Hi Thomas,
yes I agree but let see ..., I will try it. If I compare this eventual TI
simulation (i) "Gradual deleting of restraints of NON-interacting
ligand(vdw/el)" with the another TI simulation (ii) "Of decoupling ligand
from receptor binding site without using restraints" (The very
original/basic idea of the double anihilation methodology) I think that in
(i) I have much bigger chance to obtain some meaningful results (using
reasonable simul. time) although the most probably with bigger deviations
at the end.The reason is in my opinion in differences between vdw/el
potentials and harmonic restraint potentials and with this connected
differences in sampling problems during the "TI trajectory" (full set of
lambdas). Of course that the end of such TI run ((i)) should be very
carefully treated with lambdas like (... 0.98 0.99 0.9925 0.995 0.9975 1
). So let see ...
I have very last question with regard to so called "standard state".
In previously mentioned article:
--------------------------------------------------------------------------------------
Boresch, S.; Tettinger, F.; Leitgeb, M.; Karplus, M. Absolute binding free
energies:
A quantitative approach for their calculation. J. Phys. Chem. B 2003, 107,
9535-9551.
--------------------------------------------------------------------------------------
there were derived two almost identical formulas for the analytic
calculation of dAr which is energetical change corresponding to
above described transformation (i).
dAr
(R)s***(L)v----->(R)s + (L)v
In the first one ( see equation (14) ) there is as the one parameter
volume of the system (i.e. simulation box) "V" and in the second
one ( equation (32) ) there is just "V" substituted with "V0" so called
standard volume (1660 A^3) which corresponds to average volume for one
molecule (molecular pair R+L ?) in case of standard concentration of such
molecules (pairs) 1 mol/dm^3. This is the only one difference between the
formulas 14 and 32. (I remeber that similarily also Roux used this
standard concentration in his analytic correction.)
So probably if one wants to compare calculated (TI) standard free binding
energy with the experimental one,
he has to use equation 32 (to compute dAr), where the standard volume V0
is incomporated instead of the volume of the simul box,
otherwise the calculated stand. bind. energ. is not unambiguously defined.
Am I right ?
How it is in experimental part ?
Probably is imposible to do all the experimental measurements of the
standard binding energy under standard concentration C0 = 1 mol/dm^3
also simply because some molecules might be too big (with dimension higher
than cca (1660^1/3) = 12 A ) for such concentration.
So the dissociation constant Kd obtained from the experiment which is done
under some concentration (of the receptor ligand pairs) C is then
transformed (if C != C0) to the dissociation constant Kd_0 which is the
dis. constant related to the standard concentration (of ligand/receptor
pairs) C0. Am I right here ?
This is a new moment for me as until now I just considered the free
binding energy as the necessary work which has to be done to
divide given complex LR in solution into fully (infinity distance)
separated R and L pair without any obvious explicit dependence on volume.
Obviously the infinite separation is not the ideal "standard state" for
the real (experimental) word.
This new context "volume dependence of dAr and thus volume dependence of
the whole separation energy change"
was also partially the reason for suggesting to calculate dAr directly
using additional TI run. Here the volume dependence is not so "obvious"
but is there of course and especially for the lambdas near to 1 (small
constraints) will be spectrum of practically sampled energies in smaller
box different from those in bigger box as in bigger box the sufficiently
weak constraints allow for bigger deviations from the equilibrium values
(of distance, angle restraints) and thus for more diverse energy
spectrum. So I assume that I should obtain here
(if the TI run convergate in reasonable time and reasonable sampling of
lambda) some number close to the theoretical result
defined by eq. (14) (that with the volume of the simul. box "V"). This
direct calculation might be potentially useful in cases when one
uses more complex restraint network (e.g. in case of longer flexible
ligand) so that the derivation of the analytical experession of dAr
in such case might be very complicated...
Until now I have used just MM/PBSA methodology to calculate binding free
energies and so I never encounter this "volume" aspect.
If I am not wrong this is because the MM/PBSA methodology attempts simply
to calculate energy change connected with the total separation
(corresponding to infinite distance) ligand and receptor because it works
separately with energy of the complex,
energy of the ligand and energy of the receptor obtaining binding energy
as the: G(complex) - G(L)- G(R) so here is no volume dependence
and the calculated dG is really "Absolute" while in case of TI is
separation energy change volume/concentration dependent (as well as in
case of experiment).
If I am right here the results obtained from MM/PBSA cannot be directly
connected with experiment via: dG_bind_calculated =
-R*T*ln(Kd_0_experimental) as the Kd_0_experimental is related to the
standard concentration (of ligands and receptors) C0 where the maximal
separation distance of two molecules is just few angstroms. Am I right
here ?
And what about the direct "measurement" of the work which must be done to
pull the ligand smoothly from the receptor binding site
(PMF methods) ? Here probably the volume dependence is also incorporated
implicitly as the volume of the box defines the maximum available
separation distance of the ligand and the receptor. Am I right ? So
probably also here the dG_bind_calculated could not be directly compared
with -R*T*ln(Kd_0_experimental) unless is sufficiently modified to
correspond the standared concentration used in experiment. Am I right ?
Thank you very much again for your support you gave me until now and
eventually also for your next comments.
I am sorry for such probably very "trivial" questions and maybe some
nonsence thaughts. As you can see I am really not an expert here and would
like just to understand a bit ... I think it is important for anyone who
would like to put theoretical results in the context with experimental
ones properly.
