Moscow State Institute for Steel and Alloys

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Moscow State Institute for Steel and
Alloys Department of Theoretical Physics
Analytical derivation of thermodynamic
characteristics of lipid bilayer
Sergei Mukhin Svetlana Baoukina
Benasque, Spain, 2005
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Lateral pressure in lipid bilayer
amphiphilic nature elongated structure
spatial separation of different
interactions inhomogeneous pressure
profile hydrocarbon chains rotational
isomers N segments flexibility
large conformational entropy in a bilayer
collisions between chains excluded volume
effect entropic repulsion
J.Israelachvili 1985 A.Ben-Shaul 1995
lateral pressure distribution in the hydrophobic
core
total tension in a bilayer is zero
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Lipid bilayer
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Applications
Lateral pressure profile in a lipid membrane

• is difficult to measure experimentally due to
  complex intermolecular interactions and nanometer
  scale of membrane thickness
• effects the functioning of membrane proteins
  (when cross-section area varies with depth under
  protein conformational transition) R.S. Cantor,
  Chem. Phys. Lipids. 101, 45 (1999)

activation energy of protein channel, Eact
- change of the channel cross-section
area at position z under channel activation, E0
other contributions to the activation energy.
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Fluctuating chain in external potential overview
Free energy of fluctuating chain in the external
potential Mapping of the chains statistics on
the quantum particle motion in the imaginary
time Why mapping of a semi-flexible chain is
more involved then of a flexible one
flexible chain
semi-flexible chain
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Mapping on the quantum particle motion in
imaginary time
Partition function as a path integral over chain
conformations
Flexible chain case Burkhardt 1989,
ValladeLajzerowicz 1981
where Greens function obeys
Breidenich, Netz, Lipowsky 2000
Semi-flexible chain case Freed 1971,
GompperBurkhardt 1989, Leibler et al. 1989
where
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Semi-flexible chain in harmonic potential
Alternative approach S. Mukhin, 2004 S. Mukhin,
S. Baoukina, 2005
0
z
R(z)
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Derivation of lateral pressure distribution
A average area per chain
Lateral pressure profile can be found from the
system of equations
general expression
variable density case
constant density case
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Approximate solution (constant density case)
where
are eigen-functions
Anzats

where
and functions
are looked for in the form


unperturbed eigen-functions obey relations
unperturbed eigen values

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Approximate solution
lateral pressure profile
mean-squared deviation
Parameters
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S.Mukhin 2004