (low
Q range).
We can see that the two Brillouin
peaks are clearly identified and the positions of the peaks are located at around 11meV for all the
Q
values. However, for
Q
= 24.6, 27.9 and 31.2 nm-' (high
Q
range, Figure 3.13), clear
Q-dependence of the phonon excitation energy is observed. At a given
Q
value, when the
.
...........
. ...........
------
temperature exceeds TD, we see a substantial decrease in the phonon energy. This softening of the
phonons in this Q range suggests that the slowing-down
of motions involving the
intermediate-range order in a protein may be the origin of the restoration of its biological
activities.
O
-----
.BSA
T=170K
Q-4.5 nm
Data
eo -n
Fittingcore
Resolution
Fittingresult
T=220K
Q=4.5 nm
T=220K
T=220K
Q=5.6 nm 1
Q=6.7 nmn'
T=250K
Q=5.6 nmn-
'lu
In
10
0
E(meV)
-20
-10
0
E(meV)
10
20 -20
-10
0
E(meV)
10
20
Figure 3.12 Model fitting of the measured IXS spectra of BSA in the low Q range. The blue circles,
margarita solid line, green dashed line and red solid line represent respectively the measured data,
DHO model fitted curve, resolution function and Brillouin component of the DHO model. The fitted
results are shown at Q = 4.5, 5.6, 6.7 nm-' (from left to right) and at T =170, 220, 250 K (from up to
down). No dispersion was observed in this Q range.
.
........
......
:.
......
.........
..............
BSA
T=170K
00
.
T=170K
Q=27.9 nm
T=170K
Q=31.2 nm'
T=220 K
T=220 K
T=220K
Q=24.6 nm
Q=27.9 nm
Q=31.2 nm
T=250 K
T=250K
T=250K
Q=24.6 nm1
Q=27.9nm"
Q=31.2 nm-'
Q=24.6 nm"
0 24 6 nm'
0
S
0-02
-
00
Data
Fittingcore
Resolution
___ lting result
(j0.01
-
0.0
0.0
0.m
-20
-10
0
10
20
30
40
-20
E(meV)
-10
0
10
20
30
40
-20
-10
E(meV)
Figure 3.13 Model fitting of the measured IXS spectra of BSA in the high
10
0
20
30
40
E(meV)
Q range.
The blue circles,
margarita solid line, green dashed line and red solid line represent respectively the measured data,
DHO model fitted curve, resolution function and Brillouin component of the DHO model. The fitted
results are shown at Q = 24.6, 27.9, 31.2 nm- (from left to right) and at T = 170, 220, 250 K (from up
to down). At each temperature, clear Q-dependence of the phonon excitation energy is shown in the
figure. At a given Q value, the phonon energy decreases substantially when temperature exceeds TD-
3.4.4 Results and Discussion
From the results of the DHO analyses of the measured spectra, such as the ones that are
illustrated in Figure 3.12 and 3.13, we plotted the phonon dispersion relations in the full
Q range
for LYZ and BSA respectively in Figure 3.14. Two different phonon dispersion behaviors below
and above
Q
~ 15 nm' (the position of the major peak of the measured structure factor S(Q)) are
.....
clearly shown in both figures. In the low
Q range of the BSA
dispersion curves, there is no clear
temperature dependence of the excitation energies. In the high
Q range,
excitation energies have
similar dispersion curves as that had been observed in other bio-systems [12]. Since the lower
phonons in the
Q range
of 4 nm-1 to 10 nm-1 correspond to the length scale between 7 and 15
Q
A,
which reflects the inter-protein motions, we can conclude that the inter-protein motions are
temperature independent and do not induce the temperature dependent biological functions of the
proteins. On the other hand, the high
Q phonons
correspond to the length scale of about 2-3
A, are
of the secondary structure of the proteins (4-5
in the
Q range
of 20 nm-1 to 30 nm-1, which
close to the length scale of the typical distance
A) and
reflect the intra-protein collective atomic
motions. We can clearly observe the quantitative degree of the softening of phonons for both
proteins as temperature exceeds TD in Figure 3.14. This fact strongly suggests that these
temperature dependent intra-protein motions are intimately related to the biological activities of
proteins, which are also temperature dependent and strongly decrease below TD. The presence of
the structure factor peak at
Q
~ 15 nm-1 leads to a large damping of the phonons, as we can see in
panel (c) of Figure 3.14, so we cannot detect the phonons in this region (the phonons are all
damped out). The dotted lines in panel (b) of Figure 3.14, which connect the dispersion curves,
are guide lines drawn based on the previous studies of phonons in other bio-systems [88]. The
phonon damping F(Q) does not show a temperature dependence and is nearly constant at high
Q
region. This fact shows that the temperature dependence of Q is reliable.
We calculated the factor 1-fg(Q) in Eq. (3.9) and fit it by a power law. Since the factor fg(Q) is
the fraction of the elastic component, which should be proportional to the Debye-Waller factor
exp(-Q 2 (x 2)). The low
Q2 dependence
Q expansion
of fg(Q) should be proportional to
Q2 . Our
data show this
in Figure 3.14. The factor 1-fg (Q) represents the fractional spectral intensity of
the phonon-like excitation in the total intensity. When T > TD, 1~fg(Q) is larger, which indicates
that there are more phonon population due to the onset of the conformational flexibility at TD.
...........
.......................
9" "g-EP
............
*
LYZ
I
BSA
C6Ok
170 K
A
N
A _120
10-
110
6_
6
~10
> 20
-K
-5
00
20
5
E
15
I
15
10
10
0.3
~
0+3
~0.2
-A
0.1
j-
0.2
-I
-_0
-
________________0_________
0
0.0
0
5
10
A
15
20
Q (n')
25
30
35
40
45
0
5
10
15
20
Q
(1nm11)
25
30
Figure 3.14 IXS fitting results of LYZ (left) and BSA (right)respectively. (a) Structure factor S(Q) of
in a relative scale. We can see two major peaks at Q ~ 5 nmI and 15 nm-1. (b) Dispersion of the
intra-protein phonon-like energy excitations as a function of Q, below and above the second major
peak in the structure factor. The square, triangle and circle symbols indicate the phonon energies at
170, 220 and 250 K. (c) The phonon damping as a fuction of temperature. (d) Fractional area of the
Brillouin peak vs Q. The factor (1-fg) in Eq. (3.9) is found to increase proportionally to Q2
2
I -/(Q) = a()Q , where a(T) is an increasing function of T.
3.5 Conclusion
In this chapter, we studied the dynamics of protein in three different time scales. We used
neutron scattering to study the protein dynamics in long-time (a-relaxation) and mid-time
(p-relaxation). While the ac-relaxation time in globular protein like Lysozyme is too long for the
present day QENS study (in the 1pts to 1ms range), the state-of-the-art backscattering instrument
such as BASIS and HFBS is capable of studying the p-relaxation range (i.e. 10 ps to 10 ns range)
effectively. Using the asymptotic formula derived from the MCT, we are able to demonstrate that
the well-known dynamic transition temperature TD of Lysozyme can be identified as a critical
temperature Tc of the MCT. If we interpret the Tc as the crossover temperature Tx implied by the
extended mode coupling theory (eMCT) [104, 105], the well-known dynamic transition
temperature at about 220 K [6, 60, 66, 76] (or sometimes called the glass transition temperature)
can be understood as the eMCT crossover temperature.
Using IXS, we observed a well-defined dispersion relation of intra-protein phonon-like
excitations [106]. We identify a significant temperature-dependence of the slowing-down and an
increase in population of phonon-like collective motions in the
Q range
larger than 20 nm' above
the dynamic transition temperature TD. We believe that these phonon-like modes are the result of
the collective vibrational motions of the atoms in the a-helices and p-sheets. Below TD the
vibrational frequency is too high and the population of the modes is too low to be able to facilitate
the biological function. That is the reason why proteins are not good enzymes below the dynamic
transition temperature. Different from the 2-D [88] and 1-D [89] biological systems we studied
before, a protein molecule is a 3-D finite size system, which does not allow the long wavelength
intra-protein phonons to propagate. This could be the reason why in our experiment the low
Q
acoustic type phonons can still exist which may come from the inter-protein motions [90]. The
absence of dispersion in the low
Q region
is an intriguing observation, which may be observable
also by incoherent inelastic scattering of neutrons.
63
Chapter 4
Coupling of Protein and its Hydration Water
4.1 Introduction
Water molecules in protein solutions may be broadly classified into three categories: (1)
strongly bound internal water molecules that occupy internal cavities and deep clefts; (2) water
molecules that interact with the protein surface; and (3) bulk water. Internal waters, which can be
identified crystallographically and are conserved in homologous proteins [3], are extensively
hydrogen bonded and comprise an integral part of the protein structure. They have residence
times ranging from ~ 10 ns to ins, and their exchange with the bulk solvent requires local
unfolding to occur. Surface water molecules are much less well defined structurally than internal
water molecules in the sense that surface binding sites identified crystallographically are not
highly conserved among different crystal forms of the same protein. They are much more mobile,
with residence times on the order of tens of picoseconds. In addition to being important for
protein stability, and in the energetics and specicity of ligand binding, surface waters also have a
profound influence on the dynamics of a protein molecule as a whole.
In this chapter, we will show by means of neutron scattering how hydration water influent
the dynamics of protein molecules. We first show by MSD measured by elastic neutron scattering
(ENS) that protein dynamics closely follows that of the hydration water. We next carefully
analyze the QENS data of protein hydration water under different pressures and show further
dynamical properties in both protein and its hydration water. We also use the same method to
study the dynamics of other hydrated biopolymers, such as DNAs and RNAs. In the last part of
the chapter, we compare our experimental results with computer simulation results and find nice
consistency in comparison both with MC (Monte Carlo) and MD (Molecular Dynamics)
simulations.
4.2 The MSD of Hydrogen Atoms in Protein and its Hydration
Water
We have shown in chapter 3 that the slope change in MSD is a traditional method of
determining the crossover temperature both in protein and its hydration water. In this section, we
show by measured MSD that the temperature dependence of the protein dynamics closely follows
that of the hydration water under different pressures.
