| 14 |
|
replaced with dipolar entities, and charge neutral distributions were |
| 15 |
|
reduced to Lennard-Jones interaction sites. This simplification cuts |
| 16 |
|
the length scale of long range interactions from $\frac{1}{r}$ to |
| 17 |
< |
$\frac{1}{r^3}$ (Eq.~\ref{eq:dipole} vs.~ Eq.~\ref{eq:coloumb}). |
| 17 |
> |
$\frac{1}{r^3}$ (Eq.~\ref{eq:dipole} vs.~ Eq.~\ref{eq:coloumb}), |
| 18 |
> |
allowing us to avoid the computationally expensive Ewald-Sum. Instead, |
| 19 |
> |
we can use neighbor-lists and cutoff radii for the dipolar |
| 20 |
> |
interactions. |
| 21 |
|
|
| 22 |
|
\begin{align} |
| 23 |
|
V^{\text{dipole}}_{ij}(\mathbf{r}_{ij},\boldsymbol{\Omega}_{i}, |
| 32 |
|
{4\pi\epsilon_{0} r_{ij}} \label{eq:coloumb} |
| 33 |
|
\end{align} |
| 34 |
|
|
| 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 |
| 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 |
| 43 |
+ |
Fig.~\ref{fig:lipidModel}. |
| 44 |
|
|
| 45 |
< |
The main energy function in OOPSE is DUFF (the Dipolar |
| 46 |
< |
Unified-atom Force Field). DUFF is a collection of parameters taken |
| 47 |
< |
from Seipmann \emph{et al.}\cite{Siepmann1998} and Ichiye \emph{et |
| 45 |
> |
\begin{figure} |
| 46 |
> |
\includegraphics[angle=-90,width=\linewidth]{lipidModel.epsi} |
| 47 |
> |
\caption{A representation of the lipid model. $\phi$ is the torsion angle, $\theta$ % |
| 48 |
> |
is the bend angle, $\mu$ is the dipole moment of the head group, and n is the chain length.} |
| 49 |
> |
\label{fig:lipidModel} |
| 50 |
> |
\end{figure} |
| 51 |
> |
|
| 52 |
> |
Turning to the tail chains of the phospholipids, we needed a set of |
| 53 |
> |
scalable parameters to model the alkyl groups as Lennard-Jones |
| 54 |
> |
interaction sites. For this, we used the TraPPE force field of |
| 55 |
> |
Siepmann \emph{et al}.\cite{Siepmann1998} The force field is a |
| 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 |
| 61 |
> |
|
| 62 |
> |
Another advantage of using TraPPE is the constraining of all bonds to |
| 63 |
> |
be of fixed length. Typically, bond vibrations are the motions in a |
| 64 |
> |
molecular dynamic simulation. This neccesitates a small time step |
| 65 |
> |
between force evaluations be used to ensure adequate sampling of the |
| 66 |
> |
bond potential. Failure to do so will result in loss of energy |
| 67 |
> |
conservation within the microcanonical ensemble. By constraining this |
| 68 |
> |
degree of freedom, time steps larger than were previously allowable |
| 69 |
> |
are able to be used when integrating the equations of motion. |
| 70 |
> |
|
| 71 |
> |
The main energy function in OOPSE is DUFF (the Dipolar Unified-atom |
| 72 |
> |
Force Field). DUFF is a collection of parameters taken from Seipmann |
| 73 |
> |
and Ichiye \emph{et |
| 74 |
|
al.}\cite{liu96:new_model} The total energy of interaction is given by |
| 75 |
|
Eq.~\ref{eq:totalPotential}: |
| 76 |
|
\begin{equation} |
