Complexation of Ca 2+ with selenocysteine and effects on its intrinsic acidity

The interactions of Selenocysteine ( Sec ) with Ca 2+ have been investigated through the use of B3LYP/6-311+G(3df,2p)//B3LYP/6-311+G(d,p) calculations. The global minimum of the [ Sec - Ca] 2+ potential energy surface is a charge-solvated (CS) species in which the metal dication is bound to the SeH, to the amino groups and to the carbonyl oxygen. Within a gap of 5.0 kJ mol -1 in terms of free energies there are four more complexes three of which are salt-bridged (SB) structures. The interactions between Ca 2+ and the amino acid are essentially electrostatic, in contrast with what happens when Ca 2+ is replaced by Cu 2+ , where the charge transfer from Sec to the metal cation is so large that in the [ Sec -Cu] 2+ global minimum the amino acid moiety is oxidized. The significant electron density redistribution undergone by the amino acid when interacting with both doubly-charged metal ions is reflected in a significant enhancement of its intrinsic acidity, although this effect is much larger for Cu 2+ than for Ca 2+ . One of the direct consequences of the oxidation undergone by the amino acid when attached to Cu 2+ is that the complexes formed are thermodynamically unstable with respect to a proton loss since the process Sec + Cu 2+  [( Sec -H)Cu] + + H + is strongly exothermic. Conversely, a similar process when Cu 2+ is replaced by Ca 2+ is endothermic and therefore the [ Sec -Ca] 2+ complexes should be stable with respect to a proton loss.


Introduction
Selenocysteine (Sec) is considered the 21st amino acid and it is found in all kind of living beings as a building block of selenoproteins, 1 which have been found to be essential in mammals. 2 Indeed, the first selenoprotein identified in mammals, namely glutathione peroxidase, protect cells from oxidative damage. 3[5] This is, for instance the case of formate dehydrogenase which catalyzes the oxidation of formate to carbon dioxide, and in which the presence of Sec seems to play a crucial role in the mechanism of the reaction. 6It seems also well established that Sec-containing enzymes modulate and play some role in brain diseases, such as Parkinson's disease or epilepsy, 5,7 and that the deficiency of some Sec-containing enzymes seems to be closely related with stroke risk, 8 whereas several others have been implicated in the risk or development of cancer. 9Also importantly, 25 human genes encoding selenoproteins have been already identified, 10 although little is known, for the time being, about their biological functions. 11alcium is also an essential element for living organisms controlling or participating in many cell physiological activities under the form of a doubly charged ion, Ca 2+ .Actually it is well established that Ca 2+ is the single most important information carrier at the cellular level 12 with different mechanisms that regulate the intracellular Ca 2+ concentration. 13Ca 2+ also has important roles at nerve terminals as well as important postsynaptic, 14 and muscle contraction functions 15- 17 stabilizes the folded proteins 18 and increase their thermal stability. 19t the molecular level, the interactions between a base and a doubly charged metal ion usually is accompanied by a dramatic electron density redistribution within the neutral molecule interacting with the ion, due to the strong coulombic field created by the latter, 20 which in the case of ions like Cu 2+ may result in the oxidation of the base.
The specific interactions between Sec and Ca 2+ are of particular relevance because, besides the different roles mentioned above for Ca 2+ , it seems that the key proteins in cell protection against oxidative stress 21 and those which usually participate in the regulation of intracellular Ca 2+ concentration 22 are Sec-containing proteins.[25]

Computational Details
Geometry optimizations were carried out at B3LYP level using the 6-311+G(d,p) basis set.The B3LYP approach combines Becke's three parameter nonlocal hybrid exchange potential 26 with the nonlocal correlation functional of Lee et al., 27 and it has been shown to provide reliable geometries for a wide variety of compounds, 28 with a rather good accuracy/cost ratio.The same functional has been shown to yield reliable gas-phase basicities and acidities, [29][30][31] provided that a flexible enough basis set is used.In all the cases, Gaussian09 series of programs 32 were used.The harmonic vibrational frequencies were used to classify the different stationary points as local minima or transition states.The connectivity between local minima and transition states was verified by means of intrinsic reaction coordinate (IRC) calculations as implemented in the Gaussian09 suite of programs.Final total energies were obtained by single-point calculations using a 6-311+G(3df,2p) basis sets.For the subsequent analysis of the acidity of the most stable complex, the deprotonated species were optimized and the corresponding harmonic frequencies were obtained at the same level used for the neutrals.From the frequency calculations, the thermal corrections to enthalpies and Gibbs free energies were evaluated at 298.2 K.The gasphase acidity (ΔacidH) of a compound A is defined as the proton affinity of the corresponding anion (equation 1); hence, the lower the value of ΔacidH, the higher the acidity of the system.
