Acid-base equilibria of amino acids: microscopic and macroscopic acidity constants

Fritz Scholz*, Heike Kahlert Institute of Biochemistry, University of Greifswald, Felix-Hausdorff-Str. 4, 17487 Greifswald, Germany * Author for correspondence, [email protected]

Abstract A short introduction to the notation of microscopic and macroscopic acidity constants of amino acids is given. The historical pathways are discussed, which led to the contemporary understanding of the acid base reactions of amino acids and their zwitterionic nature in solutions at the isoelectric point. This text is for undergraduate studies of analytical chemistry and biochemistry.

Keywords: amino acids, microscopic acidity constants, macroscopic acidity constants, zwitterion, Georg Bredig, Friedrich Wilhelm Küster, Elliot Quincy Adams, Niels Janniksen Bjerrum, Ruth Erica Benesch, Reinhold Benesch, John Tilestone Edsall

Amino acids are ampholytic compounds According to IUPAC definitions, a compound that behaves both as an acid and as a base is called amphoteric [1]. Water is an example, as it can accept and donate protons, and so it is according to the Brønsted-Lowry theory both a base and an acid. It is said to be amphiprotic. Compounds possessing acidic and basic sites (groups) are called ampholytes. Amino acids are organic compounds with at least two carbon atoms having at least one acidic carboxyl group (

−COOH ) and at least one amino ( −NH2 ) group, and so they belong to the ampholytes. The group of protein-building (proteinogenic) amino acids comprises 22 members however, and over 500 amino acids have been identified in living matter. The structures and the different ways of classification of amino acids are available in any textbook on biochemistry, e.g., in [2], and cannot be discussed in this text. Here we confine the presentation to α-amino acids having only one carboxyl and one amino group. With a few exceptions [e.g., 3] biochemistry textbooks treat the structures, syntheses, reactions, etc. of amino acids in great detail, the description of their acid-base properties is usually restricted to the very basics, i.e., their zwitterionic forms, the isoelectric point, and their macroscopic acidity constants, usually without even mentioning the term ‘macroscopic’ and explaining that there are also microscopic acidity constants. This is not only a theoretically interesting issue, but the microspeciation of polyprotic acids has also importance for pharmacokinetics and pharmacodynamics [4].

The chemical equilibria between the four forms of amino acids with one carboxyl and one amino group

Amino acids with one carboxyl group and one amino group can exist in four different forms in an aqueous solution: (1) the neutral form, not possessing charged groups, where only the carboxylate group is

protonated (forming the carboxyl group): H2 N−− CH(R) COOH , abbreviated as HA (2) the cationic form, where both the amino and the carboxylate groups are protonated

+

(forming a carboxyl group and an ammonium group): H3 N−− CH(R) COOH ,

+ abbreviated as HA2 (3) the anionic form, where the carboxyl group is deprotonated (forming a carboxylate

− − group): H2 N−− CH(R) COO , abbreviated as A The basicity (i.e., the proton acceptor property) of the nitrogen of the amino group is stronger than the basicity of the oxygen in the water molecules of the surrounding water in an aqueous solution. As the result the amino group is more easily protonated than the water molecules. Further, the carboxyl group of amino acids is so acidic, that the proton is easily transferred to water molecules. Therefore the fourth possible form is

+ 1 − ± (4) the inner salt, or zwitterion H3 N−− CH(R) COO , abbreviated as HA . These zwitterions have to be distinguished from so-called betaines, which are inner salts with a permanent cationic part, like in the name-giving archetype betaine (trimethylglycine)

− where the nitrogen is bond to three methyl groups and the −CH2 COO group, which can be protonated. In the protonated form betaine is a cation, and in the deprotonated form a zwitterion. Betaine (trimethylglycine) is present in many plants and it was discovered in sugar beets with the Latin name Beta vulgaris, which explains the name

1 ‚Zwitter‘ is German for hermaphrodite. betaine. Figure 1 shows a scheme showing the equilibria connecting all four possible forms which exist in aqueous solutions of amino acids.

Figure 1: The four species of amino acids existing in aqueous solutions and the equilibria relating them to each other. Ka1, micro to Ka4, micro are microscopic acidity constants and Kz is the formation constant of the zwitterionic form.

