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The dependence of the distribution coefficient (logD) upon pH 5PY022 – Medicines In Development and Use

Abstract The partition coefficient (P) or distribution coefficient (D) is a ratio that compares the solubilities and distribution of a solute between two immiscible solvents. It gives an indication of whether that substance is lipophilic (tends towards the non-polar phase) or hydrophilic (favours the water). If log P is less than 0, the drug partitions more into hydrophilic areas whereas if log P is greater than 0, the drug partitions more into lipophilic areas. The aim of this experiment was investigating and determining the effect of the pH of a solution on the distribution coefficient of a drug, in this case benzoic acid. In order to carry out this investigation, a pre-prepared 0.001998 mol dm -3 stock solution of benzoic acid in ethyl acetate was used to prepare standard solutions of varying concentrations whose absorbances were measured to produce a calibration plot. A biphasic liquid of stock solution and pH 6.0 buffer was produced and the absorbance was then recorded and used to calculate the distribution coefficient of benzoic acid at this pH. The process then repeated using pH 7.0 buffer. The pH 6.0 buffer solution had resulted in a higher log D value than the pH 7.0 buffer solution and pH 8.0. This was because the aqueous phase at pH 7.0 was relatively more alkaline than at pH 6.0 and so more acid molecules were ionised and so partitioned more into the aqueous phase at pH 7.0. The outcome of this experiment was therefore determining that benzoic acid is more lipophilic at pH 6.0 than at pH 7.0 and pH 8.0.

Introduction The partition coefficient (P) or distribution coefficient (D) is essentially defined as the ratio of concentrations of an organic solute in two immiscible solvents (usually water, and a hydrophobic organic solvent such as ethyl acetate or octanol) in a liquid biphase at equilibrium, as mentioned by (Speight, 2017), and provides a numerical illustration into the lipophilicity of the molecule being tested. Lipophilicity is an important physicochemical property that needs to be tested for any potential new drug and, as both (Stolerman, 2010) and (Kerns EH., Di L., 2008) [1] state, is essentially how much an organic compound tends to partition into a non-polar medium compared to an aqueous medium. However, the key difference between these two concepts is that log P (the logarithm of the partition coefficient) is only true for compounds that cannot ionise, whereas both (Scherrer and Howard, 1977) and (Ahuja and Dong, 2005) mention that log D (the logarithm of the distribution coefficient) accounts for both the un-ionised and ionised forms (at a specified pH) in the aqueous layer while the organic layer consists of only the unionised form of the compound. This means that the pH of the aqueous layer therefore impacts LogD (Reijenga et al., 2013) [1] (termed the pH partition hypothesis), which is buffered with the sole purpose of preserving it at a selected pH value so as to not substantially alter the solution’s ambient pH when a compound is added to it (Wang et al., 2017) [1]. LogD is therefore the more useful analysis tool of the two because the pH of the solution is taken into account so is a vital component in the evaluation of how a drug behaves in different biological environments that have different pH values, which allows it to be used in the investigation as to how drugs distribute between different environments in the body.

The partition coefficient and distribution coefficient give an indication of whether the substance in question is lipophilic (and so tends towards the hydrophobic phase) or hydrophilic (so favours the aqueous phase). This is because drugs with a higher partition coefficient (logP > 0 or P > 1) usually partition into hydrophobic/lipophilic areas such as phospholipid bilayer cell membranes. On the other hand, drugs with a lower partition coefficient (logP < 0 or P < 1) normally stay in hydrophilic or aqueous regions like the blood (Wang et al., 2017) [2]. But when logP = 0 (or P = 1), the compound is similarly apportioned between the aqueous and organic layers. Optimum bioavailability is when 0 < LogP < 3. Therefore, a drug should not have too low a logD value, and certainly should not be a negative value, as this means it will stay in the aqueous region (such as the blood) when it will need to transition into the non-polar region (namely through the cell membrane bilayer). Conversely, a drug’s logD value should not be too high as it will need to go back into the blood after serving its function within the cell. The Beer-Lambert law indicates that for a certain solute molecule with the absorption measured (at a specific wavelength), absorbance will directly correlate to the concentration of said solute and that molar absorption is constant (Weast R.C., 1975). Molar absorptivity is essentially how much, at a certain wavelength of light, a compound is able to absorb light. The Beer-Lambert Law is illustrated below: A λ = εcl