The low-temperature dynamic behavior of proteins under high pressure is not as extensively
investigated as that at ambient pressure. It is well known that some bacteria can survive under
extremely high pressure and low temperature in the deep ocean. The microorganisms living in the
deepest ocean yet isolated and characterized were sampled at 11,000 m depth or 1100 bar in the
deep-sea sediments of the Marianas trench, where the Pacific oceanic lithosphere subducts into
the Earth's mantle [107]. How can proteins in the microorganisms still function under these
extreme conditions? Besides the fact that high pressure denatures most of the dissolved proteins
above 3000 bar, the behaviors of proteins under pressures below the denaturation limit (< 2000
bar) both for structure and dynamics are relevant to the biological functions of proteins and are of
great interest [51, 108, 109]. In Figure 4.1 and 4.2 we show the temperature dependence of MSD
in lysozyme hydration water at different pressures up to 1600 bar. Figure 4.1 shows the MSD of
lysozyme and its hydration water in the same scale. Figure 4.2 rescales the same data in figure 4
by a factor of 4.2 to show the synchronization in the temperature dependence of the two MSDs at
each pressure [47]. We can clearly see in both figures that at each pressure, the temperature
dependence of the protein dynamics closely follows that of the hydration water.
12-
P=1 bar
9-~
P=400 bar
H - /ysozyme
9
-
D OlLysozyme*
D2OLysozyme
A
6
x
v
XH2
3
X2H
0 H20/Lysozyme -
__
C
A
0
2
/Lysozyme
D2 0/Lysozyme
12-
P=1200 bar
P=800bar
9-
"X
0H 20/Lysozyme - D20/Lysozyme
C) D 20o/Lysozymne
A,
6-
22
v
3-
x2
Ji
2
TL
12
-
P=1500 bar
*P=
1600 bar
9 ---
--
3
xx
2X
50<
100t
15
T (K)
200
25
50
10
10>0
5
T (K)
Figure 4.1 Pressure dependence of the softness of a protein and its hydration water. It is remarkable to
see from the figure that protein at a given temperature actually becomes softer under an elevated
pressure.
....
..........
..
.
......
..
...................
.....
..... .................
..............
AA
1.0 V
V
v3-
-0.5
0.0
2-5
P=800 bar
9-
P=1200 bar
61.5 A
Ao
-1.0
V
3-
L
9 -
T
0-
T_
L
P=1500 bar
0.0
P=1600 bar
2.0
-1.5
A
0
3*
-0.
n0
50
*
100
150
T (K)
T
L
200
-0.0
250
50
100
150
200
250
T (K)
Figure 4.2 Reduced plot of pressure dependence of MSD of protein and its hydration water. It is to be
noted in this figure that the crossover temperature of the protein and its hydration water is closely
synchronized at a range of pressures below 2000 bar.
4.3 Dynamics of Protein Hydration Water Analyzed by RCM
4.3.1 RCM Analysis of Incoherent Quasi-elastic Scattering Data
In this section, we discuss the qualitative and quantitative analyses of quasi-elastic spectra of
different hydrated biopolymers, protein (lysozyme) [47], DNA [41] and RNA[42]. Our objective
......
....
.
. ..
...
................
. ..
. ............
.......
......
..........
...........
is first to show that the peak height and the peak width of the incoherent quasi-elastic spectrum is
necessarily related to each other because the area under the SH (Q,E) is in principle normalized
to unity at each Q value. From this property we can already show by plotting the peak height of
the SH(Q,E) which is SH(Q,E=0) as a function of temperature that there is a dynamic
crossover phenomenon without detailed analysis of the spectrum.
Figure 4.3 shows a series of spectra of lysozyme hydration water taken at different
temperatures at a pressure of 1500 bar and Q = 0.75 A-'. One can notice immediately that the
peak height increases as temperature decreases, indicating the narrowing of the peak width, which
is a qualitative measure of the a-relaxation time.
Figure 4.4 enlarges the peak width part in figure 4.3 and shows them together with the
resolution function of the instrument. We can clearly see the broadening of the peaks increases as
temperature increases.
170K
35
180K
Lysozyme Hydration Water
p= 1500 bar
Q=0.75A'
30
190K
200K
205K
- 210K
220K
-230K
25
20
-
240K
_1
-
10
-
5
0
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
E(geV)
Figure 4.3 The normalized QENS spectra for lysozyme hydration water at various temperatures Tat a
pressure of 1500 bar at Q = 0.75 A '. Note that as the temperature decreases the spectral width becomes
narrower and the peak intensity becomes higher.
.
. .......
. .. ......
.....
.
. . .......................
. .....
......
3.0
2.5
L-JJ
L.JLALl
AjJA1LIMAL
"Jt
V"T
&'1"
20
---
p= 1500 bar
- 21OK
1920K
Q-0.75A'
2.0
-0K
180K
170K
--
1.5--
20K(Resolution
0.5
0.0 . . . 1 ..
. . . . ..
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4
.
5
6
7
.
8
9 10
E(pieV)
Figure 4.4 The wing of the peaks, from which we extract the average relaxation time <TT>. Both peak
heights and widths indicate qualitatively the existence of a crossover temperature TL for the hydration
water. Note at 170 K the spectrum is nearly identical to the resolution function (red solid line), indicating
that it is the lowest temperature one can extract the meaningful <rT>.
In Figure 4.5 and 4.6 we use hydrated DNA and hydrated RNA to illustrate the above
mentioned fact that by plotting the peak height as a function of temperature we can already detect
the presence of the dynamic crossover temperature in a qualitative way.
WWWWV:W
............................
...........
E
'e'400
-0.003
0.000
0.003
E(mOV)
=.003
000
0.003
E(meV)
Figure 4.5 The difference neutron spectra between the H20 hydrated and the D 20 hydrated DNA
samples. Panel (A) displays the area-normalized QENS spectra at Q = 0.87 A at a series of
temperatures. Panels (B) and (C) display the heights of the peak as a function of temperature and the
wing spectral region, respectively, at those temperatures. One notes from panel (B) a cusplike transition
signaling the rate of change of peak height from a steep high temperature region to a slower low
temperature region at a crossover temperature of about 225 K. The error bars are of the size of the data
points. In panel (C), we may notice, from the wings of these spectral lines, that two groups of curves,
270-230 K and 220-185 K, are separated by the curve at temperature 220 K. In this panel, the scatter of
the experimental points gives an idea of the error bars.
0.42
(b)Peak Height
(a)
24
Hydrated RNA
0.36Q0.87A
h=0.5g H2 0/lg RNA
~2.2
9270
K
2.0
260 K
0.30 --
250K
-s-240 K
230K
~0.24
1.8>
L
-.-2
.
200
T220
TK
*210K
280
(c) Peak Width
190 K
180 K
20 K (Resolution)
o 0.18
260
18 -I
-+-200 K
---
24 0
15
>12
d1)
0.12
9 T =220K
6
0.063 --
0.00
0
-6
-4
-2
0
E(teV)
2
4
6
-6
-4
-2
0
2
4
6
E(peV)
Figure 4.6 Measured difference QENS spectra of RNA hydration water at various temperatures T. (a)
The normalized QENS spectra at Q-0.87 A-. (b) The T dependence of the logarithm of the peak
heights, which is linearly related to the MSD of the H atoms of the hydration water. (c) The wing of the
peaks, from which we extract the average relaxation time <T>. Both peak heights and widths indicate
qualitatively the existence of a crossover temperature TL for the hydration water.
In Figures 4.7-4.9, we present three examples taken from lysozyme hydration water case of a
quantitative RCM analysis by which we can extract the translational relaxation time <rT> defined
in equation (B.8) as a function of temperature. From the fitting, we obtain three parameters, r, ,
and y; and are able to calculate the theoretical ISF from equation (B.6), which are plotted in
Figure 4.9 for protein hydration water under ambient pressure and 400 bar respectively [47].
It
is important to note that using these three parameters, we can construct the ISF over a broad range
of time scale which was not covered in the original measurement within the resolution limit.
0.8
0.6
0.4
S
0.2
0.0
0.8
0.6
0.4
0.2
-4
-2
0
E (geV)
2
4 -4
-2
0
2
4
E (peV)
Figure 4.7 An example of RCM analysis of spectra taken at four different Q values at T = 210 K
and P = 400 bar for lysozyme hydration water. In practice we analyze simultaneously spectra
taken at seven Qs at a given temperature to extract the average translational relaxation time <rT>.
I
0.8
I
OExp. Data
~
0.6 - 6
W.4
0.4
-
-----
ElasticCo.
-0.
0.2
--
0. 0 -
0.4
I
_
_
-
-
0.0
-4
-2
0
E (peV)
2
4-4
-2
0
2
4
E (peV)
Figure 4.8 An example of the RCM analysis for lysozyme hydration water at 400 bar at two different
temperatures T = 210K (below TL) and 240K (above TL) respectively. Note for the higher temperature
case (T = 240K), the quasi-elastic components are much broader. And we can see clearly that for
higher T, the peak height is much lower than the lower temperature case (T = 210K).
...
............
...
......... ......
............
..............................
. ......
. .. ..................................................
....
10
1.0
0.8 -08
dC-
"'A-AM
270K
0.8
-- 20K
250K
6240K
6~
04Hydrated
1.0
-220K
2b.4
2b.4
-
.
Lysozyme 0.80
d
210K
200K
AHydrate
00
0.
0.2
0.
Q,-O 75A
1
0.
