[gmx-users] Principal Component Analysis

[Gia Maisuradze]

Hi,

I am doing MD simulations and PCA for some mutants of lambda-repressor. The 
time of simulations is 10ns. I have done two runs of MD simulations: in 
first run I have used:
rlist               =  0.8
coulombtype         =  cut-off
rcoulomb            =  1.4
rvdw                =  0.8
in mdp files, and in second run I have used:
rlist               =  0.9
coulombtype         =  PME
rcoulomb            =  0.9
fourierspacing      =  0.12
pme_order           =  4
rvdw                =  0.9
ewald_rtol          =  1e-5

When I have done PCA I have got the different behavior for first five 
principal components. In both runs for slow folder mutant the cosine 
contents are close to each other, and they are close to cosine. According to 
the paper of Berk Hess (Phys. Rev. E, 62, 8438, 2000) in this case we have 
the random diffusion. The cosine contents for both runs:
First run:
pc 1 - 0.9540
pc 2 - 0.0127
pc 3 - 0.0036
pc 4 - 0.0039
pc 5 - 0.0007

Second run:
pc 1 - 0.8246
pc 2 - 0.0485
pc 3 - 0.0007
pc 4 - 0.0038
pc 5 - 0.0148

For medium and fast folders the results are different. In first run for both 
folders we have the resemblance to cosine for first five PCA, but in second 
run the results are different. For medium folder I obtained following cosine 
contents:
First run:
pc 1 - 0.8923
pc 2 - 0.0090
pc 3 - 0.0469
pc 4 - 0.0161
pc 5 - 0.0253

Second run:
pc 1- 0.5318
pc 2 - 0.2860
pc 3 - 0.0087
pc 4 - 0.0748
pc 5 - 0.0002

For fast folder:
First run:
pc 1 - 0.9658
pc 2 - 0.0002
pc 3 - 0.0167
pc 4 - 0.0045
pc 5 - 0.0048

Second run:
pc 1 - 0.4039
pc 2 - 0.2293
pc 3 - 0.1184
pc 4 - 0.0643
pc 5 - 0.0389

Consequently the mean square displacements (MSD) are different for these 
runs. In first run for all mutants the behavior of MSD is similar to one 
given in Hess's  paper, we can see sub-diffusive and super-diffusive parts 
for 1st principal component. In second run MSD of slow folder also has the 
same behavior as in first run, but MSDs of medium and fast folders in second 
run do not show super-diffusive part for first PC.

As I know the second MD run is more reliable than first one, but the results 
of PCA from first run is "better". I was wondering what run is more 
reliable, and why I got such a different results for PCA.

Thanks,

Gia Maisuradze