Cooperative effects on the formation of intercalation sites
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《核酸研究医学期刊》
Institute of General, Inorganic and Theoretical Chemistry, University of Innsbruck, Innrain 52a, A-6020 Innsbruck, Austria
* To whom correspondence should be addressed. Tel: +43 512 507 5162; Fax: +43 512 507 5144; Email: Klaus.Liedl@uibk.ac.at
ABSTRACT
Daunomycin is one of the most important agents used in anticancer chemotherapy. It interacts with DNA through intercalation of its planar chromophore between successive base pairs. The effect of intercalation on structure, dynamics and energetics is the topic of a wealth of scientific studies. In the present study, we report a computational examination of the energetics of the intercalation process. In detail, we concentrate on the energetic penalty that intercalation of daunomycin introduces into DNA by disturbing it from its unbound conformation. For these means, we are analyzing already published molecular dynamics simulations of daunomycin–DNA complexes and present novel simulations of a bisdaunomycin–DNA and a 9-dehydroxydaunomycin–DNA intercalated complex using the MM-GBSA module implemented in the AMBER suite of programs. Using this molecular dynamics based, continuum solvent method we were able to calculate the energy required to form an intercalation site. Consequently, we compare the free energy of the duplex d(CGCGCGATCGCGCG)2 in the B-form conformation with the respective conformations when intercalated with daunomycin and a bisintercalating analog. Our results show that the introduction of one single intercalation site costs 32 kcal/mol. For double intercalation, or intercalation of the bisintercalator, the respective value for one intercalation site decreases to 27 and 24 kcal/mol, respectively, at a theoretical salt concentration of 0.15 M. This proposes that at least in these cases, a synergistic effect takes place. Although it is well known that intercalation leads to substantial disturbance of the DNA conformation, already performed investigations suggest a lower energetic penalty. Nevertheless to the best of our knowledge the calculations presented here are the most complete ones and consider hydration effects for the first time. The interaction energy between the ligand and the DNA certainly over-compensates this penalty for introducing the intercalation site and thus favors complexation. Such analyses are helpful for the description of allosteric effects in protein ligand binding.
INTRODUCTION
Small ligands can interact with DNA by groove binding or intercalation. Generally speaking, minor groove binding molecules such as netropsin or distamycin, on the one hand, fit into the groove without causing large perturbations in the DNA structure. Drug intercalation, on the other hand, is defined as the stacking of a planar chromophore between successive base pairs. Daunomycin can be accounted as a model compound for the investigation of intercalation processes and is one of the most important agents for cancer chemotherapy. To allow such an interaction, structural deformations of the DNA are necessary. Daunomycin and bisdaunomycin in this respect show a combination of these two features, as the aromatic ring-system intercalates between base pairs of the DNA double-strand, and the sugar moiety, as well as the linker in the case of bisintercalating bisdaunomycin, lie in the minor groove and influence sequence specificity as well as binding affinity. When complexed with DNA, this amino sugar enters into the minor groove while the rest of the molecule is buried between two successive base pairs. The sugar exhibits a high flexibility and builds contacts with the phosphate-backbone of the DNA. These structural and energetic effects are investigated in detail by experimental and theoretical methods (1–12). To improve the binding properties, bisintercalating ligands were developed by connecting two daunomycin molecules through a proper linker (13–15). The choice of a proper linker is crucial, as it influences the binding, and as the site size of a bisintercalator is increased relative to the monomer. Increased site size can potentially lead to increased sequence selectivity (9). One of the best linkers that optimally fits into the minor groove and conserves the binding mode of the single daunomycin molecules is a p-xylyl residue (see Figure 1) connecting two daunomycin molecules via their nitrogen atoms.
Figure 1. Structures of daunomycin (left) and bisdaunomycin (right). In 9-dehydroxydaunomycin the OH group at C9 in daunomycin is replaced by a hydrogen.
Recent investigations have treated the energetic contributions to the binding energy of different functional groups of daunomycin. The hydropathic interactions analyses of Cashman et al. (2,12) investigate contributions of different daunomycin analogs to the binding energy and also to the sequence selectivity of intercalation. They predict a free energy contribution of –3.6 ± 1.1 kcal/mol from the groove binding daunosamine sugar and a contribution of –0.7 ± 0.7 kcal/mol for the removal of the OH at position C9. The free energy G for daunomycin binding is calculated to be –10.0 ± 0.9 kcal/mol compared to the experimental value of –7.9 ± 0.3 kcal/mol from Chaires et al. (16) from comparative binding studies. Another approach that can be used to calculate binding energies was applied by Andrews et al. (17). In this approach, the binding constants and the structural components of several drugs and enzyme inibitors have been used to calculate the average binding energies of some common functional groups. Thus by dissecting the contributions of functional groups to drug–receptor interactions, binding energies can be estimated.
Despite these and other approaches for the calculation of energies in the process of binding, the question, how much energy the formation of the intercalation cavity costs, is not answered. On the other hand, several investigations concerning the stacking and unstacking interactions and energies of DNA bases were performed (18–25). In a quantum-chemical study by Sponer et al. (24), stacking energies in canonical B-DNA base-pair steps of –9.5 to –13.2 kcal/mol were found. By using our approach, we were able to calculate the energy difference between an uncomplexed DNA tetra-decamer and various DNA–intercalator complexes from molecular dynamics (MD) simulations in explicit solvent. By the accurate description at the atomic level of our system, the continuum treatment of the solvent in many cases has proven to constitute a remarkably accurate approximation. It is then possible to treat problems, such as solvation free energies, binding free energies, solvent effects on conformation and reaction rates, and pH and ionic strength effects on binding and stability, within the framework of a simple and accurate theory (26).
The Generalized Born (GB) theory is the basis of the computational method applied for the calculations performed in the present work and has been applied recently in different studies (27–32). It allows the estimation of the electrostatic free energies of solvation of diverse molecules and molecular ions. In the GB model, a molecule in solution is represented as a set of point charges, set in spherical cavities, embedded in a polarizable dielectric continuum. Finite difference Poisson–Boltzmann free energies can be approximated using GB calculations. It has been shown in previous studies that the solvation free energies are generally within 5% of the observed values using the GB method together with a simple treatment of non-electrostatic effects. The GB model is capable of reproducing solvation free energies of 32 molecules, chosen as prototypes of protein and nucleic acid constituents, with a mean unsigned error of <1 kcal (33).