1o-
o10.1
W0 1'
10, 0
10
t (PS)
101 0
1OV10
1Vol
10
j 1012
2
100 1101'C
10
10,
11W 10
--
190K
1(0'V
o 10' 101 102 103 10' 100 100
=
t (PS)
4O ba
1.0
1.0
0.8 -08
- 200K
[ %=.1
270K
------ 180K
260K
- - 250K
0.8
-0.6
HydratedLysozyme
Q.p4ObAr'
--
-0.6
2604
0.2
0.0
10
.2
t (PS)
p
1.0
0.2
09A'180K
0.0
0-0
\210K
62
)0.2
i
--
101 00 100 C0 10 102
t (ps)
-230K
220K
F190K
0.0
104-2 10' 1
+-240K
0.0
1oy310
1
1010
10
10' 100
t (ps)
10 11
10 10f
10 IV
i
1"
1 02
101
t (ps)
10'
10's0010"
Figure 4.9 An example of the intermediate scattering function (1SF) of hydrogen atoms in the
lysozyme hydration water extracted as a result of the RCM analysis at three different Q values at
different temperatures. The upper panels show the ISFs under normal pressure and the lower panels at
the pressure of 400 bar. It is seen that all the ISFs exhibit a two-step decay consisting of the beta and the
alpha relaxation processes.
4.3.2
Relaxation
time
measurements
of
hydration water in
biopolymers by QENS
For a hydrated protein at ambient pressure, it is known that below a characteristic temperature
TD= 220 K, it transforms into a glassy state and loses its conformational flexibility, showing no
appreciable biological functions [66, 110]. At and above TD, this flexibility is restored and the
protein is able to sample more conformational sub-states, thus becomes biologically active. This
"dynamic crossover" in protein is traditionally detected by observing the changing of the slope of
the MSD of hydrogen atoms vs. T plot [66, 86, 110, 111], and believed to be triggered by their
strong coupling with their hydration water, which shows a similar dynamic crossover at
approximately the same temperature [76, 87, 112-114]. This "dynamical transition" is common to
many biopolymers and believed to be triggered by their strong coupling with mobility of their
hydration water, which shows a similar "dynamic crossover" at about the same temperature. We
show experimentally that this sudden switch in dynamical behavior of hydration water on
Lysozyme [8], B-DNA [41] and RNA [42] occurs precisely at 220 K and can be described as a
Fragile-to-Strong dynamic crossover (FSC).
.
..... ..
...
.........
In this section, we give two examples of extracting the a-relaxation time of hydration water in
biopolymers. The first one is to use RCM model to calculate the ISF that fit the QENS spectra.
And then use an intuitive method to extract the a-relaxation time from the ISF graphically. The
second method is to use the fitted parameters of RCM to calculate the average translational
relaxation time by equation (B.8). In both methods, the existence of a crossover temperature is
evident from the results.
1.0
0.8
0.6
0.4
0.2
0.0 k
10 ~4
10-2
10
10~1
104
101
t (ps)
102
103
104
10"
106
Measured Alpha
Relaxation time t (Q
0)
104
Q,=0.87AI
TL= 2 2 0K
0103
p
102
,
170
180
I
190
.
.
200
I
210
,
I
I
220
230
I
I
.
240
250
260
1
270
,
~
280
T(K)
Figure 4.10 An intuitive way of extracting the relaxation time from the calculated ISF and the
evidence of the crossover behavior in the temperature dependence of the relaxation time. (A) ISF at Qo
of hydrogen atoms in RNA hydration water, as a function of temperature. (B) The alpha-relaxation
times at Qo, as a function of T, extracted from Ile points of the alpha decays of ISFs shown in panel
(A).
Figure 4.10 illustrates the first method using the case of hydration water in RNA as an example
[42]. Figure 4.11 illustrates the second method using the case of hydration water in lysozyme
under different pressures as an example [115].
227 K
TL
T
220 K,
10
H20/Lysozyme
Normial Pressure
A
EA=3.92 kcal/mol
v 10
-----
103
EA= 3 .6 1 kcal/mol
Exp.rest
VFT 1aW
Annenislaw
102
0.70
0.75
080
To/T, To
0.85
090
189 K
0.65
0.95
P = 400 bar
U
102
0.70
0.80
E =3.45 kcamol
10
0.85
,
0.65
,
,
0.70
,
,
.
0.75
,
,
,
0.85
0.80
Tf/, T=168 K
,
0-95
,'
EA=3.42 kcal/mol
P=800bar
102
0.90
T /T, To = 181 K
T= 209K
217 K
TL
0.75
P=1200bar
,
0.90
10
0.70
0.85
0.90
T/T, To=175 K
0.75
0.80
0.95
P = 1600bar
104
0.75
0-80
0.85
TfT, To = 166 K
0.90
0.95
0
4.2
4.4
4.6
4.8
5.0
52
5.4
56
5.8
6.0
TWT, To = 1000 K
Figure 4.11 the extracted <TT> plotted in a log scale against ToIT under six different pressures P =
ambient pressure, 400, 800, 1200, 1500 and 1600bar. Note for the pressures up to 1500 bar, there is a
well-defined crossover temperature; but at the pressure of 1600 bar, <rT> appears to be a smooth
curve, neither having the super-Arrhenius behavior at high temperature nor Arrhenius behavior at low
temperature.
. . ...............
.
4.3.3 The relation between dynamic crossover
FSC and the
crossover in MSD
8
105
6
A
"0
4 V
A
V
2
80
~~~-I'wW. I-*
100 120 140 160
I
.
180
.
I
200
.
i
220
.
I
240
.-
I
260
.
4j
0
280
T(K)
Figure 4.12 An example taken from RNA hydration water [42] which illustrates that the values of the
thermodynamic crossover temperature
())
vs T) and the dynamic crossover temperature
(log< rT>vs T) a re closely synchronized.
As we discussed in section 4.2, traditionally the dynamic transition temperature of a protein
is discussed in terms of the turning point of MSD vs. temperature plot [66].
One can also use
the similar plot to discuss the dynamic crossover temperature in protein hydration water, or more
generally for hydration water in biopolymers [113, 116]. However, we have recently used QENS
methods to study the protein hydration water [8].
We detect the dynamic crossover temperature
in the hydration water using Arrhenius plot of the translational relaxation time measured by
QENS. The question naturally arises whether the dynamic crossover temperatures measured by
these two different methods are identical or not. In Figure 4.12, we present a plot of MSD and the
average relaxation time of hydration water in RNA together in the same graph.
It can be seen
clearly from the graph that the crossover temperatures as determined from the elastic scan and the
quasi-elastic scattering methods are identical within the experimental error bars [42].
4.4 The Pressure Dependence of Dynamic Crossover in Protein
Hydration Water and the Pressure effects on Protein Dynamics
Previous experiments on confined water in MCM-41-S porous silica material [40, 50] have
shown that an increased applied pressure will shift the FSC temperature to a lower value. We now
show that this is also true for the interfacial water on the surfaces of protein. We further show that
while a well-defined FSC phenomenon is observed for the applied pressure up to 1500 bar, when
exceeding this pressure, the FSC phenomenon disappears. We thus identify a Widom line [117] in
the T-P plane with an end point for the case of protein hydration water which is nearly identical to
that of the confined water in MCM-41-S. This implies the existence of liquid-liquid critical point
in both the 1-D and 2-D confined water.
In Figure 4.13 we plot log<rT> vs. l/T in the same scale for four different pressures 1bar, 400
bar, 1200 bar and 1500 bar. From these plots, we can clearly see that for the same temperature,
the structural relaxation time is shorter under higher pressure. Alternatively, to maintain the same
relaxation time, the hydration water can be at a lower temperature under a higher pressure. Since
the protein dynamics is strongly coupled to that of its hydration water, a short structural relaxation
time of the hydration water enables the protein to maintain its flexibility and thus be able to
sample more conformational substates. This implies that the protein can remain active at a lower
temperature under pressure. For lower temperatures, the <Tr> obeys an Arrhenius behavior, which
can be fitted by a straight line in the log<rr> over 1/T plot; while for high temperatures, the
behavior of <rT> switches over to obey a Vogel-Fulcher-Tammann (VFT) law, which are shown
by the dashed curves in the Figure.
........
.
....
...........
...........
........
................
11
.. ..
............
...
. .............
........................
.............
....
......
...........
5.0
4.5
45
4.0
PP= 1tar
P40Obar
=
P15O0bar:
=
''3.5
3.0
2.5
2.0
1.5
0.0035
-
0.0040
0.0045
A
0.0050
-
0.0055
1/T (K )
Figure 4.13 The extracted <rT>plotted in a log scale against 1IT under different pressures P= ambient
pressure, 400, 1200, and 1500 bar. From these plots we can clearly see that for the same temperature,
the structural relaxation time is shorter under higher pressure. Or alternatively, to maintain the same
relaxation time, the hydration water can be at a lower temperature under a higher pressure.
A very distinct phenomenon in our experimental results is that
<rT>
shows a completely
different behavior at the pressure above 1600 bar (Figure 4.14). The crossover phenomenon
disappears above this pressure and <rT> appears to be a smoothly bending over curve (concave
downwards). Moreover, for the same temperature, <rT> is no longer decreasing as pressure
increases to 1600 bar. The hydration water is shown to be crossing a "liquid-liquid critical point"
around 200 K and 1600 bar [118]. To show such behavior more clearly, we thus take the MSD of
protein hydration water data from Figure 4.2 for three different pressures (ambient pressure, 1500
bar, and 1600 bar) and plot them together in Figure 4.14 (A). We can clearly see that the MSD at
higher pressures are much larger than the MSD at ambient pressure, which indicates that the
fluctuations of the hydration water are faster under pressure and further induce the fast
fluctuations of proteins. The fact that the slope in the MSD curve at 1500 bar is larger than that at
ambient pressure at low temperatures also implies that protein is softer under pressure in this
temperature region. Furthermore, the MSD curve at 1600 bar is also shown to be smoother than
the 1500 bar case and for higher temperatures, the slope of MSD at 1600 bar is smaller than
which at 1500 bar at the same temperature. This implies that protein under 1600 bar is not as soft
as it under 1500 bar. The softness of the protein is not always increasing with pressures. These
facts shown by MSD coincide with which are shown by the <r7 > curves in Figure 4.14 (B). Both
of them indicate that the relaxation of the protein hydration water is faster under pressure, which
triggers the fast relaxations and fluctuations of the proteins and improves the flexibility of the
protein. In this measured low temperature region, increasing the pressure up to 1500 bar can have
the same effect as increasing the temperature, which can make the protein more flexible and
active than at ambient pressure.
C%
A
x
V
L.
