[gmx-users] Binding Energy to Binding affinity (Kd)

[Du Jiangfeng (BIOCH)]

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?

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 appreciate any reply.

Thanks,

Jiangfeng Du, PhD Student
Cardiovascular Research Institute Maastricht
Department of Biochemistry
P.O. Box 616
Mobile: [phone]
FAX: [phone]
6200 MD Maastricht
The Netherlands

[Justin Lemkul]

Post by Du Jiangfeng (BIOCH)
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.

Post by Du Jiangfeng (BIOCH)
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
--
========================================

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

========================================

[Thomas Schlesier]

You could use 'constraint' pull-mode instead of the 'umbrella' mode.
Than the distance would change gradually and you won't observe the
fluctuations in the distance.

greetings
thomas

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.

Hi Justin, it is right I am using umbrella pulling. Now here is another
hurdle in front of me: How to select the snapshots for umbrella samples?
Since the distance between two groups went higher or lower at the beginning
of the pulling. For example, during the pulling simulation, the distance
0.46 0.42 0.46 0.43 0.44 0.42 0.45 0.44 0.43 0.45 0.44 0.45 0.43 0.44 0.44
0.54 0.52 0.63 0.65 0.72 0.8 0.92 1.2 1.5 (nm) .....
I suppose it doesn't matter which snapshots to be chosen, as long as the
snapshots can indicate a good spacing, the PMF result always should be same,
right?

You need reasonable spacing and sufficient sampling in each window to allow for
proper overlap of the umbrella potentials.
-Justin