6
Computational Schemes for Modeling Proton Transfer in Biological Systems: Calculations on the Hydrogen Bonded Complex [CH30H H NH3] + S, Topiol* and G. Mercier Department of Pharmacology, Mount Sinai School of Medicine of the City University of New York, New York, New York 10029 R. Osman and H. Weinstein Departments of Pharmacology and Physiology and Biophysics, Mount Sinai School of Medicine of the City University of New York, New York, New York 10029 Received 28 March, 1985; accepted 7 May, 1985 Different schemes are explored for the calculation of the proton transfer process in the hydrogen bonded cation [CH30H * H NH3]'. Results from ab-initio calculations with the STO-3G, 3-21G and 4-31G basis sets, are compared in search for an efficient reliable scheme to study the potential energy curves for the proton transfer. The curve constructed from the lowest energies calculated with the frozen optimized geometries of the two possible pairs of proton donor and acceptor fragments, (i.e., CH30H;/NH3 and CH30H/NH:) is in good agreement with that obtained when all the fragments of the hydrogen bonded complex are completely optimized simultaneously INTRODUCTION Proton transfer between functional groups in hydrogen bonded systems is an important part of many biological processes which de- pend on the ease with which a proton can change positions among hydrogen bonded groups. The modification of energies required for such a process constitutes, therefore, an important modulation mechanism in biologi- cal systems. Biologically active compounds such as enzyme substrates, drugs and neu- rotransmitters are often involved in modu- lation of proton transfer mechanisms, as proposed for the catalytic process in serine pr~teases'-~ and the activation of the hista- mine H2-receptor.4 Another receptor activa- tion mechanism proposed recently5 also involves ligand binding to a hydrogen bonded system. This mechanism was proposed as a model for the primary molecular event in the activation of a 5-hydroxytryptamine (5-HT; serotonin) receptor by serotonergic agonists. In this model the receptor that recognizes and binds 5-HT contains a hydrogen bonded sys- *Present Address: Berlex Laboratories, Inc., Cedar Knolls, New Jersey, 07927. tem consisting of an imidazoliudammonia cationic complex. Calculations showed that as 5-HT approaches this receptor model the indole portion of 5-HT forms a stacking com- plex with the imidazoliudammonia cation and induces the proton transfer from im- idazolium to ammonia. Thus, the stacking in- teraction causes the electric field at the two components of the hydrogen bond to be differ- entially modified and thereby facilitates the proton transfer in one direction. This transfer could be the first step in the activation pro- cess that subsequently leads to a measurable response. For such a proposed mechanism to consti- tute an acceptable model of a molecular process at a biological receptor it must dis- criminate between agonists, i.e., molecules that are recognized at the receptor and trig- ger a response, and antagonists, i.e., mole- cules that are recognized but do not elicit the same measurable response. An efficient and reliable scheme for studying the proton trans- fer which initiates the response is therefore necessary in order to investigate the effect of such different ligands on the proton transfer process. In this work we compare four schemes for studying the proton transfer be- Journal of Computational Chemistry, Vol. 6, No.6, 581-586 (1985) 01985 by John Wiley & Sons, Inc. CCC 0192-8651/85/060581-06$04.00

Computational schemes for modeling proton transfer in biological systems: Calculations on the hydrogen bonded complex [CH3OH · H · NH3]+

Embed Size (px)

Citation preview

Page 1: Computational schemes for modeling proton transfer in biological systems: Calculations on the hydrogen bonded complex [CH3OH · H · NH3]+

Computational Schemes for Modeling Proton Transfer in Biological Systems: Calculations on the Hydrogen Bonded Complex [CH30H H NH3] +

S, Topiol* and G. Mercier Department of Pharmacology, Mount Sinai School of Medicine of the City University of New York, New York, New York 10029

R. Osman and H. Weinstein Departments of Pharmacology and Physiology and Biophysics, Mount Sinai School of Medicine of the City University of New York, New York, New York 10029

