QUANTUM CHEMICAL MODELLING OF THYROID HORMONE ANALOGUES.

Wieslaw Nowak (a) and Andrzej Wojtczak (b)

(a) Institute of Physics, N. Copernicus University,
ul. Grudziadzka 5, 87-100 Torun, Poland

(b) Faculty of Chemistry, N. Copernicus University,
ul. Gagarina 7, 87-100 Torun, Poland

Contents

Abstract
  1. Introduction
  2. Methods
  3. Results
    1. Structure of molecules
    2. Charge distributions
  4. Discussion
    1. Structure of molecules
    2. Charge distributions
  5. Conclusions
Acknowledgments
References

Abstract

Thyroid hormone thyroxine (T4) and its analogues are important factors regulating a range of physiological processes, among them tissue growth and differentiation. The interaction of the hormone with the transport protein transthyretin (TTR) has been a subject of X-ray studies (A.Wojtczak, V.Cody, J.R.Luft and W. Pangborn, Acta Cryst., D52 (1996) 758) and early molecular mechanics simulations (J.Blaney, et al., J.Am.Chem.Soc., 104 (1982) 6424). In order to get a better insight into the mechanism of hormone recognition we have performed quantum chemical studies of T4, 3,3'-T2, 3',5'-dinitrothyronine, EMD21388, T4Ac and rT3 using standard ZDO (AM1, PM3) methods. For the T4 the DFT method was additionally used. The structures of isolated molecules were optimized and charge distributions and electron densities were calculated. The optimized structures are in a reasonable agreement with the available X-ray data. Results of our calculations, especially related to the electrostatics, will be used in simulations of the hormone-TTR complex dynamics.

1. INTRODUCTION

Thyroid hormone thyroxine (T4) and the product of its monodeiodination, triiodo-L-thyronine T3, regulate the tissue growth and differentiation, synthesis and metabolism of lipids and proteins as well as the tissue oxygen consumption. The hormone is delivered to the target receptors throughout the general circulation as a ligand of three transport proteins, among them transthyretin (TTR).

While bound in TTR, the thyroxine core in a skewed conformation is positioned between aliphatic side chains of Ala and Leu. Its phenolic hydroxyl interacts with the Ser side chains from two TTR subunits, and the alanyl moiety of the hormone forms the pair of salt bridges to Glu and Lys near the binding site entrance [1,2]. The protein crystal structures of TTR complexes have revealed the alternative modes of thyroxine analogues binding [2-4]. The halogen-like substituents are positioned in the hydrophobic pockets between anti-parallel beta strands of TTR. T4 iodine substituents form the alternative interactions to nucleophilic carbonyl oxygen atoms of the surrounding strands. Resulting alternative positions differ by almost 1 A, and in some cases the presence of additional water molecule mediating the binding interactions is suggested [3,5]. The position of the hormone analogue is affected by the tyrosyl ring substitution and the ether bridge flexibility. In this way the mode of the hormone substitution affects the ability to form polar interactions to Glu and Lys, differentiating the binding affinity.

The genetic disorders causing abnormalities in the hormone binding to these proteins result in hypo- or hyperthyroxinemia and severe disfunction of the organisms of affected patients. The molecular level understanding of ligand recognition and binding specificity is a prerequisite condition for an effective treatment.

Our research on the binding of thyroxine and its analogues to TTR had also indicated the possibility of multiple ligand binding modes [2]. In order to understand the molecular basis for ligand recognition in transthyretin, we have initiated a molecular modelling of ligands and TTR. Firstly, we have examined the rigidity of the thyroxine ether bridge using the molecular dynamics technique with the CHARM force field [6]. Secondly, the minimized structures and molecular electrostatic potentials of T4, 3,5,3',5'-tetraiodothyroacetic acid (T4Ac), 3,3',5'-triiodothyronine (rT3), 3,3'-diiodothyronine (T2), 3',5'-dinitro-N-acetyl-thyronine (DNNAT), 3',5'-dibromo-3-methyl-6,4'-dihydroxyflavone (EMD21388) have been calculated using standard quantum-chemical methods (mainly AM1 as implemented in the InsightII package [7]). Results for both X-ray and minimized structures were compared and the effects of conformations on the electrical properties of molecules studied. These data are compared with those of the AMBER force field obtained by the Kollman's group [8,9]. Our results will be used in simulations of the alternative binding modes of T4 in transthyretin tetramers.

