Calculation of pKa Values of Nucleobases and the Guanine Oxidation Products Guanidinohydantoin and Spiroiminodihydantoin using Density Functional Theory and a Polarizable Continuum Model

DNA-base guanine as hydrogen getter and charge-trapping layer embedded in oxide dielectrics for inorganic and organic field-effect transistors

DNA-base small molecules of guanine, cytosine, adenine, and thymine construct the DNA double helix structure with hydrogen bonding, and they possess such a variety of intrinsic benefits as natural plentitude, biodegradability, biofunctionality, low cost, and low toxicity. On the basis of these advantages, here, we report on unprecedented useful applications of guanine layer as hydrogen getter and charge trapping layer when it is embedded into a dielectric oxide of n-channel inorganic InGaZnO and p-channel organic heptazole field effect transistors (FETs). The embedded guanine layer much improved the gate stability of inorganic FETs gettering many hydrogen atoms in the gate dielectric layer of FET, and it also played as charge trapping layer to which the voltage pulse-driven charges might be injected from channel, resulting in a threshold voltage (Vth) shift of FETs. Such shift state is very ambient-stable and almost irrevocable even under a high electric-field at room temperature. So, Boolean logics are nicely demonstrated by using our FETs with the guanine-embedded dielectric. The original Vth is recovered only under high energy blue photons by opposite voltage pulse (charge-ejection), which indicates that our device is also applicable to nonvolatile photo memory.

Role of pH controlled DNA secondary structures in the reversible dispersion/precipitation and separation of metallic and semiconducting single-walled carbon nanotubes

Single-stranded DNA (ss-DNA) oligomers (dA20, d[(C3TA2)3C3] or dT20) are able to disperse single-walled carbon nanotubes (SWNTs) in water at pH 7 through non-covalent wrapping on the nanotube surface. At lower pH, an alteration of the DNA secondary structure leads to precipitation of the SWNTs from the dispersion. The structural change of dA20 takes place from the single-stranded to the A-motif form at pH 3.5 while in case of d[(C3TA2)3C3] the change occurs from the single-stranded to the i-motif form at pH 5. Due to this structural change, the DNA is no longer able to bind the nanotube and hence the SWNT precipitates from its well-dispersed state. However, this could be reversed on restoring the pH to 7, where the DNA again relaxes in the single-stranded form. In this way the dispersion and precipitation process could be repeated over and over again. Variable temperature UV-Vis-NIR and CD spectroscopy studies showed that the DNA-SWNT complexes were thermally stable even at ∼90 °C at pH 7. Broadband NIR laser (1064 nm) irradiation also demonstrated the stability of the DNA-SWNT complex against local heating introduced through excitation of the carbon nanotubes. Electrophoretic mobility shift assay confirmed the formation of a stable DNA-SWNT complex at pH 7 and also the generation of DNA secondary structures (A/i-motif) upon acidification. The interactions of ss-DNA with SWNTs cause debundling of the nanotubes from its assembly. Selective affinity of the semiconducting SWNTs towards DNA than the metallic ones enables separation of the two as evident from spectroscopic as well as electrical conductivity studies.

Molecular recognition of nucleotides in water by scorpiand-type receptors based on nucleobase discrimination

The detection of nucleotides is of crucial importance because they are the basic building blocks of nucleic acids. Scorpiand-based polyamine receptors functionalized with pyridine or anthracene units are able to form stable complexes with nucleotides in water, based on coulombic, π-π stacking, and hydrogen-bonding interactions. This behavior has been rationalized by means of an exploration with NMR spectroscopy and DFT calculations. Binding constants were determined by potentiometry. Fluorescence spectroscopy studies have revealed the potential of these receptors as sensors to effectively and selectively distinguish guanosine-5'-triphosphate (GTP) from adenosine-5'-triphosphate (ATP).

