Accepted Manuscript

Complexations of Alkali/Alkaline Earth Metal Cations with Gaseous Glutamic

Acid

Lingbiao Meng, Zijing Lin

PII: S2210-271X(14)00194-7

DOI: http://dx.doi.org/10.1016/j.comptc.2014.04.016

Reference: COMPTC 1476

To appear in: Computational & Theoretical Chemistry

Received Date: 28 February 2014

Revised Date: 16 April 2014

Accepted Date: 17 April 2014

Please cite this article as: L. Meng, Z. Lin, Complexations of Alkali/Alkaline Earth Metal Cations with Gaseous

Glutamic Acid, Computational & Theoretical Chemistry (2014), doi: http://dx.doi.org/10.1016/j.comptc.

2014.04.016

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1

Complexations of Alkali/Alkaline Earth Metal Cations with Gaseous Glutamic Acid

Lingbiao Meng1,2 and Zijing Lin1,*

1 Department of Physics & Collaborative Innovation Center of Suzhou Nano Science and Technology,

University of Science and Technology of China, Hefei 230026, China

2 Research Center of Laser Fusion, China Academy of Engineering Physics, Mianyang 621900, China

* Corresponding author. Tel: +86–551–63606345, Fax: +86–551–63606348, E–mail: zjlin@ustc.edu.cn

2

Abstract: Structures and binding energies are important information for describing the interactions

between biomolecules and metal ions. The gas phase coordination properties of the metal cations, Li+,

Na+, K+, Mg2+, and Ca2+, with glutamic acid (Glu) are thoroughly examined by considering all the likely

cation coordination modes and through the first principle conformational searches. Many important

low-energy conformers are newly located in this work. For Glu-Li+/Mg2+ complexes, the dominant

cation coordination mode is the tridentate charge solvated (CS) coordination, where the cation interacts

with the amine nitrogen, backbone carboxylic oxygen and side-chain carboxylic oxygen of canonical

Glu. For Glu-Ca2+, the tridentate salt bridge (SB) coordination where the cation interacts with the

deprotonated backbone carboxylic group and side-chain carboxylic oxygen of zwitterionic Glu is clearly

preferred. For Glu-Na+/K+, both the bidentate SB and CS coordination modes and the tridentate

coordination are predicted to coexist at the room temperature and their relative stabilities depend on the

computational methods. The effects of cation chelation on the relative stability of SB and CS isomers are

analyzed. The IR spectra of the complexes and the metal ion affinities (MIAs) are computed and agree

with the available experiments. A rule of thumb for estimating MIAs is discussed.

Keywords: Amino acid, Metalation, Conformation, Metal ion affinity, First principle calculation

3

1. Introduction

Metal cations are involved in a great number of fundamental processes of living organisms,1,2 but

their roles on the structures and functions of biological molecules such as proteins, nucleic acids, and

peptide hormones at the atomistic and electronic levels remain nebulous. Increased knowledge of the

interactions between metal cations and biomolecules is helpful for the understanding and prediction of

biomolecular properties in vivo. As significant systems either as individual biomolecules or as the

building blocks of all peptides and proteins, the naturally occurring amino acids (AAs) have been

recognized as the most important elemental models to study these interactions, and consequently, there

has been a growing interest in studying the combinations of metal cations with AAs.3–27

As a naturally occurring AA, glutamic acid (Glu) and its interactions with alkali/alkaline earth metal

cations play important roles in many biological processes. For example, Glu is the most abundant

excitatory neurotransmitter in the vertebrate nervous system,28 but excess Glu may accumulate outside

cells and causes Ca2+ to enter cells via N-methyl-D-aspartate receptor channels, leading to neuronal

damage and eventual cell death from the excessively high intracellular calcium.29 With two carboxylic

groups, a very flexible side chain and as the most acidic AA, Glu is also an interesting ligand from a

metal ion selectivity point of view. Both experimental and theoretical works have been conducted to

study the coordination properties of alkali/alkaline earth metal cations on the structures and energetics of

Glu.30–35 Bojesen et al. obtained the relative affinities of Li+ for some AAs and Na+ for all 20 AAs

determined by the Cooks’ kinetic method.30 Kish et al. derived the relative Na+ affinities of amino acids

using the kinetic method based on the dissociations of Na+ bound heterodimers of different AAs,31 and

estimated the absolute Na+ binding energy by anchoring the relative values to the Na+ affinity of alanine.

Subsequently, Heaton et al. provided the absolute Na+ and K+ affinities for Glu by the collision-induced

dissociation of cation-bound Glu complexes with Xe using a guided ion beam tandem mass

spectrometer.32,33 More recently, Williams and coworkers investigated the interactions of some

alkali/alkali earth metal cations with Glu and the role of gas-phase acidity on the zwitterionic stability by

the infrared photo–dissociation spectroscopy.34 To better understand the measured results, the recent

experiments are often accompanied with theoretical calculations.32–34 However, the existing theoretical

studies are subjected to some limitations, e.g., the candidate conformations of Glu-M+/2+ were obtained

by prescreening using the molecular force field based Monte Carlo sampling or simulated annealing

method, and the methods are prone to miss important conformations.36 Therefore, extensive systematic

conformational searches of the potential energy surfaces (PESs) of Glu-M+/2+ are required to improve

the reliabilities of the theoretical results. Moreover, to the best of our knowledge, the interactions of Glu

with these metal cations have not been considered together yet from a theoretical point of view. It is of

4

interest to analyze both the differences and similarities in the metalation conformations.