Often the existence of the zwitterionic form HA± is evoked by a comparison of the basicity of the amino group in relation to the basicity of the caboxylate group, so as, in a mechanistic view, the carboxyl group would transfer its proton to the amino group. This is in most cases a misleading view because thermodynamics can never make a mechanistic statement. The protonation state of both groups in aqueous solution results normally only from the reaction of the two groups with water controlled by the respective equilibrium constants. Only if the structure allows it, an intramolecular proton transfer can occur. Since both groups (amino group and carboxylate group) are in equilibrium with water, the above mentioned relation between the basicities of the two groups still holds, but the formation of HA± is the result of two independent equilibria.

Amino acids possessing more than one carboxyl and/or more than one amino group exist in more than four forms. Such cases are excluded from the following presentation.

In aqueous solutions, the chemical equilibria between the four forms of the simplest amino acids are as follows: ++Ka1, micro H N−− CH(R) COOH + H O o H N−− CH(R) COO−+ + H O Equilibrium 1: 3 23 3 Ka1, micro + ±+ (H22 A + H Oo HA + H3 O )

+ Ka2, micro H N−− CH(R) COO− + H O o H N−− CH(R) COO−+ + H O Equilibrium 2: 3 22 3 Ka2, micro ± −+ (HA + H23 O o A + H O )

+ Ka3, micro H N−− CH(R) COOH + H O o H N−− CH(R) COOH + H O+ Equilibrium 3: 3 22 3 Ka3, micro ++ (H22 A + H Oo HA + H3 O )

Ka4, micro H N−− CH(R) COOH + H O o H N−− CH(R) COO−+ + H O Equilibrium 4: 2 22 3 Ka4, micro −+ (HA + H23 O o A + H O )

+ + The completely protonated form H3 N−− CH(R) COOH ( HA2 ) is a dibasic acid and resembles in this respect other dibasic acids, like H24 SO , H23 CO , HS2 and (COOH)2 . However, there is an important difference: These acids exist only in one form when they have lost one proton. The oxygen atoms in H24 SO and in H23 CO are completely

− − equivalent, so that only one form O3 S( OH) (usually written as HSO4 ) and one form

− − O2 C( OH) (usually written as HCO3 ) exists. The same is true for hydrogen sulphide and oxalic acid. Therefore, the scheme shown in Figure 1 is simplified as shown in Figure 2. In

+ − case of the amino acids, the protonation sites are not identical, i.e. H3 N−− CH(R) COO

± ( HA ) differs from H2 N−− CH(R) COOH ( HA ). This difference is indicated by the two formulae HA± and HA .

Figure 2: Equilibria of a dibasic acid with identical protonation sites.

Microscopic and macroscopic acidity constants The amino acid glycine can now be used as an example to understand the difference between 5 microscopic and macroscopic acidity constants. Glycine has the following pKa values [ ]:

pKa1, micro = 2.31±0.06; pKa2, micro = 9.62±0.05, pKa3, micro = 7.62±0.04; pKa4, micro = 4.31±0.05, which are related to the concentrations of the chemical species as follows:

cc±+ HA H3 O Equation 1 Ka1,micro = c + HA2

cc−+ A HO3 Equation 2 Ka2,micro = cHA±

ccHA + HO3 Equation 3 Ka3,micro = c + HA2

cc−+ A HO3 Equation 4 Ka4,micro = cHA Thermodynamic equilibrium constants are defined on the basis of activities, and the Equations 1 to 4 are thus approximations since they are based on concentrations. The numerical values

+

pKa1, micro and pKa4, micro show that H32 N−− C(H ) COOH is a stronger acid than

H22 N−− C(H ) COOH . This relation is typical for amino acids and is described by the tautomery Equilibrium 5:

Kz + H N−− CH(R) COOH  H N −− CH(R) COO− Equilibrium 5 23 Kz (HA  HA± )

Equilibrium 5 is shifted extremely to the right side, because Kz is related to the microscopic constants as follows:

c + −−− KK Equation 5 K = H3 N CH(R) COO = a4, micro= a1, micro z c KK H2 N−− CH(R) COOH a2, micro a3, micro

It is important to note that the equilibrium constant KZ is independent of the pH!