The acidity can also be measured in terms of the corresponding Gibbs free energy, ΔacidG.A NBO (Natural Bond Orbital) analysis 33 was used to study the most prominent interactions in each molecular structure.NBO analysis allows the separation of the molecular energy into two fundamental contributions: the total energy (where delocalization is included), and the energy of the hypothetical Lewis structure.Accordingly, the electrons are strictly located in bonds and lone pairs.The interactions between occupied and empty antibonding (or Rydberg) orbitals represent the deviation of the molecule from the ideal Lewis structure and can be used as a measure of delocalizations (Edeloc = Etotal -ELewis).The formation of dative bonds, and the existence of backdonation effects are easily detected by the evaluation of second-order orbital interaction energies involving the occupied orbitals of the amino acid and the empty orbitals of the metal cation and between occupied d-orbitals of the metal and the empty antibonding orbitals of the amino acid, respectively.In the framework of the NBO approach it is also possible to calculate the Wiberg bond orders, 34 which provide additional quantitative information on the bonding between the metal and the base.All the NBO calculations were carried out at B3LYP/6-311+G(d,p).The bonding of the more stable complexes was also analyzed by means of the atoms in molecules (AIM), 35 and the electron localization function (ELF) [36][37][38] theories.By means of AIM theory we have obtained the molecular graphs showing the bond paths connecting the different bonded atoms and containing the bond critical points (BCPs), which correspond to stationary points in which the electron density is minimum along the line that connect two maxima and maximum in the other two directions.ELF is a function, which, conveniently scaled between [0,1], 37,39 permits division of the physical space in regions where electron pairs, either bonding or lone pairs, are localized.These regions or basins are usually classified as monosynaptic (core or lone pairs) and disynaptic (involving two atomic valence shells), and their electron population provides useful insights into the bonding pattern of the molecule.ELF grids and basin integrations have been evaluated with the TopMod package. 39For the three-dimensional plots, an ELF value of 0.8 is normally used.
One of the major problems associated with the theoretical study of the amino acids is the abundance of different conformers.Indeed, for L-homoselenocysteine at B3LYP level we have localized a total of seventy-seven conformers 40 .For Sec Vank et al. 41 have shown that 81 different conformers should be expected, although the potential energy surface (PES) only contains seven minima of the side chain. 42Kaur et al. 43 located a total of 33 conformers of Sec within an energy gap of 10.4 kcal mol -1 , at B3LYP/6-311++G(d,p)// B3LYP /6-31+G(d,p) level of theory, while, Spezia et al. 44 have found seven structures within an energy gap of 3.83 kcal/mol.Since the main aim of our study is not to explore the different conformations of Sec but to look at the characteristics of its complexes with Ca 2+ , for our survey, we selected the eight most stable ones, shown in Figure 1, from the five most stable conformers reported in ref. 43 and the seven conformations reported in ref. 44 after ruling out the common ones.If one assumes a Boltzmann distribution, and using the relative Gibbs free energies summarized in Table 1, Sec, in the gas phase and at room temperature (298.2K), should be an equilibrium mixture of the eight conformers summarized in Figure 1 and Table 1, with the relative abundances shown in the fourth column of that  1, which are named in alphabetic order from the most to the least stable in terms of their free energy.Note that when the complex formed corresponds to salt-bridge structure, in which the metal dication interacts with the zwitterionic form of Sec, a (z) has been added to the letter which designates the complex.Their relative energies, enthalpies and free energies are summarized in Table 1.The structures of the six more stable complexes are given in Figure 2. Thermodynamic data and the structures for the remaining complexes are shown in Table S1 and S2, respectively, of the supporting information.The global minimum of the potential energy surface for [Sec-Ca] 2+ , a, is a charge-solvated (CS) structure in which the metal dication is bound to the carbonyl group of the acidic function, the amino group and the SeH group.Similar tricoordinated CS structures have been found for other amino acids, as serine and cysteine, when interacting with Ca 2+. 