This paper reports a detailed study on the coordination chemistry of gaseous Glu with five typical

alkali/alkali earth metal cations, M = Li+, Na+, K+, Mg2+, and Ca2+, by means of quantum chemistry

calculations. The important conformations and their structural characteristics are analyzed. Metal ion

affinities (MIAs) and IR spectra of the metalated Glu are computed and compared with the available

experiments.

2. Computational Method

The complexation of a metal cation and AA may be generally classified into the two coordination

categories of charge solvation (CS) and salt bridge (SB).3,4,10,22 In the CS coordination, the metal cation

is chelated by heteroatoms of AA in a canonical conformation. In the SB coordination, the cation is

coordinated to AA in a zwitterionic form where a carboxylic hydrogen is transferred to the amino group.

As there are two carboxylic groups in Glu, there are two possible zwitterionic forms for Glu, as

illustrated in Fig.1. The zwitterions are predicted to be unstable for isolated Glu,37 but may be stabilized

by metalation. Therefore, it is necessary to consider both CS and SB species when examining the

coordination effect of metal cation.

To reliably explore the conformation space of Glu-M (M = Li+, Na+, K+, Mg2+ and Ca2+), the possible

metal-ion coordination modes for Glu as illustrated in Scheme 1 should be systematically considered.

The detailed consideration of coordination modes and the procedure of generating trial structures for

Glu-M have been described in our previous study on the interactions of Glu and transition metal ions.38

Briefly, a total of eight coordination modes of metal ion are considered for each of the canonical species

and the backbone deprotonated zwitterions (ZW.b) and side-chain deprotonated zwitterions (ZW.s).

Sixty low-energy conformers of Glu37 were used for each of the eight cation coordination modes. These

canonical conformers were also used by proton transfer to generate the initial 60 structures for each of

the ZW.b and ZW.s species. The trial structures of Glu-M were generated by all combinations of the 8

coordination modes of metal ion and the 180 Glu structures. All the trial structures of the Glu-M

complexes were first optimized at the HF/3–21G(d) level. The unique structures thus obtained were then

optimized at the B3LYP/6–31G(d) level. The low energy conformations of Glu-M were further

optimized at the B3LYP/6–311++G(d,p) level. All the low energy conformers were verified to be the

true local minima by the frequency calculations at the B3LYP/6–311++G(d,p) level. The vibrational

frequencies, zero-point vibrational energy (ZPVE) and thermal corrections to enthalpy (Hcor) and free

energy (Gcor) were then determined. The thermodynamic corrections were obtained by the standard

statistical method39 with unscaled harmonic vibrational frequencies and the rigid rotor approximation

and assuming an ideal gas for Glu-M at the standard state. The single-point energies of the low energy

5

Glu-M conformations were calculated by the methods of B3LYP, BHandHLYP and MP2 with three

basis sets of 6–311++G(d,p), 6–311++G(2d,2p) and 6–311++G(3d,2p). Unless noted explicitly, the

6–311++G(3d,2p) results are used. The single-point energies of the selected low energy Glu and Glu-Li+

conformations were calculated at the level of CCSD(T)/6–311++G(d,p). All the geometry optimizations

and energy calculations were performed with the Gaussian03/09 suite of programs.40

The metal ion affinity (MIA) was calculated as the negative of enthalpy change (–ΔH) of the gas

phase metalation reaction, Glu + M → Glu-M, at the standard state:

)()()( MGluHMHGluHHMIA −−+=Δ−= (1)

The enthalpy of isolated Glu or metalated Glu, H(A) (A=Glu or Glu-M), was determined by

conformational ensemble averaging:

∑=i ii AHAfAH )()()(

(2)

where Ai denotes the ith conformer of species A. f(Ai) is the equilibrium population of conformer Ai

determined by the relative conformational free energies (G(Aj)) according to the Boltzmann distribution:

∑ −−=j

RTAGRTAGi

ji eeAf /)(/)( /)( (3)

The enthalpy of metal ion, MH , was calculated as its electronic energy ( ME ) plus its translational

energy (3

2RT ) and PV term ( RT= ):

5

2M MH E RT= + .

The negative of free energy change (–ΔG) of the reaction was also computed. In addition to the

ensemble averaging, the contribution by the entropy of mixing41 was also considered:

∑∑ +=i iii ii AfAfRTAGAfAG )(ln)()()()(

(4)

The free energy of metal ion, G(M), was calculated by considering the contribution of translational

entropy as39:

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞⎜

⎝⎛−=

P

Tk

h

TmkRTMEMG BB

2/3

2

2ln)()(

π (5)

where m is the mass of metal ion. The basis set superposition errors (BSSEs) with the counterpoise

method42 were also considered in the single-point energy calculations for computing MIA and –ΔG.

