[gmx-users] Umbrella Sampling result

[Warren Gallin]

And a correction, I misread the Kd value.

A Kd of 0.76 µM predicts ∆G for binding is -34.9 kJ/mole, or -8.34 kcal/mole (compared to your result from the PMF of -18.3 kcal/mole.

But the basic idea holds - when you are dealing with an exponential y=e^x, the percentage error in y increases exponentially with the absolute error in x.

Warren Gallin

> On Mar 2, 2015, at 1:53 AM, Felipe Merino <felipe.merino at mpi-dortmund.mpg.de> wrote:
> 
> The problem is simpler than that, although you already pointed it out. 0.76 µM sounds like a dissociation constant, while -18 kcal/mol is in the association direction.
> 
> Incidentally, regarding the concentration problem, you are right that the equilibrium constants are dimensionless. However, there is a hidden "concentration" in the whole thing because for a bi-molecular process you have to make the free energy relative to a standard condition (usually 1M). You need to take this into account when you integrate your PMF. Check here (http://pubs.acs.org/doi/pdf/10.1021/ct3008099)
> 
> Best
> 
> Felipe
> 
> On 02/03/15 08:19, Warren Gallin wrote:
>> First, I’m assuming that you actually used 8.3144 for R, since that is the value you need to use to get the number you report.
>> 
>> I’m assuming that the “real" value of Kd that you are quoting is the concentration of the ligand at which the receptor is half saturated under the experimental conditions where the receptor is at much smaller concentration than the total ligand.
>> 
>> If you use that value to calculate the expected ∆G value from that Kd value you get -28922 J/mole., less than a 3-fold difference from the result you got form umbrella sampling.
>> 
>> So the problem is that the prediction of Kd from free energy is very sensitive to variations in free energy - basically a less than 3-fold difference in free energy in your case is associated with and 8 orders of magnitude difference in Kd values.
>> 
>> So your problem is that the free energy you got from the umbrella sampling may be off by a factor of 2-3 fold, but that causes a huge difference in the inferred Kd value.
>> 
>> So in answer to your original question, unless you know that the estimate of free energy is very accurate, the estimate of Kd can be ferociously incorrect.  Were you able to calculate a confidence interval for the value of the free energy that you got form the PMF curve?
>> 
>> Warren Gallin
>> 
>> 
>>> On Mar 1, 2015, at 10:08 PM, Alexander Law <alexander.law at pg.canterbury.ac.nz> wrote:
>>> 
>>> Great thanks, I got a value from the PMF curve as -18.3 kcal/mol (-76600 J/mol) and I did the calculation and I got an absurd result:
>>> 
>>> Kd = e^(∆G/(RT))
>>> 
>>> Kd= e^(-76600/(83144*298.15)) = 3.8032908e-14 M
>>> 
>>> The real value is 0.76 uM...
>>> 
>>> Where have I gone wrong?
>>> 
>>> Many Thanks
>>> Alex
>>> ________________________________________
>>> From: gromacs.org_gmx-users-bounces at maillist.sys.kth.se [gromacs.org_gmx-users-bounces at maillist.sys.kth.se] on behalf of Warren Gallin [wgallin at ualberta.ca]
>>> Sent: Monday, March 02, 2015 11:38 AM
>>> To: gmx-users at gromacs.org
>>> Subject: Re: [gmx-users] Umbrella Sampling result
>>> 
>>> The equation you refer to is:
>>> 
>>> ∆G=RTln(Kd)  [The extra factor in the Wikipedia entry is unnecessary, since  there is no actual unit for the “concentration terms” ; the relevant number is activity, which is dimensionless and which approaches the numerical value of the concentration when the concentrations are small.]
>>> 
>>> So there is no concentration term to consider.
>>> 
>>> Warren Gallin
>>> 
>>>> On Mar 1, 2015, at 2:27 PM, Alexander Law <alexander.law at pg.canterbury.ac.nz> wrote:
>>>> 
>>>> Dear gmx-users
>>>> 
>>>> Is it possible to produce a valid dissociation constant value from gibbs free energy value produced from umbrella sampling?
>>>> 
>>>> The equation is given at the bottom of the this wikipedia page:
>>>> 
>>>> http://en.wikipedia.org/wiki/Binding_constant
>>>> 
>>>> Is the concentration term vital since the ligand and the protein at a 1:1 mol ratio?
>>>> 
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> 
> -- 
> Felipe Merino
> Max Planck Institute for Molecular Physiology
> Department of Structural Biochemistry
> Otto-Hahn-Str. 11
> 44227 Dortmund
> Phone: +49 231 133 2306
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