45 The tricoordination of Ca 2+ is nicely reflected in the corresponding molecular graph (See Figure 3a) which shows the existence of BCPs between Ca and the aforementioned three basic sites as well as the existence of a cage (green dot) critical point.Besides, the electron localization function (ELF) theory shows the existence of disynaptic basins for Ca-O, Ca-N and Ca-Se bonds (See Figure 3b).These findings are consistent with a second-order NBO analysis which shows interactions between the lone-pairs of oxygen, nitrogen and selenium with the empty sd hybrids of Ca, with second order interaction energies of 22, 25 and 92 kJ mol -1 , respectively.Accordingly, the corresponding Wiberg bond orders of the O-Ca, N-Ca and Se-Ca bonds (0.078, 0.081 and 0.187, respectively, Figure 2) follow a similar trend.
The internal rotation of the Se-H group implies a destabilization of the complex by 1.4 kJ mol -1 yielding the third local minima, c, with a bonding pattern almost identical to that of the global minimum.The second most stable adduct b(z) corresponds to a salt-bridge (SB) form, in which Ca 2+ interacts simultaneously with the two oxygen atoms of the carboxylate group of the zwitterionic form of Sec.It is worth noting that both AIM and ELF predict these two Ca-O bonds not to be strictly identical in strength.Indeed, the electron density at the BCP and the population of the O-Ca disynaptic basin are slightly smaller for the linkage involving the oxygen atom closer to the amino group.This is due to the fact that, as illustrated in Figure 3b, the valence electron density of this oxygen atom is slightly polarized towards the nearby amino group.This SB structure is entropically stabilized.Note that in terms of enthalpy it is 7 kJ mol -1 higher in energy than the global minimum, whereas in terms of free energies the gap reduces to only 0.9 kJ mol -1 .As for the global minimum an internal rotation of the SeH group yields the d(z) structure, 2.3 kJ mol -1 higher in energy.A simultaneous internal rotation of the amino group and around the C-CSe bond leads to the fifth local minimum, e(z), 4.6 kJ mol -1 higher in energy.In this local minimum, the favorable orientation of the amino group with respect to the carboxylate one leads to the formation of an intramolecular hydrogen bond between one of the amino hydrogens and one of the carboxylate oxygens.A further rotation around the C-CSe bond yields the sixth local minimum, f(z).As shown in Figure 3a, in this structure Ca appears again tricoordinated, although the Ca-Se interaction is much weaker than that in structures a and c, as reflected in the value of the electron density at the Ca-Se BCP.
It is worth noting that complexes a and c are the result of the association of the Ca 2+ to the third more stable tautomer Sec3, and differ only on the relative orientation of the SeH group.

Conversely, complexes b(z), d(z)-f(z)
arise from the association to the zwiterionic form of the global minimum Sec1, the metal dication bridging between the two oxygen atoms of the carboxylate group.Also, in agreement with the behavior reported for serine, 25 the global minimum of the [Sec-Ca] 2+ PES is a CS structure, what is at variance with glycine, 46 where the global minimum of the PES is a SB structure.
The interconversion between local minima of the [Sec-Ca] 2+ PES is reported in Figure 4. Starting from the global minimum a, the interconversion between the CS and the SB structures requires the OH group of the carboxylic acid situated close to the amino group in order to favor the necessary proton transfer.In the neutral system this could be achieved through an internal rotation around the C-COOH bond, but for the global minimum this possibility is energetically too demanding because the COOH group is attached to Ca 2+ .An alternative mechanism maintaining the initial connectivity of Ca implies a H-shift from the OH towards the carbonyl group, which involves a rather high (136 kJ mol -1 ) energy barrier yielding the local minimum p.