Aλ = Absorbance (AU) at a specified wavelength of light (λ) ε = Molar absorption coAAAAAAAefficient (mol-1dm3cm-1) c = Concentration (mol dm-3) l = Path length of the cell used (cm)

Methods A pre-prepared stock solution consisting of 244 mg benzoic acid dissolved in 1 dm 3 of ethyl acetate (resulting in a benzoic acid concentration of 0.001998 mol dm -3) was used to prepare a set of four stock solutions at room temperature, each varying in concentration, using micropipettes and stoppered tubes through the following protocol: Tube no. Volume stock solution, μl Volume ethyl acetate, μl Total volume, μl

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1

2

3

4

5

0

400

800

1200

1600

3000

3000

2600

2200

1800

1400

0

3000

3000

3000

3000

3000

3000

Table 1: the different volumes required to prepare four standard solutions of benzoic acid dissolved in ethyl acetate from a 0.001998 mol dm-3 stock solution The absorbance of each standard solution was then obtained using a silica cuvette and a spectrophotometer set at an absorption wavelength of 270 nm, and the data obtained was then processed into a calibration plot. In order to determine the D value at pH 6.0, 5 cm 3 of pH 6.0 buffer.0 (37% 0.1 mol dm -3 citric acid and 63% 0.2 mol dm-3 disodium hydrogen phosphate v/v) and an equal volume of the benzoic acid stock solution were transferred into a 30 cm 3 sample tube using Finn pipettes and stirred using a magnetic stirrer. This was done for 5 minutes and then allowed to partition for 3 minutes until two clearly separate layers had formed. A small sample of the top ethyl acetate layer was transferred into the silica cuvette (cell) provided and the solution’s absorbance was then determined. The same procedure was repeated in order to obtain another absorbance value, but instead using a buffer solution at pH 7.0 (18% 0.1 mol dm-3 citric acid and 82% 0.2 mol dm-3 disodium hydrogen phosphate v/v).

Results Part 1: Calibration plot Moles benzoic acid = (244 mg / 1000) / 122.123 g mol -1 = 0.001998 mol [Benzoic acid] = 0.001998 mol / 1.00 dm3 = 0.001998 mol dm-3 Tube no.

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1

2

3

4

5

[Benzoic acid] (c), mol dm-3

0

0.000266

0.000533

0.000799

0.001066

0.001998

Absorbanc e at 270nm (Abs), AU

0

0.349

0.562

0.938

1.077

1.800

Table 2: the effect of changing benzoic acid concentration on the absorbance of the solution

Absorbance at 270nm (Abs), AU

[Benzoic acid] in ethyl acetate vs. Absorbance at 270nm 2.000 1.800 1.600 1.400 1.200 1.000 0.800 0.600 0.400

f(x) = 961.57 x

0.200 0.000 0.00000

0.00050

0.00100

0.00150

0.00200

[Benzoic acid]ethyl acetate (c), mol dm-3 Figure 1: calibration plot showing the effect of changing concentration on absorbance of the solution

A 270nm = εcl ε = 961.57 mol-1dm3cm-1 (from calibration plot) Part 2: Determining the concentration of benzoic acid at pH 6.0 Absorbance at pH 6.0: 1.099 AU [Benzoic acid]ethyl acetate after partitioning: c = A/εl = 1.099/(961.57 x 1) = 0.001142922512 mol dm-3 Part 3: Determining the concentration of benzoic acid at pH 7.0 Absorbance at pH 7.0: 0.182 AU [Benzoic acid]ethyl acetate after partitioning: c = A/εl = 0.182/(961.57x1) = 0.0001892737918 mol dm-3 Part 4: Treatment of results D = [Benzoic acid] ethyl acetate / [Benzoic acid]aqueous buffer Part a) D at pH 6.0 [Benzoic acid]aqueous buffer = [Benzoic acid]ethyl acetate, before partitioning - [Benzoic acid]ethyl acetate, after partitioning = 0.001998 - 0.001142922512 = 0.0008550774879 mol dm -3 D = [Benzoic acid]ethyl acetate / [Benzoic acid]aqueous buffer = 0.001142922512/0.0008550774879 = 1.336630338 LogD = log(1.336630338) = 0.1260113143 ≈ 0.126