3. Results and Discussion

As there are five electronegative atoms (four O atoms and one N atom) and a flexible side chain in

Glu, there are numerous possible metalation patterns for Glu. The metalation patterns may be generally

classified as mono-, bi-, and tridentate coordination between a metal ion and the electronegative atoms

of Glu. The tridentate M coordination modes may in principle include OOOs, OOsOs, NOOs, NOO, and

NOsOs, where O and Os denote a back-bond oxygen and a side-chain oxygen, respectively. Low energy

6

conformers are found only for the coordination modes of OOOs, OOsOs and NOOs. The bidentate M

coordination modes may include NO, NOs, OOs, OO, and OsOs. Low energy conformers are found only

for the modes of OOs, OO and OsOs. The monodentate coordination structures may be ignored due to

their high conformational energies. As the cation coordination modes may correspond to either canonical

or zwitterionic Glu, for easy identification, the suffixes of .c and .z are used to denote the canonical and

zwitterionic structures, respectively. For example, a low energy conformation of Glu-M may be denoted

as NOOs.c, OOOs.z, OOsOs.c, OOsOs.z, OO.z, OOs.c or OsOs.c. Different conformations of a given

coordination type are further differentiated with a numeral suffix to indicate their relative stabilities

ordered according to their MP2 energies, e.g., NOOs.c1 and OOOs.c2. For simplicity, a conformer may

also be denoted with the name of the metal element followed by a numeral suffix to indicate its relative

stability within all conformers ordered according to its relative MP2 energy, e.g., Na_1 and Na_2.

3.1 Conformations and Energies of Glu-M Complexes

After performing the extensive conformational searches described above, numerous low energy

structures of various coordination interactions between Glu and M are located. Table 1 shows the

relative electronic energies, dipole moment, ZPVE, Hcor and Gcor for 10 or more low energy

conformations of Glu-M for each M species. The structures of important conformers are shown in Fig.2.

An important conformer here means that the room temperature population of the conformer is over 10%

as determined by any one of the B3LYP, BHandHLYP and MP2 methods. In case there is only one

dominant conformer for a metal ion, the second most abundant conformer is also shown in Fig.2. For

comparison, the conformations known in the literatures32–35 are indicated in Table 1. As shown in Table

1, a significant number of the low-energy conformers of Glu-M are newly found in this work,

demonstrating the necessity of the present high quality conformational search that provides a much

improved description of the PESs of the Glu-M complexes.

As seen in Table 1, the B3LYP, BHandHLYP and MP2 results agree on the global minimum

conformer of Glu-Li+ that adopts a CS coordination mode of NOOs.c and that the global minimum is the

only important conformer for Glu-Li+. Similar results are obtained for Glu-Mg2+. For Glu-Na+, however,

the global minimum adopts an SB coordination of OO.z as predicted by MP2, but adopts a CS structure

of NOOs.c as predicted by both B3LYP and BHandHLYP. The difference in the relative energy of the

minima is surprisingly large as predicted by different methods, about 6.2 kcal/mol between MP2 and

B3LYP and 8.5 kcal/mol between MP2 and BHandHLYP. Probably due to the involvement of metal

cation, the methodological difference in relative conformational energy computed here is even larger

than that thought to be abnormally large found for arginylglycine and glutamine.43,44 The difference can

only be due to the methodological difference and not due to the incompleteness of the basis set used. As

shown in Table 2, the maximal error in determining the relative conformational energy is less than 2.5

7

kcal/mol for the basis set of 6–311++G(d,p) and less than 0.6 kcal/mol for 6–311++G(2d,2p). The

possible error in the relative conformational energy for 6–311++G(3d,2p) should be smaller than that for

6–311++G(2d,2p). Therefore, the 6–311++G(3d,2p) basis set used in Table 1 may be viewed as

practically convergent for determining the relative conformational energy. To resolve the conflicting

results of MP2 and B3LYP or BHandHLYP, a much higher level of theory may be required. Fortunately,

the ultimate answer rests on the experiment. The dipole moment of the MP2 global minimum of

Glu-Na+ is 5.0 Debye, while that for the global minimum of B3LYP and BHandHLYP is less than 3.5

Debye. As the dipole moments can be accurately determined experimentally,45 the theoretical results

may be unambiguously tested by the dipole moment measurement at low temperature. Together with the

theory, such a measurement of the dipole moment also provides the answer to whether the global

minimum of Glu-Na+ is a CS or SB conformer.

The global minimum of Glu-K+ is a CS structure of NOOs.c coordination as predicted by both MP2

and BHandHLYP, but is a SB conformer of OO.z coordination as predicted by B3LYP. Again, the dipole

moment of the SB conformer is larger than that of the CS conformer and the experimental measurement

may be used to test the theories. Similarly, the measurement of characteristic IR spectrum to be

discussed below may also be used to provide the answer.

All the B3LYP, BHandHLYP and MP2 results agree on that the global minimum of Glu-Ca2+ adopts a

SB conformation with the Ca2+ coordination mode of OOOs.z, while the energy for the OOsOs.z

coordination is rather high.

Overall speaking, the tridentate coordination is strongly favored by Li+/Mg2+/Ca2+, with Li+ and Mg2+

clearly favor the NOOs.c mode, while Ca2+ clearly favors the OOOs.z mode. For Na+ and K+, the

electrostatic interaction is relatively weak in comparison with the cases for Li+/Mg2+/Ca2+. The bidentate

coordination of OO.z and OOs.c becomes more competitive with the tridentate coordination as the

bidentate coordination allows for increased M-O/Os interaction with reduced distance between M and

O/Os. As a result, it is not known a priori which coordination mode the global minimum may adopt.

It is worthy pointing out that the bidentate coordination of NO.c is completely absent in the

low-energy conformations of Glu-M shown in Table 1. This is distinctly different from that found for

aliphatic AAs,4,6,18 where the cation NO.c coordination mode is ubiquitous in the low energy structures.

