Projection of trajectory onto first two eigenvectors- Does it mean that
i) the superposition of molecular structures (a set of C-alpha coordinates) over a trajectory are projected onto a plane defined by first two eigenvectors?
or
ii) the numbers (in 2D projection plot, obtained from g_anaeig) are the results of the dot products of displacement vectors of the C-alpha atoms with each of the principal eigenvectors?
I've used g_anaeig in gromacs to perform the PC analyses.
Can someone explain please?
Hi Tarak,
The principle component is just a vector desribing the relative contribution of each c-alpha atom's x,y and z component to the correlated mode of motion corresponding to that component. (Assuming you calculated your covariance matrix using c-alpha atoms only). Thus the projection of a given simulation frame onto a given PC is just the dot product of the c-alpha coordinates of that frame with the PC vector. Often one will want to see the projection on the 1st and 2nd PC which results in a projection on a 2D plane: the coordinates in this plane are the dot product with the 1st PC on one axis and the dot product with the 2nd PC on the other axis. Does that make sense?
Pawel
Thanks Pawel,
I was bit confused with the dot product of a coordinate matrix with the PC1 vector. Initially, I thought the dot product would produce a vector, but then realized it's the product of C-alpha coordinates with the principal component having one nonzero element, that essentially gives me a number. Similarly, a projection of the C-alpha coordinates onto the PC2 gives me another number. And thus, I get a (x,y) kind of coordinates onto the plane defined by PC1 and PC2 for given number of frames.
Wish you and your family a Very Very Happy New Year.....cheers.
Tarak
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