Hello –

It is ***very*** difficult to converge Coulombic interactions with finite difference calculations; hence the approach of:

· Using exactly the same grid setups for multiple steps of calculation to cancel out artifacts

· Using the solvation free energy cycle we discussed earlier with analytic Coulombic contributions

I’m fairly sure your results are not converged at 0.25 A grid spacing, hence the difference in potential values. I’d recommend exploring this with a simpler system – you might be interested in the point-pmf (http://apbs.svn.sourceforge.net/viewvc/apbs/trunk/examples/point-pmf/) or ion-pmf (http://apbs.svn.sourceforge.net/viewvc/apbs/trunk/examples/ion-pmf/) examples included with APBS that illustrate this phenomenon.

Thanks,

__________________________________________________ **Nathan Baker**

Pacific Northwest National Laboratory

Tel: +1-509-375-3997

http://nabaker.me

**From:** tj [mailto:jain.tush@gmail.com] **Sent:** Friday, June 15, 2012 6:58 PM**To:** apbs-users@googlegroups.com**Cc:** tj; (apbs-users@lists.sourceforge.net)**Subject:** Re: [apbs-users] Binding energy calcuation via two thermodynamic cycles...

Hello,

I did a follow up calculation to understand the coulomb calculations for the second question in my earlier post. Specifically, I carried out uniform dielectric calculations for the complex and the components of the complex, always centering the grid on the complex molecule. I also calculated the coulomb energies using the coulomb program. From these calculations, I estimated two coulomb binding energies by subtracting the results for the components from those for the complex.

I have plotted the results below. The 5 points are for 5 different conformations of the system. The calculations were done using APBS 1.3 at three grid resolutions: 0.25, 0.50, 0.60. The line of slope 1 is to guide the eye. The correlation between the two methods is very good. However, there is a offset that does not seem to depend on the grid resolution.

Is there a numerical reason for the offset? Is this to be expected?

Thanks.

On Thursday, June 14, 2012 10:55:35 AM UTC-7, Baker, Nathan wrote:

Hello –

The answers to your questions are:

(1) Yes.

(2) Yes, if the grids are sufficiently high resolution.

Thanks,

__________________________________________________ **Nathan Baker**

Pacific Northwest National Laboratory

Tel: +1-509-375-3997

http://nabaker.me

**From:** tj [mailto:jain.tush@gmail.com] **Sent:** Thursday, June 14, 2012 10:07 AM**To:** apbs-users@googlegroups.com**Cc:** (apbs-users@lists.sourceforge.net)**Subject:** Re: [apbs-users] Binding energy calcuation via two thermodynamic cycles...

Thanks for the reply, Nathan.

I have a couple of related questions, before I setup the calculations on a finer grid:

1) So, if the convergence was not an issue, the two approaches are expected to yield the same answer?

2) Is the delta Coulomb calculated using the coulomb program expected to be the same as the uniform_dielectric_complex - (uniform_dielectric_partner1 + uniform_dielectric_partner2) as long as the grids are "exactly" the same for the all the three uniform dielectric calculations?

Thanks.

On Wednesday, June 13, 2012 7:44:11 PM UTC-7, Baker, Nathan wrote:

Hello –

Differences like these are almost always due to lack of convergence of the results with respect to grid spacing. Given the size of the systems and the relatively high charge density of actin, I’m guessing that’s the issue here as well.

Thanks,

__________________________________________________ **Nathan Baker**

Pacific Northwest National Laboratory

Tel: +1-509-375-3997

http://nabaker.me

**From:** tj [mailto:jain.tush@gmail.com] **Sent:** Wednesday, June 13, 2012 11:44 AM**To:** apbs-users@googlegroups.com**Subject:** [apbs-users] Binding energy calcuation via two thermodynamic cycles...

Hi,

I have a question on calculating the total electrostatic binding energy using APBS, but via two thermodynamic routes:

Route1 : Calculate the solvation contribution(as in print statements for the FKBP/1d7i-dss example) + coulomb calculation(using the coulomb program). e.g.

# CHANGE IN SOLVATION ENERGY UPON BINDING

print elecEnergy complex-solv-fine - complex-ref-fine - dss-solv-fine + dss-ref-fine - 1d7i-solv-fine + 1d7i-ref-fine end

Route2 : Calculate difference of charging energies as in print statements for examples actin-dimer. e.g.

# COMBINE TO GIVE BINDING ENERGY

print elecEnergy complex - mol2 - mol1 end

In the case of the FKBP/1d7i-dss example, the two methods return approximately the same value. Details of the output produced are below:

For the example 1d7i-1dss

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

Command

-----------

apbs apbs-mol.in

Thermodynamic Cycle based on Solvation/Desolvation Energies:

------------------------------------------------------------

Coulomb complex : -1.330929222200e+05 / 2(pdie) - Using the coulomb program

Coulomb dss-min : -4.251892874134e+02 / 2(pdie)

Coulomb 1d7i-min: -1.326437989481e+05 / 2(pdie)

Binding Coulomb Energy: -11.97036 (Coulomb complex - Coulomb dss-min - Coulomb 1d7i-min)

Binding Solvation Energy : 14.42500 (complex-solv-fine - complex-ref-fine - dss-solv-fine + dss-ref-fine - 1d7i-solv-fine + 1d7i-ref-fine)

Binding Electrostatic Energy1 : 2.45464 (Binding Solvation Energy + Binding Coulomb Energy)

Thermodynamic Cycle based on Charging/Discharging Energies:

-----------------------------------------------------------------------

Binding Electrostatic Energy2 : 2.19264 => (complex-solv-fine - dss-solv-fine - 1d7i-solv-fine)

Comparison:

-----------

Binding Electrostatic Energy1 ~ Binding Electrostatic Energy2

However, for the actin-dimer example, the values are not close at all:

For the example actin-dimer

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

Command

-----------

apbs apbs-mol-auto.in

Thermodynamic Cycle based on Solvation/Desolvatin Energies:

-----------------------------------------------------------------------

Coulomb complex : -8.212523932986e+05 / 2(pdie) - Using the coulomb program

Coulomb mol2 : -4.121924924143e+05 / 2(pdie)

Coulomb mol1: -4.122022764715e+05 / 2(pdie)

Binding Coulomb Energy: 15.71188E+02 (Coulomb complex - Coulomb dss-min - Coulomb 1d7i-min)

Binding Solvation Energy : 1.054579051270E+02 => (complex - complex-ref - mol1 + mol1-ref - mol2 + mol2-ref)

Binding Electrostatic Energy1 : 16.7665E+02 (Binding Solvation Energy + Binding Coulomb Energy)

Thermodynamic Cycle based on Charging/Discharging Energies:

------------------------------------------------------------------------

Binding Electrostatic Energy2 : 1.048683060915E+02 => (complex - mol1 - mol2)

Comparison:

--------------

Binding Electrostatic Energy1 != Binding Electrostatic Energy2

In the second case the agreement is not good while in the first case it is quite good. I realize that the first route is what is usually recommended because of the grid cancellations of the self-energies. However, I have seen the binding electrostatic energy calculation done using the the second route in several examples. From my understanding of the apbs-smol-auto.in(actin-dimer exmaple), the grid is centered on the complex for all the three calculations, so I am not sure, if the difference arises because of grid artefacts.

Thanks for your help.