View source for Protein/Membrane system size

This page collects notes on how to decide how to initially setup a membrane protein simulation. ''Please do not follow these notes blindly &mdash; they are more [http://www.imdb.com/title/tt0325980/quotes guidelines] than actual rules.''

Once you've decided on box dimensions and number of lipids you can use any of the [[Membrane protein insertion]] methods to set up the system.

== System size ==
* Decide on the bilayer composition. Have you got [[Lipid FFDB|force field parameters for the lipids]]?
* System size: 
** rule of thumb 1: have at least 2-3 lipid layers between protein and periodic box boundary in the x-y plane to ensure(?) membrane-like behaviour; more may be necessary: you will need to monitor the hydrophobic mismatch and make the system big enough so that the bilayer at the box edges has its natural thickness.
** rule of thumb 2: have at least 1-1.5nm of water between protein and z-boundary (so that Coulomb forces are effectively screened)
** Especially for coarse-grained self-assembly simulations you also need to take into account the [[BONDINI#A rough guide to System Content and Membrane Structure|lipid-to-water ratio and its affect on membrane structure]].
* Add ions at eg 100 mM (+counter ions) for additional Coulomb screening
* Remember that run time scales like  <math>N \log N</math> (or even <math>N^2</math>) and <math>N</math> scales with the volume, i.e. <math>L^3</math>! Thus: keep your system small and pretty (ie the smallest system that still behaves like a big system... invariably you are trading size-artifacts versus speed and thus sampling)

== Number of lipids ==

Estimate the cross sectional area of the protein, eg using the radius of gyration

<math>A_{\mathrm{prot}} = \pi R_G</math>

and with the approximate area per lipid <math>A_l = 64</math> Å the number of lipids in two leaflets is for a box with dimensions <math>L_x</math> and <math>L_y</math>

<math>N = \frac{2(L_x L_y - A_\mathrm{prot})}{A_l}</math>.

If you are simulating a mixed bilayer, eg POPE:POPG 4:1 then you will need <math>4N/5</math> POPE lipids and <math>N/5</math> POPG ones.

== Number of ions ==
<!-- Oli Labbook p 42 -->
Once the system is solvated you can calculate the numbers of ions <math>N</math> needed for a given concentration <math>c</math> (in addition to any counter ions):

<math>c = \frac{n}{V} = \frac{N/N_A}{V}</math>

(where <math>N_A = 6.02214179 \times 10^{23} \mathrm{mol}^{-1}</math> is the [http://physics.nist.gov/cgi-bin/cuu/Value?na Avogadro constant]).

The problem is to get the water volume of the inhomogenous system, consisting of membrane and protein with the water. An approximation is to use the volume of a water molecule at standard conditions, <math>v_w = 30 \mathrm{\AA}^3</math> and calculate <math>V = N_w v_w</math> from the number of waters in the system, <math>N_w</math>. The equations become even simpler if we use the standard concentration of water, <math>c_w = n_w/(N_w v_w) = 55.5\, \mathrm{mol/l}</math>. 

Using all this we get

<math>N_+ = \frac{c_+}{V} = \frac{c_+}{c_w} N_w</math>

for the (monovalent) cations, and correspondingly for monovalent anions

<math>N_- = N_+</math>

=== Example ===
For a concentration of 100 mM = 0.1 M and 8000 water molecules we will need to add

<math>N_+ = N_- = \frac{0.1\,\mathrm{M}}{55.5\,\mathrm{M}} \times 8000 = 14</math>

ions of each kind (eg 14 sodium and 14 chloride and whatever counterions are required to make the system charge neutral).
 


[[Category:MembraneInsertion]]
[[Category:Lipids]]
[[Category:Tutorial]]