Analysis of guanine oxidation products in double-stranded DNA and proposed guanine oxidation pathways in single-stranded, double-stranded or quadruplex DNA

Guanine is the most easily oxidized among the four DNA bases, and some guanine-rich sequences can form quadruplex structures. In a previous study using 6-mer DNA d(TGGGGT), which is the shortest oligomer capable of forming quadruplex structures, we demonstrated that guanine oxidation products of quadruplex DNA differ from those of single-stranded DNA. Therefore, the hotooxidation products of double-stranded DNA (dsDNA) may also differ from that of quadruplex or single-stranded DNA, with the difference likely explaining the influence of DNA structures on guanine oxidation pathways. In this study, the guanine oxidation products of the dsDNA d(TGGGGT)/d(ACCCCA) were analyzed using HPLC and electrospray ionization-mass spectrometry (ESI-MS). As a result, the oxidation products in this dsDNA were identified as 2,5-diamino-4H-imidazol-4-one (Iz), 8-oxo-7,8-dihydroguanine (8oxoG), dehydroguanidinohydantoin (Ghox), and guanidinohydantoin (Gh). The major oxidation products in dsDNA were consistent with a combination of each major oxidation product observed in single-stranded and quadruplex DNA. We previously reported that the kinds of the oxidation products in single-stranded or quadruplex DNA depend on the ease of deprotonation of the guanine radical cation (G^•+) at the N1 proton. Similarly, this mechanism was also involved in dsDNA. Deprotonation in dsDNA is easier than in quadruplex DNA and more difficult in single-stranded DNA, which can explain the formation of the four oxidation products in dsDNA.

Reconciliation of chemical, enzymatic, spectroscopic and computational data to assign the absolute configuration of the DNA base lesion spiroiminodihydantoin

The diastereomeric spiroiminodihydantoin-2'-deoxyribonucleoside (dSp) lesions resulting from 2'-deoxyguanosine (dG) or 8-oxo-7,8-dihydro-2'-deoxyguanosine (dOG) oxidation have generated much attention due to their highly mutagenic nature. Their propeller-like shape leads these molecules to display mutational profiles in vivo that are stereochemically dependent. However, there exist conflicting absolute configuration assignments arising from electronic circular dichroism (ECD) and NOESY-NMR experiments; thus, providing definitive assignments of the 3D structure of these molecules is of great interest. In the present body of work, we present data inconsistent with the reported ECD assignments for the dSp diastereomers in the nucleoside context, in which the first eluting isomer from a Hypercarb HPLC column was assigned to be the S configuration, and the second was assigned the R configuration. The following experiments were conducted: (1) determination of the diastereomer ratio of dSp products upon one-electron oxidation of dG in chiral hybrid or propeller G-quadruplexes that expose the re or si face to solvent, respectively; (2) absolute configuration analysis using vibrational circular dichroism (VCD) spectroscopy; (3) reinterpretation of the ECD experimental spectra using time-dependent density functional theory (TDDFT) with the inclusion of 12 explicit H-bonding waters around the Sp free bases; and (4) reevaluation of calculated specific rotations for the Sp enantiomers using the hydration model in the TDDFT calculations. These new insights provide a fresh look at the absolute configuration assignments of the dSp diastereomers in which the first eluting from a Hypercarb-HPLC column is (-)-(R)-dSp and the second is (+)-(S)-dSp. These assignments now provide the basis for understanding the biological significance of the stereochemical dependence of enzymes that process this form of DNA damage.

Selection of a Mimotope Peptide of S-adenosyl-l-homocysteine and Its Application in Immunoassays

A competitive immunoassay for S-adenosyl-l-homocysteine (SAH) has been used in the clinical test for homocysteine via an enzymatic conversion reaction. Since S-adenosyl-l-homocysteine is a relatively unstable compound, we have used peptide library phage display to select a new mimotope peptide that interacts with the anti-SAH antibody. By immobilizing the synthetic peptide on solid phase as a competitive surrogate for SAH, we demonstrate its utility in a competitive ELISA assay. The linear range of the assay for SAH was 0.4–6.4 µM, in good correlation to the conventional assay using an SAH-conjugated plate. Our results show that the mimotope peptide has potential to substitute for SAH in immunoassays.