The first step in the binding process of each intercalator is the creation of the intercalation site. This process is energetically highly unfavorable and thus determines the kinetics and thermodynamics of binding. The intercalation site differs from the undisturbed DNA by a doubling of the base–base stacking distance followed by unwinding and conformational changes of the sugar phosphate backbone. Thus, a detailed energetic investigation on the formation of this intercalation site is of scientific interest. In this work, we describe the energetic analysis of already published MD simulations of daunomycin bound to d(CGCGCGATCGCGCG)2 in the B-form conformation. This sequence contains two 5'-CGA-3' daunomycin binding sites separated by four bases which enabled us to simulate the ternary complex with two daunomycin ligands as well as its bisintercalating analog and a double intercalated complex with 9-dehydroxydaunomycin. The energetic analysis was performed using the MM-GBSA module of the AMBER suite of programs. MM-GBSA is able to calculate the relative stabilities of different conformations by dividing the total free energy into its single contributions. This approach allows the calculation of the conformational free energy differences between free DNA and intercalated complexes without the need to establish an explicit sampling pathway connecting one form to the other. In this model, the free energy consists of the internal energy (Egas), the solvation free energy (GGB + Gnonpolar) and the entropic contribution to the free energy. Egas is the vacuum force-field energy and contains all intramolecular bonded (stretch, bend, torsion and improper torsion) and non-bonded (van der Waals and electrostatic) interactions. The solvation term includes both the polar and the non-polar contribution to the solvation free energy. The non-polar part is calculated by an empirical formula connecting the solvent accessible surface area (SASA) with the free energy, while the polar fraction is determined by solving the Poisson–Boltzmann equation (PBSA) or by applying the GB model (GBSA), as in the present work. The entropy is divided into the vibrational entropy, as estimated via a normal mode analysis, and the translational and rotational entropy, deduced from the coordinates and the atomic masses.
The mean MM-GBSA free energy is calculated for a set of snapshots selected from MD simulations and then compared with a reference set. Srinivasan et al. (30), for example, investigated the relative stabilities of A-DNA versus B-DNA form, by comparing the MM-PBSA free energies obtained from two MD simulations of the respective conformations. The method correctly describes the corresponding stabilities and even a phosphoramidate-modified DNA duplex gave results in good agreement with the experiment. Originally this module was written as a tool for predicting binding free energies of ligands. Therefore, the complex must be compared with the sum of the free energies of unbound ligand and receptor. We used this method for calculating the free energy of DNA alone and compared the complexed and the uncomplexed state. The difference in energy without consideration of the unbound ligand represents the energetic penalty needed for the formation of the intercalation site. In addition, we performed a calculation of total binding free energies of the ligands as described above.
MATERIALS AND METHODS
Investigation of biomolecules like DNA and DNA complexes by means of computational methods have already proven to be valuable for a deeper understanding of the structural, dynamical and energetic properties (34,35). Owing to the inclusion of the long-range electrostatic interactions by the Particle Mesh Ewald method, stable B-form DNA MD simulations are possible. All simulations were performed using the AMBER package (36,37) by adapting standard state of the art simulation protocols for our needs (38–42). We simulated the DNA sequence d(CGCGCGATCGCGCG)2 starting from its canonical B-DNA conformation, constructed using the program NUKIT. Additionally, five simulations of DNA–daunomycin complexes were performed. In one simulation one 5'-CGA-3' step was complexed, representing the single intercalation, and in second three simulations with both of these steps occupied (representing double intercalation) were performed (details to the simulation parameters) and the parametrization of the daunomycin ligand are described elsewhere (43). Furthermore, we present simulations of a ternary complex of daunomycin lacking the 9-OH group (9-dehydroxydaunomycin) and a simulation of the bisintercalating daunomycin ligand bisdaunomycin (for both see Figure 1). For the construction of the 9-dehydroxydaunomycin complex we took daunomycin, removed the OH group and performed ab initio structural minimization and calculation of the electrostatic charges. The further construction of the complex was according to the procedures already described. For the bisintercalating complex, we took the coordinates and structure of bisdaunomycin from the X-ray structure determined by Hu et al. (13) with the NDB ID code DDF072 and performed an ab initio structural minimization and calculation of the electrostatic potential for RESP (Restrained ElectroStatic Potential) (44,45) with GAUSSIAN98 (46) at the HF/6-31G* level of theory. Selection of the appropriate atom types and set up of the complex was performed with the same targeted MD approach as described previously (43). The targeted root-mean-square distance (RMSD) was chosen to be 0.0 ? and we performed a sequence of 100 ps simulations each, increasing the force constant from 1 to 2, 5 and 100 kcal/mol yielding a final RMSD of 0.087 ?. All MD simulations were performed for a total simulation time of 10–20 ns using a time step of 2 fs. The all atom force field of Cornell et al. (47) with the modifications of Cheatham et al. (48) was used. The system was solvated with TIP3P Monte Carlo water boxes requiring a 12 ? solvent shell in all directions. The long-range electrostatic interactions are considered by applying the Particle Mesh Ewald algorithm (49,50). The MM-GBSA calculations were performed for 100–200 snapshots of each simulation. These snapshots were taken every 100 ps of the 10–20 ns simulations, respectively. The vacuum free energy (Ggas) corresponds to the force field energy of the nucleic acid solute (not including counter-ions or solvent) and it was computed from the Cornell et al. (47) force field with the modifications of Cheatham et al. (48). It contains the contributions of the non-bonded and 1,4-electrostatic and van der Waals energies, as well as the internal bond, angle and dihedral energies. For each energy, the average and the standard error of the mean values are given in Tables 1–3. The solvation free energy (Gsol) is divided into the electrostatic (GGB) and the nonpolar (Gnonpolar) part. The electrostatic part was derived with the GB approximation using the model of Jayaram et al. (33), which is faster to solve than the Poisson–Boltzmann equation. Nevertheless the results of both methods are in a close agreement, illustrating that the GB-model is an effective alternative to the PB-method (33). A more detailed description of these methods is given elsewhere (26,33,51–56). The non-polar contribution to the solvation energy is dependent on the solvent accessible surface area (SASA). The term is represented as *SASA + b where the parameters and b are taken from Sanner et al. (57) and found to be 0.00542 kcal/?2 and 0.92 kcal/mol. The SASA was estimated with a 1.4 ? solvent probe radius as implemented in Sander (37). For the analysis of the salt dependence, the calculations were performed at 0, 0.1, 0.15, 0.2, 0.5 and 1.0 M theoretical salt concentrations. The solute entropy of the components is investigated by normal mode analyses of every 10th of the above mentioned 100–200 snapshots, after minimizing the snapshots and was performed with the AMBER tool NMODE. For all calculations standard parameters already described in the literature were used (58–61). The entropy was derived from a combination of the different simulations. That is, the overall change in the entropy contributions was calculated by subtracting the values from the uncomplexed DNA and from the respective ligand from the complexes. This slightly modified approach as compared to calculations where all contributions are derived from one simulation run was necessary, as the intramolecular strain in the complexes is too large as to give reasonable values for the DNA after minimization (see also Table 4).
