1
Calculations of interaction energies of ellipticine derivatives with DNA base pairs

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Properties of various derivatives of ellipticine and their stacking interactions with adenine–thymine and guanine–cytosine base pairs were investigated with an ab initio correlated method.

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The dependence of the interaction energy on the distance between an intercalator and a base-pair and on the twist angle between them was studied.

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The results were compared with three empirical potentials, two of which being based on the AMBER force field and the other one based on the Lifson–Hagler empirical potential.

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The global interaction energy minima geometries of three systems were searched.

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The performance of the empirical potentials is discussed.

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Introduction

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Ellipticine (1) is an alkaloid isolated from Ochrosia elliptica.1

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Ellipticine and its derivatives are highly toxic to malignant cells in culture2 and 2N-methyl-9-hydroxy-ellipticinium (2) and other ellipticine derivatives have reached the phase II of clinical trials.3

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These effects are believed to result from DNA-binding, with intercalation being a necessary condition for antitumor activity.2

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Little is known, however, about the specific factors involved in stabilising ellipticine–DNA complexes.

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One of the possible approaches to evaluate various factors involved in the intercalator–DNA binding is computational chemistry.

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Electrostatic energy, dispersion energy, induction energy and charge transfer are the contributions of stacking energy in the intercalated systems.4

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When the problem is treated with ab initio methods, correlated calculations are strictly required for calculations of interaction energy, because the Hartree–Fock method and the DFT methods do not include the dispersion energy.5

Type: Background | Advantage: None | Novelty: None | ConceptID: Bac4

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High level ab initio calculations are prohibitively expensive for large systems (such as an intercalator and a DNA fragment) and there is so far only one paper reporting interaction energies of intercalator–base pair systems4 and one paper reporting interaction energies of intercalator–single base.6

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Stacking interactions of various DNA bases and DNA base pairs were already studied.

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For example, in ref. 7 the interaction energies between base pairs in A-DNA and B-DNA are discussed.

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Simple empirical potentials consisting of a van der Waals term and a Coulombic term with atom-centred point charges are able to reproduce the ab initio stacking energy quite well.8

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However, this does not mean that each empirical potential is accurate.

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A comparison with the ab initio calculated data can help to evaluate the empirical potential results.4,9

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We have chosen various ellipticine derivatives (2–6) as model compounds for studying and evaluating the performance of simple empirical potentials.

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In biological reality there are more principal components that combine to stabilise DNA–drug interactions (drug structure, solution conditions and deformability of DNA strands).10

Type: Object | Advantage: No | Novelty: New | ConceptID: Obj7

22
In this study all the calculations were performed in gas phase, so other components than drug structure were omitted.

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We believe that this approach does not affect the credibility of comparison between various simple empirical potentials.

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Calculations

Geometries

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The structure and geometries of various ellipticine derivatives and of adenine–thymine and of guanine–cytosine Watson–Crick base pairs were optimised at the DFT level using the B3LYP functional and 6-31G* basis set.

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The structure of guanine–cytosine base pair was determined with the assumption of its planarity.

 nameR1R2R31EHH—29HNMEOHHCH339HEOHH—47HEHOH—5E+HHH69AE+NH2HH

Ab initio interaction energies

An ellipticine derivative and a base pair were located in coplanar “planes” (the molecules are almost planar) in such a way that the main system axes were parallel.

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Vertical separation of the subsystems was changed and energy was calculated at the MP2 level with the 6-31G* basis set with modified exponents of the polarisation functions (0.25 instead of the routinely used value 0.8, abbreviation 6-31G*(0.25)).

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This basis set is considered to be very appropriate for systems with stacking interactions.4,5,11

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The basis set superposition error (BSSE) was systematically removed by counterpoise method.12

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The interaction energy was calculated as a difference between the energy of the whole system and the sum of the energies of the subsystems (the intercalator and the base pair).

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The interaction energy is the energy necessary to separate the ellipticine derivative and the DNA base pair to infinity.

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It was shown previously that one molecule of an intercalator and one base pair is a reasonably simple model for intercalating systems4.

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Empirical potential interaction energies

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Three empirical potentials were used.

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In all of them the electrostatic energy was calculated according to the Coulomb law: Eelst = 332 Σqiqj/rijwhere qi and qj are the atomic charges and rij is the distance between the atoms i and j.

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The point charges were localised on all atomic centres and they were derived from molecular electrostatic potential (ESP)13 at the HF/6-31G*, B3LYP/6-31G* and MP2/6-31G*(0.25) levels and from restrained electrostatic potential fit (RESP)14 at the same levels.

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The RESP is a modification of original ESP method and it uses hyperbolic restraints to charges of zero for non-hydrogen atoms.

