logD - Anomolous Behavior?

Why does the logD of compound continue to change dramatically even after the changes in % ionization are very small. I have seen the following formula for calculating logD (basic compound): logD = logP - log(1+10^pKa-pH).





I can see from this formula why this happens but the results where pH is >3 units from the pKa dont seem to be chemically meaningful. I see similar behavior in your implementation of logD. Are there any plans to modify this calculation so it returns more meaningful results?

Dear Carl,





I think counter ions and support electrolytes may have enhanced effect on the logD value.


Simple models usually do not take into account the effect of counter ions. Our logD calculator contains an option for handling counter ions.





You can find more details about our counter ions –logD model:


http://www.chemaxon.com/conf/Prediction_of_distribution_coefficient_using_microconstants.pdf





For example:





Ethanamine "CCN" has pKa =10.2.


I calculated the logD-pH distribution for two different counter ion concentrations:


[Na+]=0.1 mol/l , [Cl-]=0.1mol/l


[Na+]=0.25 mol/l , [Cl-]=0.25 mol/l





See the attached pictures.





So increasing the counter ion concentration results in dumping of the logD decrease.








Please explain what do you mean by

Quote:

more meaningful results

Thank you


Jozsi

With a pKa of 10.5 I would expect the hydropbicity (or logD) to change little after pKa-3. However, the logD continues its rapid decrease well below pKa-3. The change in percent ionization between pH 7.5 and pH 7.4 is less than 0.026% but the logD decreases by 0.08 units. Compare this to the logD change between pH 9.5 and 9.6 where the % ionization changes by 2.09% and the logD also changes by 0.08 units.





The change in % ionization is 100x greater at the higher pH but the change in logD is the same for both pHs. The result is the logD continues to decrease even after the compound is essentially fully ionized. I would expect the logD to stop decreasing when the molecule stops changing its ionzation state. This is true when you look at the high pH end (pH=pKa+3) of the logD curve and should also be reflected at the low end.





I believe this behavior is due to the behavior of logarithimic functions with small numbers.





Am I missing something?

Anyone know if this behavior of logD vs pH has chemical significance? Anyone have a reference describing this behavior and how to interpret it?





logD vs. pKa (% ionization)


With a pKa of 10.5 I would expect the hydropbicity (or logD) to change little after pKa-3. However, the logD continues its rapid decrease well below pKa-3. The change in percent ionization between pH 7.5 and pH 7.4 is less than 0.026% but the logD decreases by 0.08 units. Compare this to the logD change between pH 9.5 and 9.6 where the % ionization changes by 2.09% and the logD also changes by 0.08 units.





The change in % ionization is 100x greater at the higher pH but the change in logD is the same for both pHs. The result is the logD continues to decrease even after the compound is essentially fully ionized. I would expect the logD to stop decreasing when the molecule stops changing its ionzation state. This is true when you look at the high pH end (pH=pKa+3) of the logD curve and should also be reflected at the low end.





I believe this behavior is due to the behavior of logarithimic functions with small numbers.

Dear Carl,





The logD-pH curve changes between the logP(n) of the neutral form ‘CCN’ and the logP(i) of the ionized forms 'CC[NH3+]'.


In the attached excel file you can find two calculated logD curves.


The red and the blue curves were calculated with two different logP(i) parameters. This was the only difference between the two calculations.





I don’t have experimental value for these logD-pH curves. In spite of this I think that the blue curve is better (more meaningful) than the red one.





From this can be seen that the logarithmic logD model works well if the value of the logP(i) parameter adjusted correctly. (logP(i) is a governing parameter beside of the calculated pKa and logP(n))








Our logD model contains default logP(i) values, which were obtained from experimental results.


I think we need to refresh (change or supplement) these parameters.





Jozsi

I'm trying to understand the logD behavior of 2 compounds but I need to specify their pKa's, not let the software calculate them. Is is possible for you to calculate the logD profiles of the 2 compounds below (mol files attached) using the specified pKas?





nicotinic acid - pKa1 (acidic) 5.2 pKa2 (basic) 2.6


p-aminobenzoic acid - pKa1 (acidic) 6.1 pKa2 (basic) 2.3

Dear Carl,











Specifying of two macro pKa values are not sufficient for calculating the logD of ampholytes (PABA and nicotinic acid). At least one more micro pKa value is important. Approximate calculation is of course, can be done.





Please study this review “Lipophilicity profiles of Ampholytes” : Pagliara et al. Chemical Reviews, 1997, Vol. 97, No.8








I found these pKa values:


Nicotinic acid pKa (ring N) is about 5.0


PABA acidic pKa is about 5.0





Jozsi

I cannot tell if the change in logP(i) used in the Excel spreadsheet causes a better match between changes in logD and the ionization state of molecule unless you specify the pKa that was used.





Please specify the pKa of the molecule so I can see how the logD follows the %ionization.





Thanks for your help with this.





