INT. J. Q U A N T U M CHEM.: Q U A N T U M BIOLOGY SYMP. NO. 1. 43--48 (1974)

A CNDO Estimate of the Relative Affinities of Taurine and Isethionic Acid for Alkali Metal Ions

JOHN CORNELIUS AND JOHN R. SABIN Qi i i i i i t i i i i i Tlieorj. Project. Depr t~ner i t of Phj-sics. Diiirersity of Florida,

Go inesd le , F l o r i h 3260 I

Abstract

Calculations are made. in the C N D O > ? formalism. of the re la t i~e affinities of the taurine zwitterion and the isethionic acid anion for alkali metal ions. The possible implications of the results for an un- derstanding of the antiepileptic activity of taurine are discussed.

Introduction

In studies of osmotically induced seizures it has recently been shown [ 11 that taurine (2-aminoethanesulfonic acid) has a strong protective action against the onset of such seizures. Although the mechanism of the antiepileptic action of taurine is not known, it has been proposed [ 13 that taurine may be metabolized in or on the cell membrane to isethionic acid (ISA) (2-hydroxyethylsulfonic acid), a major non- dlffusable intracellular anion.

Since both taurine and ISA are ionized at biological pH (taurine as a zwitterion and ISA as an anion). conversion of the extracellular taurine zwitterion to an in- tracellular ISA anion would be expected to increase the hyperpolarized state of the cell membrane. The increase of intracellular anions would favor increased intra- cellular potassium ions in order to maintain electroneutrality. I t is known that such an increase of intracellular potassium tends to stabilize the cellular membrane resting potential, thus decreasing the probability of repetitive firing and the onset of seizure.

There are two interesting conformations of the taurine zwitterion, namely, an extended structure and a cyclic structure with a hydrogen bond between the am- monium and sulfonic acid groups. As neutral substances are known to dlffuse more easily through the cell membrane than ions, i t is expected that the cyclic confor- mation of taurine would be more favorable to passage through the membrane. On the other hand, the extended form would be expected to have a higher affinity for alkali metal ions, and thus promote their passage through the cell membrane.

I t might then be possible for extended taurine to preferentially bind K + (rather than Na+ ) and diffuse through the cell membrane, then be converted to ISA, and release K + . Such an increase ofintracellular K+ would thereby act as an antiepileptic agent, since hyperpolarization, i.e., increased resting membrane potential, would resu 1 t.

43 @ 1974 by John Wiley & Sons. Inc.

44 CORNELIUS AND SABIN

In order to shed some light on these questions, semiempirical calculations have been carried out on taurine and ISA and their complexes with sodium and lithium ions. The preliminary results of these calculations are reported below.

Calculations

The calculations reported were of the semiempirical LCAO-MO-SCF type. They were done in the CNDO/~ [2] formalism, using a modified version [3] of a standard program [4]. Except as otherwise noted, the crystal structure of taurine [5] was used. As no determination of the crystal structure of ISA has been made, the structure was inferred from the taurine structure, using the same bond angles and lengths for the ethanesulfonic acid fragment, and replacing the ammonium group by a standard [Z] hydroxyl fragment. The structures and atom numbering for taurine and ISA are given in Figure 1.

Results and Discussion

To find the minimum energy conformation of the taurine zwitterion, the ammo- nium group was rotated about the N-C, axis. The minimum energy was found for the hydrogen-bonded configuration, with an energy barrier to full rotation of 3.95 kcal/mole, entirely consistent with an N-H,-O3 hydrogen bond. Similar results were obtained for the ISA anion, with 04-H5-03 hydrogen-bond formation in- dicated with a barrier to full rotation of 8.41 kcal/mole. This is slightly high for 0-H-0 hydrogen bond energies [6], but is not unexpected given that this is a charged system [7]. It thus would appear that both the taurine zwitterion and the ISA anion prefer a cyclic hydrogen-bonded conformation.

Calculations were then carried out for the approach of Li' and Na' to the taurine zwitterion and the ISA anion. From simple electostatic considerations it is expected that the alkali metal ion would most favorably approach these molecules from the sulfonic acid end. and this assumption was adopted here. There are two quantitatively different modes of approach which the ion might take, however, namely, along an S-0 bond axis or along the S-C, bond axis, forming a clathrate type bond between the oxygen atoms and the metal ion. Both these approach modes were

TAU ISA

I H5

Figure I . Atom numbering scheme for taurine (TAU) and isethionic acid (ISA)

ESTIMATE OF RELATIVE AFFINlTIES

E i a u )

- 95.3

- 95.8

45

-

-

-

-

-

-

-

- 1

b

I I I

I E ( a d

-101.0

- 101.5

Figure 3. Potential curves for the approach of Li+ and Na+ to the ISA anion. Curve A-Li+ along 0-S bond: curve B-Li+ along S-C bond: curve C-Na' along 0-S bond: curve D-Na+ along S-C bond.

46 CORNELIUS AND SABIN

TABLE 1. Bond energies (kcal:mole) and bond distances ( A ) for minimum-energy approach of Li+ and N a + 10 taurine zwitterion and ISA anion.

