Questions and problems?

# Nmode units questions

Are the modes produced by NMODE normalized (in particular, mass-normalized)?

The modes are originally constructed to be orthonormalized in a mass-weighted coordinate system. Before they are output, they are converted to a standard (cartesian, non-mass-weighted) basis. See the NMANAL program for an idea of how these are used to construct things like thermal fluctuations, etc.

In the printout of the modal information, are the frequencies themselves output, or their squares?

The frequencies themselves, converted to wavenumbers (i.e. the values output are proportional to the square root of the eigenvalues of the mass-weighted second derivative matrix).

The manual states something like 'projection of each normal mode onto that coordinate' but its not quite clear to me what is projected onto what and what the significance of the size or the sign of this entry is.
```>  NORMAL MODE  11  WITH FREQUENCY =    342.0154
>                                                         proj.      PE%
>  angle   O1  (  1) -  S2  (  2) -  C3  (  3)            9.85073    .45593
>  angle   O1  (  1) -  S2  (  2) -  C7  (  7)           -9.85039    .45590
>  bond    S2  (  2) -  C7  (  7)                         -.02302    .02320
>  bond    S2  (  2) -  C3  (  3)                          .02302    .02319
```

"Projection" is a scalar (dot) product between the normal mode direction vector and a displacement vector that is oriented in such a way as to change the internal coordinate in question. In your example above, moving in a positive direction along mode 11 would have (as its most important effect) an increase in the O1-S2-C3 angle and a decrease in the O1-S2-C7 angle. About 92% of the energy associated with a small displacement along mode 11 would come from the angle bending terms for these two angles. A minor component of the motion (involving about 5% of the energy) would come from a decrase in the S2-C7 bond length and an increase in the S2-C3 bond length. The PE% (which were not multiplied by 100, but I hope most people will figure that out...) are only approximate, since that calculation only works for a quadratic force field, and the AMBER force field is only approximately of that form. So all of the numbers printed should just be treated as clues to the nature of the normal modes involved. You could make an animation of each mode as an altenative analysis tool, for example.

It looks like nmode can NOT calculate normal modes if the "restrt" file is formatted : I get the following error messages at the end of the "nmout" file:
```>       Root-mean-square gradient of input coords is   3.6103208334998575E-05
>       This is greater than the requested maximum:    1.0000000000000001E-05

```
There *is* some loss of accuracy by using formated coordinates. You can either use unformatted coordinate files for the final minimization step, or just set drms to a value like 5.d-5, instead of using the default 1.d-5. There will be little change in the frequencies if you do the latter.

Some time ago I asked about NMODE problems when I tend to lost my good RMSD values between Newton-Rhapson and normal mode calcs. It really wasn't the binary/formatted kind of mistake. I worked it out calculating normal modes using iprw option to write out the nonbonded pairlist during minimization and reading it back in the beginning of normal mode calculation.

Can water in calculating normal modes of my protein?

Normal mode analysis is usually done without water, but nothing stops you from adding some or even many water molecules to the protein.

What effects will water have on protein normal modes?

The presence of solvent has various effects on the dynamics of a protein, of course, but I can't think of one that would seriously affect the outcome of a normal mode analysis.

Normal mode analysis is typically used to identify the slow large-amplitude motions of a protein. Their shape isn't perturbed much by the presence of solvent, and the frequencies and amplitudes from normal mode analysis are unreliable anyway. [Konrad Hinsen on ccl, writing of normal modes in general]