Table 1. Energy contribution of uncomplexed and complexed DNA (without ligands)
Table 2. Difference to uncomplexed DNA of the energy contribution at a theoretical salt concentration of 0.15 M
Table 3. Energy contribution of ligands alone
Table 4. Calculation of the entropy terms
RESULTS
A simulation of the uncomplexed d(CGCGCGATCGCGCG)2 tetradecamer DNA and six simulations of its complexes with intercalators were performed. In one simulation one 5'-CGA-3' binding site was complexed with daunomycin, while in the second case three different simulations where both of these binding sites were occupied. In the present study the energies of these three simulations were calculated separately, but the average values are presented. In the third simulation, the two binding sites were intercalated by the bisintercalating ligand bisdaunomycin. Finally, a complex of 9-dehydroxydaunomycin– DNA with two intercalators was carried out. In all simulations, the DNA stays stable in the B-form with a stable RMSD value after a maximum time of 350 ps. Comparing the structural parameters from the X-ray structures published by Frederick et al. (62) and Hu et al. (13) with our results, we find a good agreement. The first step in the binding process of each intercalator is the creation of the intercalation site. This process is energetically highly unfavorable and thus determines the kinetics and thermodynamics of binding. The intercalation site differs from the undisturbed DNA by a doubling of the base–base distance. Structural changes, a given B-DNA has to undergo during the intercalation process especially concern stacking interactions like DNA rise and buckle. For example, the helical rise in the complexed state is 7.5 ?, which is more than twice the value of unbound B-DNA. Besides these stacking interactions, the groove width and the structure and flexibility of the backbone are affected. It is assumed that previous to intercalation, DNA must undergo these conformational transitions to form the intercalation site. This step is also known as helical breathing. The bases must separate until the cavity is large enough that the intercalating chromophore fits. In several attempts it was tried to compute the energy necessary for forming this cavity. Nuss et al. (63) determined the destabilization energy by means of molecular mechanics calculations of drug–dinucleoside complexes to be in the range of 15–30 kcal/mol and to be essentially independent from the intercalator itself. For ethidium bromide–dinucleoside they found a net stabilization in the gas phase of 130–140 kcal/mol. Ornstein and Rein (64,65) used an empirical partitioned-potential function calculating energies for the transition between dinucleoside triphosphates in the B-DNA conformation and the corresponding intercalated state to be 17–31 kcal/mol. From experimental kinetic measurements, it appears that the activation free energy of intercalation is 15 kcal/mol (63). Owing to the fact that the activation energy and the free energy of the cavity formation are not rigorously comparable, it can be claimed, that these theoretical results are in the same range. All mentioned values did not include solvation and entropic effects. Therefore, although they are valuable for understanding the basic binding principles there is still a need for more in-depth investigations. We performed such calculations using the MM-GBSA method. We compared the free energy of the DNA conformation in the unbound state with the respective bound conformations. The MM-GBSA method allows the calculation of the mean free energy of a set of structural snapshots. As we were primarily interested in the energy that is necessary to form an intercalation site, we selected the DNA coordinates of the MD simulation of the complexes. This method benefits from computational efficiency as only the initial and final states of the system are evaluated like the energetic comparison between A-DNA and B-DNA conformations performed by Srinivasan et al. (30). In these simulations, the phase space of the complex is sampled and therefore a good description of the complexed state is achieved. MM-GBSA also includes the effect of hydration and counter-ions by means of continuum solvent models. For the estimation of the entropic effect by means of normal mode analysis, minimum energy structures are required. We were able to consider hydration effects in addition to the intramolecular energy considered in our previous calculations. For the calculation of the energy necessary to build the intercalation cavity, entropy is not considered. However, the entropy is taken into account when calculating the binding free energies from single trajectories (see Tables 4 and 5). For detailed information on the calculations and full tables, please refer to Supplementary Material.
Table 5. Energy contributions of single trajectories calculated by subtracting ligand and DNA contributions from the values of the complex
Table 1 shows the free energy values of the unbound DNA and the respective energies of the DNA conformations complexed at the 5'-CGA-3' site with one daunomycin ligand as well as the mean value of the three simulations presented by Trieb et al. (43) with two daunomycin intercalators (for details on these three different simulations please refer to Supplementary Material). For the complexes, the energies were calculated for the DNA after the removal of the intercalator. In addition, the simulation results of the complex of DNA with two 9-dehydroxydaunomcyin molecules and one bisdaunomycin are shown. The average values and standard errors of mean values were calculated from 100 to 200 snapshots, depending on the simulation length. These values are the basis for the calculation of the differences in the energetic contributions of the complexes compared with uncomplexed DNA. They are calculated by subtracting the values of the DNA from the corresponding complexes of Table 1, as presented in Table 2. The formation of the intercalation site leads to unfavorable Coulombic interactions (–136.2 kcal/mol for one daunomycin), but favorable contributions from the polar part of the solvation free energy GGB of 132.1 kcal/mol for one daunomycin. The Gtot is as expected largely positive with 32.3 kcal/mol for the formation of one and 54.4 kcal/mol for two daunomycin intercalation sites, and 50.8 kcal/mol for bisdaunomycin. Formation of the two sites for 9-dehydroxydaunomycin requires 47.8 kcal/mol. This clearly demonstrates that the formation of the cavity costs less energy, if a second daunomycin joins the first. Thus, bisdaunomycin requires even less energy for the separation of the base pairs indicates cooperativity, and shows on the one hand that the linker fits optimally into the groove without requiring additional DNA deformations and on the other hand it indicates that it optimally connects the two intercalating chromophores. In the case of a non-optimal linker, we would expect higher distortion energy of the DNA as a result of a strained ligand. Such analyses are of interest for the design of new linkers. An earlier work by Rao and Kollman (66) investigated the physical basis for the neighbor-exclusion principle, which suggests that intercalative binding can only occur at every other base-pair site. If changes in stereochemical energies, vibrational entropy, counter-ion effects or specific solvent–solute interactions are the main reason for this behavior, is still an open question.