Adenylylation, MS, and proteomics--Introducing a "new" modification to bottom-up proteomics

Although the addition of a 5'-adenosine phosphodiester group to proteins, called adenylylation, has been known for decades, the possibility that adenylylation could be a molecular switch in cellular signaling pathways has emerged recently. The distinct mass shift upon adenylation of threonine or tyrosine residues renders it a good target for MS detection and identification; however, the fragmentation of adenylylated peptides derived from proteolytic digestion of adenylylated proteins has not yet been systematically investigated. Here, we demonstrate that adenylylated peptides show loss of parts of the adenosine monophosphate (AMP) upon different fragmentation techniques. As expected, causing the least fragmentation of the AMP group, electron transfer dissociation yields less complicated spectra. In contrast, CID and higher energy collision (HCD) fragmentation caused AMP to fragment, generating characteristic ions that could be utilized in the specific identification of adenylylated peptides. The characteristic ions and losses upon CID and higher energy collision fragmentation from the AMP group turned out to be highly dependent on which amino acid was adenylylated, with different reporter ions for adenylylated threonine and tyrosine. We also investigated how adenylylation is best incorporated into search engines, exemplified by Mascot and showed that it is possible to identify adenylylation by search engines.

Y(III) interactions with guanine oligonucleotides covalently attached to aqueous/solid interfaces

The binding of Y(III) ions to surface-immobilized single-stranded 20-mers of guanine was studied using the Eisenthal χ((3)) technique and AFM. The free energy of binding for Y(III) to the G(20) sequence was found to be -39.5(8) kJ/mol. Furthermore, yttrium binds much more strongly to surface-immobilized oligonucleotides than the divalent metals previously reported. At maximum surface coverage, Y(III) ion densities range between one to three ions bound per strand. Comparatively, Mg(II) binds to the G(20)-functionalized interface in much higher ion densities. This result may be explained, in part, by the larger hydration sphere radius of Y(III) compared to that of Mg(II). The ion loading and binding free energy results, in conjunction with other surface and bulk aqueous phase studies, suggest that a fully hydrated +2 or +3 yttrium ion binds to the oligonucleotides through an outer-sphere mechanism. Tapping mode AFM results indicate that oligonucleotide height does not appreciably decrease following Y(III) binding. These results, together with the low ion densities for Y(III) ions, indicate that Y(III) strand loading may not significantly decrease the intrastrand Coulombic repulsions in order to cause a significant decrease in oligomer height.

Theoretical Determination of One-Electron Oxidation Potentials for Nucleic Acid Bases

The oxidation potentials for N-methyl substituted nucleic acid bases guanine, adenine, cytosine, thymine, uracil, xanthine, and 8-oxoguanine were computed using B3LYP and CBS-QB3 with the SMD solvation model. Acid-base and tautomeric equilibria present in aqueous solution were accounted for by combining standard redox potentials with calculated pKa and tautomerization energies to produce an ensemble averaged pH dependent potential. Gas phase free energies were computed using B3LYP/aug-cc-pVTZ//B3LYP/6-31+G(d,p) and CBS-QB3. Solvation free energies were computed at the SMD/B3LYP/6-31+G(d,p) level of theory. Compared to experimental results, calculations with the CBS-QB3 level of theory have a mean absolute error (MAE) of ca. 1 kcal/mol for the gas phase proton affinity/gas phase basicity and an MAE of ca. 0.04 eV for the adiabatic/vertical ionization potentials. The B3LYP calculations have a MAE of ∼2 kcal/mol for the proton affinity/gas phase basicity data but systematically underestimated ionization potentials by 0.14-0.21 eV. Solvent cavities for charged solute species were rescaled uniformly by fitting computed pKa data to experimentally measured pKa values. After solvent cavity scaling, the MAEs for computed pKa's compared to experimental results are 0.7 for B3LYP and 0.9 for CBS-QB3. In acetonitrile, the computed E°(XH(+•)/XH) redox potentials are systematically lower than experimentally measured potentials by 0.21 V for CBS-QB3 and 0.33 V for B3LYP. However, the redox potentials relative to adenine are in very good agreement with experimental results, with MAEs of 0.10 V for CBS-QB3 and 0.07 V for B3LYP. In aqueous solution, B3LYP and CBS-QB3 have MAEs of 0.21 and 0.19 V for E7(X(•),H(+)/XH). Replacing the methyl substituent with ribose changes the calculated E7 potentials by 0.1-0.2 V. The calculated difference between the guanine and adenine oxidation potentials is too large compared to experimental results, but the calculated difference between guanine and 8-oxoguanine is in good agreement with the measured values.