2. METHODS

The AM1 method was developed for structural and energetic studies of large organic molecules [10]. Despite of known shortcomings [11] it often gives useful and reliable information on the geometries of flexible systems (see for example [12]). In the present paper the AM1 method first time has been applied for the modelling of tyroxine hormone analogues which are presented in Fig.1:

Figure 1. Compounds studied

All initial structures obtained from the scratch (Builder module of InsightII) or crystal data (ligands of TTR) were subject to a complete energy minimization using the EF method of the MOPAC6 package [13] as implemented in InsightII v.3.5 software [7]. In all cases the PRECISE option was used and the frequencies in the minimized structures were calculated to exclude transition states.

T4 was also subject to the classical CHARMM forcefield minimization using the XPLOR package [14]. Additionaly, the DFT DMOL code [7] was used for calculations of the electrostatic potential of the T4 molecule in the AM1 optimized conformation. The molecules were also subject to geometry optimization using the PM3 method [15].

Unless otherwise indicated all partial charges were calculated using Mulliken population analysis. The ESP charges were obtained using Merz-Kollman method of fitting electrostatic potential on Williams surfaces of studied molecules.

3. RESULTS

3.1 Structure of molecules

The AM1 minimized structures are presented in the form of MOPAC archive files which may be viewed using the XMOL code (Figs. 2-7):
  • Fig. 2. T4
  • Fig. 3. T4Ac
  • Fig. 4. rT3
  • Fig. 5. T2
  • Fig. 6. DNNAT
  • Fig. 7. EMD

    The XMOL software allows for interactive studies of details of the geometry. These structures are also shown in Figs. 9-14, together with the calculated AM1 charge distributions.

    The values of torsional degrees of freedom which are most important for the general shape of hormones are presented in Tab. 1. Standard definitions of angles are shown in Fig. 8:

    Figure 8. Atom numbers and definitions of torsional angles.

    Selected geometry parameters obtained from theoretical calculations are compared with X-ray and literature data in Tab.1.

    Table 1: Thyroxine analogue geometry comparison

    		THYROXINE T4 rT3 T4Ac T2 DNNAT
    Parameter AM1 PM3 XPL crystal [1] protein
    2.0A res. [2]    		 AMB [8] AM1 * AM1 * AM1 protein
    2.0A res. [4]    		 AM1 protein
    2.2A res. [2]
    phi 77.5 83.5 86.5 108.3 102.9 90.0 83.3 105.0 22.6 93.8 39.1 94.8
    phi' 25.2 13.0 14.1 -29.2 -13.7 0.0 25.7 -19.9 59.5 19.2 43.0 65.3
    chi1 48.6 43.9 29.8 -50.0 -144.7 -- 47.0 -61.9 -57.2 -20.6 52.3 -49.8
    chi2 74.8 76.7 82.6 162.2 97.9 -- 73.7 50.9 107.4 115.8 96.9 96.0
    psi -162.3 -174.3 158.8 -159.3 93.8 -- -162.6 -- 172.6 171.0 165.4 124.1
    C-I phe 2.02 1.97 2.09 2.10 2.10 2.08 2.02 2.02 2.02 2.20** - -
    C-I tyr 2.02 1.97 2.09 2.09 2.08 2.08 2.02 2.02 2.02 2.07 - -
    C4O4C1' 116.2 117.1 121.3 120.4 123.6 125.0 115.9 116.2 116.5 127.0** 116.2 118.2

    * Crystal structures in TTR or molecular crystals unknown
    ** Deformation in the crystallographic refinement of 2.0A resolution

    AM1 = AM1 minimized structure ,
    XPL = X-PLOR minimized structure [14], CHARMM force field,
    AMB = AMBER minimized structure.