The conformation of DNA providing an intercalation cavity for one daunomycin thus exhibits an 32 kcal/mol higher Gibbs free energy than uncomplexed DNA. This value is higher than the previously estimated values as compared to our calculations with the consideration of an ensemble of snapshots and hydration and ion effects for the formation of the intercalation site. In our calculations, we are taking into account not only the energy necessary for the unstacking of the base pairs, but also the overall change in energy of the conformational changes induced in DNA.
The difference between our theoretical calculations and the lower experimental activation energy values can be explained by the fact that the formation of the cavity will not be formed totally independent of binding. Thus, during the cavity formation stabilizing DNA–ligand contacts could reduce the total free energy of the conformation transition state. The interaction energies between the ligand and the DNA are already calculated to be in the range of more than 100 kcal/mol, which is much larger in magnitude than this initial process of cavity formation and ensures the exergonic intercalation. As DNA is a highly charged molecule and the intercalating ligand also carries a charge, we expect to find a salt dependence on the formation of the intercalation cavity. In fact, we find a dependence of Gtot especially at low salt conditions (see Figure 2). For one daunomycin, for example, the Gtot is 30.9 kcal/mol at no salt and 32.8 kcal/mol at 1.0 M salt. The same is true for the other systems.
Figure 2. Dependence of Gtot for the formation of an intercalation site from salt concentration for ‘bis’ (asterisks), ‘1dau’ (closed squares), ‘2dau’ (closed triangles) and ‘2dau-9OH’ (closed circles). Values are given for one intercalating molecule.
The energy contributions of the ligands alone are presented in Table 3. These values were taken together with the values for DNA and the corresponding complexes for the calculation of binding free energies.
In the approach to calculate the entropy contributions, the problem arises, that structural and energetical minimizations of the complexed DNA with the unoccupied intercalation cavities necessary for NMODE calculations would lead to large structural deviations. Hence, we subtracted from the entropy of the corresponding complexes the contributions of the ligands and the entropy from the uncomplexed DNA structure (see Table 4). We find that the translational and rotational contributions to the entropy do not change in the different complexes and show only small differences between the ligands. The overall sum of the entropy almost exclusively results from the vibrational contribution. Owing to the loss of translational and rotational degrees of freedom (T*Strans and T*Srot), these contributions disfavor complex formation by 11–14 kcal/mol.
In a second approach, that is possible with the MM-GBSA method, the DNA, the intercalator and the complex structures are taken from single complex simulations (see Table 5). This reduces the noise that results, when comparing different MD runs with each other (29). In addition, the entropy contributions calculated in Table 4 are included. Nevertheless, this implies, that the structures and conformational freedom of the DNA and the intercalator would only change slightly, which is definitely not the case when looking at the structural deformations DNA has to undergo when forming the intercalation cavity. Hence the calculated binding free energies are too high, as the energy necessary for the deformation of the DNA is not considered.
However, when the energy for the formation of the intercalation site, calculated in our first approach, including the contribution of entropy, is subtracted, reasonable energies were obtained. This gives binding free energies for one daunomycin of –11.9 kcal/mol at 1 M salt concentration and –14.1 kcal/mol at 0.15 M salt (see Table 6). The calculated binding free energy value includes the entropic effects as described in Table 3, as the minimizations of the complexes and the unbound ligands as well as the uncomplexed DNA are possible.
Table 6. Gbinding energies at two different theoretical salt concentrations calculated by subtracting the energies necessary for the formation of an intercalation site from the binding free energies calculated from the single trajectories
This value is 4–6 kcal/mol too high, compared with the experimental values (12,14,17), which could be due to inefficiencies in the description of the counter-ions. The G value of daunomycin complexation is highly salt dependent due to the positive charge of the ligand. Cation and ligand binding are thus thermodynamically linked, and the binding of one ligand influences the binding of the other one. On the other hand, Reha et al. (23), for example, calculate stabilization energies of intercalator–base pair complexes to be 17.8 kcal/mol for a daunomycin–GC complex. The values for the bisdaunomycin intercalator, where we get binding free energies of –36.2 kcal/mol at 1.0 M and –40.5 kcal/mol at 0.15 M salt concentration, are also higher than expected. This deviation from experimental values is most probably caused by the large structural changes in DNA geometry that cannot be attributed in this second approach but that is circumvented in the first calculations.
CONCLUSION
The (CGCGCGATCGCGCG)2 sequence contains two 5'-CGA-3' binding sites for daunomycin. We simulated binary and ternary systems, in which the DNA is complexed with two daunomycin ligands. The two binding sites are separated by three base pairs. The estimated free energy for creating two binding sites (54.4 kcal/mol) at the same time is less than twice the energy needed for only one binding site (32.3 kcal/mol). This indicates that the binding of one ligand has an effect on the second binding site. Owing to this cooperativity in the case of the bisintercalator, the energy needed for the formation of the second intercalation site is further reduced to 50.8 kcal/mol. We present in this work an adaptation of the MM-GBSA method for the purpose of calculating the conformational energy necessary for the formation of an intercalation site. This method allows the comparison of the free energy between two ensembles of DNA structures. In our case, conformations of complexed DNA were compared with uncomplexed DNA as the reference state. We found that the structural transitions introduced by one or two intercalating ligands energetically disturb the DNA more than expected, but show cooperativity. This helps to understand the mechanism of this important process in more detail. The differences to kinetic data from experiment is not surprising because we believe, that the two steps of intercalation (formation of the cavity and binding) cannot be totally separated from each other. Rather, during the formation of the cavity, the ligand should already be bound and build some stabilizing contacts with the DNA and thus reduces the transition state of the experimentally measured total intercalation process. For the estimation of total binding free energies of intercalating ligands we included entropic effects. These entropic contributions are derived from a comparison of the complexes with the uncomplexed DNA and the corresponding ligands. Furthermore the Gbinding energies are corrected by the energy, that is necessary for the formation of the intercalation site and which is not accessible from the investigation of one single trajectory. Our results indicate that information from one intercalation site is transferred to the second, and a decrease in the energy, necessary to form another cavity, is observed. This is of interest for the binding affinity of bisintercalating ligands or for possible future ligands with even more than two intercalating chromophores. The investigation of the bisintercalating ligand bisdaunomycin showed also that the linker optimally fits into the groove.
SUPPLEMENTARY MATERIAL
Supplementary Material is available at NAR Online.
