Order parameters and statistics
Order parameters and statistics#
The mean order parameter of bond \(CH_j\) (i.e. the \(j^{th}\) C-H bond) is calculated using the standard formula:
where \(\theta\) is the angle between the \(CH_j\) bond and the normal to the membrane (usually the z axis), \(\langle ... \rangle\) means averaging over molecules and frames. \(S_{CH}\) can be measured by NMR which is useful to validate simulation results, as largely described in the NMRlipids project.
The order parameter output of buildH (default name OP_buildH.out
) looks like this:
# OP_name resname atom1 atom2 OP_mean OP_stddev OP_stem
#--------------------------------------------------------------------
gamma1_1 POPC C1 H11 0.01304 0.12090 0.01069
gamma1_2 POPC C1 H12 0.00666 0.09279 0.00820
gamma1_3 POPC C1 H13 -0.01531 0.09141 0.00808
[...]
Each line corresponds to a given CH. The 4 first columns contain the generic name, residue name, carbon and hydrogen names respectively. The other columns contains different statistics on order parameters (OP):
OP_mean
, also written \(\overline{S_{CH_j}}\) as described above, is the mean OP of bond \(CH_j\) averaged over all lipids and all frames of the trajectory.OP_stddev
is the standard deviation of the OP over residues, we shall write it \(\sigma(S_{CH_j})\); first we average each OP of bond \(CH_j\) (e.g. the C-H of beta1) of residue \(i\) (i.e. lipid \(i\)) over the whole trajectory:
where \(nframes\) is the total number of frames, then we calculate the standard deviation of those means over all residues:
where \(nres\) is the total number of residues (i.e. lipids).
OP_stem
is the standard error of the mean averaged in the same spirit, let’s call it \(err(S_{CH_j})\):