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\section{The DUFF Energy Function} |
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\label{sec:energyFunctionals} |
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\section{\label{sec:DUFF}The DUFF Force Field} |
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The DUFF (\underline{D}ipolar \underline{U}nified-atom |
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\underline{F}orce \underline{F}ield) force field was developed to |
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simulate lipid bilayer formation and equilibrium dynamics. We needed a |
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model capable of forming bilaers, while still being sufficiently |
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computationally efficient allowing simulations of large systems |
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(\~100's of phospholipids, \~1000's of waters) for long times (\~10's |
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of nanoseconds). |
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With this goal in mind, we decided to eliminate all charged |
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interactions within the force field. Charge distributions were |
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replaced with dipolar entities, and charge neutral distributions were |
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reduced to Lennard-Jones interaction sites. This simplification cuts |
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the length scale of long range interactions from $\frac{1}{r}$ to |
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$\frac{1}{r^3}$ (Eq.~\ref{eq:dipole} vs.~ Eq.~\ref{eq:coloumb}). |
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\begin{align} |
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V^{\text{dipole}}_{ij}(\mathbf{r}_{ij},\boldsymbol{\Omega}_{i}, |
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\boldsymbol{\Omega}_{j}) &= |
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\frac{1}{4\pi\epsilon_{0}} \biggl[ |
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\frac{\boldsymbol{\mu}_{i} \cdot \boldsymbol{\mu}_{j}}{r^{3}_{ij}} |
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- |
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\frac{3(\boldsymbol{\mu}_i \cdot \mathbf{r}_{ij}) % |
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(\boldsymbol{\mu}_j \cdot \mathbf{r}_{ij}) } |
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{r^{5}_{ij}} \biggr]\label{eq:dipole} \\ |
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V^{\text{ch}}_{ij}(\mathbf{r}_{ij}) &= \frac{q_{i}q_{j}}% |
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{4\pi\epsilon_{0} r_{ij}} \label{eq:coloumb} |
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\end{align} |
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The main energy function in OOPSE is DUFF (the Dipolar |
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Unified-atom Force Field). DUFF is a collection of parameters taken |
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from Seipmann \emph{et al.}\cite{Siepmann1998} and Ichiye \emph{et |
