## Re: [Apbs-users] Binding energies in apbs

 Re: [Apbs-users] Binding energies in apbs From: Domenico Gatti - 2008-01-08 05:10:01 ```Dear Nathan, ( Coulombic(AB) - Coulombic(A) - Coulombic(B) )/(internal dielectric constant) is exactly how I calculated the coulombic component of the "binding" energy, but I do not know what is the sign of this energy. Traditionally, the binding energy of a bound system is defined as the work done against the forces of the field to bring its components at infinite distance from each other. Thus, this "binding energy" is dissociative and its sign is positive (stronger binding=more positive energy). In the example of APBS tutorial the binding energy calculated by APBS is described as "associative" (-Delta(3)G in Fig. 5.1), that is as the work done against the forces of the field to bring the components of the complex together from infinite distance from each other, and its sign should therefore be negative (stronger binding = more negative energy). In my tests I used APBS to calculate the binding energy of a complex AB in different conditions in which A and B are actually bound or in which A and B are progressively more distant from each other. The result was that as A and B were progressively separated the coulombic binding energy calculated using the difference ( Coulombic(AB) - Coulombic(A) - Coulombic(B) )/(internal dielectric constant) became progressively smaller. This is what I expected if the energy calculated with this procedure is "dissociative" (more positive=stronger binding) and not "associative" as described in the tutorial. In contrast, solvation energy differences as defined in the tutorial, and as implemented in the example scripts, appear to provide a component of the "binding" energy that is certainly associative. Thus, my contention is that APBS solvation and coulombic energies are two different kinds of "binding" energies, the first being associative and the second dissociative, and therefore they should not be added. It's important to clarify this point, because on it depends the biochemical validity of the calculations. For example going to the test case of the actin-dimer, the APBS script gives a result of approximately 119 kJ/mol. Now, the important question is how this translates into a biochemical dissociation constant. Which one of the two equalities is true for the actin-dimer? 1) coulombicDeltaG(bind) = -RTln(1/Kd) (associative binding energy) 119/-5.7 = -20.9 = log(1/Kd) Kd = 10^21 M 2) coulombicDeltaG(bind)= -RTln(Kd) (dissociative binding energy) 119/-5.7 = -20.9 = log(Kd) Kd = 10^-21 M Case (1) appears to be correct based on my own testing, but it is not meaningful biochemically. Perhaps the situation could be clarified by calculating the solvation energies of the actin dimers and monomers. I tried to do it, but gave up after I ran in all kind of problems with the amber94 param library. It would be very helpful to have an APBS tutorial based on a complex for which an experimental Kd is available. This complex could be used to calibrate the coulombic and solvation energies calculated in APBS, and minimally to clarify whether these energies should be added or not. Thanks again for your help, Domenico On 1/7/08 9:31 AM, "Nathan Baker" wrote: > Hello -- > > If you calculated the Coulombic contribution as: > > ( Coulombic(AB) - Coulombic(A) - Coulombic(B) )/(internal > dielectric constant), > > where Coulombic(.) is the output from the 'coulomb' program in APBS, > then this would represent the coulombic energy of *binding*. Is that > what you were asking? > > Thanks, > > Nathan > > On Jan 5, 2008, at 10:27 AM, Domenico Gatti wrote: > >> Dear Nathan, >> Thanks! Sorry for asking you all these question in the middle of >> your grant >> writing. I did not divide the coulombic energy by the internal >> dielectric >> used in the solvation calculation, that will change the coulombic >> contribution by a factor of 2. I will rerun the calculations with a >> few >> finer grids to see if it makes a difference. For the rest I think I >> have >> done everything as you recommend (all the molecules are in the same >> positions in all the scripts, and the grid is always the same and >> centered >> on the complex; I have used your actin dimer script as a template). >> When I >> finish the new calculations I can send you my scripts and pqr files >> if you >> would like to see exactly what I am doing. In my last message, in >> reference >> to the second case I report, I mention the issue that perhaps the >> sign of >> the COULOMBIC contribution should be changed as it appears to >> represent a >> dissociation binding energy. Is that wrong? >> Thanks again, >> Domenico >> >> >> On 1/5/08 8:55 AM, "Nathan Baker" wrote: >> >>> Hello -- >>> >>> I'm sorry I haven't replied to your earlier e-mail yet; I've been >>> swamped with a grant deadline. >>> >>> These energies do seem too large and, without more knowledge of the >>> system, it's hard to say specifically why this might be. However, >>> here are a few of the common problems when binding energies are >>> calculated this way: >>> >>> (1) Grid is too coarse. Perhaps your grid resolution isn't fine >>> enough. This can be checked by running a subset of the calculations >>> at a finer grid spacing to see if the solvation