| 11 |
|
small number of water molecules are strongly held around the |
| 12 |
|
different parts of the headgroup and are oriented by them with |
| 13 |
|
residence times for the first hydration shell being around 0.5 - 1 |
| 14 |
< |
ns. In the second solvation shell, some water molecules are weakly |
| 15 |
< |
bound, but are still essential for determining the properties of the |
| 16 |
< |
system. Transport of various molecular species into living cells is |
| 17 |
< |
one of the major functions of membranes. A thorough understanding of |
| 18 |
< |
the underlying molecular mechanism for solute diffusion is crucial |
| 19 |
< |
to the further studies of other related biological processes. All |
| 20 |
< |
transport across cell membranes takes place by one of two |
| 21 |
< |
fundamental processes: Passive transport is driven by bulk or |
| 22 |
< |
inter-diffusion of the molecules being transported or by membrane |
| 23 |
< |
pores which facilitate crossing. Active transport depends upon the |
| 24 |
< |
expenditure of cellular energy in the form of ATP hydrolysis. As the |
| 25 |
< |
central processes of membrane assembly, translocation of |
| 26 |
< |
phospholipids across membrane bilayers requires the hydrophilic head |
| 27 |
< |
of the phospholipid to pass through the highly hydrophobic interior |
| 28 |
< |
of the membrane, and for the hydrophobic tails to be exposed to the |
| 29 |
< |
aqueous environment. A number of studies indicate that the flipping |
| 30 |
< |
of phospholipids occurs rapidly in the eukaryotic ER and the |
| 31 |
< |
bacterial cytoplasmic membrane via a bi-directional, facilitated |
| 32 |
< |
diffusion process requiring no metabolic energy input. Another |
| 33 |
< |
system of interest would be the distribution of sites occupied by |
| 34 |
< |
inhaled anesthetics in membrane. Although the physiological effects |
| 35 |
< |
of anesthetics have been extensively studied, the controversy over |
| 36 |
< |
their effects on lipid bilayers still continues. Recent deuterium |
| 37 |
< |
NMR measurements on halothane in POPC lipid bilayers suggest the |
| 38 |
< |
anesthetics are primarily located at the hydrocarbon chain region. |
| 14 |
> |
ns\cite{Ho1992}. In the second solvation shell, some water molecules |
| 15 |
> |
are weakly bound, but are still essential for determining the |
| 16 |
> |
properties of the system. Transport of various molecular species |
| 17 |
> |
into living cells is one of the major functions of membranes. A |
| 18 |
> |
thorough understanding of the underlying molecular mechanism for |
| 19 |
> |
solute diffusion is crucial to the further studies of other related |
| 20 |
> |
biological processes. All transport across cell membranes takes |
| 21 |
> |
place by one of two fundamental processes: Passive transport is |
| 22 |
> |
driven by bulk or inter-diffusion of the molecules being transported |
| 23 |
> |
or by membrane pores which facilitate crossing. Active transport |
| 24 |
> |
depends upon the expenditure of cellular energy in the form of ATP |
| 25 |
> |
hydrolysis. As the central processes of membrane assembly, |
| 26 |
> |
translocation of phospholipids across membrane bilayers requires the |
| 27 |
> |
hydrophilic head of the phospholipid to pass through the highly |
| 28 |
> |
hydrophobic interior of the membrane, and for the hydrophobic tails |
| 29 |
> |
to be exposed to the aqueous environment\cite{Sasaki2004}. A number |
| 30 |
> |
of studies indicate that the flipping of phospholipids occurs |
| 31 |
> |
rapidly in the eukaryotic ER and the bacterial cytoplasmic membrane |
| 32 |
> |
via a bi-directional, facilitated diffusion process requiring no |
| 33 |
> |
metabolic energy input. Another system of interest would be the |
| 34 |
> |
distribution of sites occupied by inhaled anesthetics in membrane. |
| 35 |
> |
Although the physiological effects of anesthetics have been |
| 36 |
> |
extensively studied, the controversy over their effects on lipid |
| 37 |
> |
bilayers still continues. Recent deuterium NMR measurements on |
| 38 |
> |
halothane in POPC lipid bilayers suggest the anesthetics are |
| 39 |
> |
primarily located at the hydrocarbon chain region\cite{Baber1995}. |
| 40 |
|
Infrared spectroscopy experiments suggest that halothane in DMPC |
| 41 |
< |
lipid bilayers lives near the membrane/water interface. |
| 41 |
> |