0-S approach S-C approach - E(kcal/mole) R ( 1 ) - E(kcal/rnole) R ( i )

L i + 101.09 2.21 133.23 2.70

Na' 56.30 2.80 80.88 3.38 taurine

L i + 104.45 2.10 215.00 2.60

Na+ 126.11 2.70 151.11 3.30 ISA

investigated for Li' and Na' approaching the taurine zwitterion or the ISA anion. The potential curves obtained for each case are depicted in Figures 2 and 3, where the distance is measured from the sulfur atom. I t is immediately apparent that the energetically preferred approach pathway is along the S-C, bond for either cation approaching either organic molecule. Also, in both cases, the stronger bond is formed with Li' rather than with Na'. The total binding energies and bond dis- tances for each case are given in Table I.

The absolute values of the binding energies reported in Table I are undoubtedly

TABLE 11. Atomic populations of taurine zwitterion and its Li' and Na' adducts at the minimum-energy geometry." and dipole moment.

+ S 4.051 4.035 4.047

01 6.595 6.530 6.557

02 6.566 6.501 6.529 03 6.629 6.565 6.593

c1 4.262 4.219 4.229

c2 3.886 3.890 3.809

N 5.030 5.029 5.029 H1 0.932 0.909 0.915 H2 0.962 0.937 0.944 H3 0.977 0.944 0.952 H4 0.950 0.937 0.941

H5 0.802 0.780 0.785 H6 0.794 0.786 0.788

n7 0.761 0.768 0.768 M 0.369 0.234

M=N a + taurine M=Li

14 (D) 16.00 8.82 10.12

"Approach along S-C, bond axis.

ESTIMATE OF RELATIVE AFFINITIES 47

TAH1.E 111. Atomic populations of ISA anion and its Li' and Na' adducts at the minimum-energy geometry." and dipole moment.

+ I S A M=Li+ M=N a

S 4.859 4.839 4.855 01 6.631 6.546 6.578

02 6.625 6.538 6.571

0 3 6.634 6.548 6.579 c1 4.246 4.196 4.205 c2 3.847 3.850 3,846 04 6.361 6.314 6.324 HI 0.982 0.954 0.962

H2 0.981 0.951 0.959

H3 1.038 1.001 1.009

H4 1.017 1.003 1.008 H5 0.778 0.801 0.798

M 0.459 0.305 ] P I (D) 15-31 6.78 11.21

"Approach along S-C, bond axis.

too large, but c N u O / 2 is well known to produce overbinding in cases such as this. The relative ordering of energies is, however, probably correct. In any case, i t is thus clear that the most energetically favorable situation in each case is an approach by Li+ along the S-C, bond axis to give a clathrate type bond.

The gross atomic populations for the taurine zwitterion, the ISA anion, and their minimum-energy adducts with Li' and Na' are given in Tables I1 and 111.

From Tables I1 and 111 it can be seen that formation of complexes of taurine or ISA with alkali metal ions results in a charge transfer from the parent molecule to the metal ion, with larger transfers to Li+ in each case. The charge is transferred primarily at the expense of the sulfonic acid oxygens in both cases and results in a considerable lessening of the dipole moment for the complex.

There is a smaller charge polarization in the Li' complexes of both taurine and ISA, resulting in a smaller dipole moment and consequently higher stability than in the analogous Na' complex. As with the case of binding energy, C N W / ~ tends tooverpolarizechargein systemssuchas this, so the trends rather than themagnitudes in Tables I1 and 111 are expected to be correct.

Conclusions

From the above data i t appears that both the taurine zwitterion and the ISA anion prefer a cyclic hydrogen-bonded conformation. Such a conformation would be expected to enhance the diffusability of taurine through the cell membrane.

48 CORNELIUS AND SABIN

The relative affinity of the taurine zwitterion and the ISA anion for the alkali metal cations is found to be Li' > Na+ in each case, and the preferred conformation ofthe complex isfound for the metal ion approach along the S-C, bond axis, leading to a clathrate like complex.

Since a variety of other studies [8] of the relative affinities of oxygen-containing compounds for alkali metal ions show the order of affinity as Li' > Na+ > K', i t is felt that the extrapolation of lessening binding energy between the taurine zwitterion or the ISA anion and an alkali metal ion in the order Li+ > Na+ > K + can reasonably be made. This trend seems to be found both theoretically and ex- perimentally in a variety of cases. Thus it is felt that some confidence may be placed in this conclusion.

It thus appears that the action of taurine as an antiepileptic agent cannot be due to its ability to preferentially transport K + acreoss the cell membrane, as the above results would indicate that Na', or Li' if it were present in the intercellular fluid, should preferentially be transported.

Acknowledgment

The authors are grateful to Prof. A. H. Nevis for suggesting this problem, and for helpful discussions during its execution. Acknowledgment is made to the College of Arts and Sciences, University of Florida, for a grant of computer time.

Bibliography

[I] N. M. VanGelder. Brain Res. 47. 157 (1972) : A. H. Nevis and M. Thursby. Preprint (1973). [2] For a detailed exposition of the method see J. A. Pople and D. L. Beveridge. Approsimcrtc, Molwitlur.

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