For glycine the formation constant of the zwitterion is: K 10−2.31 a1, micro, glycine = = 5.31 Equation 6 Kz, glycine = −7.62 10 Ka3, micro, glycine 10 Since the concentration of the neutral form HA is very small compared to that of the + ± − zwitterionic form, it is customary in textbooks to discuss only HA2 , HA and A . Now we have to explain, why the acidity constants in Figure 1 and in the equilibria 1 to 4 are called microscopic constants: The constants Ka1, micro to Ka4, micro are called microscopic acidity constants, because they all relate to the deprotonation of one specific and distinguishable acid

+ − group. From the potentiometric acid base titration of HA2 to finally A one can experimentally determine only two acidity constants Ka1, macro and Ka2, macro . They are called

+ macroscopic acidity constants, because in such a titration of HA2 , in which the pH is recorded as a function of added base ( OH− ), the neutral form HA and the zwitterionic form HA± are not distinguishable. The two equilibria

+− ± Equilibrium 6 H22 A + OH  HA + H O and

+− Equilibrium 7 H22 A + OH  HA + H O are shifted from the left to the right side at the first titration step, and the two equilibria

±− − Equilibrium 8 HA + OH  A + H2 O and

−− Equilibrium 9 HA + OH  A + H2 O are shifted to the right side at the second titration step. Thus, the two acidity constants 6 Ka1, macro and Ka2, macro are defined as follows [ ]:

(c±++ ccHA ) HA HO3 Equation 7 Ka1, macro = c + HA2

cc−+ Equation 8 K = A HO3 a2, macro + ccHA± HA These two equations can be related to the following two equilibria:

+ ±− Equilibrium 10 H22 A + H O  { HA + HA} + OH

± −− Equilibrium 11 {HA + HA} + H2 O  A + OH

cHA± Ka1, micro When the equilibrium constant Kz = = of the formation of the zwitterionic form cKHA a3, micro

is very large, i.e. at least 100, and thus ccHA±  HA , the following approximations can be made: cc±+ cc−+ HA H3 O A HO3 Ka1, macro ≈ and Ka2, macro ≈ , i.e. KKa1, macro≈ a1, micro and KKa2, macro≈ a2, micro . cHA+ cHA± The exact relations between the microscopic and macroscopic constants are as follows:

For Ka1, macro :

Kca3, micro + Ka3, micro cc±+Kc± HA2 HA H3 O a3, micro HA Using the relations cHA = = = to substitute cHA in c++ cKa1, micro Ka1, micro HO33HO Equation 7 yields:  Kca3, micro HA± cc±++ HA HO3 K cc±+KK =a1, micro =HA H3 O +=a3, micro +a3, micro KKa1, macro 11a1, micro c++ cKa1, micro Ka1, micro HA22HA  and finally

Equation 9 Ka1, macro= KK a1, micro + a3, micro

For Ka2, macro :

cc− + Ka2, micro c+± c Kc± A HO33HO HA a2, micro HA Using the relation cHA = = = to substitute cHA in Ka4, micro cK+ a4, micro Ka4, micro HO3 Equation 8 gives:

ccA−+ HO ccA−+ HO 1 KK= 33= = a2, macro + a2, micro (ccHA± HA ) Ka2, micro Ka2, micro c ± 11++ HA  KKa4, micro a4, micro and finally

KKa2, micro a4, micro Equation 10 Ka2, macro = , which can also be written as KKa2, micro+ a4, micro follows: 1 11 Equation 11 = + Ka2, macro KK a2, micro a4, micro

The titration of glycine

+ − ± Figure 3 shows the fractions of all four species ( HA , HA2 , A , HA ) of glycine as

+ function of the solution pH. Figure 4 depicts the titration curve of glycine going from HA2 to A− . How small the fraction of HA is, can be seen in Figure 3b!

c − α = i + Figure 3: The logarithm of the fractions i  of all 4 species ( i = HA , HA2 , A , Cglycine

HA± ) of glycine as function of the solution pH.

14

12

10

8 pH

6

4

2

0 0,00 0,25 0,50 0,75 1,00 1,25 1,50 τ

+  −1 − Figure 4: Titration curve of glycine hydrochloride ( HA2 , Cglycine = 0.1 mol L ) with OH . The pH is plotted versus the degree of titration τ (Greek letter tau) [15]. The letter is defined to be 1.0 for the titration of both protons.

The pH at which the concentrations of both HA± and HA have a maximum, is called the isoelectric point: ppKK+ Equation 12 pH = a1, macro a2, macro IE 2 The isolectric point of proteins is of great significance because at that pH the protein has no net charge and so it does not migrate in an electric field. In electrophoreses with a pH gradient, the so-called isoelectric focusing, the proteins will stop when they reach the zone having their specific isoelectric point [7]. The term isoelectric literally means in chemistry that a compound has equal numbers of positive and negative electric charges (in Greek language ἴσο=iso means equal) and thus it does not possess a net charge.

