Protein Hydration Dynamics

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Mans Race Against Time Saga of Discovering
Fast Dynamics in Chemical and Biological Systems
Biman Bagchi Indian Institute of Science
Bangalore - 560012
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Mans Obsession with Time from Pre-historic days
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Fast Photography
Intermediate steps in the free fall of a cat
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Eadweard Muybridge(1830-1904) Experiment
Galloping of a horse --- Is any Of the four legs
is off the ground at any one of the 16 Steps?
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Evolution of Accessible Time Scales
Eigen,Norris Porter
Herscbach, Lee
Zewail, Fleming
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Typical Laser experimental Set up
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Dynamics of Chemical and Biological Systems of
Interest

• Many chemical and biological processes have been
  found to occur with great rapidity --- hitherto
  un-suspected.
• Examples are reactions like isomerization
  dynamics, electron and proton transfer reactions,
  solvation dynamics and vibrational energy
  relaxation.

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Consequences of Ultra fast Spectroscopy

• Many old theories tumbled leading to the
  development of newer theories.
• Many hitherto un-explained phenomena could now be
  explained

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Ultra fast Isomerization Dynamics
--- an essential natural process
Stilbene, DPB, DODCI, Nile Red, Malachite Green,
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Breakdown of Kramers Theory

• Kramers theory (1940) predicted that at high
  viscosity, rate should be inversely proportional
  to viscosity ?.
• Observed rates show much weaker viscosity
  dependence at large viscosity completely at
  variance with Kramers theory.
• Generalized theory shows that residence time
  at the barrier top is crucial to understand
  solvent effects.

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Vibrational Relaxation in Liquids and Gases
Critical density fluctuations and
vibration-rotation coupling
Raman Linewidth
Temperature
SR and BB, PRL (2003)
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Optical Kerr Effect experiments have uncovered an
interesting power law behaviour still to be
fully understood.
Time dependence of orientational dynamics of the
liquid crystal, 5-OCB at 347 K on log plot
Power law
Gottke, Bagchi, Fayer JCP1 (2002), JCP2 (2002)
The time span is from 1 ps to 400 ns. Short time
shows a Power Law behavior and long time shows an
Exponential behavior
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Correlated Orientational and Translational Hopping
Translational motion ?
Orientational motion ?
Orientational Correlation function at different
time intervals ?
SB and BB, PRL (2002)
P 10.0
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Protein and Micellar Hydration Dynamics

• Dynamic Exchange Model of Slow Relaxation (1996)
• Experimental Results from Fleming, Bhattacharyya
  and Zewail Groups (2002)
• Computer Simulations on Aqueous Micelles

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Experimental Study Photon Echo Spectroscopy
Peak shift data of eosin in water (solid
circles), and lysozyme complex in water (open
triangles). Inset shows Lysozome data with fit
?
G.R. Fleming JPCB (1999)
Schematic representations of the dielectric
models used to simulate the peak shift data
?
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Potential Energy Surfaces involved in Solvation
Dynamics
Water orientational motions along the solvation
coordinate together with instantaneous
polarization P
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Sub-picosecond
15-20 fs
1 ps
Due to Librational and H-bond excitation
Roy and Bagchi (JCP, PRL)
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Hydration Layer around a Protein
Surface

• Bound water
• Quasifree water
• 3) Free Water

Change in poential experienced by the different
types of water molecules
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Theoretical Formulation of DEM
Dynamics of free water molecules
Dynamics of bound water molecules
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X-ray structure of protein Subtilisin
Carlsberg(SC). The intrinsic probe tryptophan is
shown.
X-ray structure of protein Monellin.
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Hydration Correlation Function
SC Dansyl bonded SC Monellin
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Space Filling model of the protein Monelling
Native
Two denatured states
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Hydration Correlation Function
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WATER DYNAMICS AT THE SURFACE OF
AQUEOUS MICELLES
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Distance between headgroup in the core of the
micelle along the vertical direction is around
24Å.
Snapshot of the micelle evolved after 3 ns from
the initial configuration at 350K. Red spheres
are denote the oxygens in the carboxylate
headgroup, while white ones carbon atoms along
the perfluoroctonate chain. Yellow sphere are
cesium ion.
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Solvation TCF at the micellar
surface. Note the slow decay at
the long time.
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Single Molecule Spectroscopy

• Although it is becoming a routine practice in
  many laboratories, the ability to analyze
  individual molecules still amazes even the most
  zealous practitioners of this emerging field. As
  is often the case, the introduction of a novel
  technique generates enthusiasm among the
  converted but doubts among the skeptics.
• Shimon Weiss
  Science 1999

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Two things are of great importance one
probed molecule should be under study light
emitted by the single molecule should be
distinguishable from the background noise The
first condition is met with a concentration of
about 10-10 M and a volume of 10 µm3 The
background is minimized by using small probe
volumes as the background is proportional to the
probe volume.
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• As a highly fluorescent molecule transits
  across a small probe volume on which a laser
  beam, tuned to an optical transition of the
  molecule, is focused, it is continuously cycled
  between the ground and an excited electronic
  state emitting a photon on most cycles.