Quantum Chemical Benchmarking, Validation, and Prediction of Acidity Constants for Substituted Pyridinium Ions and Pyridinyl Radicals

Sensibly modeling (photo)electrocatalytic reactions involving proton and electron transfer with computational quantum chemistry requires accurate descriptions of protonated, deprotonated, and radical species in solution. Procedures to do this are generally nontrivial, especially in cases that involve radical anions that are unstable in the gas phase. Recently, pyridinium and the corresponding reduced neutral radical have been postulated as key catalysts in the reduction of CO2 to methanol. To assess practical methodologies to describe the acid/base chemistry of these species, we employed density functional theory (DFT) in tandem with implicit solvation models to calculate acidity constants for 22 substituted pyridinium cations and their corresponding pyridinyl radicals in water solvent. We first benchmarked our calculations against experimental pyridinium deprotonation energies in both gas and aqueous phases. DFT with hybrid exchange-correlation functionals provide chemical accuracy for gas-phase data and allow absolute prediction of experimental pKas with unsigned errors under 1 pKa unit. The accuracy of this economical pKa calculation approach was further verified by benchmarking against highly accurate (but very expensive) CCSD(T)-F12 calculations. We compare the relative importance and sensitivity of these energies to selection of solvation model, solvation energy definitions, implicit solvation cavity definition, basis sets, electron densities, model geometries, and mixed implicit/explicit models. After determining the most accurate model to reproduce experimentally-known pKas from first principles, we apply the same approach to predict pKas for radical pyridinyl species that have been proposed relevant under electrochemical conditions. This work provides considerable insight into the pitfalls using continuum solvation models, particularly when used for radical species.

The electrophoretic mobility of DNA fragments differing by a single 3'-terminal nucleotide in an automated capillary DNA sequencer

The electrophoretic mobility of DNA fragments that differ by a single 3'-terminal nucleotide was assessed by capillary electrophoresis. This was accomplished using dideoxy sequencing with a 5'-fluorescently labelled primer to generate DNA fragments with 3'-hydrogen ends. The resulting DNA fragments were electrophoresed on the ABI 3730 automated capillary sequencer, and the data were analysed with the GeneMapper software to determine the electrophoretic mobility differences on addition of a 3'-terminal nucleotide. It was found that the 3'-terminal nucleotide gave rise to different electrophoretic mobility profiles depending on the identity of the terminal nucleotide. The apparent electrophoretic mobility was (faster) -C > -A > -T > -G (slower). The C-terminated fragments were the fastest and the G-terminated fragments the slowest, relative to other nucleotides. It was proposed that the terminal nucleotide effect was due to changes in partial net charges on the nucleotides that resulted in alterations in the electrophoretic mobility of the DNA fragments in the automated capillary DNA sequencer. Other alternative explanations are also discussed.

Calculation of the stabilization energies of oxidatively damaged guanine base pairs with guanine

DNA is constantly exposed to endogenous and exogenous oxidative stresses. Damaged DNA can cause mutations, which may increase the risk of developing cancer and other diseases. G:C-C:G transversions are caused by various oxidative stresses. 2,2,4-Triamino-5(2H)-oxazolone (Oz), guanidinohydantoin (Gh)/iminoallantoin (Ia) and spiro-imino-dihydantoin (Sp) are known products of oxidative guanine damage. These damaged bases can base pair with guanine and cause G:C-C:G transversions. In this study, the stabilization energies of these bases paired with guanine were calculated in vacuo and in water. The calculated stabilization energies of the Ia:G base pairs were similar to that of the native C:G base pair, and both bases pairs have three hydrogen bonds. By contrast, the calculated stabilization energies of Gh:G, which form two hydrogen bonds, were lower than the Ia:G base pairs, suggesting that the stabilization energy depends on the number of hydrogen bonds. In addition, the Sp:G base pairs were less stable than the Ia:G base pairs. Furthermore, calculations showed that the Oz:G base pairs were less stable than the Ia:G, Gh:G and Sp:G base pairs, even though experimental results showed that incorporation of guanine opposite Oz is more efficient than that opposite Gh/Ia and Sp.

