Circular Dichroism of DNA G-Quadruplexes: Combining Modeling and

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Circular Dichroism of DNA G-Quadruplexes: Combining Modeling and Spectroscopy to Unravel Complex Structures Hugo Gattuso, Angelo Spinello, Alessio Terenzi, Xavier Assfeld, Giampaolo Barone, and Antonio Monari J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b00634 • Publication Date (Web): 04 Mar 2016 Downloaded from http://pubs.acs.org on March 5, 2016

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The Journal of Physical Chemistry

Circular Dichroism of DNA G-Quadruplexes: Combining Modeling and Spectroscopy to Unravel Complex Structures Hugo Gattuso,†,‡ Angelo Spinello,¶ Alessio Terenzi,¶,§ Xavier Assfeld,†,‡ Giampaolo Barone,∗,¶ and Antonio Monari∗,†,‡ Université de Lorraine Nancy, Theory-Modeling-Simulation, SRSMC, Boulevard des Aiguillettes 54506, Vandoeuvre-lès-Nancy, France, CNRS, Theory-Modeling-Simulation, SRSMC, Boulevard des Aiguillettes 54506, Vandoeuvre-lès-Nancy, France, Universit´ a di Palermo, Dipartimento di Scienze Biologiche, Chimiche e Farmaceutiche, Viale delle Scienze, Palermo Italy, and Institute of Inorganic Chemistry University of Vienna W¨ ahringerstrasse 42 Vienna, Austria E-mail: [email protected]; [email protected]

∗

To whom correspondence should be addressed Université de Lorraine Nancy, Theory-Modeling-Simulation, SRSMC, Boulevard des Aiguillettes 54506, Vandoeuvre-lès-Nancy, France ‡ CNRS, Theory-Modeling-Simulation, SRSMC, Boulevard des Aiguillettes 54506, Vandoeuvre-lès-Nancy, France ¶ Universitá di Palermo, Dipartimento di Scienze Biologiche, Chimiche e Farmaceutiche, Viale delle Scienze, Palermo Italy § Institute of Inorganic Chemistry University of Vienna Währingerstrasse 42 Vienna, Austria †

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Abstract We report on the comparison between the computational and experimental determination of electronic circular dichroism spectra of different guanine-quadruplexes obtained from human telomeric sequences. In particular the difference between parallel, antiparallel and hybrid structures are evidenced, as well as the induction of transitions between the polymorphs depending on the solution environment. Extensive molecular dynamics simulations (MD) are used to probe the conformational space of the different quadruplexes, and subsequently state-of-the-art hybrid quantum mechanics/molecular mechanics (QM/MM) techniques coupled with excitonic semi-empirical hamiltonian are used to simulate the macromolecular induced circular dichroism. The coupling of spectroscopy and molecular simulation allows an efficient one-to-one mapping between structures and optical properties, offering a way to disentangle the rich, yet complicated, quantity of information embedded in circular dichroism spectra. We show that our methodology is robust and efficient and allows to take into account subtle conformational changes. As such it could be used as an efficient tool to investigate structural modification upon DNA/drug interactions.

Keywords DNA G-quadruplexes, human telomeres, electronic circular dichroism, QM/MM, Molecular Dynamics

Introduction The interest toward non canonical DNA structures has grown considerably in the last years. 1–5 Indeed non B-DNA conformations are nowadays no longer seen as laboratory curiosity highlighting the inherent DNA polymorphism. Instead, their fundamental biological role has been recognized and settled on very solid basis. Among biologically relevant non canonical DNA structures one should cite the so called G-quadruplexes (G4). 6–10 These are 2


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DNA sequences rich in guanine, organized in a rather peculiar way. 11 Guanine bases form planar tetramers stabilized by the so-called Hoogsteen hydrogen bond network. 12 A total of two, three or four stacked tetrameric sheets lead to a rigid structure leaving a negatively charged central channel, large enough to host stabilizing cations (usually Na+ or K+ ). Guanine rich DNA sequences are found in telomeres, 13 i.e. the non coding terminal DNA regions, as well as in some gene promoting regions; as such those regions may organize themselves in G4 arrangements. 7 Telomere regulation is extremely important since it is connected to the cell’s viability cycle. Indeed, at each replication the telomere is shortened until it reaches a critical length that induces cell apoptosis. The shortening of DNA telomere is regulated, and notably hampered, by the interaction of the strand with telomerase, a protein that is usually overexpressed in a number of invasive cancer types. 14 The interaction of G4 telomeres with other nuclear proteins has been recently evidenced, yet its role is not fully understood. 15 Indeed, the hampering of telomere length reduction induced by telomerase may be considered as one of the molecular-based reasons of cancer cell ”immortality”. As such telomeres, in G4 conformation, have emerged as a promising target for novel anticancer therapies. Indeed the interaction of external drugs resulting in the stabilization of the G4 aggregate may ultimately result in the inhibition of the telomerase, and hence in anticancer activity. 16 The preferential interaction of a drug with G4 instead of canonical DNA forms would also reduce its cytotoxicity toward healthy cells, and hence unwanted side effects of chemotherapy. 17–22 However, in order to achieve a good characterization and thus control the drug/G4 interactions a good knowledge of the structural and dynamic properties of the aggregate is absolutely needed. In this respect, G4 are more complicated than a simple picture may let one to suppose. 11 A very intricate polymorphism is indeed observed among those structure. In particular three main classes are recognized as parallel, antiparallel and hybrid (Figure 1). The classification of the G4 depends on the different orientation of the four strands forming the quadruplex structure. In particular, in the case of parallel orientation all the

