Thanks for suggestions, Jason!
How do you think how the convergence of the Principal components taken from
QHA will be altered if the simulation will be run in hight-temperature
regime or alternatively in case of the aMD boost potentials?
James
2014-12-05 16:19 GMT+01:00 Aron Broom <broomsday.gmail.com>:
> Jason,
>
> That is a great write-up! It's very valuable to have some practical pros
> and cons for these methods, and a sense of when one might be more useful
> than another. Previously my comprehension was limited to QHA approximates
> the everything has one harmonic, and NMA does them individually, but I'd
> never expanded this to understand what that might mean in terms of what was
> needed. Though I see the point about them both being "bad", in fact, I'm
> often tempted to just use the "enthalpy" (it does include the solvent
> entropy at least) when doing MMPBSA and hope the vibrational (or I guess
> configurational?) entropies are roughly similar.
>
> Is there an inherent reason that the calculations NMA performs wouldn't be
> a good fit for the GPU? In particular, couldn't energy minimization be GPU
> enhanced just as readily as MD (I don't recall at the moment if AMBER does
> this anyway when using PMEMD.cuda?).
>
> Thanks,
>
> ~Aron
>
> On Fri, Dec 5, 2014 at 8:59 AM, Jason Swails <jason.swails.gmail.com>
> wrote:
>
> > On Wed, 2014-12-03 at 09:50 -0500, Aron Broom wrote:
> > > Hi James,
> > >
> > > I've mostly ended up using the Quasi-Harmonic method for the entropy,
> as
> > > the NMA takes a very long time for each snapshot when you have a larger
> > > system. But when I did use it, I also saw a similar output. It seems
> > like
> > > it wants to be run for more steps of minimization (probably because
> your
> > > system is larger than maybe the typical test systems were) and at this
> > > point hasn't stopped being able to reduce the energy. Under the &nmode
> > > namelist thing in the input file, you can give a value for maxcyc,
> which
> > > defaults to 10,000. Keep in mind, increasing the number of cycles, and
> > > adding more snapshots is going to mean a lot more computational time
> > used.
> > > I would suggest, while that is running, to try out the quasi-harmonic
> > > option. It will give the same output, and also breakdown the entropy
> to
> > > the same terms, but will complete much faster. Also, from the minimal
> > > reading I've done on the subject, it didn't seem like the normal modes
> > > analysis was a clear cut winner in terms of the results, at least for
> > > protein sized systems. Maybe someone with more experience and
> > > understanding can comment on that?
> >
> > In my understanding, the difference between the quasi-harmonic
> > approximation (QHA) and the normal mode approximation (NMA) is subtle,
> > but important. In the former, the eigenvectors of the mass-weighted
> > covariance matrix (think principal components) are treated as pseudo
> > vibrational modes, with the eigenvectors representing their frequencies.
> > For NMA, you minimize to the closest local minimum and compute the
> > Hessian matrix directly and get the vibrational modes and frequencies
> > from the eigenvectors and eigenvalues of the Hessian. NMA is analytical
> > (for analytical second-derivatives), QHA is not.
> >
> > There are notable similarities -- i.e., both cases utilize the rigid
> > rotor approximation, assuming that you can separate the vibrational,
> > rotational, and translational modes (in reality, vibrational and
> > rotational modes are not orthogonal, since rapid rotation will "squash"
> > a globular protein and induce vibrations in the system). The _nature_
> > of the vibrations are inherently different between the two approaches,
> > though. Consider the following image of a reduced-dimensional free
> > energy surface (commonly seen in the theory of protein folding)
> > http://www.learner.org/courses/physics/visual/img_half/funnel.jpg.
> >
> > To take a look at what you do for a NMA calculation, consider picking a
> > random point on that surface. What NMA does is drop that point to the
> > "closest" local minimum and compute the Hessian. The vibrational modes
> > you get correspond to a quadratic (harmonic) function that best fits
> > that minimum at the minimum (this is why you need to minimize *well* for
> > NMA). However, not all of these basins are the same shape (some are
> > steeper, with lower vibrational entropy, and others are shallower with
> > higher vibrational entropy). So you need multiple minima to get more
> > data, with the general assumption seeming (to me) to be that more of
> > those local minima resemble the "large" harmonic well than don't.
> >
> > For QHA, though, the "harmonic well" is actually the entire sampled
> > space at that temperature (assuming "complete" sampling). So in the
> > figure I linked, the small wells are the ones from which NMA entropies
> > are approximated, whereas QHA will give you the entropy assuming the
> > entire funnel is one large harmonic well (unless I'm misunderstanding
> > exactly what the mass-weighted covariance matrix represents). This need
> > for "complete" sampling makes the QHA _very_ slow to converge in terms
> > of the number of independent snapshots you need (i.e., you need long
> > simulations in order to obtain the asymptotic limit of the QHA entropy).
> > NMA requires far fewer snapshots to "converge", but each snapshot takes
> > *much* longer due to the need to minimize thoroughly and compute the
> > Hessian. Since GPUs are making MD -- not NMA -- fast, I suspect that
> > QHA will start to win out on the grounds of computational cost.
> >
> > So while they seem very similar in theory, the QHA and NMA have strong
> > differences in their theoretical underpinnings. Here I have to agree
> > with Aron -- it isn't clear to me which is "better" (given the
> > difficulty in computing entropy, they're probably both "bad" :).
> >
> > As a fun exercise, let's try to unify them: if you sample from an ideal,
> > simple harmonic potential, there should be no difference between NMA and
> > the QHA. You can actually get pretty close to this scenario in real
> > biomolecules -- run your simulations at VERY low temperatures. When you
> > do that, the simulation will become trapped in the same local minimum
> > that you are computing the normal modes for, and will appear largely
> > harmonic if the temperature is low enough. In this case, the principal
> > components should be the same as your vibrational modes, and your
> > entropies should come out the same. One of my MMPBSA.py coauthors ran
> > one of these calculations 4-5 years ago at low temperature and indeed
> > found that the QHA converged rapidly and gave the same vibrational
> > entropies as NMA (the rotational and translational entropies are
> > analytically identical in both cases, if I recall correctly).
> >
> > If I've perpetrated a misunderstanding with respect to physical
> > significane of the mass-weighted covariance matrix here, I hope someone
> > will correct me.
> >
> > I hope this helps,
> > Jason
> >
> > --
> > Jason M. Swails
> > BioMaPS,
> > Rutgers University
> > Postdoctoral Researcher
> >
> >
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> > AMBER.ambermd.org
> > http://lists.ambermd.org/mailman/listinfo/amber
> >
>
>
>
> --
> Aron Broom M.Sc
> PhD Student
> Department of Chemistry
> University of Waterloo
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Received on Mon Dec 08 2014 - 01:00:02 PST