4-
0
0
20
40
60
80
140
100 120
160 180 200 220
240 260
T(K)
5.0
I
I
-
U
1bar
I I500bar
P.=
1I600bar
P=
4.5
4.0
2.5-
*
-*
3.5-
ilk
7Y
2.0
15
0.0035
*
0.0040
I
*
0.0045
1/T (K
0.0050
0.0055
1)
Figure 4.14 Upper Panel: MSD of hydration water molecules under three different pressures. Lower
Panel: The extracted <rT> plotted in a log scale against 1/IT under pressures P = ambient pressure,
1500, and 1600 bar. Note that the MSD at higher pressures are larger than the MSD at ambient
pressure, which indicates that the fluctuations of the hydration water are faster under pressure. This
point is also very clearly shown in the lower panel.
In order to look further into the phenomenon revealed by Figures 4.13 and 4.14, we plot the
value of
<TT>
at the crossover temperature TL as a function of pressure in Figure 4.15 (A). It is
surprising to find that although TL is pressure dependent, the <TT> values at TL are not changing
with pressure. For all the pressures we measure, this value keeps constant at around 12 ns. We
also plot the activation energy EA, which is calculated from the Arrhenius behavior of <r7r> at
low temperatures, and find it decreases with the pressure, which is coincident with previous MC
simulation result [119, 120]. Furthermore, we plot EA(P)/(kBT) as a function of P. It appears to be
independent of P again, within the error bars. The MC simulation may be able to substantiate and
elucidate its physical origin of this constancy [119, 120].We have previously shown by a
molecular dynamics (MD) simulation [117] that this super-Arrhenius to Arrhenius crossover is
due to crossing of the Widom line in the one phase region. Upon the crossing of the Widom line,
the local structure of water evolves from a predominately high density form (HDL, fragile liquid)
to a predominately low density form (LDL, strong liquid) as the temperature crosses this
characteristic temperature TL [121]. At the pressure of 1600 bar, (rT) vs. 1/T plot appears to be a
smooth curve, neither having the super-Arrhenius behavior at high temperature nor Arrhenius
behavior at low temperature. We may attribute it [50] to the phase separated mixture of the HDL
and LDL due to the crossing of the hypothetical liquid-liquid first order transition line [118]. If
these arguments are valid, then the disappearance of the FSC phenomena signals the crossing of
the state point from the Widom line to the first order liquid-liquid transition line. These two lines
are separated by the liquid-liquid critical point if it exists.
.....
.
. ...
.............................................................
... ...............
..................
0
400
800
10
1200
T>
>
1600
at TL(P)
10
4.0-O
230
TL~p
6
EA(P)
d3.8-A
3.6
220
210
-
200Q
3.4 3.2 -190
109
8
7
6
0
400
800
1200
1600
P(bar)
Figure 4.15 Pressure Dependence of the parameters extracted from analysis of the quasi-elastic
spectra by using Relaxing-Cage Model. Upper panel shows the pressure dependence of <rr> at the
corresponding crossover temperature TL(P). Middle panel shows the activation energy E(P) and TL(P)Lower panel shows the ratio of the activation energy EA(P) to k-TL. The dashed lines indicate the
linear least square fitting of these parameters.
In Figure 4.16, we thus plot the trajectory of the crossover temperature TL as a function of P
(red circles). It is remarkable to see that this Widomn line of the protein hydration water seems to
coincide with the Widom line of the confined water in MCM-41-S found in our previous
experiment [50].
280
260 -
240
-MCM-41
200
180
- -Lysozyme
H
-a-
220
£
TMD
*CL-L
L
--
160
L-L
160
T.
.........
140
*.-
....
*4....4..
----------
LDA HDA
120
1
0.0 0.2 0.4 0.6 0.8
a
1.0 1.2
1.4
kI
a.
a.
1.6 1.8 2.0 2.2 2.4 2.6
Pressure (kbar)
Figure 4.16 The pressure dependence of the measured FSC temperature TL (red circles), plotted in the
T-P plane, comparing with our previous results from water in MCM-41-S [50](purple circles). We
also show the homogeneous nucleation temperature line (TH,[122]), crystallization temperatures of
amorphous solid water (Tx,[ 123] ), and the temperature of maximum density line (TMD, [124]), taken
from known phase diagram of bulk water.
4.5 Comparison with Computer Simulation Results
4.5.1 Comparison with a 2D Model of Water
Thermodynamic and transport properties of water differs from that of normal fluids, showing
many counterintuitive trends. It has been tabulated by Martin Chaplin that physical properties of
water exhibit 66 anomalies [125].
Simulations and theories propose that many of these anomalies result from the coexistence of
two liquid phases with different local structures and hence densities. Neutron diffraction
experiments in bulk water confirm the existence of two local structures of liquid water with
............................
............
.........
. ..
.....
. ...................................
........
-- - ------
different densities [126]. But, because of inevitable freezing at low temperatures below the
homogeneous nucleation temperature TH= 235 K, one cannot ascertain whether the two structures
separate into two phases. To avoid the freezing, new experiments measure the dynamics of water at
low Ton the surface of proteins, finding a crossover from a non-Arrhenius regime at high T to a
regime that is approximately Arrhenius at low T [8]. Motivated by these experiments, Kumar et al
[119] investigated, by Monte Carlo simulations and mean field calculations on a cell model for
water in two dimensions (2D) [127], the relation of the dynamic crossover with the coexistence of
two liquid phases. They show that the crossover in the orientational correlation time
T
is a
consequence of the rearrangement of the hydrogen bonds at low T, and predict that: (i) the dynamic
crossover is isochronic, i.e. the value of the relaxation time <TT> at the crossover temperature TL is
approximately independent of pressure P; (ii) the Arrhenius activation energy EA(P) of the low-T
regime decreases upon increasing P; (iii) the crossover temperature TL(P) decreases upon
increasing P.
8.0
,
i
75 P = lbar
7.0 -
P = 400 bar
6.5
P = 800 bar
0
P = 1200 bar
0
(MC) P = 0
5.5 'o
5.0
._
4.5
0
0
.24.0
3.5
3.0 -
o
2.5
2.0
1.5
0.002
I
0.004
*
0.006
B
0.008
1/T (K 1 )
Figure 4.17 Comparison between the Monte Carlo results of a 2D model of water [119] and the QENS
data [47] for the correlation time r of supercooled water. Monte Carlo results (open symbols) are for P =
0 and are rescaled in such a way that the crossover occurs at the same T and r as the experimental data
(full symbols). The experimental data are for pressures going from ambient to 1200 bar.
.
4
.........
4.1
4.0-
3.5
-N3.93.8-
3-
LLCP
3.7
"
2.5-
N3.6
3.4
U 3.3 -
SF
2
3.2-
1.5_
-200
3.1 0
200 400 600 800 1000 1200 1400 1600
-200
0
P (bar)
200 400 600 800 1000 1200 1400 1600
P (bar)
240
230
220125
225
200 -
T
220LLCP
g1o0
160
215
-
210
-
-
SF
140-
20510
100 -
20
0
40
60
80
400 (r
600
800
(bar)
10
200-
-200 0
200 400 600 800 10001200 1400 1600
P (bar)
Figure 4.18 Monte Carlo [119] results and the QENS data [47] for the activation energy EA of the low-T
regime and the crossover temperature TL, as functions of the pressure P. Upper left panel: Monte Carlo
results for EA [119]; for sake of comparison with the experimental data, pressure is rescaled by an
arbitrary factor 1500 bar/(0.8 e/vo) and energy by a factor 16.4 kcal mol '/e z 68.7 kJ mol 1/e, both the
liquid-liquid critical point (LLCP) scenario results (circles) and the singularity free (SF) scenario results
(squares) are reported. Lower left panel: Monte Carlo results for the crossover temperature TL; pressure
is rescaled as above and temperature is rescaled by a factor 220 K/(0. 16 e/kB); symbols are as in the
previous panel. Upper right panel and lower right panel: QENS data for the lysozyme hydration water
[47].
Here, we compare these predictions with our recent quasi-elastic neutron scattering (QENS)
experiments [47] on hydrated proteins at different values of P. Figure 4.17 and 4.18 show the
comparison of the experimental results with the MC simulation results.
experiments are consistent with these three predictions.
We find that the
4.5.2 Comparison with MD Simulation Results
The plausible microscopic origin for the dynamic transition of a hydrated protein is thought
to be due to the strong coupling of the dynamics of the hydration water and those of the side
chains of the protein through their hydrogen bonds. In particular, it was shown by MD
simulations that the slow structural relaxation of the protein, which is essential for the enzymatic
function, is driven by the relaxation of the hydrogen bond network via solvent translational
displacement [128, 129].
We have shown, throughout this chapter, that this low-temperature dynamic transition of
protein, or more generally for many other biopolymers, is likely to be triggered by a
fragile-to-strong dynamic crossover (FSC) at TL ~220 K which occurs in hydration water of these
biopolymers. An important connection of this FSC with the existence of liquid-liquid critical
point (LLCP) of confined water has been made [117]: the FSC observed experimentally in a 1-d
confined water [50] is attributed to crossing of the Widom line (the line of maximum correlation
length) emanating from the LLCP, above the critical temperature and below the critical pressure
in the one phase region.
More recently, a MD simulation [9] has been made for a model of hydration water in protein
lysozyme and Dickerson dodecamer DNA and a clear evidence was given for connecting the FSC
observed in those hydration water with crossing of the Widom line. However, in this simulation
the model used was not realistic enough for hydrated powder samples used in experiments to
directly compare the temperature dependences of simulated quantities with the neutron scattering
results.
To better mimic the experimental system where we used hydrated powder protein samples,
we decided to perform MD simulations on the random powder model developed and tested by
Tarek and Tobias [102]: this model has been shown to improve the agreement with experiments
compared to the so-called protein/watercluster model used in [9], which is composed of just one
protein surrounded by its hydration water.