Some glimpses of the history of understanding acid-base equilibria of amino acids

Georg Bredig In his PhD thesis, Georg Bredig (Figure 5) has hypothesized, that betaine exists as a species having a positive and a negative charge at the same time [8]. At that time, this was a very +−− unorthodox idea. Betaine, (H32 C)3 N CH COO , (2-trimethylamino acetate or trimethylglycine) is indeed a permanent zwitterionic compound, and the archetype of the so- called betaines.

Figure 5: Georg Bredig (Glogau, Germany, Oct. 1 1868 – New York, USA April 24, 1944). Bredig studied at the Universities of Freiburg and Berlin, and made and received his PhD under the supervision of Wilhelm Ostwald in Leipzig. His major research fields were electrolyte solutions and catalysis. He was a Professor in Heidelberg and Karlsruhe. Because of his Jewish descent, he was forced to retire in 1933. He left Germany in 1939 via the Netherlands to immigrate to the USA [9].

Friedrich Wilhelm Küster The term ‘zwitterion’ goes back to the German chemist Friedrich Wilhelm Küster (Figure 6) who has assumed that 4-((4-(dimethylamino)phenyl)azo)benzenesulphonic acid exists in +−− −− − aqueous solutions as(HC3)2 HN CH66 N 2 CH 64 SO 3. He observed that this ‘Zwittergebilde’ (hermaphroditic entity) is slightly reddish, whereas the deprotonated form − −− −− 10 (HC3)2 N CH66 N 2 CH 64 SO 3 is deep yellow [ ].

Figure 6: Friedrich Wilhelm Küster (Falkenberg, Germany, April 11, 1861, – June 22, 1917, Frankfurt on the Oder, Germany). Küster studied sciences and mathematics in Berlin, Munich and Marburg. He received a PhD for studies in organic chemistry guided by Th. Zincke. In 1896 he moved to the University of Göttingen and in 1897 to the University of Breslau. From 1899/1900 he was a Professor at the Bergakademie (mining college) Clausthal. In 1903 he has published one of the first conductometric titrations (acid-base titration). Reproduced from [11].

Elliot Quincy Adams Already in 1916, US chemist Elliot Quincy Adams (Figure 7) [12] derived the Equations 9 and 10 for a dibasic acid [13]. He discussed that for symmetric dibasic acids with completely separated and identical protonation sites, all four microscopic constants are equal:

Equation 13 KKKKKa1,micro= a2,micro = a3,micro = a4,micro = . From this follows with Equations 9 and 10:

Equation 14 KKa1, macro = 2 , and

KK2 Equation 15 K = = , and for the ratio of the macroscopic a2, macro 22K constants: K Equation 16 a1, macro = 4 . Ka2, macro This ratio of 4 is the possible smallest value which only occurs if the groups are identical and completely separated. This is the so-called statistical case, when the molecule is symmetrical and the two groups do not interact, neither via bonds nor via space. Table 1 shows that for alkane diacarboxlic acids, this ratio indeed approaches 4 with the increasing number of methylene groups separating the two carboxyl groups. Unfortunately, the acidity constants of higher than sebacic acid are unknown because of their low solubility in water.

Table 1: pKa1 and pKa2 data of alkane dicarboxylic acids for 25°C, and the ratios of their acidity constants KKa1/ a2 . (The data are from different sources, and it should be noted that slightly different values are reported in various publications. However, these variations are of minor importance here.)

Common name Systematic pKa1 pKa2 K a1 K IUPAC name a2

Oxalic acid ethanedioic acid 1.23 4.19 912.0 Malonic acid propanedioic 724.4 2.83 5.69 acid Succinic acid butanedioic acid 4.16 5.61 28.2 Glutaric acid pentanedioic 12.6 4.32 5.42 acid Adipic acid hexanedioic acid 4.43 5.42 9.8 Pimelic acid heptanedioic 11.2 4.47 5.52 acid Suberic acid octanedioic acid 4.53 5.50 9.3 Azelaic acid nonanedioic 7.4 4.53 5.40 acid Sebacic acid decanedioic acid 4.72 5.45 5.0

Normally, in case of amino acids, the two constants Ka1, macro and Ka2, macro are simply denoted as Ka1 and Ka2 . It should be mentioned that Adams did not use the term microscopic acidity constants, and he called the zwitterionic form “inner salt”. However, he was the first to realize that in neutral solutions the concentration of the “inner salt”, i.e., the zwitterion ( HA± ), by far exceeds that of the uncharged form ( HA ).