Comparison between Ca 2+ and Cu 2+
As we have indicated in the introduction one of the signatures of the interactions between neutral compounds and doubly charged metal ions is the significant distortion that the latter produces on the electron density distribution of the former.These effects normally reflect the polarization produced by the strong coulombic field created by the ion and ultimately may lead to a significant charge transfer from the base towards the metal ion.As indicated in previous sections, this is actually observed in Sec-Ca 2+ complexes, in which a nonzero second-order interaction energy between the lone-pairs of the Sec and the empty orbitals of Ca are found.The situation is quantitatively different however when the doubly-charged ion is a transition metal, such as Cu 2+ .The global minimum is still a tricoordinated complex similar to structure a, in which the metal interacts simultaneously with the carbonyl oxygen atom, the SeH and the amino groups.However, the interactions with these three groups are significantly stronger than those calculated for Ca 2+ , so that the electron densities at the Cu-O, Cu-N and Cu-Se BCPs are higher (0.061, 0.088 and 0.063 a.u., respectively), as well as the corresponding Wiberg bond orders (0.169, 0.278 and 0.484, respectively).This bonding enhancement on going from Ca 2+ to Cu 2+ has a double origin.In the first place Cu 2+ is a better electron acceptor because its 4s empty orbital lies much lower in energy with respect to the 3d occupied than that of Ca 2+ with respect to the 3p occupied orbitals.In the second place, occupied 3d-orbitals of Cu(I) are much higher in energy than the 3p orbitals of Ca 2+ and easily back-donate to the antibonding orbitals of Sec.The consequence is that whereas in [Sec-Ca] 2+ complexes there is only a polarization of the lonepairs amino acid, with small orbital interaction energies, in [Sec-Cu] 2+ complexes, the interactions of the metal with the O lone-pairs are much stronger than those found for Ca (second order interaction energy 46 vs. 22 kJ mol -1 ), and with Se and N are so strong that a Se-Cu covalent bond (89.4% of Se (12.1% s, 87.8% p) + 10.6% of Cu (67.7% s, 31.7% p), occupancy = 1.85) and a half-bond N-Cu (78.4% N (14.8%s,85.2% p) + 21.6% Cu (41.3% s, 7.4% p, 51.3% d), occupancy = 0.96) are found.The obvious consequence is that while in complex a the natural charge on Ca is very close to 2 (1.81), in the [Sec-Cu] 2+ global minimum is 1.04, indicating that, upon association with Cu 2+ , Sec becomes oxidized.This is confirmed by the fact that the spin density, initially located in Cu 2+ , which is a doublet in its ground state, is mainly located on the Sec moiety when the [Sec-Cu] 2+ is formed.

Effects on the intrinsic acidity of Sec
The acidity of amino acids such as Sec is a useful information to understand the chemistry of peptides which they can formed. 47It is quite obvious from the previous discussion that the association of Sec with doubly-charged metal ions should result in drastic changes in its intrinsic properties and, in particular, in its intrinsic acidity.To analyze this question we have evaluated the intrinsic acidity of the isolated amino acid, as well as that of the six most stable [Sec-Ca] 2+ complexes.
