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From: David A Case <david.case.rutgers.edu>

Date: Wed, 28 Aug 2019 11:35:29 -0400

On Wed, Aug 28, 2019, Airy Sanjeev wrote:

*>
*

*>I want to calculate the value of Î”*G *from the umbrella sampling
*

*>methodology. Please let me know how will I calculate from The Potential of
*

*>Mean Force Profile.
*

Generally, once you have a PMF curve, you need to define two distinct

regions of the umbrella variable (call this "x") that you wish to call

states "A" and "B".

Then integrate exp(-PMF(x)/kT) over regions A and B to get the

probabilities of being in each of those two regions. Divide those two

numbers to get an equilibrium constant (ratio of probablities), then

convert to a free energy in the usual way.

The above procedure should work if "x" is just a linear combination of

Cartesian coordinates. If "x" is a dimension in a curvilinear space

(such as the distance between two proteins or groups), then you would

have to weight the integration by a Jacobian factor. Also, the generic

description above assumes a "unimolecular" transformation, where states

A and B are just a single molecular system in different regions of

conformational space. Free energies for events like the dissociation of a

dimer into monomers require specification of a standard state.

Note also, that for *qualitative* purposes, people will often just

choose two points on the PMF curve, subtract the two numbers, and call

that a "free energy difference". That's fine for intuitive arguments,

especially if one is comparing such differences between two similar

systems. This does not represent anything that could be directly

compared to an experimental value, but maybe it's all you need.

...hope this helps....dac

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Received on Wed Aug 28 2019 - 09:00:02 PDT

Date: Wed, 28 Aug 2019 11:35:29 -0400

On Wed, Aug 28, 2019, Airy Sanjeev wrote:

Generally, once you have a PMF curve, you need to define two distinct

regions of the umbrella variable (call this "x") that you wish to call

states "A" and "B".

Then integrate exp(-PMF(x)/kT) over regions A and B to get the

probabilities of being in each of those two regions. Divide those two

numbers to get an equilibrium constant (ratio of probablities), then

convert to a free energy in the usual way.

The above procedure should work if "x" is just a linear combination of

Cartesian coordinates. If "x" is a dimension in a curvilinear space

(such as the distance between two proteins or groups), then you would

have to weight the integration by a Jacobian factor. Also, the generic

description above assumes a "unimolecular" transformation, where states

A and B are just a single molecular system in different regions of

conformational space. Free energies for events like the dissociation of a

dimer into monomers require specification of a standard state.

Note also, that for *qualitative* purposes, people will often just

choose two points on the PMF curve, subtract the two numbers, and call

that a "free energy difference". That's fine for intuitive arguments,

especially if one is comparing such differences between two similar

systems. This does not represent anything that could be directly

compared to an experimental value, but maybe it's all you need.

...hope this helps....dac

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Received on Wed Aug 28 2019 - 09:00:02 PDT

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