lipid bilayers lives near the membrane/water |
| 42 |
> |
interface\cite{Lieb1982}. |
| 43 |
|
|
| 44 |
|
Molecular dynamics simulations have proven to be a powerful tool for |
| 45 |
|
studying the functions of biological systems, providing structural, |
| 46 |
|
thermodynamic and dynamical information. Unfortunately, much of |
| 47 |
|
biological interest happens on time and length scales well beyond |
| 48 |
< |
the range of current simulation technologies. Several schemes are |
| 49 |
< |
proposed in this chapter to overcome these difficulties. |
| 48 |
> |
the range of current simulation technologies. |
| 49 |
> |
%review of coarse-grained modeling |
| 50 |
> |
Several schemes are proposed in this chapter to overcome these |
| 51 |
> |
difficulties. |
| 52 |
|
|
| 53 |
|
\section{\label{lipidSection:model}Model} |
| 54 |
|
|
| 57 |
|
In a typical bilayer simulation, the dominant portion of the |
| 58 |
|
computation time will be spent calculating water-water interactions. |
| 59 |
|
As an efficient solvent model, the Soft Sticky Dipole (SSD) water |
| 60 |
< |
model is used as the explicit solvent in this project. Unlike other |
| 61 |
< |
water models which have partial charges distributed throughout the |
| 62 |
< |
whole molecule, the SSD water model consists of a single site which |
| 63 |
< |
is a Lennard-Jones interaction site, as well as a point dipole. A |
| 64 |
< |
tetrahedral potential is added to correct for hydrogen bonding. The |
| 65 |
< |
following equation describes the interaction between two water |
| 66 |
< |
molecules: |
| 60 |
> |
model\cite{Chandra1999,Fennel2004} is used as the explicit solvent |
| 61 |
> |
in this project. Unlike other water models which have partial |
| 62 |
> |
charges distributed throughout the whole molecule, the SSD water |
| 63 |
> |
model consists of a single site which is a Lennard-Jones interaction |
| 64 |
> |
site, as well as a point dipole. A tetrahedral potential is added to |
| 65 |
> |
correct for hydrogen bonding. The following equation describes the |
| 66 |
> |
interaction between two water molecules: |
| 67 |
|
\[ |
| 68 |
|
V_{SSD} = V_{LJ} (r_{ij} ) + V_{dp} (r_{ij} ,\Omega _i ,\Omega _j ) |
| 69 |
|
+ V_{sticky} (r_{ij} ,\Omega _i ,\Omega _j ) |
| 192 |
|
maintains the fast fall-off of the multipole potentials but lacks |
| 193 |
|
the normal divergences when two polar groups get close to one |
| 194 |
|
another. |
| 195 |
< |
|
| 195 |
> |
%description of the comparsion |
| 196 |
|
\begin{figure} |
| 197 |
|
\centering |
| 198 |
|
\includegraphics[width=\linewidth]{split_dipole.eps} |
| 321 |
|
with a variance estimated from the size of the van der Waals radius, |
| 322 |
|
the EDPs which are proportional to the density profiles measured |
| 323 |
|
along the bilayer normal obtained by x-ray scattering experiment, |
| 324 |
< |
can be expressed by |
| 324 |
> |
can be expressed by\cite{Tu1995} |
| 325 |
|
\begin{equation} |
| 326 |
|
\rho _{x - ray} (z)dz \propto \sum\limits_{i = 1}^N {\frac{{n_i |
| 327 |
|
}}{V}\frac{1}{{\sqrt {2\pi \sigma ^2 } }}e^{ - (z - z_i )^2 /2\sigma |
| 338 |
|
, is defined as the distance between two peaks in the electron |
| 339 |
|
density profile, calculated from our simulations to be 34.1 $\AA$. |
| 340 |
|
This value is close to the x-ray diffraction experimental value 34.4 |
| 341 |
< |
$\AA$. |
| 341 |
> |
$\AA$\cite{Petrache1998}. |
| 342 |
|
|
| 343 |
|
\begin{figure} |
| 344 |
|
\centering |
| 372 |
|
\end{itemize} |
| 373 |
|
In coarse-grained model, although there are no explicit hydrogens, |
| 374 |
|
the order parameter can still be written in terms of carbon ordering |
| 375 |
< |
at each point of the chain |
| 375 |
> |
at each point of the chain\cite{Egberts1988} |
| 376 |
|
\begin{equation} |
| 377 |
|
S_{ij} = \frac{1}{2} < 3\cos \theta _i \cos \theta _j - \delta |
| 378 |
|
_{ij} >. |
| 380 |
|
|
| 381 |
|
Fig.~\ref{lipidFigure:Scd} shows the order parameter profile |
| 382 |
|
calculated for our coarse-grained DMPC bilayer system at 300K. Also |
| 383 |
< |
shown are the experimental data of Tiburu. The fact that |
| 383 |
> |
shown are the experimental data of Tu\cite{Tu1995}. The fact that |
| 384 |
|
$\text{S}_{\text{{\sc cd}}}$ order parameters calculated from |
| 385 |
|
simulation are higher than the experimental ones is ascribed to the |
| 386 |
|
assumption of the locations of implicit hydrogen atoms which are |