Received 28 March, 1985; accepted 7 May, 1985

Different schemes are explored for the calculation of the proton transfer process in the hydrogen bonded cation [CH30H * H NH3]'. Results from ab-initio calculations with the STO-3G, 3-21G and 4-31G basis sets, are compared in search for an efficient reliable scheme to study the potential energy curves for the proton transfer. The curve constructed from the lowest energies calculated with the frozen optimized geometries of the two possible pairs of proton donor and acceptor fragments, (i.e., CH30H;/NH3 and CH30H/NH:) is in good agreement with that obtained when all the fragments of the hydrogen bonded complex are completely optimized simultaneously

INTRODUCTION

Proton transfer between functional groups in hydrogen bonded systems is an important part of many biological processes which de- pend on the ease with which a proton can change positions among hydrogen bonded groups. The modification of energies required for such a process constitutes, therefore, an important modulation mechanism in biologi- cal systems. Biologically active compounds such as enzyme substrates, drugs and neu- rotransmitters are often involved in modu- lation of proton transfer mechanisms, as proposed for the catalytic process in serine pr~teases'-~ and the activation of the hista- mine H2-receptor.4 Another receptor activa- tion mechanism proposed recently5 also involves ligand binding to a hydrogen bonded system. This mechanism was proposed as a model for the primary molecular event in the activation of a 5-hydroxytryptamine (5-HT; serotonin) receptor by serotonergic agonists. In this model the receptor that recognizes and binds 5-HT contains a hydrogen bonded sys-

*Present Address: Berlex Laboratories, Inc., Cedar Knolls, New Jersey, 07927.

tem consisting of an imidazoliudammonia cationic complex. Calculations showed that as 5-HT approaches this receptor model the indole portion of 5-HT forms a stacking com- plex with the imidazoliudammonia cation and induces the proton transfer from im- idazolium to ammonia. Thus, the stacking in- teraction causes the electric field at the two components of the hydrogen bond to be differ- entially modified and thereby facilitates the proton transfer in one direction. This transfer could be the first step in the activation pro- cess that subsequently leads to a measurable response.

For such a proposed mechanism to consti- tute an acceptable model of a molecular process at a biological receptor it must dis- criminate between agonists, i.e., molecules that are recognized at the receptor and trig- ger a response, and antagonists, i.e., mole- cules that are recognized but do not elicit the same measurable response. An efficient and reliable scheme for studying the proton trans- fer which initiates the response is therefore necessary in order to investigate the effect of such different ligands on the proton transfer process. In this work we compare four schemes for studying the proton transfer be-

Journal of Computational Chemistry, Vol. 6, No.6, 581-586 (1985) 01985 by John Wiley & Sons, Inc. CCC 0192-8651/85/060581-06$04.00

Page 2: Computational schemes for modeling proton transfer in biological systems: Calculations on the hydrogen bonded complex [CH3OH · H · NH3]+

582 Topiol et al.

tween methanol and ammonia in the cationic complex [CH,OH - H * NH,]’. A working scheme that simulates the completely opti- mized potential energy surface is proposed on that basis.

COMPUTATIONAL METHODS

All the calculations presented here were done with the optimization techniques and basis sets built into the GAUSSIAN 80 sys- tem of program^."^ We assume throughout that the proton transfer occurs along the lin- ear hydrogen bond between the oxygen of methanol and the nitrogen of ammonia. The 0 to N distance between the h drogen bonded

was chosen to secure a significant barrier to the proton transfer in the model since such a barrier is the important property in the study of the effects of ligands on the proton transfer process. Keeping the distance fixed over- comes a well known artifact of the opti- mization of hydrogen bonded systems with minimal basis sets, i.e., an underestimation of the N-0 distance and the concomitant dis- appearance of the barrier to proton t ran~fer .~”

The following four schemes were used to obtain potential energy curves for the proton transfer:

molecules was kept fixed at 3 K . This distance

I.

11.

111.

IV.