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In two of the empirical potentials van der Waals term was calculated with the Lennard-Jones potential: EvdW = ΣAij/r12ij − Bij/r6ijwhere Aij and Bij are empirical van der Waals constant.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod10

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The force field parameter set ff8615 and the more recent ff9916,17 from AMBER program package were used for calculating of constants Aij and Bij (empirical potential A-ff86 and A-ff99, respectively).

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod11

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In one of the empirical potentials (LH) the van der Waals term was calculated with the 9–6 Lifson–Hagler18 potential: EvdW = ΣAij/r9ij − Bij/r6ijand the van der Waals energies were scaled by a factor of 0.7.

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod12

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This empirical potential was shown to give good results in calculating of interaction energies of stacked DNA bases19.

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Global minima search

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In the ab initio calculations and in the comparative empirical potential calculations, the intersystem distance was changed only in one dimension.

Type: Method | Advantage: None | Novelty: Old | ConceptID: Met1

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This approach can not be used in the global energy minima search, because the molecules can move in three dimensions and can also rotate.

Type: Method | Advantage: No | Novelty: Old | ConceptID: Met1

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So we have written a Microsoft Excel macro that looks for the minima.

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It changes the position and orientation of the base pair in close neighbourhood of the intercalator and calculates the interaction energy using an arbitrary empirical potential and the analytical derivations of the energy with respect to the position (axes x, y and z) of the molecules and the twist angle (the twist angle is defined as the angle between the main subsystem axes).

Type: Model | Advantage: None | Novelty: None | ConceptID: Mod14

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Then the molecule position and the twist angle are changed with the aim to minimise the energy.

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All the conformational space is investigated, this approach ensuring that the global minimum is found.

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Results

Subsystem properties

The optimised geometries, the ESP and RESP charges (calculated from various wave functions), the energies of frontier orbitals and the AMBER atom types of five derivatives of ellipticine (2–6) and of adenine–thymine and guanine—cytosine pairs are presented in the electronic supplementary information in Tables S1–S7.

Ab initio interaction energies

The AT–E+ system

The AT–E+ (adenine–thymine–E+) system was studied more deeply and will be discussed with more details.

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The structure of the AT–E+ system is presented in Fig. 1.

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The distance between the ellipticine molecule and the adenine–thymine base pair was changed from 3.15 to 3.75 Å (in 0.15 Å step increments).

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Fig. 2 shows the dependence of the interaction energy on the intersystem distance.

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The interaction energy has a minimum at 3.33 Å, which is a typical intercalator-base pair distance.4

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For the AT–E+ system, the dependence of the interaction energy on the twist angle was also investigated.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj8

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The twist angle (defined as the angle between main axes of the subsystems) was changed from 0 to 180 degrees with a step of 30°, the intersystem distance was constant (3.3 Å).

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Fig. 3 shows the results of the ab initio calculated dependence of the stacking energy on the twist angle.

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It was also interesting to evaluate the additivity of the energy components, it means to answer the question if it is possible to calculate the interaction energy of an intercalator–base pair complex as the sum of two interaction energies of the intercalator–single base systems.

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The evaluation of the “many body term” can be helpful in calculations of interaction energies of larger systems.

Type: Object | Advantage: Yes | Novelty: New | ConceptID: Obj9

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Table 1 presents the interaction energies of the thymine–E+ and the adenine–E+ systems and compares them with the energies of the adenine–thymine–E+ system.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs4

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The many body terms are quite small.

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Other systems

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For the other ellipticine derivatives and base pairs, the interaction energy was calculated only for three intersystem distances (3.15, 3.30 and 3.45 Å).

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The minimum energy distances and minimum interaction energies are presented in Table 2.

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The minimum energy distances are always close to 3.35 Å, but the minimum energies are highly dependent on the structure of the intercalator.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res3

Comparison of the ab initio data with empirical potentials

The AT–E+ system

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In Fig. 4 the dependence of interaction energy of the AT–E+ complex on the intersystem distance calculated with the A-ff86 force field with various sets of atomic charges and the reference ab initio data are presented.

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It can be seen, that there is almost no difference between the points calculated using the ESP and RESP charges (derived from the same wave function).

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One can also see that there is practically no difference between the energies calculated using the charges derived from DFT and MP2 wave function.

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In general, the coincidence of the ab initio curve with all the A-ff86 ones is very good, the energy differences are always less then 1 kcal mol−1.

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The interaction energies evaluated by the A-ff99 force field and the energies evaluated by the LH force field together with the reference ab initio data are presented in Fig. 5 and Fig. 6, respectively.

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It can be seen again that the differences between the points evaluated by ESP and RESP charges (derived from the same wave function) are rather insignificant and also the differences between the points evaluated with the charges derived from the DFT and MP2 wave function are very small.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs8

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The coincidence of the ab initio energies with the A-ff99 ones is quite small, especially for short distances (the energy difference for 3.15 Å is almost 5 kcal mol−1).

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On the other hand the coincidence of the energies calculated with the LH force field with the ab initio energies is very good.