Oxidation of the antiviral drug acyclovir and its biodegradation product carboxy-acyclovir with ozone: kinetics and identification of oxidation products

The oxidation of the antiviral drug acyclovir (ACV) and its main biotransformation product carboxy-acyclovir (carboxy-ACV) by ozone was investigated. Both compounds have recently been detected in surface water, and carboxy-ACV has also been detected in drinking water. The experiments revealed a strong pH dependence of the oxidation of ACV and carboxy-ACV with reaction rate constants increasing by 4 orders of magnitude between the protonated, positively charged form (k(ox,PH(+)), ∼2.5 × 10(2) M(-1) s(-1)) and the deprotonated, negatively charged form (k(ox,P(-)), 3.4 × 10(6) M(-1) s(-1)). At pH 8 a single oxidation product was formed which was identified via LC-LTQ-Orbitrap MS and NMR as N-(4-carbamoyl-2-imino-5-oxoimidazolidin)formamido-N-methoxyacetic acid (COFA). Using Vibrio fischeri , an acute bacterial toxicity was found for COFA while carboxy-ACV revealed no toxic effects. Ozonation experiments with guanine and guanosine at pH 8 led to the formation of the respective 2-imino-5-oxoimidazolidines, confirming that guanine derivatives such as carboxy-ACV are undergoing the same reactions during ozonation. Furthermore, COFA was detected in finished drinking water of a German waterworks after ozonation and subsequent activated carbon treatment.

Absolute stereochemistry and preferred conformations of urate degradation intermediates from computed and experimental circular dichroism spectra

The enzymatic oxidation of urate leads to the sequential formation of optically active intermediates with unknown stereochemistry: (-)-5-hydroxyisourate (HIU) and (-)-2-oxo-4-hydroxy-4-carboxy-5-ureidoimidazoline (OHCU). In accordance with the observation that a defect in HIU hydrolase causes hepatocarcinoma in mouse, a detoxification role has been proposed for the enzymes accelerating the conversion of HIU and OHCU into optically active (+)-allantoin. The enzymatic products of urate oxidation are normally not present in humans, but are formed in patients treated with urate oxidase. We used time-dependent density functional theory (TDDFT) to compute the electronic circular dichroism (ECD) spectra of the chiral compounds of urate degradation (HIU, OHCU, allantoin) and we compared the results with experimentally measured ECD spectra. The calculated ECD spectra for (S)-HIU and (S)-OHCU reproduced well the experimental spectra obtained through the enzymatic degradation of urate. Less conclusive results were obtained with allantoin, although the computed optical rotations in the transparent region supported the original assignment of the (+)-S configuration. These absolute configuration assignments can facilitate the study of the enzymes involved in urate metabolism and help us to understand the mechanism leading to the toxicity of urate oxidation products.

Absolute pKa Values and Solvation Structure of Amino Acids from Density Functional Based Molecular Dynamics Simulation

Absolute pKa values of the amino acid side chains of arginine, aspartate, cysteine, histidine, and tyrosine; the C- and N-terminal group of tyrosine; and the tryptophan radical cation are calculated using a revised density functional based molecular dynamics simulation technique introduced previously [ Cheng , J. ; Sulpizi , M. ; Sprik , M. J. Chem. Phys. 2009 , 131 , 154504 ]. In the revised scheme, acid deprotonation is considered as a dissociation rather than a proton transfer reaction, and a correction term for treating the proton as a hydronium ion is suggested. The acidity constants of the amino acids are obtained from the vertical energy gaps for removal or insertion of the acidic proton and the computed solvation free energy of the proton. The unsigned mean error relative to experimental results is 2.1 pKa units with a maximum error of 4.0 pKa units. The estimated mean statistical uncertainty due to the finite length of the trajectories is ±1.1 pKa units. The solvation structures of the protonated and deprotonated amino acids are analyzed in terms of radial distribution functions, which can serve as reference data for future force field developments.

Effects of the salt concentration on charge regulation in tethered polyacid monolayers

Charge regulation in polyacid monolayers attached at one end to a planar surface is studied theoretically. The polyacid layers are designed to mimic single-stranded DNA monolayers. The effects of the local pH and salt concentration on the protonation states of the polyacid layer are studied using a molecular mean-field theory that includes a microscopic description of the conformations of the polyacid molecule along with electrostatic interactions, acid-base equilibrium, and excluded volume interactions. We predict that, in the case of a monovalent salt, NaCl, the amount of proton binding increases dramatically for high surface coverage of polyacid and low bulk salt concentration. When the polyelectrolyte is almost completely charge neutralized by bound protons, there is an expulsion of sodium from the layer. We show that the degree of protonation can go all the way from 0% to 100% when the bulk pH is kept fixed at 7 by changing the surface coverage of polyacid and the bulk salt concentration. The effects of increasing protonation and the expulsion of the cations from the monolayer are reduced when sodium ions are replaced by divalent magnesium ions. Our theoretical results concur with X-ray photoelectron spectroscopy studies of ssDNA monolayers on gold.

