# Comparing PCA results from two different trajectories

GROMACS version: 2019.4
GROMACS modification: No

Hello,
I have run two different simulations of my protein: one simulation with the protein on its own, and the other with the protein in complex with a ligand.

I have then performed PCA analysis on the trajectories from both of the simulations. I would now like to compare the PCA results. What is the proper way of going about this?

Is it ok to:
Calculate the eigenvectors for the apo protein, project on the apo protein trajectory, and make PC2 vs PC1 plot.
Calculate the eigenvectors for the ligand bound protein, project on the ligand bound protein trajectory, and make PC2 vs PC1 plot.
Compare the PC2 vs PC1 plots obtained from the apo protein and ligand bound protein.

Or should I:
Calculate the eigenvectors for the apo protein, project on the apo protein trajectory, and make PC2 vs PC1 plot.
Calculate the eigenvectors for the ligand bound protein, project on the apo protein trajectory, and make PC2 vs PC1 plot.
Compare the plots.

Calculate the eigenvectors for the apo protein, project on the ligand bound protein trajectory, and make PC2 vs PC1 plot.
Calculate the eigenvectors for the ligand bound protein, project on the ligand bound protein trajectory, and make PC2 vs PC1 plot.
Compare the plots.

Or is there a completely different way of comparing the PCA results?

Best wishes,
Pawel

As long was were are talking about only the PCA of the protein atoms then I would use the eigenvectors and eigenvalues from the Apo simulation and apply them to the complex (ligand-bound) simulation. In other words, project the ligand-bound trajectroy onto the PCs of the Apo simulation. This way you can compare PCs between different trajectories.

Your options (calculating eigenvectors and eigenvalues for each simulation independently) would mean that the prinipal components would be entirely different. Comparing results between two independent PCAs does not make sense.

In practise this means that you only run ‘gmx covar’ once for the Apo simulation and then use those eigenvecs and eigenvals with ‘gmx anaeig’ on a trajectory of the protein-ligand simulation.
Of course doing it vice versa is also possible.

I may be wrong but this is the only way comparing PCs makes sense to me.

Hi there, since the apo and the complex structures both have the same atoms (protein), I think it would be possible to concatenate both trajectories and do the PCA analysis. Then, you may be able to select and highlight the conformers from both structures on your PCA1 Vs PCA2 plot.

Would be great if a more experienced person could confirm this!

Hello, I am very happy to see your new ideas, I think it is very inspiring for my research, but there is something I don’t understand here, and I want to consult with you.
The coordinate system of the two trajectories after entering the PCA dimension reduction is no longer the same coordinate system. How can I find their different points?