With the additional interaction between the cation and Os of Glu, the energy of the NOOs coordination

is much reduced in comparison with that of the NO coordination, demonstrating the critical importance

of electrostatic effect on the coordination mode. Clearly, the side chain has a strong effect on the cation

coordination of AA. The results obtained with the relatively simple aliphatic AAs may not be trivially

extended to AAs with polar side chains.

3.2 Effect of Cation Chelation on the Relative Stability of SB and CS Isomers

8

The relative stabilities of AA conformations can be substantially modified by the specific noncovalent

interactions between AA and metal cations. There has been a widespread interest in understanding the

effect of metal chelation on the relative stability of SB and CS isomers. Combining the above results

with that in literatures, some useful observations may be made. Major factors influencing the

conformational stabilities of CS and SB complexes have been suggested in the literatures, which are

discussed briefly here.

(1) The size of cation. It has been suggested that the stability of SB species increases with the size of

cation.3,23,24 The argument has been that the SB conformation is favored when the electrostatic

interaction is relatively strong. The outer shell electrons of a large-sized cation have low density and

high polarisabilities and are less effective for shielding the positive charge which tends to have a strong

interaction with the electron-rich sites of AA. A small-size cation such as Li+ has little charge diffusion

and a strong tendency to accept electrons from its ligand, resulting in a relatively weak electrostatic

interaction. As seen in Table 3, this theory is partially supported by the B3LYP results for monovalent

cations only. However, the electrostatic interaction of Glu with divalent cation is clearly stronger than its

counterpart with monovalent cation. Moreover, it is difficult to imagine that the electrostatic interaction

in Glu-Li+ is weaker than that in Glu-Na+ or Glu-K+. Therefore, the effect of cation size on the relative

SB and CS structures is valid in a very limited sense at the best, and a better argument for the effect is

needed.

(2) The basicity of AA. The formation of an SB structure may be viewed as a process of proton

transfer. It is reasonable to associate a higher proton affinity of AA with a higher stability for an SB

conformation.25,31 According to this model, however, Glu should be easier than aliphatic AAs but more

difficult than histidine to form an SB structure, in strong disagreement with the known results.3,4,6,18,19

Therefore, the model is useful only for comparing different aliphatic AAs.

(3) The charge of cation. There have been experimental and theoretical evidences that increasing the

cation charge from +1 to +2 has a stabilization effect on the SB conformation.19,22,26,27 For example,

Glycine-Li+ (Gly-Li+) adopts a CS form, while Gly-Mg2+ adopts a SB conformation. This observation is

consistent with the finding for Glu-Ca2+, but contradicts with the result for Glu-Mg2+. Nevertheless, the

relative energy of the SB conformation decreases in Glu-Mg2+ in comparison with that in Glu-Li+, as

may be seen in Table 1. That is, increasing the cation charge does increase the stability of the SB species.

However, the cation charge is not the sole factor for determining the global minimum species.

From the above discussion, it is clear that all the cation charge, the cation size and the basicity of AA

are important factors influencing the global minimum configuration. In addition, the polar nature of the

side chain plays a major role in determining the global minim. Overall, the global minimum

configuration of metalated AA complex is determined by maximizing the AA - cation electrostatic

9

interaction minus the energy cost involved in forming SB structure. First, increasing the cation charge

increases the repulsion between the cation and the carboxyl hydrogen as well as the amino hydrogens.

The SB form is helpful for reducing the repulsion between the cation and the hydrogens. Consequently,

increasing the cation charge generally increases the relative stability of the SB configuration. For an

aliphatic or aromatic AA, the global minimum takes the SB form when the cation charge is increased

from +1 to +2. Second, the ratio of the distance between a cation and the carboxyl (amino) hydrogen and

the distance between the cation and the carboxyl oxygen (amino nitrogen) decreases when the cation

size increases. Relative to the attraction between the cation and the carboxyl oxygen (amino nitrogen),

the repulsion between the cation and the carboxyl (amino) hydrogen increases with the increase of

cation size. As a result, increasing the cation size usually improves the relative stability of the SB form.

However, the increased repulsion for increased cation size is meaningful only in a relative sense. The

stabilizing effect of the increased cation size on the SB stability is less definite in comparison of that

with the increased cation charge. Third, the effect of AA basicity on the SB stability is rather subtle as a

higher proton affinity often means a stronger interaction between a cation and the AA. Therefore, it is

uncertain if an increased basicity leads to an increased stability of the SB form.

A metal cation has a tendency to bind with more available active sites while avoiding the energy

penalty of forming an SB form. Therefore, polar atoms in the AA side chain have an effect of reducing

the stability of the SB form relative to that of the CS form. For example, the global minimum of

Gly-Mg2+ is an SB species, while the global minimum of Glu-Mg2+ is a CS one. An SB global minimum

is obtained only when Mg2+ is replaced by Ca2+ with a larger cation size. The charge and size of Ca2+

may be insufficient to secure an SB global minimum if the AA side chain consists of some highly active

site, e.g., the global minimum of His-Ca2+ is a CS structure.

3.3 Characteristic IR Spectra

Measurements such as the infrared multi-photo dissociation spectroscopy (IRMPD) may be employed

to provide structural information about the metal cation coordination with AA. The experimental

spectrum along with the theoretical calculations allows the determination of the likely structures of the

complexes and the proper computational methods for the systems. As indicated in Table 1, the three

methods of BHandHLYP, B3LYP, and MP2 provide similar PES results for Glu-Li+/Mg2+/Ca2+, mutually

supporting each other. Based on the data in Table 1, the measured IR spectra are expected to correspond

to the respective most stable conformations of the Glu-Li+/Mg2+/Ca2+ complexes. Indeed, the IRMPD

spectra of Glu cationized with Li+ and Ca2+ have been provided in Ref.[34] and agree with the

previous34,35 and current theoretical results due to their clear coordination modes shown in Table 1.