Figure 7: Elliot Quincy Adams (September 13, 1888 – March 12, 1971). Adams studied at MIT, and afterwards joined the General Electric laboratories in Schenectady where he worked with Irving Langmuir. In 1912, he moved to the University of California at Berkeley, where he received his PhD under the supervision of Gilbert N. Lewis in 1914. In 1917 he joined the Color Laboratory, Bureau of Chemistry of the US. Department of Agriculture in Washington DC. From 1921-1949 he worked for General Electric at Nela Park, East Cleveland, Ohio. (Courtesy of M. Vik, Technical University Liberec)

Niels Janniksen Bjerrum In 1923 Bjerrum (Figure 8) [14] came to the same conclusion about the dominance of the zwitterionic form of amino acids (in neutral solutions) as Adams in 1916. The fact that Bjerrum did not refer to Adams’ work was most likely caused by World War I, whereby the exchange of journals between the US and Europe was interrupted or delayed. It is remarkable that the time gap between the publications of Bredig (1894), Küster (1897), and Adams (1916), Bjerrum (1923) was so large. During that period, even renowned chemists like Michaelis, supposed that the concentration of the zwitterionic forms is so small that it can be neglected. Bjerrum came to his conclusion about the domination of zwitterions by drawing the analogy to ammonium acetate, which, as he wrote, consists to 99.5% of the respective ions.

Figure 8: Niels Janniksen Bjerrum (Copenhagen, Denmark, 11 March 1879, – Copenhagen, Denmark, 30 Sept. 1958) was a Danish physico-chemist. In 1905 he worked with Wilhelm Ostwald in Leipzig. From 1914 to 1949 he was a Professor at the Royal Agricultural College (Landbohøjskolen) in Copenhagen. Bjerrum is famed, among other achievements, for having introduced pH-logc diagrams [15]. (Copyright Morten J. Bjerrum, reprinted from [16]).

Ruth Erica and Reinhold Benesch Since the simple titrations of amino acids, i.e., plots of pH versus added acid or base, provide only the macroscopic acidity constants, access to the microscopic acidity constants needs specific measurements of the different species, or at least some of them. This is only possible with the help of spectroscopic techniques, which can distinguish between different species based on the differences of their structures. With spectroscopic techniques it is possible to construct “spectroscopic titration curves” which plot the concentrations of the different species as function of the solution pH (adjusted by addition of acids or bases). The first spectroscopic study for that purpose has been published in 1955 [17] by Ruth Erica Benesch and her husband Reinhold Benesch (Figure 9). They recorded the pH-dependent UV spectra of cysteine and some cysteine derivatives. Cysteine, 2-amino-3-sulfhydrylpropanoic acid, has three acidic groups: the carboxyl group, the sulfhydryl group and the ammonium group. The pKa of the carboxyl group is below 2 so that it is always deprotonated under physiological conditions. However, the sulfhydryl and ammonium groups have rather similar pKa’s and the Benesch’s wrote down the scheme shown in Figure 10.

Figure 9: Ruth Erica Benesch (neé Leroi) (Paris, Febr. 25, 1925–March 25, 2000) was raised in Berlin. In 1939 she escaped by a Kindertransport (German for children’s transport) that rescued Jewish children from Germany. Her husband Reinhold Benesch (Poland, Aug. 13, 1919–Dec. 30, 1986) was born in Poland. The most important discovery of the Beneschs was the interaction of 2,3-bisphosphoglyceric acid with deoxygenated hemoglobin by decreasing its affinity for molecular dioxygen, so it promotes the release of dioxygen bound to the hemoglobin and enhances the ability of red blood cells to release dioxygen where it is most needed [18]. (Copyright: Department of Biochemistry, Columbia University).

Ka1, micro + −+ HSRNH33 o S RNH

KKa2, micro ↑↓ ↑↓ a3, micro

− HSRNH22 o S RNH

Ka4, micro Figure 10: The acid-base equilibria of cysteine with respect to the sulfhydryl and ammonium groups. R = COO− is an anionic group, i.e., not protonated under physiological conditions.

