# [gmx-users] RE: Re: Binding Energy to Binding affinity (Kd) (Justin Lemkul)

Justin Lemkul jalemkul at vt.edu
Tue Oct 2 13:07:05 CEST 2012

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On 10/2/12 4:39 AM, Du Jiangfeng (BIOCH) wrote:
> Hi Justin,
>
> I used ~20 windows to sample ~2 nm pulling. I notice that the distance between the complex being increased during the pulling but not gradually. At the distance of 0-1nm, there are 70 snapshots (the distance sometime increased sometimes decreased). At the distance of 1-2nm, there are only 30 snapshots (the distance kept increasing always). At the distance more than >3nm, the distance increased as 0.3nm of each snapshot, is it normal and reliable?
>

I will assume you are using a harmonic potential (umbrella) to do the pulling.
In this case, your observations are totally normal.  When two species interact
strongly, it is harder to pull them apart, thus the spring extends further to
induce a larger force before displacement occurs.  As the restoring forces are
overcome, it is easier to move the pulled group through solution, so it makes
more steady progress as the molecules are separated.

> You mentioned "error estimate for each replicate", but what is it? How to define it?
>

g_wham has numerous options for statistical analysis.  I would encourage you to
read their full description in the g_wham paper, and at minimum, the short
description in g_wham -h.

> For the conversion of energy to Kd, I standardized every unit into international unit and then calculated the Kd value. Here I post my formula:
>
> \$ln="2.718281828459"; ## constant
> \$cal="4186"; ## convert kcal into J
> \$R="8.3144621"; #J/(mol*K) ideal gas constant
> \$mol=6.02214179*(10**23); ## mole numbers, constant
> \$procon=9.494/15; ## the protein concentration based on ions' concentration. mol/ml
>

This ends up being something like 633 M, which may well be correct based on size
of the molecular system, but seems very odd to me.

-Justin

> \$a=\$energy*\$cal/\$t/\$R; ## \$energy here is the binding energy calculated from umbrella sampling (kcal/mol)
> \$k=\$ln**\$a;
> \$kd=1/\$k *\$procon * (10**9); ## Kd vs Ka; unit is μM here.
>
> Thank you,
>
> Jiangfeng.
>
> On 10/1/12 4:36 AM, Du Jiangfeng (BIOCH) wrote:
>>
>> Dear Everyone,
>>
>> I have two questions about the conversion of binding energy to binding
>> affinity.
>>
>> I predicted the binding energy of a protein-membrane complex by umbrella
>> sampling (based on Justin's tutorial). After sampling, the binding energy
>> should be the substract of (min-max) PMF. I have repeated the simulation 12
>> times, and then I have done umbrella samplings also 12 times, then got 12
>> binding energies which varies from -200 Kcal/mol to -100kcal/mol, does the
>> value vary too much? or is it reasonable since the simulation results can be
>> different? Are those values too huge?
>>
>
> Without an explanation of how long your windows are and what the error estimate
> for each replicate is, it is impossible to answer this question.
>
>
>
>> When I tried to convert the binding energy to Kd by the formula
>> deltaG=-RTlnK, I am frustrated by the kd value. If the binding energy is
>> -100kcal/mol, the kd is calculated as 3.35e-59  ?M.  The kd is 1.77e-126  ?M
>> when binding energy is -200kcal/mol. This is impossible.  But what is going
>> wrong?
>>
>
> I think you are doing your calculations incorrectly (I obtain your values when
> using units of kcal/mol for dG but kJ/mol-K for the gas constant - note the
> mismatch), but even when done properly, the values are still unreasonable.
>
> -Justin
>

--
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Justin A. Lemkul, Ph.D.
Research Scientist
Department of Biochemistry
Virginia Tech
Blacksburg, VA
jalemkul[at]vt.edu | (540) 231-9080
http://www.bevanlab.biochem.vt.edu/Pages/Personal/justin

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