The Relative Thermodynamic Stability of Base Stacking in Pyrimidine and Purine Dinucleotides

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1 1st WSEAS International Conference on BIMEDICAL ELECTRICS and BIMEDICAL IFRMATICS (BEBI '08) The Relative Thermodynamic Stability of Base Stacking in yrimidine and urine Dinucls igel Aylward School of hysical and Chemical Sciences Queensland University of Technology George St., Brisbane, Queensland 4000 AUSTRALIA Abstract: - Consistent relative stacking interaction energies have been calculated for triply ionised dinucl structures in the g-g- conformation. For UpUp, UpCp, CpUp and CpCp, the stacking energies in the ZKE approximation including zeropoint energies were found to be , , , / h, respectively. The corresponding free energy values at K were found to be: , , , / h, respectively. For ApAp, ApGp, GpAp and GpGp, the stacking energies in the ZKE approximation including zero-point energies were found to be , , , / h, respectively. The corresponding free energy values at K were found to be: , , , / h, respectively. These values enable the preferred structures of sequences to be determined in the nearest neighbor Ising model of a polyribonucl. The highest and lowest enthalpy values for the sequences of a pyrimidine hexanucl were recorded as UpUpUpUpUpUp = h, and CpCpCpCpCpCp = h The highest and lowest enthalpy values for the sequences of a purine nucl tetranuclwere recorded as ApApApAp = h and GpGpGpGp = h The most stable interaction determined was the GpCp interaction where the enthalpy change is calculated as h The stacking interactions were calculated for the overall enthalpy changes in the ZKE approximation at the F and M2 /6-31G* level. Key-Words: Thermodynamic data, base stacking, pyrimidine and purine dinucl ISS: ISB:

2 1st WSEAS International Conference on BIMEDICAL ELECTRICS and BIMEDICAL IFRMATICS (BEBI '08) 1 Introduction The nucleic acid bases, uracil, thymine, cytosine, adenine and guanine are known to stack in aqueous solution as free bases (1), nucleosides and nucls (2). The stacking also occurs in single strand polymers (3), and in double helices (4). Extensive studies of nucleic acid base stacking have been undertaken, both experimental (5) and theoretical (6) to determine the factors stabilising DA, to determine the flexibility, curvature, thermal stability (7), or to simulate melting curves (8). The theoretical studies have included pure ab initio (9), and semi-empirical calculations (10). This study is to accurately determine the relative stacking energies of the bases to test the hypothesis that the original genes were formed by stacking that preceeded a slow polymerisation reaction that proceeded down the chain. If correct, this hypothesis predicts that the stability of the stacks formed and subsequently polymerised were assembled according to their thermodynamic stability, and these stable sequences were trapped for all time in the genes of living organisms. ne suggestion for nucls that could have polymerised were the amino acyl derivatives of cyclic-3,5 -nucls (11). In this project the sixteen base-base interactions of triply ionised dinucls are determined by a pure ab initio method (12). The total energy of the polymer may then be calculated according to the one-dimensional Ising model (13). 2 roblem Formulation The computations tabulated in this paper used the GAUSSIA98 [14] commercial package. The standard calculations at the F and M2 levels including zero-point energy corrections [12], together with scaling [15], using the same basis set, 6-31G*. are as previously published [16]. Enthalpy changes at the M2 level not including scaled zero point energies are designated as (M2). The complexes are less stable when calculated at the artree Fock level [12]. The method of calulating the relative stacking interactions in the gas phase was to optimize the dinucl structure and determine the enthalpy change for the formation of the glycosidic bond and the stacking interaction as shown in Fig.1. The enthalpy change for the formation of the glycosidic bond was then determined separately as shown in Fig.2. This enabled the stacking interaction to be isolated. In these reactions the coordinates of bonding functional groups were not fixed, and allowed to vary during the optimization. ITER STA ACTI CKIG GLYCSIDIC ITER STA ACTI CKIG GLYCSIDIC BD BD (2) (1) Fig.1 The formation of the glycosidic bond and stacking interactions where the enthalpy change is 3 (5) (4) GLYCSIDIC BD (3) - ISS: ISB:

3 1st WSEAS International Conference on BIMEDICAL ELECTRICS and BIMEDICAL IFRMATICS (BEBI '08) Fig.2 The formation of the glycosidic bond where the enthalpy change is = 3 where 1 is defined as the stacking interaction. 3 roblem Solution 3.1 Conformations and Stacking Energies of the Stacked Dinucls The geometry of the optimized dinucls is characterised by the dihedral angles shown in Fig.3. (17) C 2 α β γ δ C 2 ε ζ - Base χ5 Base χ3 Fig.3. The dihedral angles used to define the structure of the dinucls. A representative stacked conformation of GpGp is shown in Fig.4. Fig.4. The optimized stacked conformation of GpGp. The dihedral angles are recorded in Table 1. Table 1 The dihedral angles of pyrimidine and purine dinucls. Enthalpy changes for stacking. Dinucl α β γ δ ε UpUp CpUp UpCp CpCp GpGp GpAp ApAp ApGp Table1 (cont) Dinucl χ (5') χ (3') 273 (stacked) UpUp CpUp UpCp CpCp GpGp GpAp ApAp ApGp Also recorded are the enthalpy changes where the model is M2, basis set 6-31G* and the zero point energies (F) have been scaled and included. These values are given in Table.2 Table 2 ISS: ISB:

