Protein Hydration Dynamics

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Dynamics in Complex Chemical Systems
Biman Bagchi Indian Institute of Science
Bangalore - 560012
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Complex Chemical Systems of Interest
1. Vibrational Relaxation Near the Gas-Liquid
Critical Point.
2. Kerr (Orientational) Relaxation Near the
Isotropic-Nematic Phase transition in Liquid
Crystalline Materials
3. Transport in Supercooled Liquids.
4. Micellar and Protein Hydration Dynamics
5. Folding of Globular and Non-globular proteins
Correlation Between Energy Landscape, Topology
and Kinetics

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Experimental Observation
The Linewidth of fundamental (0,1) (isotropic)
Raman band of N2 along, the solid-gas
coexistence line, the liquid-gas coexistence
line, and In the isochoric state for critical
(circles) and supercritical sample (squares).
M. Musso et al. JCP 116, 8015 (2002)
PRL 85, 3850 (2003)
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What is dephasing ?
If the state of a single two-level atom is

???(t) or ???(t) are the population densities of
states ? and ?.
The density matrix, rij(t), is defined as
When laser beams with different k-vectors excite
the atom, rij(t) tends to have a spatially
sinusoidal variation.
A grating is said to exist if ?aa(t) or ?bb(t) is
spatially sinusoidal, A coherence is said to
exist if rab(t) or rba(t) is spatially sinusoidal.
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The main questions attempted to answer

• According to Mukamel, Ronis et al., the
  divergence of linewidth reflect the growing
  critical fluctuations near the gas-liquid
  critical point (CP).
• However, the decay of frequency modulation time
  correlation function is rather fast 100 fs
  (0.1 ps)
• Understanding the role of vibration-rotation
  coupling to the dephasing rate near CP

Mukamel et al. PRL 50, 590 (1983)
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Theoretical Analysis Kubo-Oxtoby Formalism
The isotropic Raman Spectrum is given by
Polarizability along Q coordinate
The Raman Line shape can be written as,
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The fluctuation in energy between the ground
state and the nth quantum level is given by
Resonance Term
Density Term
The Vibration-Rotation (VR) contribution to the
broadening of the line shape is given by
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Simulation Results
Tc
?-shaped Raman linewidth of Nitrogen
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Simulation Results
Tc
The RMS Frequency fluctuation (?) vs.
temperature (T) along the critical isochore for
N2. We fitted all simulation points with Gaussian.
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Dynamical heterogeneities near the critical point
(T 125.3K).
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Mode Coupling Theory analysis (MCT)
? The density (?) dependent frequency
modulation time correlation function
? Near Critical Point (CP), k ?0

The MCT gives the cross-correlation between VR
coupling and density term in terms of triplet
direct correlation
?
The large enhancement of vibration-rotation
coupling near critical point (CP) arises from the
non-Gaussian behavior of density fluctuation and
this enters through a nonzero value of the
triplet direct correlation
Roychowdhury and Bagchi JCP 119, 3278 (2003)
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V is the oscillator-medium interaction potential
and the fluctuation in overtone frequency between
the 0 and n-th level of ith molecule
MCT gives the density dependence frequency
fluctuations time correlation function
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The large enhancement vibration-rotation coupling
near gas-liquid critical point arises from the
non-Gaussian behavior of triple direct
correlation function ( using MCT)
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Summary

• ? The nonmonotonic dependence of RMS frequency
  fluctuation on temperature along critical
  isochore..
• ? A ?-shaped dependence of linewidth near the CP.
• A near divergence of linewidth near the CP.
• Enhanced role of vibration-rotation coupling not
  anticipated in earlier studies.
• Mode coupling theory analysis and growth of
  heterogeneity.

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II. Vibrational dephasing via Concentration
fluctuations of Binary liquid mixtures
? The role of density and concentration
fluctuations in liquid binary mixture on the
linewidth of vibrational spectra.
? Concentration fluctuations are most promising
mechanism for experimentally observing the
effects of attractive intermolecular forces on
vibrational motion.
Lindenberger et al. J. Phys. Chem. A
1999,103,5655-5660
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Experimental Result
Measured effective dephasing time T2(open
squares) and average correlation time ?c (full
points) of the ?1 mode of CH3I vs. mole fraction
x of CH3I in the mixture with CDCl3.
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NPT Simulation Result Binary Liquid mixture
Non-monotonic composition dependence as observed
in experiments
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Model Binary Mixture
The LJ parameters for the A system were taken as
?A/kB 146.46K and ?A 3.85A and, for the B as
?B/kB 400K and ?B 4A. The LJ parameters of
AB intermolecular interaction are taken as ?AB/kB
467K and ?AB 4.6 A
Partial radial distribution functions, gAA(r)
(solvent-solvent), gBB(r) (solute-solvent), and
gAB(r) (solute-solute) at 0.5 solute composition
(?A). r r/?A, where ?A is the molecular
diameter of species A.
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Ultrafast decay
Slow decay
The frequency modulation time correlation
functions C?(t) at different compositions of
the solute (?A). Inset show the same up to 0.4 ps.
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The frequency dependent Raman line shape at four
different compositions in the binary mixture.
Note that the frequency is in reduced unit.
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The probability distribution of the frequency
modulation at the different compositions, (a) ?A
0.20, (b) ?A 0.50, (c) ?A 0.75, and (d) ?A
1.00.
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The mean square frequency modulation (lt??2(0) gt)
of A - B bond at different compositions of solute
(?A).
The values of lt ??2(0) gt?c at different mole
fraction of the solute (?A). We fitted all the
points with the third degree polynomial (cubic
fit).
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The calculated average dephasing time (solid
circle, ?v) and the viscosity (star, ?) for
different mole fractions A. The solid line is the
quadratic fit for v and the dotted line is the
spline fit for ?.
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The values of the product v at different
compositions of solute (?A) in the binary mixture.
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Protein and Micellar Hydration Dynamics

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

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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
27
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