    Torsion angles: phi' = C4-O4-C1'-C2', phi = C3-C4-O4-C1', chi2 = C8-C7-C1-C2, chi1 = N8-C8-C7-C1, psi = N8-C8-C9-O10, bonds C-I phe = phenolic ring C-I, C-I tyr = tyrosyl ring C-I, angle C4O4C1' = C4-O4-C1' (see also Fig. 8)

    The AM1 geometry of EMD analog is shown in Fig.9 (bond lengths) and in Fig. 10 (bond angles):

    Figure 9. AM1 calculated bond lengths in EMD

    Figure 10. AM1 calculated bond angles in EMD

    3.2 Charge distributions

    There are numerous ways of obtaining the charge distribution in organic molecules using quantum chemical methods. In Figs. 11-16 we present selected charges calculated within the AM1 method for the minimized structures. All AM1 charges for each compound may be extracted from the MOPAC *.arc files (for example T4). The charges related to the most important atoms and groups of analogues are presented in the Table 2. In this table the DFT charges obtained with BLYP functional (DMOL code [7]) and those used by J.M.Blaney et.al. in their AMBER modelling for T4 are also shown. Below the AM1 charge distribution calculated for the EMD molecule is presented as an example:

    Fig.11. Charge distribution in T4.

    Fig.12. Charge distribution in T4Ac.

    Fig.13. Charge distribution in rT3.

    Fig.14. Charge distribution in T2.

    Fig.15. Charge distribution in DNNAT.

    Fig.16. AM1 charge distribution in EMD.

    Table 2: AM1, PM3, DFT and AMBER charges on selected atoms

    atom (group) T4 AM1 T4 PM3 (a) T4 DFT (b) T4 DFT (c) T4 AMBER - (d) T4Ac rT3 T2 DNNAT EMD
    O4 (ether) -0.152 -0.109 -0.104 -0.496 -0.24 -0.149 -0.158 -0.144 -0.145 --
    O4 (phenol) -0.230 -0.195 -0.173 -0.636 -0.40 -0.231 -0.231 -0.233 -0.199 -0.223
    H (phenol) 0.234 0.203 0.121 0.503 0.40 0.234 0.234 0.227 0.277 0.239
    I3' (phenol) 0.162 0.058 0.060 0.037 -0.07 0.160 0.161 0.183 -0.125 (a) 0.095 (Br)
    I5' (phenol) 0.185 0.082 0.091 0.058 -0.07 0.184 0.184 -- ?? 0.075 (Br)
    I3 (tyrosyl) 0.179 0.084 0.066 0.056 -0.07 0.182 0.192 0.185 -- --
    I5 (tyrosyl) 0.200 0.116 0.103 0.081 -0.07 0.188 -- -- -- --
    O10 (carboxy) -0.454 -0.460 -0.310 -0.474 -0.543 -0.357(b) -0.453 -0.443 -- --
    O11 (carboxy) -0.526 -0.577 -0.331 -0.494 -0.543 -0.311(c) -0.528 -0.535 -- --
    N8 (amino) -0.060 0.675 -0.006 -1.119 -0.364 -- -0.061 -0.062 -- --
    H (amino) 0.203 -0.011 0.153 0.491 0.332 -- 0.231 0.282 -- --
    H (amino) 0.283 0.013 0.173 0.574 0.332 -- 0.284 0.280 -- --
    H (amino) 0.230 0.115 0.138 0.503 0.332 -- 0.232 0.224 -- --


    (a) PM3 optimized geometry
    (b) AM1 geometry used, Hirshfeld partition method
    (c) AM1 geometry used, Mulliken partition method
    (d) AMBER parameters used, data from [8]

