I've performed small test using 50ns of the production run as the input
performing 2 MMGBSA with 1)QHA and 2) NMA for enthropy calculations (below
logs):
1)Using QHA
|--------------------------------------------------------------
|&general
|startframe= 1, interval=1, keep_files=2, entropy=1,
strip_mask=:WAT:Cl-:NA+:K+:PPC, netcdf=1
|/
|&gb
|igb=5, saltcon=0.150,
|/
|--------------------------------------------------------------
|All units are reported in kcal/mole.
|All entropy results have units kcal/mol (Temperature is 298.15 K).
-------------------------------------------------------------------------------
-------------------------------------------------------------------------------
ENTROPY RESULTS (QUASI-HARMONIC APPROXIMATION) CALCULATED WITH PTRAJ:
Translational Rotational Vibrational Total
Complex: 16.9764 17.7080 4275.0995 4309.7839
Receptor: 16.9725 17.7077 4243.1059 4277.7861
Ligand: 12.1595 9.0509 41.3388 62.5492
DELTA S: -12.1556 -9.0506 -9.3452 -30.5514
Free Energy:
-------------------------------------------------------------------------------
Differences (Complex - Receptor - Ligand):
Energy Component Average Std. Dev. Std. Err. of
Mean
-------------------------------------------------------------------------------
VDWAALS -28.1255 2.8115
0.0385
EEL -6.9265 3.5042
0.0480
EGB 8.9388 2.3158
0.0317
ESURF -4.4972 0.2938
0.0040
DELTA G gas -35.0520 4.3997
0.0602
DELTA G solv 4.4416 2.2824
0.0313
DELTA TOTAL -30.6104 4.0461
0.0554
-------------------------------------------------------------------------------
-------------------------------------------------------------------------------
Using Quasi-harmonic Entropy Approximation: DELTA G binding = -0.0590
-------------------------------------------------------------------------------
-------------------------------------------------------------------------------
2)With the NMA
|--------------------------------------------------------------
|&general
|startframe= 1, interval=50, keep_files=2,
strip_mask=:WAT:Cl-:NA+:K+:PPC, netcdf=1
|/
|&gb
|igb=5, saltcon=0.150,
|/
|&nmode
|nmstartframe=1, nminterval=1, nmode_igb=1, nmode_istrng=0.15,
|/
|--------------------------------------------------------------
ENTROPY RESULTS (HARMONIC APPROXIMATION) CALCULATED WITH NMODE:
Complex:
Entropy Term Average Std. Dev. Std. Err. of
Mean
-------------------------------------------------------------------------------
Translational 16.9764 0.0000
0.0000
Rotational 17.6664 0.0106
0.0010
Vibrational 3228.5220 7.1795
0.6941
Total 3263.1648 7.1841
0.6945
Receptor:
Entropy Term Average Std. Dev. Std. Err. of
Mean
-------------------------------------------------------------------------------
Translational 16.9725 0.0000
0.0000
Rotational 17.6648 0.0112
0.0011
Vibrational 3212.5911 7.3649
0.7120
Total 3247.2285 7.3697
0.7125
Ligand:
Entropy Term Average Std. Dev. Std. Err. of
Mean
-------------------------------------------------------------------------------
Translational 12.1595 0.0000
0.0000
Rotational 9.2911 0.0601
0.0058
Vibrational 12.1290 0.9353
0.0904
Total 33.5795 0.9366
0.0905
Differences (Complex - Receptor - Ligand):
Entropy Term Average Std. Dev. Std. Err. of
Mean
-------------------------------------------------------------------------------
Translational -12.1556 0.0000
0.0000
Rotational -9.2896 0.0604
0.0058
Vibrational 3.8018 4.8664
0.4705
DELTA S total= -17.6431 4.8641
0.4702
-------------------------------------------------------------------------------
Differences (Complex - Receptor - Ligand):
Energy Component Average Std. Dev. Std. Err. of
Mean
-------------------------------------------------------------------------------
VDWAALS -28.3625 2.7322
0.2641
EEL -6.8004 3.3622
0.3250
EGB 8.8860 2.1574
0.2086
ESURF -4.5019 0.2698
0.0261
DELTA G gas -35.1629 4.0793
0.3944
DELTA G solv 4.3840 2.1221
0.2052
DELTA TOTAL -30.7789 3.8018
0.3675
-------------------------------------------------------------------------------
-------------------------------------------------------------------------------
Using Normal Mode Entropy Approximation: DELTA G binding = -13.1358 +/-
6.1355
-------------------------------------------------------------------------------
-------------------------------------------------------------------------------
Conclusions:
In that case I've obtained true value using NMA (compared with the
experimental values) but with the significant error!. In comparison QHA
resulted in 2 times lower entropy (this time intervals for calculations
were equal to 5000 steps as the snapshots have been saved to the trajectory
during MD). Are there any possibilities to fix QHA?
James
2014-12-08 9:35 GMT+01:00 James Starlight <jmsstarlight.gmail.com>:
> 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
>> >
>> >
>> > _______________________________________________
>> > AMBER mailing list
>> > AMBER.ambermd.org
>> > http://lists.ambermd.org/mailman/listinfo/amber
>> >
>>
>>
>>
>> --
>> Aron Broom M.Sc
>> PhD Student
>> Department of Chemistry
>> University of Waterloo
>> _______________________________________________
>> AMBER mailing list
>> AMBER.ambermd.org
>> http://lists.ambermd.org/mailman/listinfo/amber
>>
>
>
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Received on Tue Dec 09 2014 - 00:00:02 PST
