| 1 |
|
|
| 2 |
+ |
\section{\label{sec:DUFF}The DUFF Force Field} |
| 3 |
|
|
| 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 |
| 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). |
| 11 |
|
|
| 12 |
< |
\section{The DUFF Energy Functionals} |
| 13 |
< |
\label{sec:energyFunctionals} |
| 12 |
> |
With this goal in mind, we decided to eliminate all charged |
| 13 |
> |
interactions within the force field. Charge distributions were |
| 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}). |
| 18 |
|
|
| 19 |
< |
The main energy functional set in OOPSE is DUFF (the Dipolar |
| 19 |
> |
\begin{align} |
| 20 |
> |
V^{\text{dipole}}_{ij}(\mathbf{r}_{ij},\boldsymbol{\Omega}_{i}, |
| 21 |
> |
\boldsymbol{\Omega}_{j}) &= |
| 22 |
> |
\frac{1}{4\pi\epsilon_{0}} \biggl[ |
| 23 |
> |
\frac{\boldsymbol{\mu}_{i} \cdot \boldsymbol{\mu}_{j}}{r^{3}_{ij}} |
| 24 |
> |
- |
| 25 |
> |
\frac{3(\boldsymbol{\mu}_i \cdot \mathbf{r}_{ij}) % |
| 26 |
> |
(\boldsymbol{\mu}_j \cdot \mathbf{r}_{ij}) } |
| 27 |
> |
{r^{5}_{ij}} \biggr]\label{eq:dipole} \\ |
| 28 |
> |
V^{\text{ch}}_{ij}(\mathbf{r}_{ij}) &= \frac{q_{i}q_{j}}% |
| 29 |
> |
{4\pi\epsilon_{0} r_{ij}} \label{eq:coloumb} |
| 30 |
> |
\end{align} |
| 31 |
> |
|
| 32 |
> |
|
| 33 |
> |
The main energy function in OOPSE is DUFF (the Dipolar |
| 34 |
|
Unified-atom Force Field). DUFF is a collection of parameters taken |
| 35 |
|
from Seipmann \emph{et al.}\cite{Siepmann1998} and Ichiye \emph{et |
| 36 |
|
al.}\cite{liu96:new_model} The total energy of interaction is given by |
| 59 |
|
|
| 60 |
|
The torsion functional has the form: |
| 61 |
|
\begin{equation} |
| 62 |
< |
V_{\phi} = \sum ( k_1 \cos^3 \phi + k_2 \cos^2 \phi + k_3 \cos \phi + k_4) |
| 62 |
> |
V_{\phi} = \sum ( k_3 \cos^3 \phi + k_2 \cos^2 \phi + k_1 \cos \phi + k_0) |
| 63 |
|
\label{eq:torsionPot} |
| 64 |
|
\end{equation} |
| 65 |
|
Here, the authors decided to use a potential in terms of a power |
