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From: John Chodera <jchodera.gmail.com>

Date: Thu, 10 Apr 2008 10:47:57 -0700

Hi David,

It's important to note that WHAM can only be applied to *equilibrium*

data. In order to compute the potential of mean force (PMF) along

something like a pulling coordinate using WHAM, typical practice is to

conduct a number of umbrella sampling simulations where the positions

and spring constants of harmonic restraints are carefully chosen to

ensure good overlap in the distribution of sampled distances along the

pulling coordinate. Each simulation has to be long enough to reach

equilibrium and then sample enough uncorrelated configurations to give

a precise estimate. The initial equilibration period of each

simulation must be discarded, and correlation times of the production

period are analyzed to determine the number of uncorrelated

configurations in the dataset. Typically, you want something like 40

such uncorrelated configurations per simulation, but if you use a

method that gives you statistical uncertainties as well as your PMF,

this will let you know how large the statistical uncertainty is in

your final estimate, and may give you clues to where you need more

sampling.

Benoît Roux has an excellent paper on the theory behind applying WHAM

to umbrella sampling simulations:

M. SOUAILLE and B. ROUX, "Extension to the Weighted Histogram Analysis

Method: Combining Umbrella Sampling with Free Energy Calculations",

Comput. Phys. Comm. 135, 40-57 (2001).

I would, however, suggest you use an estimator that gives you

statistical uncertainties as well. Michael Shirts and I have recently

produced one called MBAR (for "Multistate Bennett acceptance ratio")

which is pretty much a drop-in replacement for WHAM:

http://arxiv.org/abs/0801.1426

http://www.simtk.org/home/pymbar

Finally, methods such as "reverse cumulative averaging" can help you

automatically judge when each simulation has reached equilibrium and

how many correlation times you have in your dataset:

http://dx.doi.org/10.1063/1.1638996

The protocol you describe sounds like it would continue to perturb the

Hamiltonian at a rate that would not allow the system to come to

equilibrium before the umbrella restraint is moved again. As such,

you cannot use WHAM to analyze this data, as it will be

nonequilibrium.

To rectify this, you can either (1) increase the time spent before the

umbrella restraint is moved again to be sufficiently large to allow

the system to come to equilibrium and many equilibrium samples to be

collected from each window, or (2) accumulate the total work done on

the system during each pushing run and use this collection of work

measurements (one per pushing simulation) with a nonequilibrium

estimator, such as one based on the Jarzynski relation, to recover the

equilibrium free energy difference as a function of pulling

coordinate.

For option (2), the extraction of the PMF along the pulling coordinate

is a little bit tricky, since it's not the same as the free energy of

the system as a function of the umbrella equilibrium position. See,

for example, this paper by David Minh and Artur Adib of the NIH for

how it is done for bidirectional pulling experiments (where you pull

from both directions at equal rate):

http://arxiv.org/abs/0802.0224

I'm not entirely sure what the best estimator to use for

unidirectional pulling experiments is, but I am sure we can dig that

up if you think that nonequilibrium pulling is the way you'd like to

go. You would probably need many, many more pulling simulations than

10-20 to get this to converge, however.

My own suggestion would be to stick with umbrella sampling, especially

since these simulations can be run in parallel. The umbrellas

probably don't need to be so close as 0.025 A between umbrella

centers. You can probably start with a crude spacing, run some

simulations, and then examine the distribution of pulling distances

sampled and fill in the gaps where needed.

Best,

John

Date: Thu, 10 Apr 2008 10:47:57 -0700

Hi David,

It's important to note that WHAM can only be applied to *equilibrium*

data. In order to compute the potential of mean force (PMF) along

something like a pulling coordinate using WHAM, typical practice is to

conduct a number of umbrella sampling simulations where the positions

and spring constants of harmonic restraints are carefully chosen to

ensure good overlap in the distribution of sampled distances along the

pulling coordinate. Each simulation has to be long enough to reach

equilibrium and then sample enough uncorrelated configurations to give

a precise estimate. The initial equilibration period of each

simulation must be discarded, and correlation times of the production

period are analyzed to determine the number of uncorrelated

configurations in the dataset. Typically, you want something like 40

such uncorrelated configurations per simulation, but if you use a

method that gives you statistical uncertainties as well as your PMF,

this will let you know how large the statistical uncertainty is in

your final estimate, and may give you clues to where you need more

sampling.

