Re: Various practical colvar module related questions

From: JťrŰme Hťnin (jhenin_at_ifr88.cnrs-mrs.fr)
Date: Wed Jan 19 2011 - 09:46:23 CST

Hi Ajasja, it's been a while...

2011/1/18 Ajasja Ljubetińć <ajasja.ljubetic_at_gmail.com>:
> Dear all (especially¬†J√©r√īme:),
> I am about to start some more extensive ABF/metadynamics calculations, but I
> have some practical problems/questions:
> 1) How to choose the values for the constants such as (LangevinDamping,
> fullSamples, width of colvar, lowerWallConstant, upperWallConstant)?
> Chipot and Henin,2005 have tested the effect of these parameters by
> comparing them to a longer reference unconstrained MD simulation. All the
> parameters can significantly effect the calculated FES. But I find it hard
> to choose the rigth values without a reference MD run.
> And overdameped system does not diffuse efficiently, large or small
> WallConstatns can affect the potential at the borders, and the fullSamples
> seems to affect the standard error. In Fig 3c why is the error so large? I
> would think that the more samples one has the better the estimate of the
> average force.

fullSamples is not the total number of samples collected. It is the
samples collected in each bin in the preliminary, unbiased part of the
simulation. The larger the value, the longer the delay before the bias
starts, so the longer it takes to explore high-free-energy regions.

> I'll be working in water and membrane (probably using projections along a
> vector as colvars), so I'm thinking of:
> rigidbonds all
> timestep 2 ps
> nonbondedFreq       1
> fullElectFrequency  2
> langevinDamping    1 1/ps
> fullSamples 500???
> width 0.4 A
> lowerWallConstant 5???
> How can one be sure the choice of the parameters is correct? Is it better to
> have smaller bins and less fullSamples or more fullSamples and larger bins?

To some degree, I'd recommend smaller bins and a smaller fullSamples.
The other parameters look okay. You could try a higher wall constant.

> 2) Must ABF simulations be preformed in a NVT ensembe? What about
> metdynamics?
> The free energy is the sensible measure in a NVT ensemble. What happens if
> one runs ABF simulations at  NPT? (I suppose it would be to naive to expect
> that one obtains the free enthalpy:). But in liquid systems the pV term is
> small, so does this even matter?

No, it doesn't matter much. ABF and metadynamics are often run in NPT.

> 3)How does one know when/if an ABF simulation has converged?
> This one is probably easy, I would imagine when the histogram of the colvars
> becomes flat (at least in the region of interest)? Does the same hold for
> metadynamics? Or perhaps it's enough just to see if the FES does not change
> any more (like it says in the ABF tutorial)

In real life, diffusive sampling is inefficient, so the histogram
never becomes very flat. An interesting quantity is to look at RT
times log of the histogram, in other words, the residual free energy
associated with the distribution actually sampled. It is a crude
measure of the uncertainty in the PMF.

> 4)Can a metadynamics simulation also be split in to smaller regions
> (windows)?

I don't see why not.

> Is it feasible to split the FES into smaller regions?

Is that a separate question? I don't get it.

> When using multiple
> walkers the simulations get slower and slower (because one cannot use
> grids).

True.

> 5)How does one obtain the probability density from the free energy profile?
> In a NVT ensemble the probabilty of a state with energy Ej is given by the
> Boltzmann distribution.
>
> Pj=exp(-beta*Ej)/sum_over_j(exp(-beta*Ej)).

This is true of a microstate, that is, a single point in phase space.
Free energy profiles describe states that are defined by a value of
the RC, that is, iso-RC surfaces in phase space. Those have a kind of
entropy. But they are not true macrostates either - if I had to give
them a name, I would call them mesostates. They are not very physical,
mostly just a theoretical construct (like microstates).

> But equation (3) in Henin and Chipot,2004 seems to imply I'm missing
> something:
> A(x)=-1/beta*ln(P(x)) + A0

Indeed.

> ==> P(x) =exp(-beta*Ej)/exp(A0)

Not true, because coordinate x does not describe a microstate here. If
the reaction coordinate was the full set of Cartesian coordinates,
then the free energy "profile" would just be the potential energy, and
the identity you wrote would hold. And then, entropy would indeed be
constant across those states.

Best,
Jerome

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