| 4 |
|
The DUFF (\underline{D}ipolar \underline{U}nified-atom |
| 5 |
|
\underline{F}orce \underline{F}ield) force field was developed to |
| 6 |
|
simulate lipid bilayer formation and equilibrium dynamics. We needed a |
| 7 |
< |
model capable of forming bilaers, while still being sufficiently |
| 7 |
> |
model capable of forming bilayers, while still being sufficiently |
| 8 |
|
computationally efficient allowing simulations of large systems |
| 9 |
|
(\~100's of phospholipids, \~1000's of waters) for long times (\~10's |
| 10 |
|
of nanoseconds). |
| 35 |
|
Applying this standard to the lipid model, we decided to represent the |
| 36 |
|
lipid model as a point dipole interaction site. Lipid head groups are |
| 37 |
|
typically zwitterionic in nature, with sometimes full integer charges |
| 38 |
< |
seperated by only 5 to 6~$\mbox{\AA}$. By placing a dipole of |
| 38 |
> |
separated by only 5 to 6~$\mbox{\AA}$. By placing a dipole of |
| 39 |
|
20.6~Debye at the head groups center of mass, our model mimics the |
| 40 |
< |
dipole of DMPC.\cite{Cevc87} Then, to account for the steric henderanc |
| 41 |
< |
of the head group, a Lennard-Jones interaction site is also oacted at |
| 42 |
< |
the psuedoatom's center of mass. The model is illustrated in |
| 40 |
> |
dipole of DMPC.\cite{Cevc87} Then, to account for the steric hindrance |
| 41 |
> |
of the head group, a Lennard-Jones interaction site is also located at |
| 42 |
> |
the pseudoatom's center of mass. The model is illustrated in |
| 43 |
|
Fig.~\ref{fig:lipidModel}. |
| 44 |
|
|
| 45 |
|
\begin{figure} |
| 56 |
|
unified-atom representation of n-alkanes. It is parametrized against |
| 57 |
|
phase equilibria using Gibbs Monte Carlo simulation techniques. One of |
| 58 |
|
the advantages of TraPPE is that is generalizes the types of atoms in |
| 59 |
< |
an alkyl chain to keep the number of pseudoatoms to a minimum. |
| 60 |
< |
%( $ \mbox{CH_3} $ %-$\mathbf{\mbox{CH_2}}$-$\mbox{CH_3}$ is the same as |
| 59 |
> |
an alkyl chain to keep the number of pseudoatoms to a minimum; the |
| 60 |
> |
$\mbox{CH}_2$ in propane is the same as the central and offset |
| 61 |
> |
$\mbox{CH}_2$'s in pentane, meaning the pseudoatom type does not |
| 62 |
> |
change according to the atom's environment. |
| 63 |
|
|
| 64 |
|
Another advantage of using TraPPE is the constraining of all bonds to |
| 65 |
|
be of fixed length. Typically, bond vibrations are the motions in a |
| 66 |
< |
molecular dynamic simulation. This neccesitates a small time step |
| 66 |
> |
molecular dynamic simulation. This necessitates a small time step |
| 67 |
|
between force evaluations be used to ensure adequate sampling of the |
| 68 |
|
bond potential. Failure to do so will result in loss of energy |
| 69 |
|
conservation within the microcanonical ensemble. By constraining this |
| 70 |
|
degree of freedom, time steps larger than were previously allowable |
| 71 |
|
are able to be used when integrating the equations of motion. |
| 72 |
|
|
| 73 |
+ |
After developing the model for the phospholipids, we needed a model |
| 74 |
+ |
for water that would complement our lipid. For this we turned to the |
| 75 |
+ |
soft sticky dipole (SSD) model of Ichiye \emph{et |
| 76 |
+ |
al.}\cite{liu96:new_model} This model is discussed in greater detail |
| 77 |
+ |
in Sec.~\ref{sec:SSD}. The basic idea of the model is to reduce water |
| 78 |
+ |
to a single Lennard-Jones interaction site. The site also contains a |
| 79 |
+ |
dipole to mimic the partial charges on the hydrogens and the |
| 80 |
+ |
oxygen. However, what makes the SSD model unique is the inclusion of a |
| 81 |
+ |
tetrahedral short range potential to recover the hydrogen bonding of |
| 82 |
+ |
water, an important factor when modeling bilayers, as it has been |
| 83 |
+ |
shown that hydrogen bond network formation is a leading contribution |
| 84 |
+ |
to the entropic driving force towards lipid bilayer |
| 85 |
+ |
formation.\cite{Cevc87} |
| 86 |
+ |
|
| 87 |
+ |
BREAK |
| 88 |
+ |
|
| 89 |
+ |
END OF CURRENT REVISIONS |
| 90 |
+ |
|
| 91 |
+ |
BREAK |
| 92 |
+ |
|
| 93 |
+ |
|
| 94 |
+ |
|
| 95 |
+ |
|
| 96 |
+ |
|
| 97 |
|
The main energy function in OOPSE is DUFF (the Dipolar Unified-atom |
| 98 |
|
Force Field). DUFF is a collection of parameters taken from Seipmann |
| 99 |
< |
and Ichiye \emph{et |
| 74 |
< |
al.}\cite{liu96:new_model} The total energy of interaction is given by |
| 99 |
> |
and The total energy of interaction is given by |
| 100 |
|
Eq.~\ref{eq:totalPotential}: |
| 101 |
|
\begin{equation} |
| 102 |
|
V_{\text{Total}} = |
| 127 |
|
\end{equation} |
| 128 |
|
Here, the authors decided to use a potential in terms of a power |
| 129 |
|
expansion in $\cos \phi$ rather than the typical expansion in |
| 130 |
< |
$\phi$. This prevents the need for repeated trigonemtric |
| 130 |
> |
$\phi$. This prevents the need for repeated trigonometric |
| 131 |
|
evaluations. Again, all $k_n$ constants were based on those in TraPPE. |
| 132 |
|
|
| 133 |
|
\subsection{Non-Bonded Interactions} |