Since as mentioned above in the gas phase and at 298.2 K Sec is an equilibrium mixture of eight conformers, we have evaluated the acidity of these eight forms considering that OH, SeH and amino deprotonation would be possible.From this theoretical survey we can conclude that the deprotonation of the amino group never competes with OH or SeH deprotonation.However, there are conformers which behave as oxygen acids, whereas others behave as Se acids.Similar findings have been reported in the literature. 43The results obtained through B3LYP/6-311+G(3df,2p)//B3LYP/6-31+G(d,p) calculations have been summarized in Table 2.It can be observed that whereas the global minimum, Sec1, as well as Sec4, Sec5 and Sec8 behave as a Se acids, the second local minimum and Sec3, Sec6 and Sec7 are predicted to be oxygen acids, the deprotonation of the OH group being 12, 6, 23, and 15 kJ mol -1 more favorable than the deprotonation of the SeH group, respectively.Taking into account that Sec is an equilibrium mixture of these eight conformers with the relative abundance given in Table 1, the expected acidity of this amino acid should be 1390.9kJ mol -1 .To the best of our knowledge the gas-phase acidity of Sec is not known, but our estimated value predict Sec to be less acidic than previous theoretical estimates. 43he association of Sec with Ca 2+ leads to two important changes regarding the intrinsic acidity of the system.Firstly, there is an expected and huge acidity enhancement.Indeed the global minimum a is 815 kJ mol -1 more acidic than the isolated amino acid.Secondly, regardless of the kind of complex (CS or SB) which undergoes the deprotonation, the SeH group is the most acidic site.Among the complexes investigated f(z) is the strongest acid followed by complex c, which is predicted to be 1.3 kJ mol -1 less acidic.The estimated acidity enhancement for Cu 2+ complexes (993 kJ mol -1 ) is larger than for Ca 2+ as a consequence of the oxidation undergone by the amino acid when associated with the transition metal ion.However, the most important observation is that whereas the overall deprotonation process is strongly exothermic when the interaction involves Cu 2+ , it is slightly endothermic if the metal ion is Ca 2+ .As shown in Figure 5a for both the most stable CS and the most stable SB structures the [(Sec-H)Ca] + + H + dissociation limit lies respectively 9 and 87 kJ mol -1 higher in energy than the Sec + Ca 2+ entrance channel.Conversely, when Ca 2+ is replaced by Cu 2+ , the corresponding dissociation limits (See Figure 5b) lie 736 and 581 kJ mol -1 lower in energy than the Sec + Cu 2+ entrance channel.This implies that whereas the formation of the [Sec-Cu] 2+ is thermodynamically instable with respect to the loss of a proton and should undergo a spontaneous deprotonation, the [Sec-Ca] 2+ is stable with respect to same process.

Conclusions
The global minimum of the [Sec-Ca] 2+ potential energy surface is a CS species in which the metal dication is bound to the three basic groups of the amino acid, namely the carbonyl oxygen, the SeH and the amino groups, but within a gap of 5.0 kJ mol -1 in terms of free energies there are other four complexes, three of which are SB structures.Actually, the second local minimum of the PES, is a SB complex entropically stabilized which lies only 0.9 kJ mol -1 higher in energy than the CS global minimum.The interactions between Ca 2+ and the amino acid are essentially electrostatic, in contrast with what happens when Ca 2+ is replaced by Cu 2+ , where the charge transfer from Sec to the metal cation is so large that in the [Sec-Cu] 2+ global minimum the amino acid moiety is oxidized.The significant electron density redistribution undergone by the amino acid when interacting with both doubly-charged metal ions is reflected in a significant enhancement of its intrinsic acidity, although this effect is much larger for Cu 2+ than for Ca 2+ .Whereas the conformers of the isolated Sec are oxygen or selenium acids, the complexes with Ca 2+ are always Se acids.One of the direct consequences of the oxidation undergone by the amino acid when attached to Cu 2+ is that the complexes formed are thermodynamically unstable with respect to a proton loss since the process Sec + Cu 2+  [(Sec-H)Cu] + + H + is strongly exothermic.Conversely, a similar process when Cu 2+ is replaced by Ca 2+ is endothermic and therefore the [Sec-Ca] 2+ complexes should be stable with respect to a proton loss.

Figure 3 .
Bonding of the more stable [Sec-Ca] 2+ complexes (a) Molecular graphs.Red, yellow and green dots denote bond, ring and cage critical points, respectively.Electron densities are in a.u.(b) ELF plots.Blue and red lobes denote core and lone-pair monosynaptic basins.Green lobes correspond to disynaptic basins between heavy atoms.Yellow lobes denote disynaptic basins corresponding to bonds between heavy and hydrogen atoms.Populations are in e -.