ACKNOWLEDGEMENTS
This work was supported by a grant from the Austrian Science Fund (grant number P16176 -TPH), for which we are grateful.
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* To whom correspondence should be addressed. Tel: +43 512 507 5162; Fax: +43 512 507 5144; Email: Klaus.Liedl@uibk.ac.at
ABSTRACT
Daunomycin is one of the most important agents used in anticancer chemotherapy. It interacts with DNA through intercalation of its planar chromophore between successive base pairs. The effect of intercalation on structure, dynamics and energetics is the topic of a wealth of scientific studies. In the present study, we report a computational examination of the energetics of the intercalation process. In detail, we concentrate on the energetic penalty that intercalation of daunomycin introduces into DNA by disturbing it from its unbound conformation. For these means, we are analyzing already published molecular dynamics simulations of daunomycin–DNA complexes and present novel simulations of a bisdaunomycin–DNA and a 9-dehydroxydaunomycin–DNA intercalated complex using the MM-GBSA module implemented in the AMBER suite of programs. Using this molecular dynamics based, continuum solvent method we were able to calculate the energy required to form an intercalation site. Consequently, we compare the free energy of the duplex d(CGCGCGATCGCGCG)2 in the B-form conformation with the respective conformations when intercalated with daunomycin and a bisintercalating analog. Our results show that the introduction of one single intercalation site costs 32 kcal/mol. For double intercalation, or intercalation of the bisintercalator, the respective value for one intercalation site decreases to 27 and 24 kcal/mol, respectively, at a theoretical salt concentration of 0.15 M. This proposes that at least in these cases, a synergistic effect takes place. Although it is well known that intercalation leads to substantial disturbance of the DNA conformation, already performed investigations suggest a lower energetic penalty. Nevertheless to the best of our knowledge the calculations presented here are the most complete ones and consider hydration effects for the first time. The interaction energy between the ligand and the DNA certainly over-compensates this penalty for introducing the intercalation site and thus favors complexation. Such analyses are helpful for the description of allosteric effects in protein ligand binding.
INTRODUCTION
Small ligands can interact with DNA by groove binding or intercalation. Generally speaking, minor groove binding molecules such as netropsin or distamycin, on the one hand, fit into the groove without causing large perturbations in the DNA structure. Drug intercalation, on the other hand, is defined as the stacking of a planar chromophore between successive base pairs. Daunomycin can be accounted as a model compound for the investigation of intercalation processes and is one of the most important agents for cancer chemotherapy. To allow such an interaction, structural deformations of the DNA are necessary. Daunomycin and bisdaunomycin in this respect show a combination of these two features, as the aromatic ring-system intercalates between base pairs of the DNA double-strand, and the sugar moiety, as well as the linker in the case of bisintercalating bisdaunomycin, lie in the minor groove and influence sequence specificity as well as binding affinity. When complexed with DNA, this amino sugar enters into the minor groove while the rest of the molecule is buried between two successive base pairs. The sugar exhibits a high flexibility and builds contacts with the phosphate-backbone of the DNA. These structural and energetic effects are investigated in detail by experimental and theoretical methods (1–12). To improve the binding properties, bisintercalating ligands were developed by connecting two daunomycin molecules through a proper linker (13–15). The choice of a proper linker is crucial, as it influences the binding, and as the site size of a bisintercalator is increased relative to the monomer. Increased site size can potentially lead to increased sequence selectivity (9). One of the best linkers that optimally fits into the minor groove and conserves the binding mode of the single daunomycin molecules is a p-xylyl residue (see Figure 1) connecting two daunomycin molecules via their nitrogen atoms.
Figure 1. Structures of daunomycin (left) and bisdaunomycin (right). In 9-dehydroxydaunomycin the OH group at C9 in daunomycin is replaced by a hydrogen.
Recent investigations have treated the energetic contributions to the binding energy of different functional groups of daunomycin. The hydropathic interactions analyses of Cashman et al. (2,12) investigate contributions of different daunomycin analogs to the binding energy and also to the sequence selectivity of intercalation. They predict a free energy contribution of –3.6 ± 1.1 kcal/mol from the groove binding daunosamine sugar and a contribution of –0.7 ± 0.7 kcal/mol for the removal of the OH at position C9. The free energy G for daunomycin binding is calculated to be –10.0 ± 0.9 kcal/mol compared to the experimental value of –7.9 ± 0.3 kcal/mol from Chaires et al. (16) from comparative binding studies. Another approach that can be used to calculate binding energies was applied by Andrews et al. (17). In this approach, the binding constants and the structural components of several drugs and enzyme inibitors have been used to calculate the average binding energies of some common functional groups. Thus by dissecting the contributions of functional groups to drug–receptor interactions, binding energies can be estimated.
Despite these and other approaches for the calculation of energies in the process of binding, the question, how much energy the formation of the intercalation cavity costs, is not answered. On the other hand, several investigations concerning the stacking and unstacking interactions and energies of DNA bases were performed (18–25). In a quantum-chemical study by Sponer et al. (24), stacking energies in canonical B-DNA base-pair steps of –9.5 to –13.2 kcal/mol were found. By using our approach, we were able to calculate the energy difference between an uncomplexed DNA tetra-decamer and various DNA–intercalator complexes from molecular dynamics (MD) simulations in explicit solvent. By the accurate description at the atomic level of our system, the continuum treatment of the solvent in many cases has proven to constitute a remarkably accurate approximation. It is then possible to treat problems, such as solvation free energies, binding free energies, solvent effects on conformation and reaction rates, and pH and ionic strength effects on binding and stability, within the framework of a simple and accurate theory (26).
The Generalized Born (GB) theory is the basis of the computational method applied for the calculations performed in the present work and has been applied recently in different studies (27–32). It allows the estimation of the electrostatic free energies of solvation of diverse molecules and molecular ions. In the GB model, a molecule in solution is represented as a set of point charges, set in spherical cavities, embedded in a polarizable dielectric continuum. Finite difference Poisson–Boltzmann free energies can be approximated using GB calculations. It has been shown in previous studies that the solvation free energies are generally within 5% of the observed values using the GB method together with a simple treatment of non-electrostatic effects. The GB model is capable of reproducing solvation free energies of 32 molecules, chosen as prototypes of protein and nucleic acid constituents, with a mean unsigned error of <1 kcal (33).