    4. DISCUSSION

    4.1 Structure of molecules

    The theoretical prediction of geometries of large, flexible molecules is a non-trivial task. A comparison of calculated and experimental X-ray structures gives useful hints as to whether the semiempirical method AM1 can be used in further modelling of thyroxine hormones. Thyroxine is a derivative of amino acid tyrosine. Therefore the geometry of T4 and it's analogues is discussed in terms of torsional angles generally used to describe the conformation of the polypeptide chain and amino acid side chain conformations. Below a short discussion of optimized structures is presented for the each compound separately.
    T4 - Thyroxine
    Both crystal structures, X-PLOR, AMBER, PM3 and AM1 minimized structures have the skewed conformation of the ether bridge close to ideal (90,0). This conformation might be expected as to be a predominant due to the steric efects of tyrosyl iodines. The tyrosyl chi1 angle is found to be +gauche in AM1, PM3 and X-PLOR, -gauche in T4 crystal structure and -144 deg. in the TTR-T4 complex, reflecting three most probable conformations of the side chain. The tyrosyl chi2 is about 90 deg. in AM1 and X-PLOR minimization, as well as in a protein complex, while in the T4 crystal structure is of 162 deg., probably due to the packing forces in the crystal lattice. The angle corresponding to main chain psi angle is found to be -160 deg. in both AM1 and T4 crystal structure and 160 deg. in X-PLOR, the conformation from the allowed but not the most favoured region of the Ramachandran plot. In the protein complex psi of 94 deg. corresponds to the beta conformation. The difference reflects the contribution of two salt bridges formed by the T4 alanyl moiety to Glu-54 and Lys-15 in the protein environment of transthyretin. The C-I distances in the AM1 structure (2.02 A) are slightly shorter than those in crystal structures or predicted by X-PLOR (2.09A). The ether bridge angle about 120 deg. is similar in all methods. The T4 structures obtained from the T4 crystals, crystals of complexes of T4 with TT4, XPLOR and the AM1 methods are compared in Fig.17.
    T4Ac tetraiodothyroacetic acid
    The ether bridge conformation found using the AM1 method (skewed) is consistent throughout the whole series. The tyrosyl moiety conformation -60/50 deg. is the most frequent of those found in proteins. The chi2 of 50 deg. is slightly smaller than the expected 90 deg. value but still in an acceptable range for the crowded protein environment with the tight packing interactions.
    rT3 3,3',5'-triiodothyronine
    The AM1 results gave the skewed conformation of the ether bridge (26/83 deg.) which is consistent with the crystal structure of thyroxine (T4) [1] and the ligand conformation found in transthyretin complexes of 3,3'-T2 [4] and T4 [2]. Such a conformation is caused by restricted flexibility of the ether bridge due to steric effects of the bulky iodine substituents. The tyrosyl moiety conformation is +gauche (47/74 deg.) and is not the most favourable for the side chains in proteins. However, the same conformation is calculated with AM1 for T4 and DNNAT. This energy minimum is allowed for the isolated amino acid with no steric hindrance from the adjacent residue in the polypeptide chain. The AM1 value of the analogue of the main chain psi angle of -162.6 deg is not favoured in proteins. However, it is in an acceptable range.
    T2 3,3'-diiodothyronine
    Phenolic C-I distance of 2.20 A and the ether bridge angle of 127 deg. result from deformations in the 2.0A resolution crystallographic refinement with PROLSQ. The ether bridge conformation in the TTR complex structure is skewed (90,0) deg. while for the isolated molecule minimization with AM1 gives a structure between anti-skewed and twisted. This reflects the increased conformational flexibility for the analogue with the mono substituted tyrosyl ring. The conformations of the tyrosyl moiety in the protein complex and in the AM1 minimized structure are similar (-gauche). The psi angle of 170 deg. is identical in both the crystal structure and AM1 results.
    DNNAT 3,3'-dinitro-N-acetyl-thyronine
    The ether bridge conformation (95,65) is found to be close to perpendicular (90,90) deg. in the transthyretin complex. The AM1 calculations result in a twisted structure (45,45) deg.. The difference is probably due to the protein binding effects compared to isolated molecule minimization. The different conformation reflects the increased flexibility of the bridge in the hormone analogue not substituted in the tyrosyl ring. In this analogue the tyrosyl side chain conformations 52/97 (AM1) and -50/96 (protein complex) correspond to two preferred conformations in proteins. The AM1 structure is much less probable, and may suggest that a local minimum in the rotational space was found. The psi angle of 165 deg. in AM1 and 124 deg. in the protein complex are similar to those observed in T4. The difference seems to be a systematic effect of the isolated molecule minimization. The ether bridge angle is almost an identical in the theoretical calculation and the crystal structure.
    EMD21388
    The most important bond lengths and bond angles are presented in Fig.9 and Fig.10 respectively. Selected geometrical AM1 data are compared with the EMD crystal structure (V. Cody - [16]) in Tab. 3. For the numbering of atoms used in this table Fig.18 should be consulted:


    Figure 18. The numbering of atoms in EMD.