The proton was moved to different posi- tions along the line connecting the methanol oxygen and the ammonia ni- trogen with the methanol portion kept frozen in the optimized structure of the protonated methanol (CH,OH,)+, and the ammonia portion kept frozen in the optimized structure of neutral ammonia. Same as scheme I but using the opti- mized structures of neutral methanol and ammonium cation. The lower energy of schemes I and I1 was taken at each proton position. All the geometrical parameters of each fragment were varied as the proton was moved to a new position. In these optimizations only the N to 0 distance was kept fixed, and the entire molecule was optimized. In order to obtain the geometries and energies of the two minima and the transition state, the position of the proton was also included as a variable parameter. The transi-

For

tion state was obtained by imposing the requirement that one of the eigen- values of the force constant matrix be negative. schemes I, I1 and I11 the location of the

two minima and of the transition state point were obtained from fitting a quartic equation to the potential energy curve, and the ener- gies at these points were recalculated with the corresponding basis set. In scheme I11 both possible neutralkation pairs were used to calculate the energy at the transition state and the one with the lower energy was select- ed. In scheme IV the extrema and the entire potential energy curve were obtained by di- rect optimization, and are compared to the values calculated at extrema points obtained from fitting a quartic equation to the poten- tial energy curve.

RESULTS AND DISCUSSION

We have studied the four different schemes presented above with the STO-3G, 3-21G, and 4-31G basis sets. In these studies the 4-31G results can be used as a reasonable standard which reproduces results obtained with much larger basis sets and including correlation ef- fects (see ref. 9 and references therein). The results of calculations with the STO-3G basis set using the different schemes for the proton transfer process are presented in Figure 1 and in Table I. All four schemes have two

-60 -50 L --*--- 6 8 1 1 2 1 4 1 6 1 8 2 2 2 2 4

R (0-H) CANGSTROM)

Figure 1. Potential energy curves for proton transfer in the cationic complex [CH30H - H * NHJ calculated with the STO-3G basis set according t o the four schemes described in Methods. Scheme I (-**O...); Scheme I1 (- - - 0 - - -); Scheme I11 (- - - - - - -); Scheme IV (-A-). Energies are relative to the dissociated com- ponent molecules (see Table I). Note that Scheme I yields lower energies than Scheme I1 to the left of the transition state and that the situation is reversed on the right.

Page 3: Computational schemes for modeling proton transfer in biological systems: Calculations on the hydrogen bonded complex [CH3OH · H · NH3]+

Schemes for Modeling Proton Transfer in Biological Systems 583

Table I. Characteristics of the potential energy curves for proton transfer calculated with the STO-3G basis set.

Scheme I I1 I11 IV IVd

A. Positions (R) and Energies (E) of Extremum Points" R(M) 1.055 1.082 1.069 1.046 1.066 E(M) - 169.435395 - 165.425847 - 169.435219 - 169.435848 - 169.435879 R(T) 1.479 1.429 1.449 1.443 1.445 E(T) - 169.409650 - 169.411594 - 169.409739' - 169.414581 -169.413794

R(A) 1.909 1.910 1.911 1.920 1.911 E(A) - 169.436222 - 169.448941 -169.448950 -169.451115 -169.451900

-169.411935

B. Relative Energiesb ETS(M) 16.2 8.9 14.6 13.3 13.9 ETS(A) 16.7 23.4 23.2 22.9 23.9 E(M)-E(A) 0.5 14.5 8.6 9.6 10.1

"Distances of proton from the methanol oxygen (in A") are given for the extrema near the methanol (M), the transition state (TI and near the ammonia (A). Energies (in hartrees) of optimized fragments are CH30H =

bETS(M) and ETS(A) are the energies (in Kcal/mole) of the transition state relative to the corresponding minima. 'First value is obtained from the protonated methanol/ammonia complex and the second from the methanol/

dEstimated from fitting the energies in Scheme IV to a quartic equation.

-113.549193, CH3OHl = -113.929594, NH3 = -55.455420, NH: = -55.868846.

ammonium complex.

minima in the potential energy curve corre- sponding to the two possible neutraucation pairs. This is also true for the results ob- tained from calculations with the 3-21G and 4-31G basis sets (see Tables I1 and 111, and Figures 2 and 3).

Scheme IV represents the best possible pro- cedure for the calculation of the potential en- ergy curve of proton transfer because in this scheme the proton movement is the reaction coordinate while the rest of the structure is

optimized a t each point (column 4 , Tables 1-111). Because it is of interest to evaluate whether the additional optimiza- tions (i.e., of the two minima and the transi- tion state) are necessary for the calculation of the properties of the potential curves, we fit- ted a quartic equation to the data obtained from scheme IV (Figs. 1-3), calculated the positions of the extrema and interpolated the energies at these points (Tables 1-111). The energies are shown in the fifth column of

Table 11. Characteristics of the potential energy curve for proton transfer calculated with the 3-21G basis set.