Part b) D at pH 7.0 [Benzoic acid]aqueous buffer = [Benzoic acid]ethyl acetate, before partitioning - [Benzoic acid]ethyl acetate, after partitioning = 0.001998 - 0.0001892737918 = 0.001808726208 mol dm -3 D = [Benzoic acid]ethyl acetate / [Benzoic acid]aqueous buffer = 0.0001892737918/0.001808726208 = 0.1046447997 LogD = log(0.1046447997) = -0.9802823489 ≈ -0.98

Discussion It can be seen that the absorbance of the ethyl acetate layer at pH 6.0 was 1.099 AU, which resulted in [benzoic acid]ethyl acetate to be 0.00144 mol dm -3 and the logD value to be 0.126. The absorbance for when the buffer was at pH 7.0 was 0.182 AU, resulting in a concentration of 0.00019 mol dm-3 and the logD value to be -0.98. However, the theoretical log P value for benzoic acid is 1.88 (Haynes, 2016). At pH 8.0, it can be seen through calculation involving the Henderson-Hasselbalch equation (as shown below) that benzoic acid will have a D value of 0.02374877304 and therefore a logD value of -1.62 which indicates that at pH 8.0 benzoic acid will tend to be very hydrophilic as a very large proportion of it has partitioned into the aqueous phase. D=P x fu Figure 2: the distribution coefficient (D)

Figure 3: the fraction of unionised species present at a given pH fu at pH 6.0 = 1/(10 pH-pKa + 1) = 1/(10 6 – 4.202 + Pneutral species = D6.0/fu = 1.336630338/0.0156725476 = 85.28481598

1)

=

0.0156725476

∴ fu at pH 8.0 = 1/(10pH-pKa + 1) = 1/(108 D8.0 = Pneutral species x fu = 85.28481598 x LogD8.0 = log(0.0135769611) = -1.867197426 ≈ -1.87

–

4.202

+ 1) = 0.0001591955255 0.0001591955255 = 0.0135769611

So why is there a difference between the distribution coefficient ( D) of benzoic acid at pH 6.0, 7.0 and 8.0? pKa is an indication of the strength of an acid and is essentially the pH value at which a compound becomes ionised by gaining or losing a proton. It is perhaps noteworthy to mention that pKa can also be thought of as the pH at which the drug is 50% ionised and 50% unionised (Kerns EH., Di L., 2008) [2]. An acid is classed as a strong acid – so is able to give

off a proton easily – if it has a low pKa value, meaning if pH > pKa the acid molecule will be ionised in an aqueous environment, and vice versa (if pH < pKa, the acid molecule is classed as a weak acid and so will be present as more of the unionised species in an aqueous environment). As the pH of the ambient aqueous solution increases, the environment will become more alkaline. This will cause the neutral molecules to become more likely to donate their protons to the environment. Therefore, as this ionised molecule cannot interact in the non-polar environment, it will tend to move into the aqueous phase thus causing the distribution coefficient to become smaller as there are more molecules in the aqueous phase. The relation between pKa and pH, along with the concentrations of the ionic and neutral species (Reijenga et al., 2013) [2] is mathematically illustrated by figure 4, the Henderson-Hasselbalch equation. A−¿ ¿ Figure 4: The Henderson-Hasselbach equation (Kerns EH., Di L., 2008) [2] ¿ pH = pKa + log ¿ It was determined experimentally that there was a greater Log D value at pH 6.0 than at pH 7.0 and (through calculation) pH 8.0, which meant more of the benzoic acid molecules were present within the ethyl acetate layer at pH 6.0. This is because the pKa of benzoic acid is 4.202 in H2O at 25 oC (Harris D., 2010) and so even though the pH of the aqueous layer at pH 6.0, 7.0 and pH 8.0 were already greater than the pKa, meaning the acid molecules will already be ionised to some degree, the environment in the aqueous layer was relatively more basic at pH 7.0 and 8.0 than at pH 6.0. This meant a larger fraction of the acid molecules were ionised at pH 8.0 and 7.0 and so more partitioned into the aqueous layer, yielding a greater [benzoic acid] aqueous buffer thus decreasing the Log D value at these pH values (Watson, D. G., 2011).