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The comparison of selected empirical potentials and ab initio calculated interaction energies of the twisted AT–E+ complex are presented in Fig. 7.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj12

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In this case, the best coincidence of the empirical potential calculated energies with the ab initio data gave the LH force field.

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Other systems

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Figs. 8–13 present the empirical potential calculated interaction energies and the reference ab initio data for the other ellipticine derivative-base pair complexes.

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The same conclusions as for the adenine–thymine–E+ system can be done.

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The differences between the ESP and RESP charges derived from the same wave function are very small and the differences between the charges derived from DFT and MP2 wave functions are also very small.

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For neutral systems (AT-9HE, AT-7HE, GC-9HE, Figs. 8, 9 and 13), the electrostatic term contribution is less then 1 kcal mol−1 and therefore the differences between the HF and MP2 derived charges are also rather insignificant.

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In general, the A-ff86 empirical potential gives the best results in comparison to the reference ab initio calculated energies.

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The differences between the ab initio calculated energies and the A-ff86 (ESP-MP2) ones are always less than 1 kcal mol−1, only for the AT-9HE and AT-7HE systems are closed to 2 kcal mol−1.

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The performance of the LH empirical potential is also quite good, the worst results gives the A-ff99 empirical potential, where the differences for 3.15 Å are in the range 2–5.5 kcal mol−1.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs15

Global minima search

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For the AT–E+, AT–9HNME and GC–9AE+ systems, the global energy minima geometries were searched as was described above.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj13

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The A-ff86 empirical potential and the ESP-MP2 sets of charges were used for the search.

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Table 3 presents the number of minima found and the global energy minimum for each complex.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs16

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Figs. 14–16 present the global energy minima geometries for the three systems.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs17

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For three arbitrary selected minima of each system, the energies of interaction were also recalculated ab initio and with the other empirical potentials.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj14

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The results are summarised in Table 4.

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The order of the interaction energies of the minima is the same for all the empirical potentials used but the order of the interaction energies calculated ab initio is different.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs19

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For example for the AT–E+ system, the minimum 6 has the lowest ab initio calculated interaction energy.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs20

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These empirical potentials are not very suitable for the search of global energy minima geometries.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res8

The performance of the empirical potentials

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Fig. 17 presents the correlation of the ab initio calculated interaction energies with the empirical potentials (with ESP-MP2 charges).

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj15

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The figure shows very good agreement between the ab initio method and the A-ff86 and LH force fields.

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The maximal positive and negative deviations, the average absolute deviations, the slopes, intercepts and correlation coefficients for the three empirical potentials with the HF and MP2 derived atomic charges are presented in Table 5.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs21

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The importance of the electrostatic energy term is illustrated in Fig. 18.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs22

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Fig. 18, left, presents the van der Waals term and Fig. 18, right, the total interaction energies calculated with the A-ff86 (ESP-MP2) force field for all intercalator-base pair systems studied.

Type: Object | Advantage: None | Novelty: New | ConceptID: Obj16

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One can see from Fig. 18 that the van der Waals term (dispersion energy) is almost the same for all systems, but the total interaction energy differs considerably (8 kcal mol−1) according to the structure of the intercalator.

Type: Observation | Advantage: None | Novelty: None | ConceptID: Obs23

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It means that the electrostatic term is crucial when drug–DNA interactions are calculated.

Type: Result | Advantage: None | Novelty: None | ConceptID: Res10

Conclusions

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(i) The A-ff86 force field reproduced the ab initio calculated interaction energies very well.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con2

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This empirical potential takes into account only the electrostatic energy and the dispersion energy contributions, which means that the induction and charge transfer energy contribution are rather small.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con3

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(ii) The ESP-DFT derived atomic charges give almost the same electrostatic energy as the charges derived from the MP2 wave function.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con4

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(iii) The use of the RESP charges does not affect the magnitude of the interaction energy.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con5

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(iv) The A-ff99 force field gave worse results then the A-ff86 one.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con6

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It can be surprising that the older parameters (ff86) are better than the new parameters (ff99), but the ff99 parameters are designated for calculations with explicitly expressed water molecules.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con7

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On the other hand, the ff86 parameters were used for calculations in vacuum (as the ab initio calculations in this study are) and for calculations where the presence of solvent was simulated with distance dependent dielectric constant.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con7

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(v) The LH force field also reproduced the ab initio interaction energies very well.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con8

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Especially good results were given by the LH force field for the twisted AT–E+ system.

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(vi) The empirical potentials used in this study did not find the global energy minima geometries well.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con10

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The surface of the potential energy of stacked systems is quite flat6,19 and the energy differences between minima are rather small.

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Small errors of the interaction energy calculations can cause bad order of the minima.

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The doubts about the global energy minima geometries could resolve, for example, an NMR experiment.

Type: Conclusion | Advantage: None | Novelty: None | ConceptID: Con12