The UV spectra of cysteine show a shift of maximum absorption from (236–238) nm to (230–

−+ 232) nm with decreasing pH since the maximum of S RNH3 is at somewhat shorter

− −+− wavelength than that of S RNH2 . A plot of %(S RNH3 +S RNH2 ) versus pH shows that 2/3 of the thiol sites are deprotonated at the first titration step and 1/3 at the second step, i.e., 1/3 of the ammonium group is deprotonated at the first step together with 2/3 of the thiol sites group. With the help of the spectroscopic data the Beneschs solved the following equation

+ c−+−+ cc−+ − (S RNH32 S RNH ) = S RNH3 S RNH 2 max ++ + c−+−+ c+ cc −+ HSRNH c− Equation 13 (S RNH32 S RNH ) HSRNH 3 S RNH 3 2 S RNH2 KK+ Kc+ = a1, micro a2, micro a4, micro H + ++ cKKKKcHH++a2, micro a1, micro a2, micro a4, micro 1

max in which c − +− is the maximum concentration of the deprotonated sulfhydryl group, (S RNH32+ S RNH ) for Ka1, micro , Ka2, micro , and Ka4, micro with 3 parallel equations in which they used experimental values. Ka4, micro can be derived from the other acidity constants, because the ratio

KKa1, micro a2, micro= KK a4, micro a3, micro holds. Table 1 gives the experimentally determined data. Only slightly deviating data, also based on spectrophotometry, have been published later [19]

17 Table 1: The microscopic pKa data of cysteine as determined by Benesch and Benesch [ ].

pKa1, micro pKa2, micro pKa3, micro pKa4, micro 8.53 8.86 10.36 10.03

An important development was later the application of Nuclear Magnetic Resonance Spectroscopy for the determination of the fractional deprotonation of acidic groups pioneered by Dallas L. Rabenstein, then at the University of Alberta, Canada [20, 21]. For a review of the NMR titration see [22]. Even with spectroscopic techniques it is not possible to determine all microscopic constants when the number of protonation sites exceeds three [23, 24, 25]. Finally, it should be mentioned, that before the spectroscopic techniques have been developed to determine microscopic acidity constants, a “chemical approach” has been chosen (see [26]):

The two macroscopic acidity constants Ka1, macro and Ka2, macro were determined by classical pH titration (as shown in Figure 4) taking the pH values reached for 50% titration of the first step and 50% of the second step as pKa1, macro and pKa2, macro , respectively. Then a good approximate of pKa3, micro was determined by titrating an ester of the amino acid, as that possesses only one acidic group, i.e., the ammonium group. Of course, the real pKa3, micro value of the amino acid slightly deviates from that of the ester, but this deviation is very minor. When Ka3, micro is known, the Equation 9 allows to calculate Ka1, micro . Then Equation 5

Ka4, micro provides Kz , which is equal to the ratio . Equations 5 and 11 can be combined to Ka2, micro calculate the two unknown data Ka2, micro and Ka4, micro

Ka 2, macro Equation 14 KKa2, micro= a 2, macro /1− Kz

Equation 15 Ka4, micro= KK z( a 2, macro +1)

Understandably, the calculated microscopic constants slightly deviate from the true values. The glycine data given above Equation (1) have been similarly determined by an acid-base titration of glycine giving the two macro constants, and titrating the methylester of glycine 5 giving a good approximation of the Ka3, micro [ ].

John Tilestone Edsall Only in 1936, John Tilestone Edsall (Figure 11) has provided in a very early Raman spectroscopic study the proof of the zwitterionic nature of amino acids at their isoelectric point [27]. Edsall performed these studies in the group of the US-biochemist Edwin Joseph Cohn (1892‒1953) at Harvard Medical School. Cohn and Edsall published in 1943 a groundbreaking book [28], in which Edsall lucidly presented the theory of acid-base equilibria of amino acids; however, without using the terms microscopic and macroscopic acidity constants. It seems that Terrell L. Hill2 [29] used these terms for the first time in a paper in 1943 [30]. The terms ‚microscopic‘ and ‚macroscopic‘ are literally taken wrong. It would be better to call the microscopic constants ‘real constants’, and the macroscopic constants ‘apparent constants’. However, as they belong to the established nomenclature since long, they can be used as long as their meaning is correctly understood.

Figure 11: John Tilestone Edsall (Philadelphia, Nov 3, 1902 ‒ Boston, June 12 2002) [31] was an eminent US biochemist. He conducted his undergraduate studies under the supervision of Lawrence J. Henderson (famous for the Henderson-Hasselbalch equation of buffers!) at Harvard College. In 1954 he moved to Harvard University. For 10 years, he was Editor-in- Chief of the Journal of Biological Chemistry and for 50 years of Advances in Protein Chemistry. He had a strong commitment to call for freedom of science [32]. Copyright: 2002 Elsevier Science B.V.

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