    Table 3: A comparison of selected AM1 internal coordinates of EMD21388 with the X-ray data

    coordinate AM1 (in A or deg.) X-ray (in A or deg.)
    C4-Br5 1.873 1.887
    C9-Br10 1.875 1.901
    C1-C27 1.467 1.497
    C19-O20 1.239 1.234
    C6-O7 1.367 1.350
    C15-O13 1.377 1.360
    C21-O22 1.385 1.378
    C27-O22 1.388 1.378
    C27-C28 1.358 1.331
    C28-C29 1.480 1.500
    O22-C27-C1-C2 43.93 45.31
    C21-O22-C27 117.35 118.92
    O22-C27-C1 109.54 107.90

    As one can see, the AM1 minimized geometry is in very good agreement with the protein crystal structure, however the AM1 C-Br bond lengths are 0.026 and 0.014 A shorter than observed in the crystal. The torsional angle of 45.8 deg. is close to the 43.9 deg. observed in a crystal, which suggests that the crystal packing does not involve any special strain imposed on this torsion. From comparison of structures we conclude that the AM1 model gives a reasonable description of the geometry of the EMD analogue.

    4.2 Charge distribution

    The specific electrostatic interactions may be responsible for the negative cooperativity observed in the TTR tetramers. Therefore it is very important to study the effects of different structures and conformations of the "tail" tyrosyl group or its equivalents on the charge distribution in the "head" phenol ring moiety. The most important partial charges are collected in Tab.2. In all iodinated analogues the AM1 charges on I3' and I5' are similar (+0.16 and +0.18) and do not depend on details of the tyrosyl group stucture. A slight asymmetry between I3' and I5' results from the interaction of I5' with the hydrogen atom of the hydroxyl group. The charges of O4' (hydroxyl) and the corresponding H atom are also very similar in all derivatives including EMD. A slightly higher charges of H in DNNAT indicate on a greater acidity of the -OH group in this analogue. The PM3 method gives lower positive charges on iodine atoms (+0.05, +0.08) but very similar to the AM1 on the hydroxyl group. The AM1 charges on bromine atoms in EMD are smaller (0.095 and 0.075) than those of iodines so we expect that the halogene interactions of EMD with protein nucleofilic groups should be smaller than the interactions of iodinated compounds. Since in the first modelling of T4 interactions with proteins AMBER parameters with the negative values of charges located on all iodines have been used (see Tab.2), perhaps the electrostatic interactions were not correctly represented in that model.

    The DFT partial charges obtained for T4 using the Mulliken population analysis are quite different from those based on the Hirshfeld method, the later beeing more consistent with semiempirical calculations.

    It is worthwhile to note that in all zwitterionic molecules ( T4, T2 and rT3) we observe a clear asymmetry of the AM1/PM3 charge distribution on oxygens in the carboxy group. This observation indicates that O10 and O11 are not equivalent with respect to their H-bonding abilities since the "cis" orientation of the COO- and NH3+ groups leads to the preferential interaction of one of the oxygens with the amino group.

    The total charges calculated for the NH3+ group are identical in all charged compounds but the PM3 and AM1 methods give different distributions of the charges on N and H atoms.

    The sum of partial charges of atoms belonging to the nitro group of DNNAT is negative (-0.125) while all calculated partial charges for iodine atoms are positive. Since sizes of the iodine substituent and the nitro group are similar (in terms of Van der Waals radius) the detailed differences in electron density distribution must be responsible for the different binding properties of T4 (T2) and DNNAT. Indeed, electron density contoured at the same level reveals relatively lower values on iodines compared to the nitro group substituent (see Fig. 19 below). This confirms the role of protein nucleophilic group interactions with ligand halogenes for the ligand recognition and effective binding in transthyretin.

    Fig.19. Comparison of AM1 electron density distribution in T4 (white) and DNNAT (purple).

    The calculated distribution of the electron density is consistent with the observation based on the protein crystal structures that iodines of T4 interact with nucelofilic carbonyl groups of polypeptide main chains while similarly positioned nitro substituents of DNNAT H-bond to the serine side chain hydroxyles.

    The electrostatic potential derived charges, based on the AM1 electron density distribution gave reasonable results only for DNNAT e.g. the only analogue without iodine or bromine substituents. The selected ESP charges are presented in Fig.20 and all values may be obtained from the modified MOPAC archive file dnnatesp.arc

    Fig.20. Electrostatic potential charges based on the AM1 charge distribution in DNNAT.

    In the other cases the ESP InsightII option led to very high (1.5-3.5) values of point charges located on the phenol ring carbon atoms. In our opinion these results of the fitting procedure indicate on the deficiency of the standard point charge model of electrostatics in iodinated hormones. Perhaps, higher moments should be included or dummy potential sites should be introduced to describe correctly lone pairs of iodine and bromine atoms [18]. The high asymmetry of electrostatic potential in the vicinity of the phenol ring is demonstrated in Fig. 21.