We show in this section that this realistic powder model can actually reproduce experimental
data within the statistical error bars. In particular, we show the striking agreements of MD
calculations with the temperature dependences of the measured mean-square hydrogen atom
displacements of the protein and its hydration water and the translational alpha-relaxation time of
the hydration water, <rT>, calculated from the self-intermediate scattering functions (SISF). The
significance of these comparisons is the following: we demonstrate that the dynamic crossover we
observed in experiments can be attributed sorely to the crossover phenomenon resulting from
evaluation of the average translational alpha-relaxation time by analyses of the long-time decays
(in the range of 100 ps - 50 ns) of the SISF of the hydrogen atoms attached rigidly to a typical
water molecule [130-132]. It is the signature of crossing of the Widom line in a 2-d confined
water. At high temperatures the fragile behavior arises from water structure dominated by a high
density form (HDL), which is more fluid, and at low temperatures, upon crossing TL, the water
structure evolves into a predominantly low-density form (LDL), which is less fluid, and has a
strong behavior. This sudden switch in mobility of hydration water at TL serves to trigger the
dynamic transition in protein, in agreement with the previous MD simulation results [128, 129].
Since our interest was mainly on dynamics of hydration water, we decided to use the
TIP4P-Ew water model [133]. This model has a computed self-diffusion constant in excellent
agreement with the experimental values. Furthermore, it has a very good correspondence of the
temperature scale (its density maximum is at 274 K, only 3 K below the correct value) at least
down to 230 K. Accordingly, we had to choose an all-atom force field for the protein developed
with the TIP4P model in mind. So we decided to implement the OPLS-AA force field for the
lysozyme molecules [134].
As mentioned above, Tarek and Tobias [102] pointed out the poor agreement with
experiments of the so-called cluster model, composed of a single protein covered by a shell (thin
or thick) of water, which lacks the characteristic feature of the powder protein. They found that it
produces serious errors and artifacts for any calculated properties. Instead, a crystal model
(composed of at least 2 proteins) or a powder model (8 proteins, oriented or random) resulted in a
realistic model to reproduce neutron scattering data [128, 135], with little differences between
them.
Therefore, we put in a box two OPLS-AA lysozyme molecules randomly oriented and 484
TIP4P-Ew water molecules (h = 0.3 for each protein): after an energy minimization of 5000 steps
with the Steepest Descent algorithm, we equilibrated the system in a NPT ensemble
(isobaric-isothermal) for 10 ns at 300 K and for another 50 ns at 200 K. We then performed 11
simulations at different temperatures (from 180 K to 280 K, with 10 K of interval) with a
parallel-compiled version of GROMACS [136], starting each simulation from the final
configuration of the closest temperature. The Lennard-Jones interactions were truncated beyond
1.4 nm, while electrostatic interactions, calculated with the Particle Mesh Ewald method [137]
were truncated at 0.9 nm. All bonds were constrained at their equilibrium values using the LINear
Constraint Solver algorithm (LINCS, [138]). Simulations were performed using a triclinic cell
with periodic boundary conditions and each MD simulation length was 50 ns after the
equilibration time.
32 A
37A
43A
Figure 4.19 Snapshot from a MD simulation at T = 250 K and P = 1 atm of the hydrated lysozyme
powder model, containing two protein molecules and 484 water molecules around them (hydration
level h = 0.3) [8].
(a) 1.00.90.80.7-
0.60.50.410-2
10
10
10
10
10
t (ps)
(b)
* MD Smianifelio
Ardtenio fit
E,-
3.38 kca~rlan
kalmo9.I9Df
4al=u43
T, - 182K
4T,, = 176 K, 191)
T, =221 K
IT,,=w22K,1910
101-
A
V
V
e QENS
* ND
40 43
3.0
iwwrwl
102.
45
10ooff (K~')
Figure 4.20 (a) Water proton incoherent self-intermediate scattering functions calculated at six
different temperatures. (inset) ISF at five different Q-values (from top to bottom, 0.4, 0.5, 0.6, 0.7, and
0.8 A-'). The choice of the Q range was dictated by the low-limit value of Q = 0.2 A imposed by the
box dimensions and the high-limit value of Q = 1 A', below which rotational motions can be
neglected. The solid curves are fits to the relaxing cage model in a wide time range of 7 orders of
magnitude, between 2 fs and 20 ns. (b) Temperature dependence of the average translational
relaxation time, < V >, from MD simulation; To is the ideal glass transition temperature. Numerical
data are fitted with a Vogel-Fulcher-Tammann (VFT) law at high temperatures and with an Arrhenius
law at low temperatures (solid lines) but with the same prefactor [8].
A perspective view of the simulation box is shown in Figure 4.19, where the two proteins and
the hydration water surrounding them are displayed, together with the box dimensions. It should
be noted that there are only a few water molecules sandwiched between the two proteins while
there are more water molecules around other parts of protein surface. But on the average, h = 0.3
is supposed to be only one monolayer of water covering each protein. The resulting density of the
modeled hydrated powder protein is between 1.2 and 1.3 g/cm 3, depending on the temperature, in
agreement with experimental data for lysozyme crystals (1.23 g/cm 3, [139]).
Figure 4.20(a) shows the calculated self-intermediate scattering function (SISF) for the
protons attached to a rigid molecule of hydration water for different temperatures, as a function of
time at fixed Q-value (0.6 A-'), while the inset shows the ISF at T= 220 K for different Q-values.
The solid lines are the best fits to the ISF according to the RCM described above. The RCM fits
of the ISF, both the time dependence and the Q-dependence, are excellent allowing us to extract
the <TT> as a function of temperature as shown in Figure 4.20(b). The crossover feature is clearly
visible looking at the decay of the ISF below and above TL. We fitted the fragile part with a VFT
law, and the strong part with an Arrhenius law. The crossover temperature is determined to be TL
= 221 K, very close to the experimental value of 220 K [8].
4.6 Conclusion
In this chapter, we have made an extensive series of studies on the pressure dependence of
the average translational relaxation time (or c-relaxation time) of protein hydration water by
high-resolution QENS. We find strong evidence that the pressure dependence of the dynamic
crossover temperature in protein follows that of the pressure dependence of the FSC temperature
of hydration water. We find the Widom line of the 2-D confined protein hydration water is nearly
coincident with the 1-D confined water in MCM-41-S with cylindrical pore of diameter 15A. This
strongly suggests that the liquid-liquid critical point of water CLL, if it exists, is located at
approximately Tc = 200 ± 5K, Pc = 1550 ± 50 bars in both confined geometries. We also observe
an abnormal deviation from the VFT law, just above the crossover temperature in the Arrhenius
plot of<rT> at P= 1500bar (see Figure 4.16), which is very close to the predicted critical pressure.
We may consider this deviation to come from the large density fluctuation of hydration water near
the critical point. This may be another evidence that our predicted location of critical point is
close to the actual one.
At the end of this chapter, we demonstrated by MD simulations that the low temperature
crossover phenomenon is due to the average translational motion of all the water molecules in the
hydration layer, not to the long-range proton diffusion coupled to the motion of the so-called
Bjerrum-type defects [130, 131]. Furthermore, by a simulation using a realistic powder model,
one can quantitatively account for the temperature dependence of the Neutron Scattering data.
93
Chapter 5
Summary
In summary, we study the low temperature dynamics of both protein (Chapter 3) and its
hydration water (Chapter 2). We can detect the dynamic crossover temperature TL by either the
MSD vs T plot or by the Arrhenius plot of the a-relaxation time vs 1/T. The two methods give the
same crossover temperature (see Chapter 4). The slope of MSD vs T plot gives information on
softness of the protein and its hydration water. The pressure dependence of an Arrhenius plot of
the relaxation time gives a plausible evidence of the existence of the second critical point in
supercooled confined water. The crossover temperature depends on pressure but the relaxation
time at the crossover temperature is independent of the pressure (so-called isochronic)
-<rr>
about 10-20 ns. Proteins remain soft at lower temperatures under pressure. The crossover
temperature TL is lower by 35 K for water confined in a hydrophobic substrate DWNT than in a
hydrophilic substrate (Chapter 2). The so-called glass transition temperature is universal in all
biopolymers because it is synchronized with the dynamic crossover temperature TL in their
hydration water-the so-called "slaving" phenomenon [76]. This is the consequence of the HDL
to LDL transition taking place at the TL. There is strong experimental evidence that the crossover
phenomenon is a general property of all the glass-forming liquids [140]. MD simulation of a
realistic hydrated powder model of lysozyme reproduces the dynamic crossover phenomenon in
the protein hydration water.
95
Appendix A
Incoherent Neutron Scattering for Studying
Dynamics of Water
Incoherent Elastic Neutron Scattering (ENS), Quasielastic Neutron Scattering (QENS) and
Inelastic Neutron Scattering (INS) methods offer many advantages for the study of hydrogen
atom dynamics in a protein and its hydration water. The main reason is that the scattering cross
section of hydrogen is about 80 barns, and is much larger (at least 20 times) than that of other
atoms in the protein-hydration-water system, composed of oxygen, carbon, nitrogen and sulfur
atoms. Furthermore, neutron scattering cross section of a hydrogen atom is mostly incoherent so
that QENS and INS spectra reflect, essentially, the self-dynamics of the hydrogen atoms in the
protein or water. Combining this dominant cross section of hydrogen atoms with the use of
spectrometers having different energy resolutions, we can study the molecular dynamics of water
in a wide range of time-scale, encompassing picoseconds to tens of nanoseconds. In addition,
investigating different Q values (Q being the magnitude of the wave vector transfer in the
scattering) in the range from 0.2^-1
Q
2.0 A-1, the spatial characteristics of water dynamics
can be investigated at the sub-nanometer level.
It can be shown generally [141] that the double differential scattering cross section is
proportional to the self-dynamic structure factor of hydrogen atoms SH (Q,E) through the
following relation:
d
-2.N
=
dQdE
where E=Ei -E
H(Q, E)
Hf
(A.1)
47rh k,
=hoj is the energy transferred by a neutron to the sample in the collision
process; and hQ=hk,-hkj, the momentum transferred in the scattering process; and N, the
number of hydrogen atoms in the scattering volume. The self-dynamic structure factor, SH (Q,E)
embodies the elastic, quasi-elastic and inelastic scattering contributions. It can be expressed as a
Fourier transform of the self-ISF of a typical hydrogen atom according to:
SH(Q, E)= 2zAhf dte^ FH(Q, t)
(A.2)
FH(Q,t) is the atom density-density time correlation function of the tagged hydrogen atom
being measured by the neutron scattering. It is, thus, the primary quantity of theoretical interest
related to the experiment. It can be calculated by a model, such as the relaxing cage model (RCM),
or by a molecular dynamics (MD) simulation based on a phenomenological potential model of
water.
