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Home > Computational estimation of the acidities of purines and indoles
Computational estimation of the acidities of purines and indoles
Kara L. Geremia1 & Paul G. Seybold
Introduction
The purines comprise a key class of biochemically active compounds, and the purine skeleton is said to be the most widely distributed N-heterocycle in naturer [1]. Although best known for containing the nucleobases adenine and guanine, the purines, along with related compounds such as the indoles, encompass an enormous diversity of bioactive compounds, ranging from natural products to medicines and pharmaceuticals. Accordingly, it is useful to develop theoretical methods for estimating the physical and chemical properties of these compounds. In particular, the acidities of these compounds as expressed by their pKa values are of special interest since, among other things, these values determine the particular forms (neutral and ionic) that will prevail under different circumstances.
Several theoretical approaches can be taken when estimating the pKa values of chemical compounds [2–7]. In a first-principles approach, one directly employs quantum-chemical methods and solvent models independent of experimental data, which has the disadvantage that quite demanding computational methods are generally required to achieve reasonable accuracy [2, 8, 9]. In some cases, improvements can be obtained by adding explicit solvent molecules to the calculations (see, e.g., Adam [10] and Thapa and Schlegel [11]). Quantitative structure–activity relationship (QSAR) methods [4, 12–14] search for molecular features (Bdescriptors) associated with specific molecular properties such as the pKa, and thus rely on existing experimental data, but at the same time such methods allow the use of less demanding computational levels. In addition, QSAR methods typically produce general equations that can be applied to other related compounds beyond those in the initial test set. A third approach, used in a number of commercial programs, relies on a large database of experimental values and substituent features such as Hammett constants to estimate molecular pKa values [15, 16]. In this report, we employ the latter two methods to estimate the pKa values of a collection of purines and related com- pounds and to provide QSAR equations for wider appli- cation to this class of compounds.
Methods
The atom numbering scheme for purines is somewhat idiosyncratic [17], as it treats the purine framework as a six-membered pyrimidine ring fused to an imidazole ring, whereas the more customary atom numbering scheme is used for the heterocyclic rings in indoles. These schemes are shown below.
In the initial stage of this study, experimental data for the pKa values of selected compounds—purines and related ring heterocycles such as indoles in the present case—were col- lected. The pKa values given in the literature for the 31 select- ed compounds are shown in Table 1. Here we define the cation→ neutral dissociation as pKa1 and the neutral → anion dis- sociation as pKa2. Also included in this table for comparison purposes are the pKa values determined via the Advanced Chemical Development (ACD/Labs, Toronto, Canada) PhysChem Suite commercial program.
A complication arises for the nitrogen heterocyclic ring systems studied in this work because these compounds typically exist in a variety of tautomeric forms [18–21]. We have used density functional theory B3LYP/6–31 + G** computa- tions as implemented by the Spartan’10 computational pro- gram (Wavefunction, Inc., Irvine, CA, USA) along with the aqueous SM8 solvent model of Marenich et al. [22] to study the relative stabilities of the possible tautomers of each compound. (These studies will be reported in the future.) For sim- plicity, for dissociations 1 and 2, we assumed that the most stable tautomer (as determined computationally) of each spe- cies (cation or neutral) is the dissociating species. [For exam- ple, the 1,9(H)-P+ form of the basic purine cation species, protonated at the 1 and 9 positions, is computed to be the most stable cation tautomer in aqueous solution; in process 1, this species dissociates to form the most stable neutral tautomer 9H-P, which is protonated at nitrogen 9, and this in turn dissociates in process 2 to form the anion P− with none of the ring nitrogen atoms protonated.
We were first interested in ascertaining whether the B3LYP/6–31 + G** level of theory was adequate for accurate- ly determining the pKa values of these compounds using the relation ΔG°= -RTpKa. The Spartan’10 computational pro- gram cannot evaluate the Gibbs energy change in solution because of the complications introduced by solute–solvent interactions, but calculations can be tested against gas-phase data where available. The NIST chemical database lists experimental gas-phase rG° values for the reaction A− + H+ ⇌ AH for five of the compounds listed in Table 1. (The vacuum Gibbs energy G°(H+) is −26.3 kJ/mol at 298.15K [5].) The experimental and calculated ΔrG°= G°(A−)+ G°(H+) − G°(HA) values are shown in Table 2. The experimental and calculated ΔrG° values are seen to be in excellent agreement and are strongly correlated (R2 = 0.996), supporting the use of the present level of computation. As noted, it is not possible to calculate G° values directly within a solvent using the Spartan program, so we wished to find a surrogate descriptor for the pKa regression calculations. The energy change ΔE has previously been used successfully in a number of studies, and was deemed a reasonable descrip- tor candidate [24–26]. To examine this connection further, we determined the correlation between the calculated vacuum ΔE values and the experimental gas-phase ΔGr° value for the compounds in Table 2. The correlation was found to be excel- lent (R2 = 0.999), further supporting the premise that ΔE could serve as a surrogate for ΔG° under more general conditions, e.g., within the solvent environment.
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