Conclusion It can therefore be said that the distribution coefficient is in fact dependent upon pH. This is because benzoic acid has been shown to become more hydrophilic as the pH of the solution increases away from the pKa as the logD of benzoic acid in fact decreases with increasing pH (logD6.0 > logD7.0 > logD8.0).

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2)

Stolerman, I.P., 2010. Lipophilicity. Encyclopedia Of Psychopharmacology. 2nd ed. Berlin: Springer, pp.707-710. ISBN: 9783540686989

3) Kerns, EH. and Di, L., 2008. [1] Chapter 5: lipophilicity, 5.1: lipophilicity fundamentals. Drug-Like Properties: Concepts, Structure Design And Methods: From ADME To Toxicity Optimization. 2nd ed. Academic Press, Elsevier, pp.43. ISBN: 9780123695208

4) Scherrer, R. and Howard, S., 1977. Use of distribution coefficients in quantitative structure-activity relations. Journal of Medicinal Chemistry, 20(1), pp.53. DOI: 10.1021/jm00211a010. American Chemical Society (ACS). Available at: https://pubs.acs.org/doi/abs/10.1021/jm00211a010 5) Ahuja, S. and Dong, M., 2005. Chapter 17: LC/MS application in high-throughput ADME screen, 17.2: measurement of physicochemical properties, 17.2b: Lipophilicity. Handbook Of Pharmaceutical Analysis By HPLC. 6th ed. Amsterdam: Elsevier Academic Press, p.418. ISBN: 9780120885473 6) Reijenga, J., van Hoof, A., van Loon, A. and Teunissen, B., 2013. [1] Development of Methods for the Determination of pKa Values. Analytical Chemistry Insights, vol. 8, p.63. DOI: 10.4137/ACI.S12304 7) Wang, Z., Wille, U. and Juaristi, E. (2017) [1]. Encyclopedia of physical organic chemistry. Chapter 12: Molecule-medium relationships. 1st ed. New Jersey: John Wiley & Sons Ltd., p.559. ISBN: 9781118470459 8) Wang, Z., Wille, U. and Juaristi, E. (2017) [2]. Encyclopedia of physical organic chemistry. Chapter 14: LogP. 1st ed. New Jersey: John Wiley & Sons Ltd., p.629. ISBN: 9781118470459

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R.C. (1975). Handbook of Chemistry Cleveland: CRC Press LLC. ISBN: 9780878194551

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11) Kerns, EH. and Di, L., 2008. [2] Chapter 6: pKa, 6.1: pKa fundamentals. Drug-Like Properties: Concepts, Structure Design And Methods: From ADME To Toxicity Optimization. 2nd ed. Academic Press, Elsevier, pp.49. ISBN: 9780123695208 12) Reijenga, J., van Hoof, A., van Loon, A. and Teunissen, B., 2013. [2] Development of Methods for the Determination of pKa Values. Analytical Chemistry Insights, vol. 8, p.54. DOI: 10.4137/ACI.S12304 13) Harris, D. (2010). Quantitative Chemical Analysis (8 ed.). New York: W. H. Freeman and Company. pp. 165. ISBN: 9781429239899 14) Watson, D., 2011. Pharmaceutical Chemistry. Livingstone/Elsevier, p.154. ISBN: 9780443072321

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