Scheme I I1 I11 Iv IVd

A. Positions (R) and Energies (E) of Extremum Points" R(M) 1.059 1.090 1.072 1.045 1.074

R(T) 1.446 1.400 1.416 1.391 1.417 E(M) - 170.653095 -170.647116 - 170.652858 - 170.654652 - 170.654919

E(T) - 170.639278 - 170.639367 - 170.639146' -170.642858 -170.642317 -170.639593

R(A) 1.923 1.926 1.962 1.942 1.926 E(A) - 170.666963 - 170.675891 - 170.675903 -170.677718 -170.678476

ETS(M) 8.7 4.9 8.6 7.4 7.9 ETS(A) 17.4 22.9 23.1 21.9 22.7 E(M)-E(A) 8.7 18.1 14.5 14.5 14.8

B . Relative Energiesb

"Distances (in A") as defined in Table I. Energies (in hartrees) of optimized fragments are CH30H = -114.398019,

bETS(M) and ETS(A) are the energies (in Kcal/mole) of the transition state relative to the corresponding minima. 'First value is obtained from the protonated methanol/ammonia complex and the second from the methanol/

dEstimated from fitting the energies in Scheme Iv to a quartic equation.

CHSOH,' = -114.724919, NH, = -55.872203, NHf = -56.233856.

ammonium complex.

Page 4: Computational schemes for modeling proton transfer in biological systems: Calculations on the hydrogen bonded complex [CH3OH · H · NH3]+

584 Topiol et al.

30.

20. n W 4 10.

Table 111. Characteristics of the potential energy curves for proton transfer calculated with the 4-31G basis set.

-.

-.

--

Scheme I I1 I11 IV IVd

A. Positions(R) and Energies(E) of Extremum Points R(M) 1.053 1.057 1.046 1.045 1.046

R(T) 1.435 1.401 1.407 1.392 1.416 E(T) -171.323313 - 171.326740 -171.323317' - 171.330228 -171.329629

R(A) 1.915 1.941 1.942 1.959 1.941 E(A) - 171.354221 - 171.369344 -171.369367 -171.371319 - 171.371747

E(M) - 171.342045 - 171.339478 - 171.342261 -171.346682 -171.346165

-171.326812

B. Relative Energiesb ETS(M) 11.8 8.0 9.7 10.3 10.4 ETS(A) 19.4 26.7 26.7 25.8 26.4 E(M)-E(A) 7.6 18.7 17.0 15.5 16.1

"Distances (in A") as defined in Table I. Engeries (in hartrees) of optimized fragments are CH30H = -114.871521,

bETS(M) and ETS(A) are the energies (in Kcal/mole) of the transition state relative to the corresponding minima. 'First value is obtained from the protonated methanol/ammonia complex and the second from the methanol/

dEstimated from fitting the energies in Scheme IV to a quartic equation.

CH3OH2' = -115.190165, NH3 = -56.106692, NH: = -56.458884.

ammonium complex.

.....m..... SCHEME I ----O-.- SCHEME I1

-A-SCHEME I V SCHEME I11 - - - . - _ _

.6 . 8 I. 1.2 1.4 1.6 1 .8 2. 2 . 2 2 .4

R C0-H) <ANGSTROM>

Figure 2. Potential energy curves for proton transfer in the cationic complex [CH30H * H * NHJ+ calculated with the 3-21G basis set according to the four schemes described in Methods. Scheme I (*..O...); Scheme I1 (-*-O-.-); Scheme I11 ( - - - - - - - I ; Scheme IV (-A-). Energies are relative to the dissociated component molecules (see Table 11). Note that Scheme I yields low- er energies than Scheme I1 to the left of the transition state and that the situation is reversed on the right.

Tables 1-111. The differences between the op- timized and the interpolated energies do not exceed 0.5 kcal/mol and the differences be- tween the optimized and interpolated posi- tions of the extrema do not exceed 0.029A. Thus, the potential energy curve for the pro- ton transfer can be adequately represented by a quartic equation fitted to the data and the estimated energies and positions of the proton at the extremum points can be estimated with reasonable precision. The actual geometry of the entire complex at the minima and at the

4cI I ......m.... SCHEME 1

SCHEME I1

-A-SCHEME IV - - - . - - - SCHEME I11

t

-I 10. 0

n W

L

-I a \ 0 .