4 1st WSEAS International Conference on BIMEDICAL ELECTRICS and BIMEDICAL IFRMATICS (BEBI '08) M2 /6-31G* total energies and zero point energies (hartrees) for the respective equilibrium geometries. Molecule M2 ZE (F) hartree hartree UpUp CpUp UpCp CpCp GpGp GpAp ApGp ApAp The Thermodynamic Data for Stacked yrimidine Dinucls at K, F Model, Basis Set 6-31G*. The Gaussian program also produces the following thermodynamic data in which the zero-point energy is not scaled. Table 2. The thermodynamic data for the stacking and glycosidic bond formation in the pyrimidine dinucls. Energies are in hartree (1 h = kcal.mol -1 ) (12). E (F) Total Electronic Energy ZE Zero- oint Energy. Η Εlectr. + Therm Enthalpy. UpUp (1) rpup (2) Up (3) rp (4) U (5) UpCp (1) rpcp (2) Up (3) rp (4) U (5) CpUp (1) rpup (2) Cp (3) rp (4) C (5) CpCp (1) rpcp (2) Cp (3) rp (4) C (5) Table.2 (cont). G (F) Electronic + Thermal Free Energy S Entropy (cal K -1 mol -1 ) G stacking and G glycosidic bond UpUp (1) G stacking rpup (2) = Up (3) rp (4) G glycosidic U (5) = UpCp (1) G stacking rpcp (2) = Up (3) rp (4) G glycosidic U (5) = CpUp (1) G stacking rpup (2) = Cp (3) rp (4) G glycosidic C (5) = CpCp (1) G stacking rpcp (2) = Cp (3) rp (4) G glycosidic C (5) = The Thermodynamic Data for Stacked urine Dinucls at K, F Model, Basis Set 6-31G*. The corresponding thermodynamic data for the purine dinucls is given in Table 3. Table 3. The thermodynamic data for the stacking and glycosidic bond formation in the purine dinucls. Energies are in hartree (1 h = kcal.mol -1 ) E (F) Total Electronic Energy ZE Zero- oint Energy. Η Εlectr. + Therm Enthalpy. ISS: ISB:

5 1st WSEAS International Conference on BIMEDICAL ELECTRICS and BIMEDICAL IFRMATICS (BEBI '08) ApAp (1) rpap (2) Ap (3) rp (4) A (5) ApGp (1) rpgp (2) Ap (3) rp (4) A (5) GpAp (1) rpap (2) Gp (3) rp (4) G (5) GpGp (1) rpgp (2) Gp (3) rp (4) G (5) Table.3 (cont). G (F) Electronic + Thermal Free Energy S Entropy (cal K -1 mol -1 ) G stacking and G glycosidic bond ApAp (1) G stacking rpap (2) = Ap (3) rp (4) G glycosidic A (5) = ApGp (1) G stacking rpgp (2) = Ap (3) rp (4) G glycosidic A (5) = GpAp (1) G stacking rpap (2) = Gp (3) rp (4) G glycosidic G (5) = GpGp (1) G stacking rpgp (2) = Gp (3) rp (4) G glycosidic G (5) = Comparison of the Calculated Frequency of the Dinucls with those in the 5S Ribosomal RA of Escherichia Coli. With only eight of the sixteen interactions calculated accurately at the M2 / 6-31G* level of accuracy it is premature to make a comparison with the frequency of dinucls in the 5S ribosomal RA of Escherichia Coli, or other RA. owever, with the data complete for the pyrimidine nucls and the purine nucls it is possible to separately generate ensembles of all sequences according to the Ising model. The interaction energies are just added and then weighted according to the Boltzman principle to enable the calculation of the theoretical frequency. It is clear from the relative thermodynamic data, of which the most reliable should be that from the M2 values, that the UpUp frequency will be low, or non-existant, whilst the frequency of both CpCp and GpGp will be higher. The frequency of the remaining five dinucls will lie in between. The frequencies found in the 5S ribosome RA of Escherichia Coli (18) are as follows: UU=0.0, UC=3.36, CU=4.20, CC=11.77, AA=4.20, AG=7.56, GA=6.72, GG= Further work may support the hypothesis that the bases stacked before they polymerised and all living organisms contain an afterglow of biological creation. 4. Conclusion The results are broadly in agreement with literature gradations (10,19-21), and experimental studies (5). owever, the values for the enthalpies of stacking are generally much larger in the gas phase where the bases are able to tilt, and approach to very close van der Waals distances. These calculations are time consuming and expensive. More comprehensive studies with larger resources may alter the data values. The separation of values appears sufficient for them to have possibly influenced the formation of the first genes. Acknowledgements Appreciation is expressed to J..Jenkinson, D.Singelton and R.Kobayashi of the Australian ISS: ISB:

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Relative Thermodynamic Stacking Constants of Deoxyribo Dinucleotides

igel Aylward Relative Thermodynamic Stacking Constants of Deoxyribo Dinucls IGEL AYLWARD Queensland University of Technology George St., Brisbane, Queensland 4000 AUSTRALIA n.aylward@alumni.qut.edu.au