| 121 |
|
protein like hen egg white lysozyme (PDB code: 1LYZ) yields an |
| 122 |
|
effective protein concentration of 100 mg/mL.\cite{Asthagiri20053300} |
| 123 |
|
|
| 124 |
< |
Typically {\it total} protein concentrations in the cell are on the |
| 124 |
> |
{\it Yotal} protein concentrations in the cell are typically on the |
| 125 |
|
order of 160-310 mg/ml,\cite{Brown1991195} and individual proteins |
| 126 |
|
have concentrations orders of magnitude lower than this in the |
| 127 |
|
cellular environment. The effective concentrations of single proteins |
| 387 |
|
\item The convex hull is computed and facets are identified. |
| 388 |
|
\item For each facet: |
| 389 |
|
\begin{itemize} |
| 390 |
< |
\item[a.] The force from the pressure bath ($-PA_f\hat{n}_f$) is |
| 390 |
> |
\item[a.] The force from the pressure bath ($-\hat{n}_fPA_f$) is |
| 391 |
|
computed. |
| 392 |
|
\item[b.] The resistance tensor ($\Xi_f(t)$) is computed using the |
| 393 |
|
viscosity ($\eta$) of the bath. |
| 498 |
|
is 180.32 GPa, while previous calculations on the QSC potential in |
| 499 |
|
periodic-boundary simulations of the bulk crystal have yielded values |
| 500 |
|
of 175.53 GPa.\cite{QSC} Using the same force field, we have performed |
| 501 |
< |
a series of relatively short (200 ps) simulations on 40 \AA~ radius |
| 501 |
> |
a series of 1 ns simulations on 40 \AA~ radius |
| 502 |
|
nanoparticles under the Langevin Hull at a variety of applied |
| 503 |
|
pressures ranging from 0 -- 10 GPa. We obtain a value of 177.55 GPa |
| 504 |
|
for the bulk modulus of gold using this technique, in close agreement |
| 602 |
|
\subsection{Molecular orientation distribution at cluster boundary} |
| 603 |
|
|
| 604 |
|
In order for a non-periodic boundary method to be widely applicable, |
| 605 |
< |
they must be constructed in such a way that they allow a finite system |
| 605 |
> |
it must be constructed in such a way that they allow a finite system |
| 606 |
|
to replicate the properties of the bulk. Early non-periodic simulation |
| 607 |
|
methods (e.g. hydrophobic boundary potentials) induced spurious |
| 608 |
|
orientational correlations deep within the simulated |
| 624 |
|
likely that there will be an effective hydrophobicity of the hull. |
| 625 |
|
|
| 626 |
|
To determine the extent of these effects, we examined the |
| 627 |
< |
orientationations exhibited by SPC/E water in a cluster of 1372 |
| 627 |
> |
orientations exhibited by SPC/E water in a cluster of 1372 |
| 628 |
|
molecules at 300 K and at pressures ranging from 1 -- 1000 atm. The |
| 629 |
< |
orientational angle of a water molecule is described |
| 629 |
> |
orientational angle of a water molecule is described by |
| 630 |
|
\begin{equation} |
| 631 |
|
\cos{\theta}=\frac{\vec{r}_i\cdot\vec{\mu}_i}{|\vec{r}_i||\vec{\mu}_i|} |
| 632 |
|
\end{equation} |
| 685 |
|
|
| 686 |
|
To further test the method, we simulated gold nanopartices ($r = 18$ |
| 687 |
|
\AA) solvated by explicit SPC/E water clusters using the Langevin |
| 688 |
< |
hull. This was done at pressures of 1, 2, 5, 10, 20, 50 and 100 atm |
| 688 |
> |
hull. This was done at pressures of 1, 2, 5, 10, 20, 50, 100 and 200 atm |
| 689 |
|
in order to observe the effects of pressure on the ordering of water |
| 690 |
|
ordering at the surface. In Fig. \ref{fig:RhoR} we show the density |
| 691 |
|
of water adjacent to the surface as a function of pressure, as well as |
| 715 |
|
The Langevin Hull samples the isobaric-isothermal ensemble for |
| 716 |
|
non-periodic systems by coupling the system to a bath characterized by |
| 717 |
|
pressure, temperature, and solvent viscosity. This enables the |
| 718 |
< |
simulation of heterogeneous systems composed of materials of |
| 718 |
> |
simulation of heterogeneous systems composed of materials with |
| 719 |
|
significantly different compressibilities. Because the boundary is |
| 720 |
|
dynamically determined during the simulation and the molecules |
| 721 |
< |
interacting with the boundary can change, the method and has minimal |
| 721 |
> |
interacting with the boundary can change, the method inflicts minimal |
| 722 |
|
perturbations on the behavior of molecules at the edges of the |
| 723 |
|
simulation. Further work on this method will involve implicit |
| 724 |
|
electrostatics at the boundary (which is missing in the current |
| 773 |
|
The individual hull operations scale with |
| 774 |
|
$\mathcal{O}(\frac{n}{p}\log\frac{n}{p})$ where $n$ is the total |
| 775 |
|
number of sites, and $p$ is the number of processors. These local |
| 776 |
< |
hull operations create a set of $p$ hulls each with approximately |
| 777 |
< |
$\frac{n}{3pr}$ sites (for a cluster of radius $r$). The worst-case |
| 776 |
> |
hull operations create a set of $p$ hulls, each with approximately |
| 777 |
> |
$\frac{n}{3pr}$ sites for a cluster of radius $r$. The worst-case |
| 778 |
|
communication cost for using a ``gather'' operation to distribute this |
| 779 |
|
information to all processors is $\mathcal{O}( \alpha (p-1) + \frac{n |
| 780 |
|
\beta (p-1)}{3 r p^2})$, while the final computation of the system |
| 782 |
|
|
| 783 |
|
For a large number of atoms on a moderately parallel machine, the |
| 784 |
|
total costs are dominated by the computations of the individual hulls, |
| 785 |
< |
and communication of these hulls to so the Langevin hull sees roughly |
| 785 |
> |
and communication of these hulls to create the Langevin hull sees roughly |
| 786 |
|
linear speed-up with increasing processor counts. |
| 787 |
|
|
| 788 |
|
\section*{Acknowledgments} |