A.1 Incoherent Elastic Scattering (E = )
The intermediate scattering function (ISF) for a hydrogen atom harmonically bound to a
molecule can be written as
FH (Q, t)
=
(exp(- iQXH (0))exp(iQXH (t))).
(A.3)
where Q is the magnitude of the Q vector, pointing in the x-direction in the isotropic powder
sample. Then it can be shown that in the Gaussian approximation, which is exact for the
harmonically bound particle, one can write [142]
FH (Q, t) = exp(- Q2 (X 2 ))exp(Q2 (X, (O)XH(t))
(A.4)
where the first factor, exp(-Q2(X/j)), is called the Debye-Waller factor, which gives rise to the
elastic scattering, and the second factor, which involves the displacement-displacement time
correlation function, gives rise to the inelastic scattering such as phonons. In the classical regime,
the eq. (A.4) can further be written into the form
F/I(Q, t) = exp
(A.5)
iQ2W(t)
where the width function can be written as [13]
W(t) = 2VO2 dco
fH()_CS
(1-cos wt).
(A.6)
fH (co) is the Fourier transform of the normalized velocity of the correlation function of a
hydrogen atom, which is sometime called the spectral density function of the hydrogen atom.
10
f (
where
((VVH2)
0
kB
H.
x"()V,(t))
2;T -0VH0
In eq. (A.4), the elastic scattering corresponds to t =
the second factor become unity, and
(A.7)
2f fdte'"
o,
where
FH (Q,oo) = exp(-Q2(X2 ))), which is just the Debye-Waller
factor. Combining this equation with eq. (A.5), we finally obtain a very useful result,
X2)=o
W(oo)=V fdco H
(A.8)
The mean-square deviation (MSD) of the hydrogen atoms can be obtained from the integral of the
reduced spectraldensityfunction of the hydrogen atoms.
A.2 Inelastic Scattering (E
= hco #
0)
From the inelastic scattering intensity dominated by the incoherent scattering from hydrogen
atoms, the Q-dependent vibrational Density-Of-States (Q-DOS) of hydrogen atoms can be
calculated by
2
GH(Q, E)=
MH
2
h2
E
(Q2
n(E)+1
epQ
XH
2
(A.9)
(Q, E)
Q
in the case of protein. But in the case of hydration water,
2
GH2O(QCO)
The true hydrogen DOS fH (w) is obtained in the
of water,
Q -+ 0
(A.10)
Q22 SH2O(Q,C,
Q -+ 0
limit of the GH (Q,E). In the case
limit in practice means Q <1A~:
GH (co) = lim GH2
Q-+M0
H2 o (o) -
T
MH2
(A.11)
A.3 Incoherent quasielastic scattering (E 0)
In principle, the single-particle dynamics of bulk or confined water should include both the
translational and the rotational motions of a rigid water molecule. Given the fact that in the
process of QENS data analysis, we only focus our attention to ISF with
Q
1.1 A1 , we can
safely neglect the contribution of the rotational motion to the total dynamics [143], which means
FH (Q, t)
FT(Q, t), where FT(Q,t) is the translational part of the ISF.
Appendix B
Relaxing-Cage
Model
(RCM)
for
the
Single-Particle Dynamics of Water
During the past several years, our group has developed the RCM for the description of the
translational and the rotational dynamics of water at supercooled temperatures. This model has
been tested with MD simulations of SPC/E water, and has been found to be accurate. It has been
used to analyze many QENS data from supercooled bulk water as well as interfacial water
[144-148].
On lowering the temperature below the freezing point, around a given water molecule, there is
a tendency to form a hydrogen-bonded, tetrahedrally coordinated first and second neighbor shells
(cage). At short times, less than 0.05 ps, the center of mass of a water molecule performs
vibrations inside the cage. At long times, longer than 1.0 ps, the cage eventually relaxes and the
trapped particle can migrate through the rearrangement of a large number of particles surrounding
it. Therefore, there is a strong coupling between the single particle motion and the density
fluctuations of the fluid. The mathematical expression of this physical picture is the so-called
RCM.
The RCM assumes that the short-time translational dynamics of the tagged (or the trapped)
water molecule can be treated approximately as the motion of the center of mass in an isotropic
harmonic potential well provided by the mean field generated by its neighbors. We can, then,
write the short time part of the translational ISF in the Gaussian approximation, connecting it to
the velocity auto-correlation function, (icm (t)'
VcM
(0)), in the following way:
Fj(Q t) = exp =exp
-
Q2
[
()
2
(t - rXcC(0)-
Since the translational density of states, Zr (CO),
Vcm
(r))dr
is the time Fourier transform of the
normalized center of mass velocity auto-correlation function, one can express the mean squared
deviation, (r&M(t)) as follows:
- 22
(t)
r2(\rM
3
//
where (v2)=(vi)+(v2)+(v)
)
2(B2(1 -
CMy do)CO
(B.2)
cos wt)
is the average center of mass square velocity, and M
= 3v2= 3
is the mass of water molecule.
Experiments and MD results show that the translational harmonic motion of a water molecule
in the cage gives rise to two peaks in Zr(co) at about 10 and 30-meV, respectively [149]. Thus,
the following Gaussian functional form is used to represent approximately the translational part of
the density of states:
ZT()=
(1 -C)o
2
V12 F2C 12
__2
exp[-
CC
Cco2
+
2,cm2 2
2
2
2com
c(B.3)
C2
exp[-
2
2W2
Moreover, the fit of MD results using Eq. (B.3) gives C = 0.44,
C02
co =10.8 THz, and
= 42.0 THz. Using Eq. (B.2) - Eq. (B.3), we finally get an explicit expression for Fj(Q,t):
Fj (Q,t) = exp{-Q
[(1 2
1-exp(-
2
)2+ C 2r1-xP(
2
) ]}
(B.4)
Eq. (B.4) is the short-time behavior of the translational ISF. It starts from unity at t = 0 and
decays rapidly to a flat plateau determined by an incoherent Debye-Waller factor A (Q), given
by:
A(Q)= exp - -Q2 v2 (1 C) +
=
C
exp[- Q2a 2 /3]
(B.5)
where a is the root mean square vibrational amplitude of the water molecules in the cage, in
which the particle is constrained during its short-time movements. According to MD simulations,
a ~0.5A is fairly temperature independent [150].
On the other hand, the cage relaxation at long-time can be described by the standard
a-relaxation model, according to the Mode-Coupling Theory (MCT), with a stretched exponential
having a structural relaxation time
T
and a stretch exponent P. Therefore, the translational ISF,
valid for the entire time range, can be written as a product of the short time part and a long time
part:
(B.6)
FT(Q,t) = Fj(Qt)exp -i-TT )
The fit of the MD generated FT(Q,t) using Eq. (B.6) shows that
Tr
is Q -dependent,
obeying the power-law:
Tr
where
r
= Vo (aQ)T
is <2, with a slight dependency on Q and T, and
(B.7)
p8 < 1
is slightly Q and
T dependent as well. In the Q -- 0 limit, one should approach the diffusion limit, where
and
p -> 1. Thus the translational
r-
2
ISF can be written as: FT (Q, t)= exp(-DQ2t), D being the
self-diffusion coefficient. In QENS experiments, this low Q limit is not usually reached, and
both 8 and y can be considered Q-independent in the limited Q range of 0 s Q 51 [146,
147].
We define a Q-independent average translational relaxation time
(r )= --(o
/
p)1-( 1/,p)
(B.8)
which is a convenient quantity to be extracted from the experimental data by the fitting process of
RCM. This quantity can be identified to be proportional to the a -relaxation time which
dominates the long-time decay of the ISF in low temperature water. Combining Eqs. (A.1), (B.4),
and (B.6), we can calculate the theoretical values of SHO(Qco) and compare it directly with its
experimental spectral data.
In actual QENS experiment, we have to take into account the signal coming from the hydrogen
atoms in the hydration water only, by taking the difference of the spectra of H2 0 and D20
hydrated samples [151, 152]. Denoting the fraction of the elastic scattering coming from the
bound hydrogen atom in protein by p we can analyze the experimental data according to the
following model:
S(Q, o) = pR(QO, co) + (1 - p)FTFH (Q, t)R(Q0 , t)}
(B.9)
where FH (Q, t) ~ FT (Q, t) is the ISF of hydrogen atoms which defines the quasielastic
scattering, R(Qo,t) is the experimental resolution function, and the symbol FT denotes the
Fourier transform from time t to frequency co.
Appendix C
A list of publications
C.1
Experimental
evidence
of
fragile-to-strong
dynamic
crossover in DNA hydration water
Authors: Sow-Hsin Chen, Li Liu, Xiang-qiang Chu, Yang Zhang, Emiliano Fratini, Piero
Baglioni, Antonio Faraone, and Eugene Mamontov
Journal: Journal of Chemical Physics
Abstract: We used high-resolution quasielastic neutron scattering spectroscopy to study the
single-particle dynamics of water molecules on the surface of hydrated DNA samples. Both H20 and
D20 hydrated samples were measured. The contribution of scattering from DNA is subtracted out by
taking the difference of the signals between the two samples. The measurement was made at a series
of temperatures from 270 down to 185 K. The relaxing-cage model was used to analyze the
quasielastic spectra. This allowed us to extract a Q-independent average translational relaxation time
<-rT> of water molecules as a function of temperature. We observe clear evidence of a
fragile-to-strong dynamic crossover (FSC) at TL = 222 ± 2 K by plotting lOg<TT> versus T. The
coincidence of the dynamic transition temperature T, of DNA, signaling the onset of anharmonic
molecular motion, and the FSC temperature TL of the hydration water suggests that the change of
mobility of the hydration water molecules across TI. drives the dynamic transition in DNA.
