Nova Biotechnol Chim (2021) 20(2): e1010 DOI: 10.36547/nbc.1010 1 Nova Biotechnologica et Chimica Formation of carnosine - an ab initio study Roman Boča, Beáta Vranovičová Department of Chemistry, Faculty of Natural Sciences, University of SS. Cyril and Methodius in Trnava, Nám. J. Herdu 2, Trnava 91701, Slovakia  Corresponding author: roman.boca@ucm.sk Article info Article history: Received: 11th June 2021 Accepted: 8th September 2021 Keywords: Carnosine Histidine Beta-alanine ab initio calculations Molecular properties Equilibrium constant Note: used non-SI units kcal mol-1 = 4.184 kJ.mol-1, debye, D = 3.336 × 10-30 Ams, bohr, a0 = 5.292 ×10 −11 m, angstrom, Å = 10-10 m, atm = 101,325 Pa Abstract Formation of carnosine from histidine and -alanine is studied by ab initio MO- LCAO-SCF method followed by the perturbative configuration interaction (MP2) in vacuo. After the full geometry optimization at the SCF level, the molecular properties were evaluated and followed by the vibrational-rotational analysis. Consequently, the energy, entropy and free energy were evaluated for the reactants and products of the reaction histidine + -alanine → carnosine + H2O and finally, the equilibrium constant was enumerated. © University of SS. Cyril and Methodius in Trnava Introduction Carnosine (beta-alanyl-L-histidine) is a simple peptide formed by the condensation reaction of histidine and -alanine (Eq. 1). histidine + -alanine → carnosine + H2O (1) The molecular structures are viewed in Fig. 1. Carnosine is a substance with multi-beneficial effects (Boldyrev et al. 2013). It is synthesized in organisms by the carnosine-synthase (Eq. 2) ATP + L-histidine + -alanine → ADP + phosphate + carnosine (2) Fig. 1. From top to bottom: structure of the histidine, - alanine, and carnosine (zwitterionic forms) as extracted from the CCDC (Cambridge Crystallographic Data Centre). CCDC codes: 1889705, 1105698, and 1105666. Colours: C – dark grey, N – blue, O – red, H – white. mailto:roman.boca@ucm.sk Nova Biotechnol Chim (2021) 20(2): e1010 2 and it is metabolized by the canosinase. Beneficial effects of the carnosine were proven in many areas and the most important of them are: prevention of neurodegeneration, improvement of memory, antidepresive action, and suppressing of cancer (Schön et al. 2019). As carnosine penetrates the blood-brain barrier (BBB) and causes only little side effects, it possesses high utility potential. It serves also as a reservoir of histidine which is transformed to histamine by L-histidine- decarboxylase; the histamine itself does not penetrate BBB. Experimental X-ray structure data for the reactants and products of the reaction (Eq. 1) have been retrieved from the CCDC database (Cambridge Crystallographic Data Centre). These solid-state structures were used as an initial guess for the full geometry optimization in vacuo. For such a purpose the ab initio MO- LCAO-SCF method was utilized using the 6- 31G** basis set (Hyperchem 2008). The dilemma of the zwitterionic versus amino forms in vacuo was solved by considering both of them. At the SCF level a number of molecular properties were evaluated: the energies of the HOMO (the highest occupied molecular orbital) and LUMO (the lowest unoccupied molecular orbital), the adiabatic ionization energy Ei and electron affinity Eeg based upon the positively and/or negatively charged open-shell system after geometry optimization, followed by the evaluation of the Mulliken electronegativity  = (Ei - Eeg)/2 and the Pearson hardness  = (Ei + Eeg)/2 (Pearson 1977; Sen 1993). For the electroneutral molecule also the dipole moment p and the polarizability volume  (one-third trace of the polarizability tensor) were calculated at the SCF level. The molecular electrostatic potential (Politzer et al. 1985; Politzer and Murray 2002) was displayed as a 3D contour map on the isovalue surface of charge density; this shows the acidic/basic sites along the molecular skeleton suitable for nucleophilic and/or electrophilic interactions. The energetic properties were improved by a partial inclusion of the correlation energy by employing the 2nd-order perturbative configuration interaction using the Moller-Plesset partitioning (MP2). The above results have been compared with those obtained by the enlarged basis set 6-311G(d,p) after the full geometry optimization at the MP2 level. The optimized geometry has been a starting point for the full vibrational-rotational analysis yielding the corresponding energy levels. They enter the partition function allowing the evaluation of the