0 -10.

-20.

-30.

-40.

-50.

-60.

8

.6 . 8 I . 1.2 1.4 1.6 1.8 2 . 2.2 2.4 R a- to <ANGSTROM)

Figure 3. Potential energy curves for proton transfer in the cationic complex [CH30H * H - NH31+ calculated with the 4-31G basis set according to the four schemes described in Methods. Scheme I (. - 0 - - *); Scheme I1 (-.-O-*-); Scheme I11 ( - - - - - - - I ; Scheme IV (-A-). Energies are relative to the dissociated component molecules (see Table 111). Note that Scheme I yields lower energies than Scheme I1 to the left of the transi- tion state and that the situation is reversed on the right.

transition state cannot be deduced in a simi- lar way due to the unknown changes in all the other geometrical parameters in the opti- mization. However, inspection of the geome- tries closest to the critical points indicates that the structures are similar to those ob- tained from the full optimization.

Comparison of columns 1 or 2 to column 4 in the tables indicates that neither scheme I nor scheme I1 is adequate to describe the pro- ton transfer process: The transition barriers

Page 5: Computational schemes for modeling proton transfer in biological systems: Calculations on the hydrogen bonded complex [CH3OH · H · NH3]+

Schemes for Modeling Proton Transfer in Biological Systems 585

30.

20. n w 0 r -1 10.-

from the protonated methanol, ETS(M), are always overestimated in scheme I and always underestimated in scheme 11. Conjointly, the transition barriers from the ammonium side, ETS(A), a r e always underestimated in scheme I and overestimated in scheme 11. The difference between the energies of the protonated methanol/ammonia couple and the methanol/ammonium couple, i.e., E(M) - E(A), is also consistently under- estimated by scheme I and overestimated by scheme 11. Thus, both the relative energies of the minima and the transition barriers depend on which of the two schemes (I or 11) is used.

The curve of scheme I11 was constructed from the lowest energies of schemes I and I1 because scheme I better approximates the movement of the proton near the methanol portion and scheme I1 better approximates the movement near the ammonia portion. Re- sults from this scheme are presented in column 3 of the tables. Schemes I11 and IV give similar values for the relative energies of the transition state with respect to the minimum when the proton is near the oxygen (ETS(M)) and near the nitrogen (ETS(A)). Likewise, the difference between the ener- gies of minima obtained from scheme I11 is similar to that obtained from scheme IV.

The agreement with the fully optimized scheme IV indicates that the protonated methanol/ammonia and the methanol/ ammonium structures should be used in scheme I11 to evaluate the minimum near the oxygen (E(M)) and near the nitrogen (E(A)), respectively. However, for the transition state it is not clear, a priori, which of these struc- tures would yield the better result. Both structures were therefore calculated and the one which gave the lower energy was used in scheme 111.

Interesting internal consistencies in com- parisons among various schemes were ob- served with all the basis sets used: (i) The methanol/ammonium structure always had a lower energy than the protonated methanol/ ammonia structure. (ii) Within each basis set, scheme I11 is a good approximation to scheme IV, both energetically and in the lo- cation of the extremum points. For the latter two schemes (111 and IV) the sensitivity of the results to the choice of basis set is similar to that usually obtained for intramolecular geo-

.. -.

-0- STO-3G ......A ___._. 3-216 ---0---4-316 P

. 7 . Q 1 . 1 1 .3 1.5 1 . 7 1.9 2.1 2 . 3

R CO-H> CANGSTRONS>

Figure 4. Comparison of potential energy curves for the proton transfer in the fully optimized structure (Scheme IV) obtained with different basis sets. STO-3G (-0-1; 3-21G (*..A**-); 4-31G (--0--). Energies are relative to the dissociated component molecules (see Tables 1-111).

