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} |