Benoît Roux has an excellent paper on the theory behind applying WHAM

to umbrella sampling simulations:

M. SOUAILLE and B. ROUX, "Extension to the Weighted Histogram Analysis

Method: Combining Umbrella Sampling with Free Energy Calculations",

Comput. Phys. Comm. 135, 40-57 (2001).

I would, however, suggest you use an estimator that gives you

statistical uncertainties as well. Michael Shirts and I have recently

produced one called MBAR (for "Multistate Bennett acceptance ratio")

which is pretty much a drop-in replacement for WHAM:

http://arxiv.org/abs/0801.1426

http://www.simtk.org/home/pymbar

Finally, methods such as "reverse cumulative averaging" can help you

automatically judge when each simulation has reached equilibrium and

how many correlation times you have in your dataset:

http://dx.doi.org/10.1063/1.1638996

The protocol you describe sounds like it would continue to perturb the

Hamiltonian at a rate that would not allow the system to come to

equilibrium before the umbrella restraint is moved again. As such,

you cannot use WHAM to analyze this data, as it will be

nonequilibrium.

To rectify this, you can either (1) increase the time spent before the

umbrella restraint is moved again to be sufficiently large to allow

the system to come to equilibrium and many equilibrium samples to be

collected from each window, or (2) accumulate the total work done on

the system during each pushing run and use this collection of work

measurements (one per pushing simulation) with a nonequilibrium

estimator, such as one based on the Jarzynski relation, to recover the

equilibrium free energy difference as a function of pulling

coordinate.

For option (2), the extraction of the PMF along the pulling coordinate

is a little bit tricky, since it's not the same as the free energy of

the system as a function of the umbrella equilibrium position. See,

for example, this paper by David Minh and Artur Adib of the NIH for

how it is done for bidirectional pulling experiments (where you pull

from both directions at equal rate):

http://arxiv.org/abs/0802.0224

I'm not entirely sure what the best estimator to use for

unidirectional pulling experiments is, but I am sure we can dig that

up if you think that nonequilibrium pulling is the way you'd like to

go. You would probably need many, many more pulling simulations than

10-20 to get this to converge, however.

My own suggestion would be to stick with umbrella sampling, especially

since these simulations can be run in parallel. The umbrellas

probably don't need to be so close as 0.025 A between umbrella

centers. You can probably start with a crude spacing, run some

simulations, and then examine the distribution of pulling distances

sampled and fill in the gaps where needed.

Best,

John

-- Dr. John D. Chodera <jchodera.gmail.com> | Mobile : 415.867.7384 Postdoctoral researcher, Pande lab | Lab phone : 650.723.1097 Department of Chemistry, Stanford University | Lab fax : 650.724.4021 http://www.dillgroup.ucsf.edu/~jchodera On 10/04/2008, David Cerutti <dcerutti.mccammon.ucsd.edu> wrote: > Hello, > > I'm just starting into the wide world of WHAM, but I want to do a very > thorough study. Starting very soon, I intend to perform 10-20 simulations > for pushing biotin out of strepatvidin. My basic data collection is as > follows: > > 1.) 15ns total pushing run, with 0.025A perturbations every 30ps at a 1.5fs > time step (1000 steps = 1.5ps) > > 2.) Collect data on the restraining potential with: > &wt type='DUMPFREQ', istep1=10 > > 3.) Write energy output data every 10 steps (0.015ps) > > 4.) Write coordinates every 1000 steps (1.5ps) > > Is this a sufficent amount of data collection? Primarily, I'm concerned > whether my rate of coordinate output is all right, because the example in > the AMBER9 manual doesn't seem to need coordinates output at a high rate. > Since I'll have all the restart files, I could certainly go back on many > processors and resample the conformations if I needed denser sampling, but > it'd be much better to get enough readouts the first time. > > Thanks, > Dave > ----------------------------------------------------------------------- > The AMBER Mail Reflector > To post, send mail to amber.scripps.edu > To unsubscribe, send "unsubscribe amber" to majordomo.scripps.edu > ----------------------------------------------------------------------- The AMBER Mail Reflector To post, send mail to amber.scripps.edu To unsubscribe, send "unsubscribe amber" to majordomo.scripps.eduReceived on Fri Apr 18 2008 - 21:18:25 PDT

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