Pages: 171103
Volume: 125
Year: 2006
Reference: S. -H. Chen, L. Liu, X.-Q. Chu, Y. Zhang, E. Fratini, P. Baglioni, A. Faraone,
and E. Mamontocv, "Experimental Evidence of Fragile-to-Strong Dynamic Crossover in
DNA Hydration Water", J Chem. Phys. 125, 171103 (2006).
C.2 Observation of a dynamic crossover in water confined in
double-wall carbon nanotubes
Authors: Xiang-qiang Chu, Alexander I. Kolesnikov, Alexander P. Moravsky, Victoria
Garcia-Sakai and Sow-Hsin Chen
Journal: Physical Review E
Abstract: High-resolution quasielastic neutron scattering spectroscopy was used to measure H2 0
hydrated double-wall carbon nanotubes (DWNT). The measurements were made at a series of
temperatures from 250 K down to 150 K. The relaxing-cage model was used to analyze the
quasielastic spectra. We observed clear evidence of a fragile-to-strong dynamic crossover (FSC)
at TL = 190 K in the confined water. We further show that the mean-square atomic displacement
of the hydrogen atoms in water exhibits a sharp change in slope at approximately the same
temperature 190 K. Comparing the result with that obtained from the confined water in
hydrophilic porous silica material MCM-41, we demonstrate experimentally that water confined
in a hydrophobic substrate exhibits a lower dynamic crossover temperature by ATL approximate
to 35 K.
Pages: 021505
Volume: 76
Year: 2007
Reference: X.-Q. Chu, A. I. Kolesnikov, A. P. Moravsky, V. Garcia-Sakai, and S.-H. Chen,
"Observation of a Dynamic Crossover in Water Confined in Double-Wall Carbon Nanotubes",
Phys. Rev. E 76, 021505 (2007).
C.3 Observation of a dynamic crossover in RNA hydration
water which triggers a dynamic transition in the biopolymer
Authors: Xiang-qiang Chu, Emiliano Fratini, Piero Baglioni, Antonio Faraone and Sow-Hsin
Chen
Journal: Physical Review E
Abstract: High-resolution quasielastic neutron scattering spectroscopy was used to measure H2 0
and D2 0 hydrated RNA samples. The contribution of scattering from RNA was subtracted out by
taking the difference of the signals between the two samples. The measurements were made at a
series of temperatures from 270 K down to 180 K. The relaxing-cage model was used to analyze
the difference quasielastic spectra. We observed clear evidence of a fragile-to-strong dynamic
crossover (FSC) at TL = 220 K in RNA hydration water. We further show that the mean-square
displacements of the hydrogen atoms in both RNA and its hydration water exhibit a sharp change
in slope at approximately the same temperature 220 K. This latter fact suggests that the dynamic
transition in RNA is triggered by the abrupt change of mobility of the hydration water at its FSC
temperature.
Pages: 011908
Volume: 77
Year: 2008
Reference: X.-Q. Chu, E. Fratini, P. Baglioni, A. Faraone, and S. -H. Chen, "Observation of a
Dynamic Crossover in RNA Hydration Water which Triggers the Dynamic Transition in the
Biopolymer", Phys. Rev. E 77, 011908 (2008).
C.4 The low-temperature dynamic crossover phenomenon in
protein hydration water: Simulations vs experiments
Authors: M. Lagi, X. Q. Chu, C. S. Kim, F. Mallamace, P. Baglioni and S. H. Chen
Journal: Journal of Physical Chemistry B
Abstract: A super-Arrhenius-to-Arrhenius dynamic crossover phenomenon has been observed in
the translational (x-relaxation time and in the inverse of the self-diffusion constant both
experimentally and by simulations for lysozyme hydration water in the temperature range of TL =
223 ± 2 K. MD simulations are based on a realistic hydrated powder model, which uses the
TIP4P-Ew rigid molecular model for the hydration water. The convergence of neutron scattering,
nuclear magnetic resonance and molecular dynamics simulations supports the interpretation that
this crossover is a result of the gradual evolution of the structure of hydration water from a
high-density liquid to a low-density liquid form upon crossing of the Widom line above the
possible liquid-liquid critical point of water.
Pages: 1571-1575
Volume: 112
Year: 2008
Reference: M. Lagi, X.-Q. Chu, C. Kim, F. Mallamace, P. Baglioni and S.-H. Chen, "The
Low-Temperature Dynamic Crossover Phenomenon in Protein Hydration Water: Simulations vs
Experiments", J Phys. Chem. B, 112, 1571 (2008).
C.5 Dynamic crossover phenomenon in confined supercooled
water and its relation to the existence of a liquid-liquid critical
point in water
Authors: Sow-Hsin Chen, Francesco Mallamace, Li Liu, Dazhi Liu, Xiang-qiang Chu, Yang Zhang,
Chansoo Kim, Antonio Faraone, Chung-Yuan Mou, Emiliano Fratini, Piero Baglioni, Alexander I.
Kolesnikov, Victoria Garcia-Sakai
Book Series: AIP CONFERENCE PROCEEDINGS
Abstract: We have observed a Fragile-to-Strong Dynamic Crossover (FSC) phenomenon of the
alpha-relaxation time and self-diffusion constant in confined supercooled water. The alpha-relaxation
time is measured by Quasielastic Neutron Scattering (QENS) experiments and the self-diffusion
constant by Nuclear Magnetic Resonance (NMR) experiments. Water is confined in 1-d geometry in
cylindrical pores of nanoscale silica materials, MCM41-S and in Double-Wall Carbon Nanotubes
(DWNT). The crossover phenomenon can also be observed from appearance of a Boson peak in
Incoherent Inelastic Neutron Scattering experiments. We observe a pronounced violation of the
Stokes-Einstein Relation at and below the crossover temperature at ambient pressure. Upon applying
pressure to the confined water, the crossover temperature is shown to track closely the Widom line
emanating from the existence of a liquid-liquid critical point in an unattainable deeply supercooled
state of bulk water. Relation of the dynamic crossover phenomenon to the existence of a density
minimum in supercooled confined water is discussed. Finally, we discuss a role of the FSC of the
hydration water in a biopolymer that controls the biofunctionality of the biopolymer.
Pages: 39-52
Volume: 982
Year: 2008
Reference: S. -H. Chen, F. Mallamace, L. Liu, D. Z. Liu, X. Q. Chu, Y. Zhang, C. Kim, A.
Faraone, C. -Y. Mou, E.Fratini, P. Baglioni, A.I. Kolesnikov, V. Garcia-Sakai, "Dynamic
Crossover Phenomenon in Confined Supercooled Water and its Relation to the Existence of a
Liquid-Liquid Critical Point in Water", an invited paper at the 5th InternationalWorkshop on
Complex Systems, Sendai, Japan, Sep. 25-28, 2007, Proceedings: Complex Systems, AIP
Conference Proceedings 982, Eds: M. Tokuyama, I. Oppenheim, H. Nishiyama, pp 39-52 (2008).
C.6 Studies of Phononlike Low-Energy Excitations of Protein
Molecules by Inelastic X-Ray Scattering
Authors: Dazhi Liu, Xiang-qiang Chu, Marco Lagi, Yang Zhang, Emiliano Fratini, Piero Baglioni,
Ahmet Alatas, Ayman Said, Ercan Alp, and Sow-Hsin Chen
Journal: Physical Review Letters
Abstract: Molecular dynamics simulations and neutron scattering experiments have shown that
many hydrated globular proteins exhibit a universal dynamic transition at TD = 220 K, below which
the biological activity of a protein sharply diminishes. We studied the phononlike low-energy
excitations of two structurally very different proteins, lysozyme and bovine serum albumin, using
inelastic x-ray scattering above and below TD. We found that the excitation energies of the high-Q
phonons show a marked softening above TD. This suggests that the large amplitude motions of
wavelengths corresponding to this specific Q range are intimately correlated with the increase of
biological activities of the proteins.
Pages: 135501
Volume: 101
Year: 2008
Reference: D. Liu, X.-Q. Chu, M. Lagi, Y. Zhang, E. Fratini, P. Baglioni, A. Alatas, A. Said, E.
Alp, and S.-H. Chen, "Studies of Phonon-like Low Energy Excitations of Protein Molecules by
Inelastic X-ray Scattering", Phys. Rev. Lett. 101, 135501 (2008).
C.7 Pressure effects in supercooled water: comparison between
a 2D model of water and experiments for surface water on a
protein
Authors: Giancarlo Franzese, Kevin Stokely, Xiang-qiang Chu, Pradeep Kumar, Marco G.
Mazza, Sow-Hsin Chen and H. Eugene Stanley
Journal: Journal of Physics: Condensed Matter
Abstract: Water's behavior differs from that of normal fluids, having more than sixty anomalies.
Simulations and theories propose that many of these anomalies result from the coexistence of two
liquid phases with different densities. Experiments in bulk water confirm the existence of two local
arrangements of water molecules with different densities, but, because of inevitable freezing at low
temperature T, cannot ascertain whether the two arrangements separate into two phases. To avoid the
freezing, new experiments measure the dynamics of water at low T on the surface of proteins, finding
a crossover from a non-Arrhenius regime at high T to a regime that is approximately Arrhenius at low
T. Motivated by these experiments, Kumar et al (2008 Phys. Rev. Lett. 100, 105701) investigated, by
Monte Carlo simulations and mean field calculations on a cell model for water in two dimensions
(2D), the relation of the dynamic crossover with the coexistence of two liquid phases. They show that
the crossover in the orientational correlation time tau is a consequence of the rearrangement of the
hydrogen bonds at low T, and predict that: (i) the dynamic crossover is isochronic, i. e. the value of
the crossover time XL is approximately independent of pressure P; (ii) the Arrhenius activation energy
EA(P) of the low-T regime decreases upon increasing P; (iii) the temperature T*(P) at which r reaches
a fixed macroscopic time r* ;> rL decreases upon increasing P; in particular, this is true also for the
crossover temperature TL(P) at which r = rLPages: 494210
Volume: 20
Year: 2008
Reference: G. Franzese, K. Stokely, X.-Q. Chu, P. Kumar, M. G. Mazza, S.-H. Chen and H. E.