thermodynamic functions, such as the internal energy U, entropy S, the free energy A and the Gibbs energy G at the room temperature. Results and Discussion The MO-LCAO-SCF calculations started from the experimental solid-state geometry that is a zwitterionic form for histidine, -alanine and also carnosine. The full geometry optimization converged to the zwitterionic form (hereafter Z) as displayed in Fig. 2 for histidine. There exists a five- membered ring H(NH2)CCO with the short contact NH…O forming a bent hydrogen bond. The molecular electrostatic potential shows that the (H2N)H site is positively charged as opposite to the –COO residue. Zwitterionic form Amino acid form Optimum geometry at the SCF level Start form the CCDC geometry (zwitterion), final zwitterionic form with the NH…O contact Start from the reallocated hydrogen atom Molecular electrostatic potential; contour 0.03 ea0 -1 Fig. 2. Optimized structure and molecular electrostatic potential for histidine. (a0 – bohr). In addition, the calculations were done for the amino-acid form (hereafter A) in which the Nova Biotechnol Chim (2021) 20(2): e1010 2 hydrogen atom from the ammonium site was reallocated to the distant oxygen atom. For histidine this canonical form is a bit more stable by 17 kcal.mol-1 at the SCF level and 10 kcal.mol-1 at the MP2 level (Table 1). The molecular properties of the Z- and A-forms are almost analogous; the only marked difference exhibits the dipole moment that for the Z-form is very high. The Pearson hardness reflects the resistance of the molecule against the electron transfer and for the histidine it is high (155, 161 kcal.mol-1) relative to the series of other amino acids (Vranovičová and Boča 2021). Table 1. Calculated properties of histidine. a a All energy quantities in units of kcal mol-1. -alanine belongs to the simplest amino acids and it crystallizes in the zwitterionic form. However, the geometry optimization resulted in travelling of the hydrogen atom from the NH3 + site to the –COO– residue where a six-membered ring (H2N)CCCOH is formed with the bent N…HO hydrogen bond (Fig. 3). The ground state molecular energy for the Z- and A- forms are almost identical, favouring the A-form only by 0.6 kcal.mol-1 (Table 2). The calculated molecular properties are very similar, again except the dipole moment. The molecular electrostatic potential is rather unique with a positive tail at the HO– edge pointing to the negatively charged NH2– group. The hardness is high: 160 and 167 kcal.mol-1. For this small molecule the geometry optimization was performed also at the MP2 level. The final geometry is almost identical with that fixed at the SCF level and it is stabilized by only 2 kcal.mol-1. Zwitterionic form Amino acid form Optimum geometry at the SCF level Start from the CCDC geometry (zwitterion), final amino acid form with the N…HO contact Start from the reallocated hydrogen atom Molecular electrostatic potential; contour 0.03 ea0 -1 Fig. 3. Optimized structure and molecular electrostatic potential of -alanine. Table 2. Calculated properties of -alanine. a a All energy quantities in units of kcal.mol-1. Zwitterion Amino acid HOMO -215 -201 LUMO 101 116 E+ -342,138 -342,136 E0 (optimized geometry) -342,323 -342,340 E− -342,220 -342,252 Ei(SCF) 185 204 Eeg(SCF) 103 88 M(SCF) 41 58 P(SCF) 144 146 E+(MP2) -343,183 -343,177 E0(MP2) -343,399 -343,409 E−(MP2) -343,305 -343,318 Ei(MP2) 216 232 Eeg(MP2) 94 91 M(MP2) 61 70 P(MP2) 155 161 Dipole moment p/debye 12.99 6.20 Polarizability /Å3 75.6 75.6 Surface area S /Å2 321 325 Volume V/Å3 475 482 Zwitterion Amino acid HOMO -261 -247 LUMO 116 124 E+ -201,788 -201,778 E0 (optimized geometry) -201,985.2 -201,985.8 E− -201,878 -201,890 Ei(SCF) 197 208 Eeg(SCF) 107 96 M(SCF) 45 56 P(SCF) 152 152 E+(MP2) -202,361 -202,351 E0(MP2) -202,593 -202,591 E−(MP2) -202,505 -202,496 Ei(MP2) 232 240 Eeg(MP2) 88 95 M(MP2) 72 72 P(MP2) 160 167 Dipole moment p/debye 6.75 2.97 Polarizability /Å3 40.7 40.5 Surface area S/Å2 242 242 Volume V/Å3 331 331 3 Nova Biotechnol Chim (2021) 20(2): e1010 2 The molecule of carnosine during the geometry optimization becomes folded as shown in Fig. 4. Zwitterionic form Amino acid form Optimum geometry at the SCF level Start from the CCDC geometry (zwitterion) with spatially separated NH3 + and COO- groups Start from the reallocated hydrogen atom Molecular electrostatic potential; contour 0.03 ea0 -1 Fig. 4. Optimized structure and molecular electrostatic potential of carnosine. Table 3. Calculated properties of carnosine. Zwitterion [kcal.mol-1] Amino acid [kcal.mol-1] HOMO -162 -200 LUMO 38 115 E+ -496,423 -496,451 E0 (optimized geometry) -496,552 -496,619 E− -496,526 -496,540 Ei(SCF) 129 168 Eeg(SCF) 26 79 M(SCF) 51 44 P(SCF) 77 123 E+(MP2) -496,846 -496,870 E0(MP2) -498,113 -498,171 E−(MP2) -496,959 -496,967 Ei(MP2) 1,267 1,301 Eeg(MP2) 1,154 1,204 M(MP2) 56 48 P(MP2) 1,210 1,252 Dipole moment p/debye 25.24 4.95 Polarizability /Å3 113.8 112.3 Surface area S/Å2 438 445 Volume V/Å3 677 689 The A-form is preferred against the Z-form by 67 and 58 kcal.mol-1, respectively. The inclusion of the correlation energy via the MP2 method causes a dramatic increase of the ionization energy, electron affinity and consequently the Pearson hardness. The effect to the Mulliken electronegativity is small (Table 3). The molecule of water possesses rather high ionization energy and electron affinity (Table 4). The calculated ionization energy Ei(MP2) = 283 matches the experimental value of 291 kcal.mol-1. The Pearson hardness P(MP2) = 202 kcal.mol -1 refers to the class of hard molecules. Table 4. Calculated properties of water.a HOMO -312 LUMO 135 E+ -47,455 E0 (optimized geometry) -47,706 E− -47,577 Ei(SCF) 251 Eeg(SCF) 129 M(SCF) 61 P(SCF) 190 E+(MP2) -47,547 E0(MP2) -47,830 E−(MP2) -47,708 Ei(MP2) 283 Eeg(MP2) 122 M(MP2) 80 P(MP2) 202 Dipole moment p/debye 2.15 Polarizability /Å3 4.87 Surface area S/Å2 116 Volume V/Å3 117 a Experiment: Ei (vertical) = 12.62 eV = 291 kcal.mol -1. All energy quantities in units of kcal.mol-1. The free energies of the reactants and products allow determining the overall change A(T) for the reaction (Eq. 1) which enters the equilibrium constant lnK = -A/RT. As evident from Table 5, for the amino-acid forms at the SCF level there is A ~ 0 at 300 K which yields K ~ 1. This value leads to the conclusion that the formation of carnosine and its hydrolysis via Eq. 1 are equally probable processes. This result gives a thermodynamic (not kinetic) predisposition to the carnosine hydrolysis. Hydrolysis of carnosine has been observed as an enzyme-assisted process (Pegova et al. 2000). The results obtained in an analogous way but using the enlarged basis set 6-311G(d,p) and MP2- optimized geometry gave almost the same results as evident from Table 5. With expectations, all 4 Nova Biotechnol Chim (2021) 20(2): e1010 2 molecular energies are a bit lower. Amino acid and zwitterionic forms of histidine, -alanine, and carnosine are close in energy. With G = -0.32 kcal mol-1 the equilibrium constant reads K = exp (-G/RT) = 1.14. Table 5. Energies, entropies, and free energies of the reactants and products at 300 K.a Histidine -alanine Carnosine H2O Reaction (Eq.1) SCF level, 6-31G** E0, Z-form -342,323 -201,985.2 -496,552 -47,706 50.2 E0, A-form -342,340 -201,985.8 -496,619 -47,706 0.8 U, 300 K -342,225 -201,908 -496,444 -47,689 0 S, 300 K 0.0984 0.0785 0.1283 0.0450 -0.0036 A, 300 K -342,254 -201,932 -496,483 -47,703 0 Evib 113.4 75.8 172.9 14.6 -1.7 Erot 0.89 0.89 0.89 0.89 0 Etrans 0.89 0.89 0.89 0.89 0 Svib 0.0283 0.0138 0.0544 0 0.0123 Srot 0.0290 0.0253 0.0317 0.0103 -0.0122 Strans 0.0411 0.0394 0.0422 0.0347 -0.0036 MP2 level, 6-31G** E0, Z-form -343,399 -202,593 -498,113 -47,830 49 E0, A-form -343,409 -202,591 -498,171 -47,830 -1 MP2 level, 6-311G(d,p) (5D, 7F) E0, Z-form -344,886 -203,472 -500,247 -48,046 65.4 E0, A-form -344,885 -203,470 -500,307 -48,046 1.57 U, 300 K -344,782 -203,396 -500,141 -48,031 6.73 S, 300 K 0.1084 0.0804 0.1365 0.0465 -0.0058 G, 300 K, 1 atm -344,805 -203,420 -500,181 -48,044 -0.32 a Energies in kcal mol-1, entropies in kcal K-1 mol-1. Z – zwitterion, A – amino acid form. Conclusions Ab initio MO-LCAO-SCF calculations show that the amino acid forms of the -alanine, histidine, and carnosine are more stable than the zwitterionic form in vacuo. The large Pearson hardness of the carnosine means that it is very resistant against the electron transfer. The formation of the carnosine from the -alanine and histidine via Eq. 1 is an equally probable process as its hydrolysis, K ~ 1. Acknowledgments Grant agencies of Slovakia are acknowledged for the financial support (projects VEGA 1/0013/18, APVV 16-0039 and ITMS No 313011ASN4). Conflict of Interest The authors declare that they have no conflict of interest. References Boldyrev AA, Aldini G, Derave W (2013) Physiology and pathphysiology of carnosine. Physiol. Rev. 93: 1803- 1845. Cambridge Crystallographic Data Centre, https://www.ccdc.cam.ac.uk/. HyperChem (2008) Molecular modeling system, ver. 8.0.6. Hypercube Inc. 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