    Fig.21. Electrostatic potential contours (in hartree) based on the DFT charge distribution in T4 0.001 - white, 0.010 - red, dots - VdW radii.

    There is also a possibility that we have encountered a case in which a standard least squares fitting procedure is inadequate (see for example [19] ). Thus the problem of ESP charges in iodinated derivatives requires further studies.

    5. CONCLUSIONS

    The AM1 method is suitable for the structural studies of analogues of thyroxine hormones. Minimized structures compare well with the available X-ray data. Calculated electron density distributions indicate for the basically different type of interactions with protein receptors in DNNAT and iodinated analogues. The AM1 charges, despite of their "reasonable" values, perhaps should be used only with caution in a classical MD modelling of these hormones. Large gradients of molecular electrostatic potentials near the iodinated phenol group lead to the "exotic" values of ESP AM1 charges. The DFT study of tyroxine analogues, which is now in progress in our laboratory, should give a better grounded model of electrostatics in these systems.

    Acknowledgments

    A support from the Polish State Commitee for Scientific Research grant no. 6 P04A 032 11, project BiMol (FNP) and UMK grants no. 328-F and 389-F is acknowledged. Authors thanks also Mr K.Wejer for this assistance in HTML editing and Mr G. Bakalarski for DFT calculations.

    References:

    1. V.Cody, Acta Cryst., B37 (1981) 1685.
    2. A.Wojtczak, V.Cody, J.Luft and W.Pangborn, Acta Cryst., D52 (1996) 758.
    3. P. de la Paz, J.M.Burridge, S.J.Oatley and C.C.F.Blake, in "The Design of Drugs to Macromolecular Targets", C.R. Beddell (Ed.), J.Wiley & Sons Ltd., London , 1992, pp.119-172.
    4. A.Wojtczak, J.Luft and V.Cody, J.Biol.Chem. 267(1992) 353-357.
    5. C.C.F. Blake, S.J. Oatley, Nature, 268 (1977) 115.
    6. W. Nowak, unpublished results.
    7. InsightII v.2.3.7, Biosym Technologies, Inc., USA, 1995.
    8. J.Blaney, P.K.Weiner, A.Dearing, P.A.Kollman, E.C.Jorgensen, S.J.Oatley, J.M.Burridge and C.F.F. Blake, J. Am. Chem. Soc. 104 (1982) 6424.
    9. T.A.Andrea, S.W.Dietrich, W.J.Murray, P.A.Kollman E.C.Jorgensen and S.Rothenberg, J.Med.Chem., 22 (1979) 221; J.M.Blaney, E.C.Jorgensen, M.L.Connolly, T.E.Ferrin R.Langridge, S.J.Oatley, J.M.Burridge and C.F.Blake J.Med.Chem. 25 (1982) 785.
    10. M.J.S.Dewar, E.G.Zoebisch, E.F.Healy and J.J.P. Stewart, J.Am.Chem.Soc., 107 (1985) 3902.
    11. J.P.Stewart, in "Reviews in Computational Chemistry", K.B.Lipkowitz and D.B.Boyd, Eds., vol.3, VCH Publishers, Inc., 1991, New York, p.45.
    12. W.Nowak, M.Wierzbowska, J.Mol.Struct. (Theochem), 00 (1996) 000.
    13. J.J.P. Stewart, Journal of Computer-Aided Molecular Design, 4 (1990) 1.
    14. A.Brunger, 1992, XPLOR Manual, Yale Univ. Press.
    15. J.J.P.Stewart, J.Comp.Chem., 10 (1989) 209.
    16. V.Cody, J.Luft, M.McCourt and K.Irmscher, Struct.Chem., 2 (1991) 601.
    17. E.C. Jorgensen, in "Hormonal Proteins and Peptides", C.H.Li (Ed.), Vol. 6, Academic Press, New York, 1971, pp. 57-105.
    18. D.E.Williams, in "Reviews in Computational Chemistry", K.B. Lipkowitz and D.B. Boyd, Eds., vol.3, VCH Publishers, Inc., 1991, New York, pp.219-271.
    19. M.M.Francl, Ch.Carey, L.M.Chirlian and D.M.Gange, J.Comp.Chem., 17 (1996) 367.