I am running "Principal Components Analysis (PCA)" for my protein at three different temperatures using "g_covar_mpi -s XXXXX.tpr -f XXXXXX.xtc".
The results I am getting are :
At 300 K:
(1) Trace of the covariance matrix: 14.966 (nm^2)
(2) Sum of the eigenvalues: 14.966 (nm^2)
At 350 K:
(1) Trace of the covariance matrix: 26.4201 (nm^2)
(2) Sum of the eigenvalues: 26.42 (nm^2)
At 375 K:
(1) Trace of the covariance matrix: 11.1512 (nm^2)
(2) Sum of the eigenvalues: 11.1512 (nm^2).
Can anyone explain this output? I need a proper answer. Does this mean that "At 375 K, Trace of the covariance matrix is lesser than other temperatures. So the protein is better and stable at this temperature??
Thanks
No, the trace of the covariance matrix doesn't tell you anything about the stability of the protein. Covariance values can be positive or negative, so the trace in this case either means (1) the positive covariance values are small or (2) there are more offsetting positive and negative covariance values in the matrix at 375 K. Covariance tells you about the cooperativity of motion, not stability.
So, more offsetting positive and negative values at 375 K indicates??
On its face, nothing. You need to use the covariance matrix to see which parts of the protein have positive and negative covariance to see the direction of the dynamics.
In reply to Justin Lemkul; covariances can be positive or negative but the trace is the sum of the leading diagonal, so the trace is just the sum of the individual variances. Variances can't be negative.
However, you still cannot draw much information from the trace unless you know a lot about the variables that go into it. It is perfectly possible for the variance of an unimportant variable to drop drastically while the variance of a key indicator of stability increases somewhat (or vice versa). Further, the trace will depend heavily on whether you have scaled the variables or not before calculating the covariances; if you haven't, variables with large values will (depending on their range) tend to dominate the trace - and again you need to know which variables are important indicators of stability to understand how the trace will be affected.
Finally, reduced variation does not necessarily imply stability. If some property drops to zero or goes to an asymptote at higher temperature (for example because the protein is entirely denatured) the variance is likely to be near zero too - so on a bad day, a very small variance could simply mean 'irrevocably broken'.
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