The first step in the binding process of each intercalator is the creation of the intercalation site. This process is energetically highly unfavorable and thus determines the kinetics and thermodynamics of binding. The intercalation site differs from the undisturbed DNA by a doubling of the base–base stacking distance followed by unwinding and conformational changes of the sugar phosphate backbone. Thus, a detailed energetic investigation on the formation of this intercalation site is of scientific interest. In this work, we describe the energetic analysis of already published MD simulations of daunomycin bound to d(CGCGCGATCGCGCG)2 in the B-form conformation. This sequence contains two 5'-CGA-3' daunomycin binding sites separated by four bases which enabled us to simulate the ternary complex with two daunomycin ligands as well as its bisintercalating analog and a double intercalated complex with 9-dehydroxydaunomycin. The energetic analysis was performed using the MM-GBSA module of the AMBER suite of programs. MM-GBSA is able to calculate the relative stabilities of different conformations by dividing the total free energy into its single contributions. This approach allows the calculation of the conformational free energy differences between free DNA and intercalated complexes without the need to establish an explicit sampling pathway connecting one form to the other. In this model, the free energy consists of the internal energy (Egas), the solvation free energy (GGB + Gnonpolar) and the entropic contribution to the free energy. Egas is the vacuum force-field energy and contains all intramolecular bonded (stretch, bend, torsion and improper torsion) and non-bonded (van der Waals and electrostatic) interactions. The solvation term includes both the polar and the non-polar contribution to the solvation free energy. The non-polar part is calculated by an empirical formula connecting the solvent accessible surface area (SASA) with the free energy, while the polar fraction is determined by solving the Poisson–Boltzmann equation (PBSA) or by applying the GB model (GBSA), as in the present work. The entropy is divided into the vibrational entropy, as estimated via a normal mode analysis, and the translational and rotational entropy, deduced from the coordinates and the atomic masses.
The mean MM-GBSA free energy is calculated for a set of snapshots selected from MD simulations and then compared with a reference set. Srinivasan et al. (30), for example, investigated the relative stabilities of A-DNA versus B-DNA form, by comparing the MM-PBSA free energies obtained from two MD simulations of the respective conformations. The method correctly describes the corresponding stabilities and even a phosphoramidate-modified DNA duplex gave results in good agreement with the experiment. Originally this module was written as a tool for predicting binding free energies of ligands. Therefore, the complex must be compared with the sum of the free energies of unbound ligand and receptor. We used this method for calculating the free energy of DNA alone and compared the complexed and the uncomplexed state. The difference in energy without consideration of the unbound ligand represents the energetic penalty needed for the formation of the intercalation site. In addition, we performed a calculation of total binding free energies of the ligands as described above.
MATERIALS AND METHODS
Investigation of biomolecules like DNA and DNA complexes by means of computational methods have already proven to be valuable for a deeper understanding of the structural, dynamical and energetic properties (34,35). Owing to the inclusion of the long-range electrostatic interactions by the Particle Mesh Ewald method, stable B-form DNA MD simulations are possible. All simulations were performed using the AMBER package (36,37) by adapting standard state of the art simulation protocols for our needs (38–42). We simulated the DNA sequence d(CGCGCGATCGCGCG)2 starting from its canonical B-DNA conformation, constructed using the program NUKIT. Additionally, five simulations of DNA–daunomycin complexes were performed. In one simulation one 5'-CGA-3' step was complexed, representing the single intercalation, and in second three simulations with both of these steps occupied (representing double intercalation) were performed (details to the simulation parameters) and the parametrization of the daunomycin ligand are described elsewhere (43). Furthermore, we present simulations of a ternary complex of daunomycin lacking the 9-OH group (9-dehydroxydaunomycin) and a simulation of the bisintercalating daunomycin ligand bisdaunomycin (for both see Figure 1). For the construction of the 9-dehydroxydaunomycin complex we took daunomycin, removed the OH group and performed ab initio structural minimization and calculation of the electrostatic charges. The further construction of the complex was according to the procedures already described. For the bisintercalating complex, we took the coordinates and structure of bisdaunomycin from the X-ray structure determined by Hu et al. (13) with the NDB ID code DDF072 and performed an ab initio structural minimization and calculation of the electrostatic potential for RESP (Restrained ElectroStatic Potential) (44,45) with GAUSSIAN98 (46) at the HF/6-31G* level of theory. Selection of the appropriate atom types and set up of the complex was performed with the same targeted MD approach as described previously (43). The targeted root-mean-square distance (RMSD) was chosen to be 0.0 ? and we performed a sequence of 100 ps simulations each, increasing the force constant from 1 to 2, 5 and 100 kcal/mol yielding a final RMSD of 0.087 ?. All MD simulations were performed for a total simulation time of 10–20 ns using a time step of 2 fs. The all atom force field of Cornell et al. (47) with the modifications of Cheatham et al. (48) was used. The system was solvated with TIP3P Monte Carlo water boxes requiring a 12 ? solvent shell in all directions. The long-range electrostatic interactions are considered by applying the Particle Mesh Ewald algorithm (49,50). The MM-GBSA calculations were performed for 100–200 snapshots of each simulation. These snapshots were taken every 100 ps of the 10–20 ns simulations, respectively. The vacuum free energy (Ggas) corresponds to the force field energy of the nucleic acid solute (not including counter-ions or solvent) and it was computed from the Cornell et al. (47) force field with the modifications of Cheatham et al. (48). It contains the contributions of the non-bonded and 1,4-electrostatic and van der Waals energies, as well as the internal bond, angle and dihedral energies. For each energy, the average and the standard error of the mean values are given in Tables 1–3. The solvation free energy (Gsol) is divided into the electrostatic (GGB) and the nonpolar (Gnonpolar) part. The electrostatic part was derived with the GB approximation using the model of Jayaram et al. (33), which is faster to solve than the Poisson–Boltzmann equation. Nevertheless the results of both methods are in a close agreement, illustrating that the GB-model is an effective alternative to the PB-method (33). A more detailed description of these methods is given elsewhere (26,33,51–56). The non-polar contribution to the solvation energy is dependent on the solvent accessible surface area (SASA). The term is represented as *SASA + b where the parameters and b are taken from Sanner et al. (57) and found to be 0.00542 kcal/?2 and 0.92 kcal/mol. The SASA was estimated with a 1.4 ? solvent probe radius as implemented in Sander (37). For the analysis of the salt dependence, the calculations were performed at 0, 0.1, 0.15, 0.2, 0.5 and 1.0 M theoretical salt concentrations. The solute entropy of the components is investigated by normal mode analyses of every 10th of the above mentioned 100–200 snapshots, after minimizing the snapshots and was performed with the AMBER tool NMODE. For all calculations standard parameters already described in the literature were used (58–61). The entropy was derived from a combination of the different simulations. That is, the overall change in the entropy contributions was calculated by subtracting the values from the uncomplexed DNA and from the respective ligand from the complexes. This slightly modified approach as compared to calculations where all contributions are derived from one simulation run was necessary, as the intramolecular strain in the complexes is too large as to give reasonable values for the DNA after minimization (see also Table 4).