energies change >>> significantly. >>> >>> (2) Coulombic energies weren't scaled properly. Did you divide your >>> Coulombic energies by the internal dielectric constant used for the >>> polar solvation energy calculations? >>> >>> (3) Parameter/surface mismatch. Which parameter sets and surface >>> definitions did you use? Along the same lines, what were your APOLAR >>> settings and radii used for those calculations? >>> >>> When the structures of A and B don't change upon complex formation, I >>> often prefer to calculate polar solvation energies directly through 3 >>> calculations: G(AB) - G(A) - G(B), where G(.) represents the total >>> electrostatic energy of a structure. When performing such >>> calculations, it's very important to ensure that A is exactly in the >>> same place on the grid as it is in AB when performing those two >>> calculations (same for B). The examples/actin-dimer test case gives >>> an example of this kind of calculation. >>> >>> Hope this helps, >>> >>> Nathan >>> >>> On Jan 4, 2008, at 11:20 PM, Domenico Gatti wrote: >>> >>>> Dear APBS Users, >>>> >>>> Being new to APBS I would really appreciate if you could tell me >>>> whether >>>> I am understanding correctly the meaning of the binding energies >>>> calculated >>>> by the various scripts. In equations 5.1, 5.2, and 5.3 of the >>>> tutorial the >>>> "Binding Free Energy" for a two component complex of molecules mol1 >>>> and mol2 >>>> is defined as an "association" binding free energy (-Delta3G of the >>>> cycle >>>> shown in Fig. 5.1), and therefore, >>>> >>>> DeltaG(bind)= -RTln(1/Kd) >>>> >>>> For example, I have used apbs to calculate the binding free energy >>>> for two >>>> monomers A and B forming the homodimer AB (from one of our X-ray >>>> structures). The following are the various components in kJ/mol with >>>> their >>>> signs as they appear in the log files: >>>> >>>> AB B A AB- >>>> B-A >>>> >>>> SOLV APOLAR 9866 4702 4710 >>>> 454 >>>> >>>> SOLV POLAR -9540 -5254 -5000 >>>> 714 >>>> >>>> COULOMBIC 362000 181000 180471 >>>> 529 >>>> ___________________________________________________________________________>>>> _ >>>> >>>> DeltaG(bind) 362326 180448 180181 >>>> 1697 >>>> >>>> >>>> 1697/-5.7 = -298 = log(1/Kd) >>>> >>>> Kd = 10^298 M >>>> >>>> >>>> >>>> This is not an isolated case in my hands. In another >>>> crystallographic >>>> complex (this time a dimeric protein (AB) that binds to a receptor >>>> C) I get >>>> the following results: >>>> >>>> ABC C AB ABC- >>>> C-AB >>>> >>>> SOLV APOLAR 15778 8115 7148 >>>> 515 >>>> >>>> SOLV POLAR -17301 -10161 -7810 >>>> 670 >>>> >>>> COULOMBIC 76928 40505 35794 >>>> 629 >>>> ___________________________________________________________________________>>>> _ >>>> >>>> DeltaG(bind) 75405 38459 35132 >>>> 1814 >>>> >>>> >>>> 1814/-5.7 = -318 = log(1/Kd) >>>> >>>> Kd = 10^318 M >>>> >>>> >>>> Clearly, I must not be interpreting correctly the signs of the >>>> energies for >>>> the various components, or perhaps I am summing things that are not >>>> supposed >>>> to be summed. For example, if I calculate the COULOMBIC contribution >>>> by >>>> using a pqr file that contains all the molecules of the complex, but >>>> separated in space by over 40 angstroms, the energy goes down to >>>> almost >>>> nothing, suggesting that the COULOMBIC component represents a >>>> "dissociation" >>>> binding free energy. As such it should be subtracted from the >>>> solvation >>>> energy rather then added (as it is in the two tables above). In the >>>> second >>>> case that would give a binding free energy of 515+670-629=556 kJ/mol >>>> >>>> 556/-5.7 = -98 = log(1/Kd) >>>> >>>> Kd = 10^98 M >>>> >>>> >>>> On the other hand, if all my signs are wrong that would become >>>> >>>> Kd = 10^(-98) M >>>> >>>> which is equally hard to believe. >>>> >>>> I would be happy to send you my scripts, logs and pdb/pqr. >>>> >>>> Thanks again for your help and Happy New Year! >>>> >>>> Best, >>>> Domenico >>>> >>>> Domenico Gatti, MD PhD >>>> Assoc. Professor >>>> Biochemistry & Mol. Biology >>>> Wayne State University School of Medicine >>>> 540 E. Canfield Avenue >>>> Detroit, MI 48201 >>>> Tel: 313-577-0620 or 313-993-4238 >>>> Fax: 313-577-2765 >>>> dgatti@... >>>> >>>> >>>> >>>> >>>> >>>> >>>> >>>> >>>> >>>> ------------------------------------------------------------------------- >>>> This SF.net email is sponsored by: Microsoft >>>> Defy all challenges. Microsoft(R) Visual Studio 2005. >>>> http://clk.atdmt.com/MRT/go/vse0120000070mrt/direct/01/ >>>> _______________________________________________ >>>> apbs-users mailing list >>>> apbs-users@... >>>> https://lists.sourceforge.net/lists/listinfo/apbs-users >>> >>> -- >>> Associate Professor, Dept. of Biochemistry and Molecular Biophysics >>> Center for Computational Biology, Washington University in St. Louis >>> Web: http://cholla.wustl.edu/ >>> >>> >>> >> >> >> > > -- > Associate Professor, Dept. of Biochemistry and Molecular Biophysics > Center for Computational Biology, Washington University in St. Louis > Web: http://cholla.wustl.edu/ > > > Domenico Gatti, MD PhD Assoc. Professor Biochemistry & Mol. Biology Wayne State University School of Medicine 540 E. Canfield Avenue Detroit, MI 48201 Tel: 313-577-0620 or 313-993-4238 Fax: 313-577-2765 dgatti@... ```