Hence, the discussion here focuses on the cases for Na+ and K+ as very different energy profiles are

predicted by different computational methods.

10

As seen in Table 1, the dominant coordination mode for Glu-Na+ is OO.z as predicted by MP2, but is

NOOs.c as predicted by B3LYP and BHandHLYP. Fig.3(a) compares the theoretical IR spectra of

Glu-Na+ at T = 298K obtained with the conformational distributions determined by the MP2 and B3LYP

methods and a scaling factor of 0.9646 for the computed vibrational frequencies. The IR spectrum by

BHandHLYP is similar to that by B3LYP.

As shown in Figure 3(a), there are two frequency ranges, the range of 1400–1800 cm–1 and the range

of 2800–3400 cm–1, that are obviously different in the MP2 and B3LYP spectra. There are three strong

bands in the range of 1440–1673 cm–1 in the MP2 spectrum. The bands are due to the NH3+ symmetric

deformation and C=O stretching vibrations in the Na+ coordination mode of OO.z. Only one strong band

at 1704 cm–1 due to the C=O stretching vibration is observed in the B3LYP spectrum. There are also

three clear bands for the N-H stretching vibrations in the range of 2840–3380 cm–1 in the MP2 spectrum.

The IR strengths of the three bands are highly reduced in the B3LYP spectrum and only the vibrational

mode at about 2840 cm–1 may be easily identified. Due to the characteristically different features in the

IR spectra, the experimental measurement may be used to determine which theory is more reliable for

predicting the global minimum conformation of the Glu-Na+ complex.

As may be inferred from Table 1, there is no overwhelmingly dominant coordination mode for Glu-K+

at the room temperature due to the small energy difference among the conformations of different

coordination modes. The IR spectrum for T=298K should therefore be composed of substantial

contributions from different coordination modes, even though the major component of the coordination

modes is seen to be NOOs.c, OO.z and NOOs.c as predicted by MP2, B3LYP and BHandHLYP,

respectively. To clearly distinguish the results of different computational methods, the IR spectrum

measured at low temperature is helpful as it is determined by the lowest energy conformer. Fig.3(b)

compares the IR spectra of Glu-K+ at T = 98K determined by the MP2 and B3LYP methods. As may be

seen by comparing Figures 3(a) and 3(b), the major features of the IR spectrum of Glu-K+ predicted by

MP2 (B3LYP) and the IR spectrum of Glu-Na+ predicted by B3LYP (MP2) are roughly the same as they

are dominated by the NOOs.c (OO.z) coordination mode. Similar to the case for Glu-Na+, the

experimental measurements would provide the definite answer about the dominant coordination mode as

well as finding out the proper computational method for Glu-K+.

3.4 Meta Ion Affinities

Table 3 shows the theoretical MIAs computed by different methods and compared with the available

experimental results. As seen in Table 3, the computational results of MP2, B3LYP and BHandHLYP for

the MIA of K+ are quite similar and agree well with the experiment. The MIA results for Na+ computed

by MP2 and B3LYP differ by more than 6 kcal/mol. However, both the results are in reasonable

agreement with the experiments when the experimental uncertainty is considered. The BHandHLYP

11

result is about 9 kcal/mol higher than the MP2 result and clearly overestimates the MIA of Na+. Similar

differences are found among the MIAs of Li+ computed by the methods of MP2, B3LYP and

BHandHLYP. The MP2 result is almost the same as the CCSD(T) result and is likely more trust worthy

than the results of B3LYP and BHandHLYP for Li+. The assessment is further supported by comparing

the theoretical and experimental results for the MIA of Gly with Li+ and the difference between the

MIAs of Gly and Glu with Li+ at the experimentally estimated temperature of 373K,47 as shown in Table

4. The MP2 and CCSD(T) results agree with each other and with the experiment. The B3LYP and

BHandHLYP results fall outside the experimental uncertainty, with the BHandHLYP method provides

the largest overestimates. The overestimates produced by the B3LYP and BHandHLYP computations

may be associated with the delocalization error of DFT when involving a substantial amount of charge

transfer.48

Due to the good agreement with the CCSD(T) result and reasonably good agreement with the

available experiments shown in Tables 3 and 4, the MP2 result is preferred over its DFT counterpart

when the charge transfer is relatively large. This observation may be applied to the cases with Mg2+ and

Ca2+ and the MP2 results for the MIAs of Mg2+ and Ca2+ are recommended. The large amounts of

overestimation by B3LYP and BHandHLYP may again be understood in terms of their delocalization

errors. The charge transfers are generally larger for the divalent cations than for the monovalent cations.

As a result, the MIA for Mg2+ is highly overestimated by BHandHLYP and B3LYP. The MIA for Ca2+ is

also substantially overestimated by BHandHLYP and B3LYP.

It is worth noting that the delocalization error of DFT has little effect on the geometry optimizations.

For example, test is done by re-optimizing the structures of the two lowest-energy conformers of Glu,

Glu-Li+ and Glu-Mg2+ at the MP2/6-311++G(d,p) level. It is found that the MP2 structures are

essentially the same as the B3LYP structures and affect the MIA results by < 0.5 kcal/mol.