metrical parameters,1° as demonstrated by changes in bond length associated with changes in basis set (see Tables 1-111). How- ever, the comparison of the energetic char- acteristics of the potential energy curves reveals some consistent differences which are illustrated in Figure 4. A comparison to the 4-31G calculations, taken as a relative stan- dard, reveals that the STO-3G calculations overestimate the barrier in one direction (ETS(M)) and underestimate it in the other direction (ETS(A)). The relative energy of the minima (E(M)-E(A)) is grossly underesti- mated in the calculations (compare Tables I and 111). Inspection of the relative energies of the extremum points with respect to the sepa- rated components of the complex shows that these differences come from the under- estimated stabilization of the transition state and of the methanol/ammonium complex (Fig. 4). The 3-21G calculations show a con- sistent underestimation of the barriers and of the relative energies of the minima (compare Tables I1 and 111). This arises from a non- uniform overestimation of the stabilization of the complex with respect to the separated molecules.

We conclude that while the curves con- structed from one neutralkation pair do not provide a reliable description of the proton transfer process, the lowest energy mixture of these, scheme 111, appears to serve as an accu- rate approximation to the potential energy curve obtained with fully optimized struc- tures in scheme IV. Furthermore, although

Page 6: Computational schemes for modeling proton transfer in biological systems: Calculations on the hydrogen bonded complex [CH3OH · H · NH3]+

586

the barriers and the relative minima in the potential energy curve for the proton transfer depend on the basis set chosen, scheme I11 is a good approximation to scheme IV when the same basis set is used. Thus, the potential energy curves for proton transfer between the two members in a hydrogen bonded system can be adequately approximated by the curve constructed from combining the two possible neutralkation potential energy curves as de- scribed in scheme 111. This scheme should be applicable to other cationic hydrogen bonded systems which serve as models for functional groups in biological systems.

We wish to thank Dr. L. Rubenstein for many valu- able discussions. This work was supported by the Na- tional Institute on Drug Abuse (NIDA) under grant DA-01875 and the National Science Foundation (NSF) under grant BNS83-0337. S. Topiol is recipient of an Irma T. Hirschl Career Scientist Award. H. Weinstein is recipient of Research Scientist Development Award DA-00060 from NIDA.

A generous grant of computer time from the Univer- sity Computing Center of the City University of New York is gratefully acknowledged. Analysis of results in this work was carried out in part on the PROPHET System, a national computer resource, sponsored by NIH through the Chemical/Biological Information Handling Program, Division of Research Resources.

Topiol et al.

References

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

D. M. Blow, J. J. Birktoft, and B. S. Hartley, Nature (London), 221, 337 (1969). H. Umeyama, S. Hirono, and S. Nakagawa, Proc. Natl. Acad. Sci. USA, 81, 6266 (1984). S. Scheiner and W. N. Lipscomb, Proc. Natl. Acad. Sci. USA, 73, 432 (1976). (a) H. Weinstein, D. Chou, C. L. Johnson, S. Kang and J.P. Green, Mol. Pharmacol., 27, 1531 (1976). (b) S. Topiol, H. Weinstein and R. Osman, J. Med. Chem., 27, 1531 (1984). R. Osman, H. Weinstein, S. Topiol and L. Ruben- stein, Clinical Physwl. Biochem., 3, 80 (1985). J.S. Binkley, R.A. Whiteside, R.A. Krishnan, R. Seeger, D. J. DeFrees, H. B. Schlegel, S. Topiol, R. Kahn, and J. A. Pople, GAUSSIAN 80, IBM ver- sion, unpublished. (a) W.J. Hehre, R.F. Stewart and J.A. Pople, J. Chem. Phys., 53,2651 (1969). (b) J. S. Binkley, J. A. Pople and W. J. Hehre, J. Am. Chem. SOC., 102,939 (1980). (c) R. Ditchfield, W. J. Hehre, and J. A. Pop- le, J. Chem. Phys., 54, 724 (1970). P. A. Kollman in: Modern Theoretical Chemistry, vol. 4, Applications of Electronic Structure Theory, H. Schaefer 111, Ed. Plenum Press, New York, 1977. S. Scheiner, M. M. Szczesniak, and L. D. Bigham, Int. J. Quant. Chem., 23, 793 (1983). J. A. Pople in: Modern Theoretical Chemistry, vol. 4, Applications of Electronic Structure Theory, H. F. Schaefer 111, Ed. Plenum Press, New York, 1977.