I have done 100ns simulations for my protein using gromacs, and then subjected to PCA analysis from gromacs (g_cova, g_anaeig). In order to see the dominant motion within the proteins (WT and mutant type), I have used -extr option in gromacs. With 50 frames of the whole trajectory and generated a movie from 50 PDB frames using chimera. As this is my first MD simulation study, I have some confusion at this stage.
This type of global motions analysis is similar or same with NMA? Also the above said approach is acceptable to publish along with movies?
Suggestions please.
This is a long topic to discuss, but I'll try to make it as short as I can.
NMA, in its conventional form, is not applied to MD trajectories but to a SINGLE energy-minimized structure. NMA is based on the assumption that potential energy landscape in the vicinity of the minimized atomic structure is close to quadratic, and so can be approximated by the first three terms of Taylor series expansion. Unfortunately this very nice simplifying assumption only holds at very low temperatures, mainly due to the anharmonic (nonlinear and nonstationary) and usually collective motions of atoms. Hence, NMA should be only valid in very a limited time and spatial scale. On the other hand, it is rather interesting that NMA holds in a much wider range and there have been numerous studies showing the similarity of normal modes obtained from a single minimized crystal structure and large scale collective displacements obtained from experimental methods. I will not write about possible reasons to explain this observation, since it is (though, of course, related but still) separate topic from your question. In short, NMA is applied to a single conformation.
PCA, on the other hand, is a multivariate statistical technique, which aims to reduce the high-dimensional space of variables to a lower one. When it comes to MD simulations of proteins, in its simplest sense, we may assume that each snapshot from the simulation is a sample conformation from the equilibrated fluctuations of a protein (of course, PCA may be applied also to non-equilibrium simulations, but I try to make it as simple as it can be). Furthermore, we assume that samples we obtain from the MD simulation spans most of the "essential dynamics" of the protein (Beware: it is usually this assumption which usually does not hold!). Hence, with a well-sampled essential dynamics of the protein at hand, we reduce the high number of degrees of freedom, which is equal to 3N-6 (where N is the number of atoms used in PCA, usually Ca atoms), to a much lower dimension, which is easier to monitor and intrepret. This number (the number of PCs), depending on different studies, ranges between 3-20. In summary, PCA is applied on an MD trajectory.
Although the input data processed by these two techniques are different, not only both techniques aim to identical objectives, i.e. to determine the large-scale collective motions, but also their results converge in the following hypothetical case: If the protein fluctuations under physiological conditions were completely harmonic and MD simulations were long enough to capture the equilibrated dynamics of proteins, NMA and PCA would give the same results. However, since neither of these assumptions are completely satisfied, there are always more or less differences between these methods. Again there's a huge literature comparing these two methods.
I hope this helps.
This is a long topic to discuss, but I'll try to make it as short as I can.
NMA, in its conventional form, is not applied to MD trajectories but to a SINGLE energy-minimized structure. NMA is based on the assumption that potential energy landscape in the vicinity of the minimized atomic structure is close to quadratic, and so can be approximated by the first three terms of Taylor series expansion. Unfortunately this very nice simplifying assumption only holds at very low temperatures, mainly due to the anharmonic (nonlinear and nonstationary) and usually collective motions of atoms. Hence, NMA should be only valid in very a limited time and spatial scale. On the other hand, it is rather interesting that NMA holds in a much wider range and there have been numerous studies showing the similarity of normal modes obtained from a single minimized crystal structure and large scale collective displacements obtained from experimental methods. I will not write about possible reasons to explain this observation, since it is (though, of course, related but still) separate topic from your question. In short, NMA is applied to a single conformation.
PCA, on the other hand, is a multivariate statistical technique, which aims to reduce the high-dimensional space of variables to a lower one. When it comes to MD simulations of proteins, in its simplest sense, we may assume that each snapshot from the simulation is a sample conformation from the equilibrated fluctuations of a protein (of course, PCA may be applied also to non-equilibrium simulations, but I try to make it as simple as it can be). Furthermore, we assume that samples we obtain from the MD simulation spans most of the "essential dynamics" of the protein (Beware: it is usually this assumption which usually does not hold!). Hence, with a well-sampled essential dynamics of the protein at hand, we reduce the high number of degrees of freedom, which is equal to 3N-6 (where N is the number of atoms used in PCA, usually Ca atoms), to a much lower dimension, which is easier to monitor and intrepret. This number (the number of PCs), depending on different studies, ranges between 3-20. In summary, PCA is applied on an MD trajectory.
Although the input data processed by these two techniques are different, not only both techniques aim to identical objectives, i.e. to determine the large-scale collective motions, but also their results converge in the following hypothetical case: If the protein fluctuations under physiological conditions were completely harmonic and MD simulations were long enough to capture the equilibrated dynamics of proteins, NMA and PCA would give the same results. However, since neither of these assumptions are completely satisfied, there are always more or less differences between these methods. Again there's a huge literature comparing these two methods.
I hope this helps.
In NMA you diagonalize Hessian matrix whereas in PCA the covariance matrix. Try to figure out, what is the difference between their matrix elements...
Thank you Burak alakent and Michal Kolar for your suggestions. It helps me a lot
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