According to the data in Table 3, MIAs for the alkali metal ions are less than 80 kcal/mol, while that

for the alkaline earth metal ions are over 150 kcal/mol. As often commented in literature, the results are

consistent with the primary importance of the electrostatic interaction on MIA. Based on the

electrostatic interaction alone, the ratio of MIAs may be estimated by the ratio on )( 2−+Ocation rr

Z ,

where Z is the charge of cation, rcation the radius of cation and −2Or the radius of oxygen ion.

Considering that the ionic radii of K+, Na+, Li+, Ca2+ and Mg2+ are respectively 133, 95, 60, 99 and 65

pm, and the covalent radius of O2- is 66 pm, the corresponding MIA ratios are 1:1.24:1.58:2.41:3.04.

The ratios of the MP2 MIAs shown in Table 3 are 1:1.23:1.93:4.21:5.70. Therefore, a large portion of

the difference in MIAs may indeed be attributed to the electrostatic interaction. However, it is also

evident that the ratio concerning cation with more charge or smaller radius is significantly

12

underestimated. This is understandable as a cation with more charge or smaller radius has a higher

electron affinity and tends to attracts more electrons to its valence orbital, as discussed above. The role

of charge transfer on changing the MIA ratios caused by the electrostatic force may be roughly

incorporated by replacing the ratio of cation charges with the ratio of their electron affinities, Ee. Ee is

equivalent to the first atomic ionization energy for the monovalent cation or the second atomic

ionization energy for the divalent cation. That is, the MIA ratio may be estimated by the ratio of

)( 2−+Ocation

err

E instead of )( 2−+Ocation rr

Z . According to this revision, the corresponding MIA ratios

are 1:1.46:1.96:3.30:5.26. Compared to the estimate by electrostatic interaction alone, the revised model

represents a clear improvement. Naturally, such a simple model can only be approximate and MIAs may

be accurately determined only by electronic structure calculation.

4. Summary

The conformational spaces of Glu-M, M= Li+, Na+, K+, Mg2+ and Ca2+, are carefully searched by

optimizing trial structures generated by combinations of isolated Glu conformers with the possible

cation coordination modes. In addition to find the low energy conformers known in literatures, a number

of new important conformations are found, demonstrating the power of the searching approach adopted

and the necessity of the conformational search performed here.

The metal cation coordination modes, relative energies and dipole moments of all important

conformations as calculated by the methods of MP2, B3LYP and BHandHLYP are presented. The

relative stabilities of different coordination modes are dependent on the cation examined. The global

minimum for Glu-Li+ or Glu-Mg2+ adopts a tridentate CS coordination mode of NOOs.c. For Glu-Ca2+,

the tridentate SB coordination mode of OOOs is clearly preferred. For Glu-Na+/K+, both the bidentate

SB and CS coordination modes and the tridentate coordination are predicted to coexist at the room

temperature and their relative stabilities depend on the computational methods. For Glu-Na+, the global

minimum adopts an SB coordination of OO.z as predicted by MP2, but adopts a CS coordination of

NOOs.c as predicted by both B3LYP and BHandHLYP. The global minimum of Glu-K+ is a CS structure

of NOOs.c coordination as predicted by MP2 and BHandHLYP, but is an SB conformer of OO.z

coordination as predicted by B3LYP. The computational results for Glu-Na+/K+ may be resolved

experimentally as the dipole moments of the NOOs.c and OO.z conformers are substantially different.

The effects of cation chelation on the relative stability of SB and CS isomers of AAs are analyzed in

combination with the literature data. The cation charge and size and the reactivity of the AA side chain

are important factor affecting the relative SB and CS stabilities. Increased cation charge and size and

reduced side chain reactivity increases the stability of SB isomer. The basicity of AA is an influential

13

factor for the SB stability only when the side chain is inactive.

The IR spectra of the Glu-M complexes are computed and are closely related to the cation

coordination modes of the global minima. The theoretical IR spectra agree with the available

experiments for Glu-Li+ and Glu-Ca2+. For Glu-Na+/K+ with different coordination modes of the global

minima are predicted by different computational methods, spectral regions of characteristically different

features are identified and may be easily tested by future experiments.

MIAs are computed and compared with the available experiments. Though the K+ affinities

determined by MP2, B3LYP and BHandHLYP are similar, BHandHLYP and B3LYP seem to provide

substantial overestimates for the Glu affinities of Li+, Mg2+ and Ca2+. The MP2 results are in agreement

with the available experiments on Na+ and K+ as well as on the relative Li+ affinity between Glu and Gly

and are deemed to be the most reliable. The computational results confirm the primary importance of

electrostatic interaction for the MIAs. The results also indicate the important influence of the cation

electron affinity on MIA.

Acknowledgement

The financial support of the National Natural Science Foundation of China (11074233 & 11374272),

the State Key Development Program for Basic Research of China (2012CB215405) and the Specialized

Research Fund for the Doctoral Program of Higher Education (20113402110038 & 20123402110064)

are gratefully acknowledged.

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18

Figure Captions

Scheme 1. Representative coordination modes of metal glutamic acid complexes. Other coordination

modes may be obtained by interconversion: OH↔O and NH2↔NH3+.

Figure 1. Proton transfer reaction paths for neutral glutamic acid (CN: canonical neutral, ZW.b:

Zwitterion with the backbone deprotonated; ZW.s: Zwitterion with the side chain deprotonated.)

Figure 2. Important conformations of Glu-M (M=Li+, Na+, K+, Mg2+, and Ca2+) complexes. The

interatomic distances shown are in angstroms.