Table 1. Energy contribution of uncomplexed and complexed DNA (without ligands)
Table 2. Difference to uncomplexed DNA of the energy contribution at a theoretical salt concentration of 0.15 M
Table 3. Energy contribution of ligands alone
Table 4. Calculation of the entropy terms
RESULTS
A simulation of the uncomplexed d(CGCGCGATCGCGCG)2 tetradecamer DNA and six simulations of its complexes with intercalators were performed. In one simulation one 5'-CGA-3' binding site was complexed with daunomycin, while in the second case three different simulations where both of these binding sites were occupied. In the present study the energies of these three simulations were calculated separately, but the average values are presented. In the third simulation, the two binding sites were intercalated by the bisintercalating ligand bisdaunomycin. Finally, a complex of 9-dehydroxydaunomycin– DNA with two intercalators was carried out. In all simulations, the DNA stays stable in the B-form with a stable RMSD value after a maximum time of 350 ps. Comparing the structural parameters from the X-ray structures published by Frederick et al. (62) and Hu et al. (13) with our results, we find a good agreement. The first step in the binding process of each intercalator is the creation of the intercalation site. This process is energetically highly unfavorable and thus determines the kinetics and thermodynamics of binding. The intercalation site differs from the undisturbed DNA by a doubling of the base–base distance. Structural changes, a given B-DNA has to undergo during the intercalation process especially concern stacking interactions like DNA rise and buckle. For example, the helical rise in the complexed state is 7.5 ?, which is more than twice the value of unbound B-DNA. Besides these stacking interactions, the groove width and the structure and flexibility of the backbone are affected. It is assumed that previous to intercalation, DNA must undergo these conformational transitions to form the intercalation site. This step is also known as helical breathing. The bases must separate until the cavity is large enough that the intercalating chromophore fits. In several attempts it was tried to compute the energy necessary for forming this cavity. Nuss et al. (63) determined the destabilization energy by means of molecular mechanics calculations of drug–dinucleoside complexes to be in the range of 15–30 kcal/mol and to be essentially independent from the intercalator itself. For ethidium bromide–dinucleoside they found a net stabilization in the gas phase of 130–140 kcal/mol. Ornstein and Rein (64,65) used an empirical partitioned-potential function calculating energies for the transition between dinucleoside triphosphates in the B-DNA conformation and the corresponding intercalated state to be 17–31 kcal/mol. From experimental kinetic measurements, it appears that the activation free energy of intercalation is 15 kcal/mol (63). Owing to the fact that the activation energy and the free energy of the cavity formation are not rigorously comparable, it can be claimed, that these theoretical results are in the same range. All mentioned values did not include solvation and entropic effects. Therefore, although they are valuable for understanding the basic binding principles there is still a need for more in-depth investigations. We performed such calculations using the MM-GBSA method. We compared the free energy of the DNA conformation in the unbound state with the respective bound conformations. The MM-GBSA method allows the calculation of the mean free energy of a set of structural snapshots. As we were primarily interested in the energy that is necessary to form an intercalation site, we selected the DNA coordinates of the MD simulation of the complexes. This method benefits from computational efficiency as only the initial and final states of the system are evaluated like the energetic comparison between A-DNA and B-DNA conformations performed by Srinivasan et al. (30). In these simulations, the phase space of the complex is sampled and therefore a good description of the complexed state is achieved. MM-GBSA also includes the effect of hydration and counter-ions by means of continuum solvent models. For the estimation of the entropic effect by means of normal mode analysis, minimum energy structures are required. We were able to consider hydration effects in addition to the intramolecular energy considered in our previous calculations. For the calculation of the energy necessary to build the intercalation cavity, entropy is not considered. However, the entropy is taken into account when calculating the binding free energies from single trajectories (see Tables 4 and 5). For detailed information on the calculations and full tables, please refer to Supplementary Material.
Table 5. Energy contributions of single trajectories calculated by subtracting ligand and DNA contributions from the values of the complex
Table 1 shows the free energy values of the unbound DNA and the respective energies of the DNA conformations complexed at the 5'-CGA-3' site with one daunomycin ligand as well as the mean value of the three simulations presented by Trieb et al. (43) with two daunomycin intercalators (for details on these three different simulations please refer to Supplementary Material). For the complexes, the energies were calculated for the DNA after the removal of the intercalator. In addition, the simulation results of the complex of DNA with two 9-dehydroxydaunomcyin molecules and one bisdaunomycin are shown. The average values and standard errors of mean values were calculated from 100 to 200 snapshots, depending on the simulation length. These values are the basis for the calculation of the differences in the energetic contributions of the complexes compared with uncomplexed DNA. They are calculated by subtracting the values of the DNA from the corresponding complexes of Table 1, as presented in Table 2. The formation of the intercalation site leads to unfavorable Coulombic interactions (–136.2 kcal/mol for one daunomycin), but favorable contributions from the polar part of the solvation free energy GGB of 132.1 kcal/mol for one daunomycin. The Gtot is as expected largely positive with 32.3 kcal/mol for the formation of one and 54.4 kcal/mol for two daunomycin intercalation sites, and 50.8 kcal/mol for bisdaunomycin. Formation of the two sites for 9-dehydroxydaunomycin requires 47.8 kcal/mol. This clearly demonstrates that the formation of the cavity costs less energy, if a second daunomycin joins the first. Thus, bisdaunomycin requires even less energy for the separation of the base pairs indicates cooperativity, and shows on the one hand that the linker fits optimally into the groove without requiring additional DNA deformations and on the other hand it indicates that it optimally connects the two intercalating chromophores. In the case of a non-optimal linker, we would expect higher distortion energy of the DNA as a result of a strained ligand. Such analyses are of interest for the design of new linkers. An earlier work by Rao and Kollman (66) investigated the physical basis for the neighbor-exclusion principle, which suggests that intercalative binding can only occur at every other base-pair site. If changes in stereochemical energies, vibrational entropy, counter-ion effects or specific solvent–solute interactions are the main reason for this behavior, is still an open question.
