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 −+ H2 N−− CH(R) COOH + H22 O o H N−− CH(R) COO + H3 O Equilibrium 4: 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 o H N −− CH(R) COO− Equilibrium 5 23 Kz (HA o 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.