Figure 3. Comparison of the theoretical IR spectra of (a) Glu-Na+ at T = 298K and (b) Glu-K+ at T =

98K as determined by the theories of B3LYP and MP2 with the basis set of 6–311++G(3d,2p).

19

Scheme 1. Representative coordination modes of metal glutamic acid complexes. Other coordination

modes may be obtained by inter-conversion: OH↔O and NH2↔NH3+.

20

Figure 1. Proton transfer reaction paths for neutral glutamic acid (CN: canonical neutral, ZW.b:

Zwitterion with the backbone deprotonated; ZW.s: Zwitterion with the side chain deprotonated.)

21

Figure 2. Important conformations of Glu-M (M=Li+, Na+, K+, Mg2+, and Ca2+) complexes. The

interatomic distances shown are in angstroms.

22

(a)

(b)

Figure 3. Comparison of the theoretical IR spectra of (a) Glu-Na+ at T = 298K and (b) Glu-K+ at T =

98K as determined by the theories of B3LYP and MP2 with the basis set of 6–311++G(3d,2p).

23

Tables

Table 1: Relative Electronic Energies, Relative Thermal Corrections, Dipole Moments and Coordination Modes (Coordination) for the Lowest Energy Conformers of Glu-Li+/Na+/K+ Complexes in Gas Phase.a,b