The conformation of DNA providing an intercalation cavity for one daunomycin thus exhibits an 32 kcal/mol higher Gibbs free energy than uncomplexed DNA. This value is higher than the previously estimated values as compared to our calculations with the consideration of an ensemble of snapshots and hydration and ion effects for the formation of the intercalation site. In our calculations, we are taking into account not only the energy necessary for the unstacking of the base pairs, but also the overall change in energy of the conformational changes induced in DNA.
The difference between our theoretical calculations and the lower experimental activation energy values can be explained by the fact that the formation of the cavity will not be formed totally independent of binding. Thus, during the cavity formation stabilizing DNA–ligand contacts could reduce the total free energy of the conformation transition state. The interaction energies between the ligand and the DNA are already calculated to be in the range of more than 100 kcal/mol, which is much larger in magnitude than this initial process of cavity formation and ensures the exergonic intercalation. As DNA is a highly charged molecule and the intercalating ligand also carries a charge, we expect to find a salt dependence on the formation of the intercalation cavity. In fact, we find a dependence of Gtot especially at low salt conditions (see Figure 2). For one daunomycin, for example, the Gtot is 30.9 kcal/mol at no salt and 32.8 kcal/mol at 1.0 M salt. The same is true for the other systems.
Figure 2. Dependence of Gtot for the formation of an intercalation site from salt concentration for ‘bis’ (asterisks), ‘1dau’ (closed squares), ‘2dau’ (closed triangles) and ‘2dau-9OH’ (closed circles). Values are given for one intercalating molecule.
The energy contributions of the ligands alone are presented in Table 3. These values were taken together with the values for DNA and the corresponding complexes for the calculation of binding free energies.
In the approach to calculate the entropy contributions, the problem arises, that structural and energetical minimizations of the complexed DNA with the unoccupied intercalation cavities necessary for NMODE calculations would lead to large structural deviations. Hence, we subtracted from the entropy of the corresponding complexes the contributions of the ligands and the entropy from the uncomplexed DNA structure (see Table 4). We find that the translational and rotational contributions to the entropy do not change in the different complexes and show only small differences between the ligands. The overall sum of the entropy almost exclusively results from the vibrational contribution. Owing to the loss of translational and rotational degrees of freedom (T*Strans and T*Srot), these contributions disfavor complex formation by 11–14 kcal/mol.
In a second approach, that is possible with the MM-GBSA method, the DNA, the intercalator and the complex structures are taken from single complex simulations (see Table 5). This reduces the noise that results, when comparing different MD runs with each other (29). In addition, the entropy contributions calculated in Table 4 are included. Nevertheless, this implies, that the structures and conformational freedom of the DNA and the intercalator would only change slightly, which is definitely not the case when looking at the structural deformations DNA has to undergo when forming the intercalation cavity. Hence the calculated binding free energies are too high, as the energy necessary for the deformation of the DNA is not considered.
However, when the energy for the formation of the intercalation site, calculated in our first approach, including the contribution of entropy, is subtracted, reasonable energies were obtained. This gives binding free energies for one daunomycin of –11.9 kcal/mol at 1 M salt concentration and –14.1 kcal/mol at 0.15 M salt (see Table 6). The calculated binding free energy value includes the entropic effects as described in Table 3, as the minimizations of the complexes and the unbound ligands as well as the uncomplexed DNA are possible.
Table 6. Gbinding energies at two different theoretical salt concentrations calculated by subtracting the energies necessary for the formation of an intercalation site from the binding free energies calculated from the single trajectories
This value is 4–6 kcal/mol too high, compared with the experimental values (12,14,17), which could be due to inefficiencies in the description of the counter-ions. The G value of daunomycin complexation is highly salt dependent due to the positive charge of the ligand. Cation and ligand binding are thus thermodynamically linked, and the binding of one ligand influences the binding of the other one. On the other hand, Reha et al. (23), for example, calculate stabilization energies of intercalator–base pair complexes to be 17.8 kcal/mol for a daunomycin–GC complex. The values for the bisdaunomycin intercalator, where we get binding free energies of –36.2 kcal/mol at 1.0 M and –40.5 kcal/mol at 0.15 M salt concentration, are also higher than expected. This deviation from experimental values is most probably caused by the large structural changes in DNA geometry that cannot be attributed in this second approach but that is circumvented in the first calculations.
CONCLUSION
The (CGCGCGATCGCGCG)2 sequence contains two 5'-CGA-3' binding sites for daunomycin. We simulated binary and ternary systems, in which the DNA is complexed with two daunomycin ligands. The two binding sites are separated by three base pairs. The estimated free energy for creating two binding sites (54.4 kcal/mol) at the same time is less than twice the energy needed for only one binding site (32.3 kcal/mol). This indicates that the binding of one ligand has an effect on the second binding site. Owing to this cooperativity in the case of the bisintercalator, the energy needed for the formation of the second intercalation site is further reduced to 50.8 kcal/mol. We present in this work an adaptation of the MM-GBSA method for the purpose of calculating the conformational energy necessary for the formation of an intercalation site. This method allows the comparison of the free energy between two ensembles of DNA structures. In our case, conformations of complexed DNA were compared with uncomplexed DNA as the reference state. We found that the structural transitions introduced by one or two intercalating ligands energetically disturb the DNA more than expected, but show cooperativity. This helps to understand the mechanism of this important process in more detail. The differences to kinetic data from experiment is not surprising because we believe, that the two steps of intercalation (formation of the cavity and binding) cannot be totally separated from each other. Rather, during the formation of the cavity, the ligand should already be bound and build some stabilizing contacts with the DNA and thus reduces the transition state of the experimentally measured total intercalation process. For the estimation of total binding free energies of intercalating ligands we included entropic effects. These entropic contributions are derived from a comparison of the complexes with the uncomplexed DNA and the corresponding ligands. Furthermore the Gbinding energies are corrected by the energy, that is necessary for the formation of the intercalation site and which is not accessible from the investigation of one single trajectory. Our results indicate that information from one intercalation site is transferred to the second, and a decrease in the energy, necessary to form another cavity, is observed. This is of interest for the binding affinity of bisintercalating ligands or for possible future ligands with even more than two intercalating chromophores. The investigation of the bisintercalating ligand bisdaunomycin showed also that the linker optimally fits into the groove.
SUPPLEMENTARY MATERIAL
Supplementary Material is available at NAR Online.
ACKNOWLEDGEMENTS
This work was supported by a grant from the Austrian Science Fund (grant number P16176 -TPH), for which we are grateful.
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