Regards,





Carl

Jozsi wrote:

Dear Carl, The logD-pH curve changes between the logP(n) of the neutral form ‘CCN’ and the logP(i) of the ionized forms 'CC[NH3+]'. In the attached excel file you can find two calculated logD curves. The red and the blue curves were calculated with two different logP(i) parameters. This was the only difference between the two calculations. I don’t have experimental value for these logD-pH curves. In spite of this I think that the blue curve is better (more meaningful) than the red one. From this can be seen that the logarithmic logD model works well if the value of the logP(i) parameter adjusted correctly. (logP(i) is a governing parameter beside of the calculated pKa and logP(n)) Our logD model contains default logP(i) values, which were obtained from experimental results. I think we need to refresh (change or supplement) these parameters. Jozsi

Hi,

Quote:

Please specify the pKa of the molecule so I can see how the logD follows the %ionization.

"CCN" has pKa =10.2.





(Draw the structure into the Marvin and calculate the pKa.)








Jozsi

Now that I know the pKa, I agree the blue curve appears more realistic. The changes in logD more closely mirror the changes in % ionization. Do you think comparing the logD profile to the % ionization curve could be used to estimate appropriate logP(i) values?

Jozsi wrote:

Hi, Quote: Please specify the pKa of the molecule so I can see how the logD follows the %ionization. "CCN" has pKa =10.2. (Draw the structure into the Marvin and calculate the pKa.) Jozsi

Hi,

Quote:

...could be used to estimate appropriate logP(i) values?

Yes. logD=logP(i) since at low pH value the amine will be fully protonated.








Jozsi

Hi Jozsi,





Does Chemaxon have any plans to investigate the use of comparing the logD profile to % ionization curve to improve estimates of logP(i)? If so, please keep me informed of any progress.





Thanks





Carl

Jozsi wrote:

Hi, Quote: ...could be used to estimate appropriate logP(i) values? Yes. logD=logP(i) since at low pH value the amine will be fully protonated. Jozsi

Hi,

Quote:

...comparing the logD profile to % ionization curve to improve estimates of logP(i)?

Yes, if experimentally determined logD-pH curve available then we apply this method to extract logP(i) values.








Could you sketch the logD-pH curve of the "CCN” what you would consider to be fine from "chemical point of view"? You can use the Excel and any dummy values for this purpose. I am just wondering the characteristic of your "dream" curve.


I have attached the logD-pH points of our curve. Copy these data points into the Excel and then modify the logD values as you think.








pH logD


0.00 -3.72


0.50 -3.72


1.00 -3.72


1.50 -3.72


2.00 -3.72


2.50 -3.72


3.00 -3.72


3.50 -3.72


4.00 -3.71


4.50 -3.71


5.00 -3.71


5.50 -3.69


6.00 -3.65


6.50 -3.53


7.00 -3.29


7.50 -2.92


8.00 -2.47


8.50 -2.00


9.00 -1.52


9.50 -1.07


10.00 -0.70


10.50 -0.46


11.00 -0.34


11.50 -0.29


12.00 -0.28


12.50 -0.27


13.00 -0.27


13.50 -0.27


14.00 -0.27








Thanks.





Jozsi

Hi Jozsi,





Could you adjust the logP(i) in this example until the logD profile more closely matches the % ionzation at pKa-3 and repost the spreadsheet? This is where the model breaks down (in my opinion) for both acids (pKa+3) and bases (pKa-3). See attached spreadsheet.





Please inlcude the logP(i) estimates used for all cases in the reposted spreadsheet.





Carl

Jozsi wrote:

Hi, Quote: ...comparing the logD profile to % ionization curve to improve estimates of logP(i)? Yes, if experimentally determined logD-pH curve available then we apply this method to extract logP(i) values. Could you sketch the logD-pH curve of the "CCN” what you would consider to be fine from "chemical point of view"? You can use the Excel and any dummy values for this purpose. I am just wondering the characteristic of your "dream" curve. I have attached the logD-pH points of our curve. Copy these data points into the Excel and then modify the logD values as you think. pH logD 0.00 -3.72 0.50 -3.72 1.00 -3.72 1.50 -3.72 2.00 -3.72 2.50 -3.72 3.00 -3.72 3.50 -3.72 4.00 -3.71 4.50 -3.71 5.00 -3.71 5.50 -3.69 6.00 -3.65 6.50 -3.53 7.00 -3.29 7.50 -2.92 8.00 -2.47 8.50 -2.00 9.00 -1.52 9.50 -1.07 10.00 -0.70 10.50 -0.46 11.00 -0.34 11.50 -0.29 12.00 -0.28 12.50 -0.27 13.00 -0.27 13.50 -0.27 14.00 -0.27 Thanks. Jozsi

Hi,








The logP(i) value seems to be correct in our logD model.





The logP(i) <-3 is a reasonable value for the 'CC[NH3+]' ion.











Probably the next two reasons can lead to the difference between the experimental and the predicted logD curves.





1. The effect of the support electrolyte on the ionized/unionized molecule is not considered correctly


2. The accuracy of the experimental techniques is limited in case of ionized molecules.














Jozsi

Jozsi,





At pH < pKa-2 the rate of change of logD remains constant well after the rate of change of ionization state slows dramatically (see attachment). Chromatography is routinely used to estimate logP and the chromatographic retention behavior of ionized analytes follows the % ionization curve closely. logD however shows large departures from the expected change. logD continues to change at a constant rate even though the %ionization is changing very little. This does not make sense.





