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

Du Jiangfeng (BIOCH) j.du at maastrichtuniversity.nl
Tue Oct 2 10:39:27 CEST 2012

```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?

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

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

\$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

```