Best wishes,
Marek
Dne Thu, 10 May 2012 09:33:34 +0200 <steinbrt.rci.rutgers.edu> napsal/-a:
> Hi Marek,
>
> I never tried what you describe. It is in principle a good idea, but
> would
> produce enormous sampling problems:
>
> The non-interacting, non-restrained ligand has the entire box as
> accesible
> phase space, so for a converged simulation it would have to repeatedly
> cover every spot therein. This is almost guaranteed not to happen with
> even the smallest restraints, so in terms of phase space overlap between
> initial and final state, this is about the worst case possible in a free
> energy simulation. So, yes you can try running that, but I doubt it will
> give a meaningful result.
>
> Thomas
>
> On Wed, May 9, 2012 11:43 am, Marek Maly wrote:
>> Thanks Thomas !
>>
>> I have just the last particular question.
>>
>> In spite the fact that the very last part of the ligand decoupling from
>> the receptor (using restraints):
>>
>> dAr
>> (R)s***(L)v----->(R)s + (L)v
>>
>>
>> (i.e. calculation of the free energy change connected with the
>> "anihilation" of the restraints
>> which are applied on already non-interacting (vdw/el) ligand) is
>> possible
>> to calculate analytically,
>> I would like to verify it numerically by TI with this setup:
>>
>> V0 = Receptor + Ligand (in water) where all the ligand atoms are DUMMY
>> atoms.
>> Ligand is restrained in V0 with target restraints (defined in the RST
>> file)
>> (ifsc=0, scmask='', crgmask='')
>> dvdl_norest=0
>>
>> V1 = Receptor + Ligand (in water) where all the ligand atoms are DUMMY
>> atoms.
>> Ligand is free to move in V1 (no restraints)
>> (ifsc=0, scmask='', crgmask='')
>> dvdl_norest=0
>>
>>
>> Might it be correct for the given purpose ?
>>
>> Thank you very much again !
>>
>> Best wishes,
>>
>> Marek
>>
>>
>>
>>
>>
>>
>> Dne Wed, 09 May 2012 17:08:52 +0200 <steinbrt.rci.rutgers.edu>
>> napsal/-a:
>>
>>> Hi,
>>>
>>>> Regarding the scaling constant (which "preventively" scale restraints)
>>>> when SC pot. are used: 1/lambda versus 1/(1-lambda) maybe it is not
>>>> the "full typo" as this is probably dependent on simulated process.
>>>> For
>>>> the ligand "disappearing" scaling constant
>>>> is 1/(1-lambda) for the opposite process (appearing) perhaps 1/lambda
>>>> is
>>>> used. This would correspond to the disappearing/appearing
>>>> SF-potentials where in case of disappearing multiplicative constant
>>>> (1-lambda) is used and in case of appearing it is just lambda.
>>>
>>> True, maybe that was my idea when writing it. However, I think only the
>>> setup in which whole restrained ligands disappear has ever been used.
>>>
>>>> #1 - appearing of the restraints while ligand is fully (vdw/el)
>>>> interacting with receptor during this process
>>>>
>>>> Here I would use this approach:
>>>>
>>>> V0 = Receptor + Ligand (in water)
>>>> no restraint is applied in V0 ( ifsc=0, scmask='',crgmask='' )
>>>> dvdl_norest=0
>>>>
>>>>
>>>> V1 = Receptor + Ligand (in water)
>>>> Ligand is restrained in V1 with target restraints (defined in the RST
>>>> file) (ifsc=0, scmask='',crgmask='')
>>>> dvdl_norest=0
>>>
>>> yes, that is how I would do it. This linearly increases the restraint
>>> strength with lambda, which is what you want.
>>>
>>>> #2 Decoupling (vdw/el) the fully restrained ligand.
>>>>
>>>> Here I would use this setup:
>>>>
>>>> V0 = Receptor + Ligand (in water)
>>>> Ligand is restrained in V0 with target restraints (defined in the RST
>>>> file) (ifsc=1, scmask=':LIGAND',crgmask='')
>>>> dvdl_norest=1
>>>>
>>>>
>>>> V1 = just Receptor (in water)
>>>> ( ifsc=1, scmask='',crgmask='' )
>>>> dvdl_norest=1
>>>>
>>>
>>> that is also right, but I think dvdl_norest can be left out in V1, it
>>> has
>>> no real effect there. It is necessary in V0. In this setup, the ligand
>>> will decouple, but will still be restrained with unchanged strength.
>>>
>>>> Anyway the second possibility for V1 might be here:
>>>>
>>>> V1 = Receptor + Ligand (in water) where all the ligand atoms are DUMMY
>>>> atoms.
>>>> Ligand is restrained in V1 with target restraints (defined in the RST
>>>> file) (ifsc=1, scmask=':LIGAND' or scmask='' ???, crgmask='')
>>>> dvdl_norest=1
>>>>
>>>
>>> No, that is not useful. Dummy atoms and softcore are mutually exclusive
>>> ways to do the same thing and they cannot be mixed like this. Stick to
>>> the
>>> first way you suggested.
>>>
>>> Kind Regards,
>>>
>>> Thomas
>>>
>>> Dr. Thomas Steinbrecher
>>> formerly at the
>>> BioMaps Institute
>>> Rutgers University
>>> 610 Taylor Rd.
>>> Piscataway, NJ 08854
>>>
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>>
>>
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>
>
> Dr. Thomas Steinbrecher
> formerly at the
> BioMaps Institute
> Rutgers University
> 610 Taylor Rd.
> Piscataway, NJ 08854
>
> _______________________________________________
> AMBER mailing list
> AMBER.ambermd.org
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>
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> (20120509) __________
>
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>
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>
>
>
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Received on Thu May 10 2012 - 16:00:03 PDT