One way to reconcile this would be to change the slope of the logD curve so logPi is achieved at pH = pKa-3 for for bases and pH = pKa+3 for acids.





For example, in the logPi = -3.09 case you posted earlier at pH = 9.2 (pKa-1) the % ionization changes by 1.73% with a 0.1 pH unit decrease and the logD changes by 0.09. At pH = 8.2 (pKa-2) the % ionization changes by 0.2% with a 0.1 pH unit decrease and the logD changes by 0.08 units. So both a 1.73% and 0.2% change in %ionization gives a nearly equivalent change in logD. The change in logD should more closely mirror the change in ionization state of the molecule. ONe way to achieve this with the same logPi would be to increase the rate of change of logD vs pH.





Also, this discrepancy is reflected in the logD profile where the logD changes much more as the pH decreases below the pKa than when the pH increases above the pKa. It seems there should be more symmetry here. This symmetry IS observed in chromatographic retention. In fact, this behavior is used to determine pKa values from chromatographic retention.





Any thoughts?





Regards,





Carl

jszegezdi wrote:

Hi, The logP(i) value seems to be correct in our logD model. The logP(i) <-3 is a reasonable value for the 'CC[NH3+]' ion. Probably the next two reasons can lead to the difference between the experimental and the predicted logD curves. 1. The effect of the support electrolyte on the ionized/unionized molecule is not considered correctly 2. The accuracy of the experimental techniques is limited in case of ionized molecules. Jozsi

Hi,








.

Quote:

..would be to increase the rate of change of logD vs pH.

But in this case the slope D(logD)/D(pH) of the linear region would be abnormally large.





Your assumption that the logD must not change outside of the pKa+-3.0 boundaries is incorrect.


If you look at an experimental logD-pH curves of amines or acids you will see that the pKa+-4.0 or pKa +-4.5 would be a better practical boundary. Please check this on some experimental curves.

Quote:

...should be more symmetry here.

As far as the symmetry is concerned it can hold only for zwitterions. In case of simple acidic or basic compounds no symmetry exist.





Jozsi

Jozsi,





What criterion are you using regarding a "normal" slope for D(logD)/D(pH)? I'm using the slope of the %ionization curve.





In chromatography retention changes very little, if any, after pKa-3 for bases. In fact, the retention change vs. pH follows the %ionization curve closely.





What do you feel is the primary contributor to decreasing hydrophobicity with changes in pH? Conventional wisdom is the ionized form is more soluble in water than the neutral form. Once the molecule is fully ionized (for bases pKa-3) why should the hydrophobicity continue to change?





This is the key point I'm trying to understand and the main failing, in my opinion, of the logD calculations currently in use (Marvin and others):





Once the molecule is fully ionized (for bases pKa-3) why should the hydrophobicity continue to change?








Am I missing something?





Again, in chromatography (which is used to estimate logP and pKa) the retention profile of a simple acid or base follows the %ionization curve closely.





As for symmetry, I am referring to the symmetry of the % ionization curve for simple acids and bases. pKa-1 and pKa+1 gives the same change in %ionization. It seems the logD profile should show this same behavior.





Carl

jszegezdi wrote:

Hi, . Quote: ..would be to increase the rate of change of logD vs pH. But in this case the slope D(logD)/D(pH) of the linear region would be abnormally large. Your assumption that the logD must not change outside of the pKa+-3.0 boundaries is incorrect. If you look at an experimental logD-pH curves of amines or acids you will see that the pKa+-4.0 or pKa +-4.5 would be a better practical boundary. Please check this on some experimental curves. Quote: ...should be more symmetry here. As far as the symmetry is concerned it can hold only for zwitterions. In case of simple acidic or basic compounds no symmetry exist. Jozsi

Hi,

Quote:

What criterion are you using regarding a "normal" slope for D(logD)/D(pH)? I'm using the slope of the %ionization curve.

The linear region of the experimental logD-pH curve usually has unit slope or smaller.

Quote:

...Am I missing something?

I think you don't consider that the logD is a logarithmic function of hydrophobicity.








I depicted both the logD-pH and the D-pH curves. They have different characteristics. It seems that your thinking is in good agreement with the D-pH curve.











Jozsi

Not sure I agree. I'll have to think about it a bit more but both hydrophobicity (as logP) and pH are logarithmic functions. In my opinion it is this property of logarithms that is not being handled correctly in logD.





The primary problem is logD continues to change significantly when no significant physical change in the molecule is occuring.





Check what happens at pH = 99.0% ionzation (pKa+2) vs. pH = 99.9% (pKa+3) for a simple basic compound. The change in physical properties with this small change in ionization (with a 1 unit change in pH) are not expected to be significant but the logD continues to change at approximately the same rate as when ionzation changes from 50% to 90%, also a 1 unit change in pH.





This is the primary problem I see with logD.





Carl