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Fluorescence Spectrum From Single Molecule
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Hydrogen Bond Definition
PHGC-WO dist lt 4.35Å WO-WO dist lt
3.50Å PHGO-WO dist lt 3.50Å WO-WH
dist lt 2.45Å PHG-Water Eng lt -6.25Kcal/mole
O-O-H Angle lt 30
Population Variable
h(t) 1, if a pair of atoms are bonded at time
t 0, otherwise H(t) 1, if a pair of
atoms are continuously bonded
between time 0 and t 0, otherwise
TCFs
and
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Schematic Representation of Interfacial Waters
(a) IBW1
(b) IBW2
Numerical Values of the geometrical parameters
are obtained from the MD run
PHGO denotes the Oxygen of the polar Head group
of the Surfactant, and PHGC is the Carbon atom
in the head group.
WO and WH are the Oxygen and Hydrogen atoms of
the Water
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Oxygen-Oxygen Radial Distribution Function of
Different Interfacial Water
molecules
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Hydrogen-Bond length Distribution
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Hydrogen Bond Angle Distribution
(O---H-O Angle)
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Monomer Energy Distribution (Single Particle
Energy)
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Potential Energy Distribution for Pairs of
molecules of the type, IFW-Water, IBW1-Water,
IBW2-Water
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Potential Energy Distribution for Pairs of
molecules of the type, IFW-PHG, IBW1-PHG,
IBW2-PHG
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Partial Solvation Time Coorelation
Function
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Temperature Dependence of Solvation TCF
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Orientational correlation function of water
molecules at the micellar surface,At
varying distances.
Top to bottom, within 4.5Å, 6Å, 10Å and far 28Å
respectively
Slow orientational Correlation function Of water
molecules At the surface (within 10 Å ).
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Temperature Dependence of Dipolar TCF
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Dipolar TCF for different Interfacial water
molecules
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Water-PHG Hydrogen bond TCF
tavg6.8ps
tavg43.7ps
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Water-Water Hydrogen-bond TCF
For SLWW(t) tavg 0.56ps
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Trajectory of Four Water Molecules
Dwph-G Shortest distance of each of the water
molecules to the micellar surface
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Species Hydrogen bond Life-time Correlation
Function
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Species Life-time Correlation Function
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Moment-moment TCF for all Waters in the
Micellar Solution
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Moment-moment TCF for all waters in the
1ETN Protein Solution (System
Under Study)
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Acknowledgement
Dr. S. Balasubramanian
Mr. Subrata Pal
Dr. N. Nandi
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Misfolding Related Diseases
Misfolding and Association
Formation of Fibrils
Less change in radius of Gyration Non-globular
protein
Neurotic Plaque and Neurofibrillary tangles
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Main Unsolved Problems
How does the association take place ?
Is it due to nucleation or aggregation like a
sol-gel transition ?
Experiments suggest that in the refolded states,
both monomer-dimer and aggregates are in
equilibrium
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The AlzheimerS Disease Amyloid A4 Peptide
(Residues 1-40) 20 NMR structures
Eur J Biochem 233 pp. 293 (1995)
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Alzheimer disease amyloid- ? peptide
(1-28)
NMR, Minimized Average Structure
Biochemistry 33 pp. 7788 (1994)
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Amyloid ? peptide (25-35), NMR 20
structures
11 residue , 73 atoms
Biochemistry 35 pp. 16094 (1996)
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Structure of Amyloid Protein (25-35)
Comparison between model and real structure .
RMSD 1.2 A
--- application of the MSB scheme
AM and BB, JCP2 (2003)
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Alzheimer disease and ?-amyloid
Before Alzheimer
After Alzheimer
Cerebral Cortex
Basal forebrain
Hippocampus essential for memory storage
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Conclusions
Minimalistic model with the help of Hydropathy
scale and helix propensity can show many aspects
of the STRUCTURAL and DYNAMICAL aspects of
protein folding
Correlation between hydrophobic topological
contact and relative contact order points out to
the nature of folding
Contact pair correlation function probes the
multistage dynamics from microscopic detail
Self-aggregation and association formation could
be addressed from theoretical model of
nucleation or diffusion controlled reaction
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Use of Helix propensity scale to Helix
Potential
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• Simulations in Self-organized Assemblies
• Translational Diffusion similar to bulk Water
• Reorientation and Solvation Dynamics
• One component 100 times slower than bulk
  water
• Bagchi-Bala, Chandra, Berkowitz, Experiment
  

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Predictions of the Dynamic Exchange Model
Wuthrich and Halle (1991) Nandi And Bagchi
(1996)

• The orientational relaxation at protein/micelle
  surface is
• non-exponential, with the short time component
  equal to that
• For free water while the long time component is
  equal to the
• inverse of the rate of bound ?free transition.

2. Solvation time correlation function is also
non-exponential, With the short time component
identical to bulk water but the long time
component is again determined by the rate of
bound ? free transition.
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Orientations of the free and bound water
Fluctuating densities of the free and bound water
Rotational diffusion const. for free and bound
water
Orientation of molecule does not change during
the bound ?free reaction
In absence of protein surface and in long time
limit (small z)
Wave-number and frequency dependent friction
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• Simulations in Self-organized Assemblies
• and at Protein Surfaces (Hydration dynamics)
• Translational Diffusion similar to bulk Water
• Reorientation and Solvation Dynamics
• One component 100 times slower than bulk
  water
• Bagchi-Bala, Chandra, Berkowitz, Experiment
  

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Hydration Correlation Function of NATA
N-acetyltryptophanamide (NATA) included in a
micelle
Hydration correlation function
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