Relative electronic energiesc Relative thermal correctionsd

Complex Coordination MP2 B3LYP BHandHLYP ΔZPVZ ΔHcor ΔGcor Dipolese Refsf

Glu-Li+

1 NOOs.c1 0.00 0.00 0.00 0.00 0.00 0.00 2.50 g

2 NOOs.c2 1.58 1.79 1.81 0.05 0.05 0.10 2.87

3 NOOs.c3 5.05 4.93 5.20 -0.16 -0.11 -0.25 2.54

4 NOOs.c4 6.01 5.87 6.26 -0.18 -0.15 -0.20 4.35

5 OOs.c1 6.82 5.96 6.72 -0.51 -0.32 -0.82 2.76

6 NOOs.c5 7.16 7.63 8.41 -0.19 -0.14 -0.35 4.97

7 OO.z1 7.30 7.96 10.36 -0.25 -0.09 -0.80 4.41

8 NOOs.c6 7.45 8.78 9.38 -0.11 -0.11 0.00 5.66

9 OO.z2 7.83 8.07 10.55 -0.38 -0.12 -1.04 4.82 g

10 OOs.c2 8.09 5.86 6.72 -0.78 -0.54 -1.32 3.24

Glu-Na+

1 OO.z1 0.00 0.00 0.00 0.00 0.00 0.00 5.00 h

2 OO.z2 0.61 0.16 0.24 -0.10 -0.02 -0.15 5.51 h

3 OOs.c1 2.12 1.02 -0.75 -0.48 -0.33 -0.35 3.32 h

4 OOs.c2 2.99 2.01 0.22 -0.71 -0.50 -0.87 3.36 h

5 NOOs.c1 3.05 -0.80 -3.15 -0.16 -0.07 0.26 3.84 h

6 OOs.c3 3.14 1.88 0.21 -0.61 -0.38 -1.03 3.05

7 NOOs.c2 3.61 -0.06 -2.38 -0.30 -0.22 0.27 2.53

8 OOs.c4 3.75 1.33 -0.33 -0.79 -0.55 -0.96 3.98

9 NOOs.c3 4.28 -1.91 -4.26 -0.18 -0.08 0.19 3.25 h

10 OOs.c5 4.60 2.23 0.62 -0.45 -0.24 -0.84 2.19

Glu-K+

1 NOOs.c1 0.00 0.00 0.00 0.00 0.00 0.00 4.12 i

2 OO.z1 0.51 -1.06 1.32 0.49 0.24 0.42 5.21 i

3 NOOs.c2 0.86 0.92 1.05 0.01 0.03 -0.09 4.63

4 OO.z2 1.20 -0.84 1.65 0.32 0.16 0.16 5.59 i

5 OOs.c1 1.23 0.04 0.76 -0.05 -0.09 -0.11 3.81

6 OOs.c2 1.65 1.65 2.58 -0.18 -0.17 -0.36 3.12

7 NOOs.c3 1.65 1.37 1.52 -0.12 -0.11 0.03 3.39

8 OOs.c3 1.73 0.69 1.38 -0.23 -0.23 -0.48 4.03 i

9 OOs.c4 1.91 0.69 1.46 -0.18 -0.16 -0.52 3.93

10 OOsOs.c1 2.83 3.81 4.70 0.14 -0.12 0.85 3.87

11 OOs.c5 3.03 0.61 1.47 -0.40 -0.32 -0.85 4.59 i

12 OsOs.c1 3.22 2.11 4.31 -0.83 -1.03 -1.25 8.42 i

13 OsOs.c2 3.50 1.82 4.16 -0.76 -0.90 -1.19 9.20 i

24

14 OOs.c6 4.05 1.56 2.49 -0.07 -0.03 -0.62 2.89

Glu-Mg2+

1 NOOs.c1 0.00 0.00 0.00 0.00 0.00 0.00 5.75

2 OOOs.z1 2.23 5.23 6.55 0.32 0.57 0.04 4.67

3 NOOs.c2 2.87 2.60 2.70 0.05 0.08 -0.11 5.87

4 OOOs.z2 3.05 5.98 7.36 0.24 0.49 0.00 4.42

5 NOOs.c3 3.53 3.46 3.53 -0.06 -0.01 -0.14 3.52

6 NOOs.c4 5.91 5.80 6.11 -0.10 -0.08 -0.08 5.87

7 OOOs.z3 6.28 9.14 10.54 0.08 0.40 -0.45 4.89

8 OOOs.z4 7.79 10.43 12.02 0.04 0.36 -0.42 5.37

9 NOOs.c5 9.19 8.69 9.17 -0.15 -0.06 -0.49 5.89

10 NOOs.c6 15.79 17.48 19.47 -0.66 -0.51 -0.86 8.43

Glu-Ca2+

1 OOOs.z1 0.00 0.00 0.00 0.00 0.00 0.00 4.90 g, j

2 OOOs.z2 0.72 0.75 0.83 -0.11 -0.10 -0.11 4.69

3 OOOs.z3 2.46 2.66 2.59 -0.31 -0.26 -0.42 4.02

4 OOOs.z4 4.71 4.44 4.71 -0.30 -0.22 -0.57 4.39

5 NOOs.c1 4.83 2.58 1.42 -0.47 -0.62 -0.28 7.67 g, j

6 NOOs.c2 6.93 4.73 3.61 -0.41 -0.56 -0.25 7.88

7 NOOs.c3 7.37 5.16 4.03 -0.56 -0.67 -0.50 5.09

8 NOOs.c4 7.47 5.48 4.25 -0.52 -0.68 -0.37 6.81

9 OOsOs.z1 10.31 10.79 11.45 -0.09 -0.42 0.59 6.83

10 NOOs.c5 10.47 8.07 7.23 -0.60 -0.72 -0.45 7.04 a All energies in kcal/mol and Dipole moments in Debye. b Structures calculated at the B3LYP/6–311 ++G(d,p) level. c Electronic energies calculated at B3LYP, BHandHLYP, and MP2 methods with the 6–311++G(3d,2p) basis set.d Thermal corrections calculated at the B3LYP/6–311++G(d,p) level. e Dipole moments calculated at the MP2/6–311++G(3d,2p) level. f Structures reported: g ref 34, h ref 32, i ref 33, j ref 35.

25

Table 2: Maximal Differences in Relative Conformational Energies (Δmax(ΔE)) Determined by Different

Basis Sets.a

Δmax(ΔE) Methods Basis Set Glu-Li+ Glu-Na+ Glu-K+ Glu-Mg2+ Glu-Ca2+ B3LYP 6–311++G(d,p) b

6–311++G(2d,2p) c

1.30 0.27

0.77 0.23

0.38 0.20

1.58 0.30

0.89 0.21

MP2 6–311++G(d,p) b

6–311++G(2d,2p) c 1.93 0.22

1.92 0.57

2.50 0.23

2.10 0.44

1.80 0.46

a All energies in kcal/mol; b maximal difference in relative conformational energies between the basis

sets of 6–311++G(2d,2p) and 6–311++G(d,p); c maximal difference in relative conformational energies

between the basis sets of 6–311++G(3d,2p) and 6–311++G(2d,2p).

26

Table 3: Metal Ion Affinities and Gibbs Free Energy Changes at the Standard State for Glutamic Acid Binding with Li+, Na+, K+, Mg2+, and Ca2+. All values are in kcal/mol.

Li+ Na+ K+ Mg2+ Ca2+ MP2 -ΔH298 70.9 a 45.4 36.7 206.4 152.6

69.0 b 44.2 35.8 204.2 150.7 -ΔG298 57.8 b 34.4 27.1 191.6 139.4

B3LYP -ΔH298 75.2 a 51.7 36.0 219.7 158.5 74.6 b 51.0 35.7 218.8 158.0 -ΔG298 63.3 b 41.0 27.2 206.0 146.6

BHandHLYP -ΔH298 78.2 a 54.1 37.0 222.8 157.3 77.7 b 53.5 36.7 222.0 156.9 -ΔG298 66.4 b 43.2 28.1 209.2 145.6

CCSD(T) -ΔH298 73.8 a 69.1 b -ΔG298 57.8 b

Exp. -ΔH298

48.8±1.9c 48.0±1.2d 36.3±1.7e

a BSSEs ignored. b BSSE corrections included. c ref 31. d ref 32. e ref 33.

27

Table 4: Theoretical and Experimental Reaction Free Energy Changes (in kcal/mol) for Gly-Li+ and Glu-Li+ at T = 373K.

ΔG373(Gly-Li+) ΔG373(Glu-Li+)–ΔG373(Gly-Li+) ΔG373(Glu-Li+)MP2 43.9 11.1 55.0

B3LYP 48.3 12.1 60.4 BHandHLYP 50.7 12.9 63.6

CCSD(T) 43.2 11.8 55.0 Exp.47 41.6±3.0 11.3±1.5 52.9±3.0

28

Graphical abstract:

29

Highlights:

►Coordination properties of Glu with Li+, Na+, K+, Mg2+, and Ca2+ are thoroughly examined by conformational

searches.

►Important new conformations are found.

►Coordination effects on the stabilities of salt bridge (SB) and charge solvation (CS) conformations are analyzed.

►Metal ion affinities are calculated by B3LYP, MP2, BHandHLYP and CCSD(T) and agree with the available

experiments.

►Measurements of dipole moments or IR spectra are required to ascertain the coordination modes of Glu-Na+/K+.