Mechanistic aspects of the formation of guanidinohydantoin from spiroiminodihydantoin under acidic conditions

Experimentally, it was observed that the oxidized guanine lesion spiroiminodihydantoin (Sp) contained in highly purified oligodeoxynucleotides slowly converts to guanidinohydantoin (Gh). The reaction is accelerated in the presence of acid. The possible mechanisms of this transformation have been analyzed computationally. Specifically, the potential energy surface for formation of Gh from Sp has been mapped using B3LYP density functional theory, the aug-cc-pVTZ and 6-31+G(d,p) basis sets, and the integral equation formalism for the polarizable continuum model (IEF-PCM) solvation model. The results favor a mechanism in which proton-assisted hydration of the C6 carbonyl group forming a gem-diol leads to ring opening of the iminohydantoin ring. The resulting species resembles a beta-ketoacid in its ability to decarboxylate; tautomerization of the resulting enol forms Gh. The results of these studies indicate that incubation of nucleosides or oligonucleotides containing Sp should be avoided in acidic media when high purity or an accurate assessment of the amounts of hydantoin lesions is desired.

Substitution of Ala for Tyr567 in RB69 DNA polymerase allows dAMP and dGMP to be inserted opposite Guanidinohydantoin

Continuous oxidative damage inflicted on DNA produces 7,8-dihydro-8-oxoguanine (8-oxoG), a commonly occurring lesion that can potentially cause cancer by producing G → T transversions during DNA replication. Mild oxidation of 8-oxoG leads to the formation of hydantoins, specifically guanidinohydantoin (Gh) and spiroiminodihydantoin (Sp), which are 100% mutagenic because they encode almost exclusively the insertion of dAMP and dGMP (encoding G → T and G → C transversions, respectively). The wild-type (wt) pol α family DNA polymerase from bacteriophage RB69 (RB69pol) inserts dAMP and dGMP with low efficiency when situated opposite Gh. In contrast, the RB69pol Y567A mutant inserts both of these dNMPs opposite Gh with >100-fold higher efficiency than wt. We now report the crystal structure of the "closed" preinsertion complex for the Y567A mutant with dATP opposite a templating Gh (R-configuration) in a 13/18mer primer-template (P/T) at 2.0 Å resolution. The structure data reveal that the Y to A substitution provides the nascent base pair binding pocket (NBP) with the flexibility to accommodate Gh by allowing G568 to move in the major-to-minor groove direction of the P/T. Thus, Gh is rejected as a templating base by wt RB69pol because G568 is inflexible, preventing Gh from pairing with the incoming dATP or dGTP base.

Comparison of nine programs predicting pK(a) values of pharmaceutical substances

Knowledge of the possible ionization states of a pharmaceutical substance, embodied in the pK(a) values (logarithm of the acid dissociation constant), is vital for understanding many properties essential to drug development. We compare nine commercially available or free programs for predicting ionization constants. Eight of these programs are based on empirical methods: ACD/pK(a) DB 12.0, ADME Boxes 4.9, ADMET Predictor 3.0, Epik 1.6, Marvin 5.1.4, Pallas pKalc Net 2.0, Pipeline Pilot 5.0, and SPARC 4.2; one program is based on a quantum chemical method: Jaguar 7.5. We compared their performances by applying them to 197 pharmaceutical substances with 261 carefully determined and highly reliable experimental pK(a) values from a literature source. The programs ADME Boxes 4.9, ACD/pK(a) DB 12.0, and SPARC 4.2 ranked as the top three with mean absolute deviations of 0.389, 0.478, and 0.651 and r(2) values of 0.944, 0.908, and 0.894, respectively. ACD/pK(a) DB 12.0 predicted all sites, whereas ADME Boxes 4.9 and SPARC 4.2 failed to predict 5 and 18 sites, respectively. The performance of the quantum chemical-based program Jaguar 7.5 was not as expected, with a mean absolute deviation of 1.283 and an r(2) value of 0.579, indicating the potential for further development of this type of approach to pK(a) prediction.