Stanley, "Pressure effects in supercooled water:comparison between a 2D model of water and
experiments for surface water on a protein", J. Phys.: Condens. Matter 20, 494210 (2008).
C.8 Proteins Remain Soft at Lower Temperatures under
Pressure
Authors: Xiang-qiang Chu, Antonio Faraone, Chansoo Kim, Emiliano Fratini, Piero Baglioni,
Juscelino B. Leao and Sow-Hsin Chen
Journal: Journal of Physical Chemistry B
Abstract: The low-temperature behavior of proteins under high pressure is not as extensively
investigated as that at ambient pressure. In this paper, we study the dynamics of a hydrated
protein under moderately high pressures at low temperatures using the quasielastic neutron
scattering method. We show that when applying pressure to the protein-water system, the
dynamics of the protein hydration water does not slow down but becomes faster instead. The
degree of "softness" of the protein, which is intimately related to the enzymatic activity of the
protein, shows the same trend as its hydration water as a function of temperature at different
pressures. These two results taken together suggest that at lower temperatures, the protein remains
soft and active under pressure.
Pages: 5001-5006
Volume: 113
Year: 2009
Reference: X.-Q. Chu, A. Faraone, C. Kim, E. Fratini, P. Baglioni, J. B. Leao, and S.-H. Chen,
"Proteins Remain Soft at Lower Temperatures under Pressure", J. Phys. Chem. B 113, 5001
(2009).
C.9 Dynamical Coupling between a Globular Protein and its
Hydration Water Studied by Neutron Scattering and MD
Simulation
Authors: Sow-Hsin Chen, Xiang-qiang Chu, Marco Lagi, Chansoo Kim, Yang Zhang, Antonio
Faraone, Juscelino B. Leao, Emiliano Fratini, Piero Baglioni, and Francesco Mallamace
Journal: WPI-AIMR-2009 Proceedings
Abstract: This review article describes our neutron scattering experiments made in the past three
years and the understanding derived from these results, in regards to the coupling of dynamics
between a protein and its hydration water. We emphasize the fact that the key to this strong
coupling is the existence of a fragile-to-strong dynamic crossover (FSC) phenomenon occurring
at around TL= 225 ± 5 K in the hydration water. On lowering of the temperature toward FSC, the
structure of hydration water makes a transition from predominantly the high density form (HDL),
a more fluid state, to predominantly the low density form (LDL), a less fluid state, derived from
the existence of a liquid-liquid critical point at an elevated pressure. We show experimentally that
this sudden switch in the dynamical behavior of hydration water on Lysozyme, B-DNA and RNA
triggers the so-called glass transition in these biopolymers. In the glassy state, the biopolymers
lose their vital conformational flexibility resulting in a sharp decrease in their biological
activities.
Pages:
Volume:
Year: 2009
Reference: S.-H.Chen, X.-Q. Chu, M. Lagi, C. Kim, Y. Zhang, A. Faraone, J. B. Leao, E. Fratini,
P. Baglioni, and F. Mallamace, "Dynamical Coupling between a Globular Protein and its
Hydration Water Studied by Neutron Scattering and MD Simulation", WPI-AIMR-2009
Proceedings (2009).
C.10
Neutron
Scattering
Studies
of
Dynamic
Crossover
Phenomena in a Coupled System of Biopolymer and Its
Hydration Water
Authors: Sow-Hsin Chen, Francesco Mallamace, Xiang-qiang Chu, Chansoo Kim, Marco Lagi,
Antonio Faraone, Emiliano Fratini, Piero Baglioni
Journal: Journal of Physics: Conference Series
Abstract: We observed a Fragile-to-Strong Dynamic Crossover (FSC) phenomenon of the
a-relaxation time and self-diffusion constant in hydration water of three biopolymers: lysozyme,
B-DNA and RNA. The mean squared displacement (MSD) of hydrogen atoms is measured by Elastic
Neutron Scattering (ENS) experiments. The a-relaxation time is measured by Quasielastic Neutron
Scattering (QENS) experiments and the self-diffusion constant by Nuclear Magnetic Resonance
(NMR) experiments. We discuss the active role of the FSC of the hydration water in initiating the
dynamic crossover phenomenon (so-called glass transition) in the biopolymer. The latter transition
controls the flexibility of the biopolymer and sets the low temperature limit of its biofunctionality.
Finally, we show an MD simulation of a realistic hydrated powder model of lysozyme and
demonstrate the agreement of the MD simulation with the experimental data on the FSC phenomenon
in the plot of logarithm of the a-relaxation time vs. l/T.
Pages: 012006
Volume: 177
Year: 2009
Reference: S.-H. Chen, F. Mallamace, X.-0. Chu, C. Kim, M. Lagi, A. Faraone, E. Fratini, P.
Baglioni, "Neutron Scattering Studies of Dynamic Crossover Phenomena in a Coupled System of
Biopolymer and Its Hydration Water", JPhys: ConfSeries [JPCS] 177, 012006 (2009).
C.11 The Dynamic Response Function XT(Qt) of Confined
Supercooled Water and its Relation to the Dynamic Crossover
Phenomenon
Authors: Sow-Hsin Chen, Yang Zhang, Marco Lagi, Xiangqiang Chu, Li Liu, Antonio Faraone,
Emiliano Fratini, Piero Baglioni
Journal: Zeitschrift Fur Physikalische Chemie-International Journal of Research in Physical
Chemistry & Chemical Physics
Abstract: We have made a series of Quasi-Elastic Neutron Scattering (QENS) studies of
supercooled water confined in 3-D and 1-D geometries, specifically, interstitial water in aged
cement paste (3-D)and water confined in MCM-41-S and Double Wall Nano Tube DWNT (1-D).
In addition, we also include the cases of hydration water oil protein surface and other biopolymer
surfaces (Pseudo 2-D). By analyzing the QENS spectra using Relaxing Cage Model (RCM), we
are able to extract accurately the self-intermediate scattering function of hydrogen atoms FH(Q, t),
at low-Q as a function of temperature T, showing an a-relaxation process at long time. We can
then construct the Dynamic Response Function XT(Q, t) = -dFH(Q, t)/dT. Z7 (Q,t) as a function of t
at constant Q shows a single peak at the characteristic alpha-relaxation time (t), the amplitude of
which grows as we approach the dynamic crossover temperature TL observed before in each of
these geometries. However, the peak height ofZr(Q,t) decreases after passing the crossover
temperature TL. We make all argument to relate the occurrence of the extremum of the peak
height in %rto the existence of the dynamic crossover temperature in each of these cases.
Pages: 109-131
Volume: 224
Year: 2010
Reference: S.-H.Chen, Y. Zhang, M. Lagi, X.-Q. Chu, L. Liu, A. Faraone, E. Fratini, and P. Baglioni,
"The Dynamic Response Function XT (Q,t) of Confined Supercooled Water and its Relation to the
Dynamic Crossover Phenomenon", Z. Phys. Chem. 224, 109-131(2010).
C.12 Experimental Evidence of Logarithmic Relaxation in
Single-particle Dynamics of Hydrated Protein Molecules
Authors: Xiang-qiang Chu, Marco Lagi, Eugene Mamontov, Emiliano Fratini, Piero Baglioni, and
Sow-Hsin Chen
Journal: Soft Matter
Abstract: Quasielastic neutron scattering (QENS) was used to study the intermediate-time
single-particle dynamics of a D20 hydrated globular protein, Lysozyme, in the f-relaxation range.
Measurements are made in the temperature range of 220-320K, suggested by a recent molecular
dynamics (MD) simulation on the same hydrated protein powder [Phy. Rev. Lett. 103,
108102(2009)]. We observe a logarithmic-like decay of the intermediate scattering function (ISF)
of the hydrogen atoms in the protein molecule in the time interval from 10 ps to Ins. We analyze
the ISF, FH(Q, t), in terms of an asymptotic expression proposed by mode coupling theory (MCT).
The result clearly shows that this logarithmic stretching of the p-relaxation range is real,
substantiating the prediction of the MD simulation results that used the formula proposed by
MCT for the analysis of ISF.
Pages:
Volume:
Year: 2010
Reference: X.-Q.Chu, M. Lagi, E. Mamontov, E. Fratini, P. Baglioni, and S.-H. Chen,
"Experimental Evidence of Logarithmic Relaxation in Single-particle Dynamics of Hydrated
Protein Molecules", to appear in Soft Matter., 2010.
C.13 Low Temperature Dynamics of Water Confined in a
Hydrophobic Mesoporous Material CMK-1
Authors: Xiang-qiang Chu, Kao-Hsiang Liu, Madhu Sudan Tyagi, Chung-Yuan Mou, and Sow-Hsin
Chen
Journal:
Abstract: Quasielastic neutron scattering (QENS) was used to study the dynamics of a 3-D confined
water in a hydrophobic mesoporous material CMK-1-14 in the temperature range from 250 K to 170
K. By analyzing the QENS spectra using relaxing cage model (RCM), we are able to extract the
average translational relaxation time and calculate the self-intermediate scattering function of
hydrogen atoms. Previously we observe that water confined in hydrophobic double wall carbon
nanotubes (DWNT) has a slightly lower crossover temperature than that confined in hydrophilic
MCM-41-S (a silica porous material). By comparing the result of this experiment with previous ones,
we find an interesting phenomenon that the crossover temperature of water confined in CMK-1
occurs in-between the above two. This provides the first evidence that besides the obvious surface
effect brought about by the hydrophobic confinements, the value of the crossover temperature is also
dependent on the dimensionality of the geometry of the confinement.
Pages:
Volume:
Year: 2010
Reference: X.-Q. Chu, K.-H. Liu, M. S. Tyagi, C.-Y. Mou, and S.-H. Chen, "Low Temperature
Dynamics of Water Confined in a Hydrophobic Mesoporous Material CMK- 1", submitted to J.
Phys. Cond.Matt., 2010.
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