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(Figure 2).

!"#$%&%''('# )"#*+,&-.#

/"#!012%&%''('# Figure 2: Representative structures of the G-quadruplexes in cartoon representation extracted from the Molecular Dynamic trajectories. Backbone is represented as ribbon, while basis as ellipsoidal objects. Stabilizing cations are in van der Waals representation, in purple for K+ and yellow for Na+ cations. The bases forming the G4 core are in light blue, flanking bases in dark blue and light green. A) Parallel, B) Hybrid, and C) Antiparallel. One of the most used technique in molecular biology to infer the structure of a macromolecular arrangement is doubtlessly electronic circular dichroism (ECD). Unlike other techniques such as mass or NMR spectrometries, ECD is of simple and economic realization and can be routinely performed. The sensitivity of macromolecular ECD to the structural variation of multichromophoric arrangements makes it capable to capture the subtle changes induced by temperature fluctuation or interactions with drugs. 25 Indeed, ECD is nowadays commonly used to unravel structural modification of proteins and polypeptides 26–29 as well as nucleic acid conformations. 30–35 However, the density and quality of information contained in ECD spectra although remarkable, is somehow difficult to relate the subtle modification

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of spectral features to non-equivocal structural deformations or conformations. It is in that context that the use of a general approach combining simulation and modeling with experimental spectroscopies proves to be extremely helpful. It is possible to use molecular dynamics (MD) techniques to perform a large scale exploration of the configuration and conformational space of a number of biological polymers, also taking into account their interactions with drugs and the subsequent modification. At the same time state-of-the art quantum mechanics/molecular mechanics (QM/MM) methods allow to obtain a good description of the excited states of complex biological systems taking into account the environmental influence as well as the dynamic and vibrational effects when coupled with MD. 36–40 Hence such a protocol appears as extremely promising since it allows building in silico a set of possible conformations, test their stability via MD, simulate their spectra and compare them with available experimental data to discriminate between the different structures. 41 However, in the case of ECD the situation is further complicated by the fact that the observable (ECD spectrum) is actually the result of the interaction of a multichromophore system. 42,43 In order to restrain the QM partition to treatable sizes some approaches have been developed, whether based on semiempirical Frenkel excitonic Hamiltonian, 42,44 or on specifically tailored QM methodologies, such as complex polarization propagator. 43,44 The simulation of ECD spectra have nowadays been performed on different biological macromolecules such as proteins or nucleic acids, 45 as well as in artificial auto-organizing materials. 46,47 Very recently Mennucci’s group reported the study of ECD of DNA in canonical and non-canonical arrangements. 48 In the present contribution we apply our protocol 42 combining QM/MM and MD to the determination of ECD spectra of G4 in the different conformations and compare them to the experimental results. On the one hand, we will validate the possibility to properly describe the dynamic conformation of different G4 polymorphs by means of force field calculations. On the other hand, we will provide and validate a general protocol that will allow mapping the ECD spectra to structural conformations of the G4 manifold. Hence, we will have

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a powerful tool that could be successfully used to interpret the interactions between G4 and different molecules, and hence strongly support the rational design of novel specific therapeutic agents.

Computational Methodology All along the present contribution the simulation of the ECD has been performed at QM/MM level following a preliminary exploration of the G4 conformational space by MD techniques. In order to achieve a good convergence of the sampling a rather large number of snapshots has been taken into account. For that reason a relatively small QM partition is necessary in order to avoid too heavy computational burdens. To achieve such a compromise we used the so called Frenkel excitonic model to take into account the interactions between the chromophores, i.e. the DNA nucleobases. For the reader convenience we briefly recall the basic foundation of Frenkel excitonic coupling and in particular its application to supramolecular ECD determination. 42

Frenkel Hamiltonian for ECD It is well known that non-chiral chromophores arranged in a chiral multichromophoric system display an optically active ECD, whose characteristics strongly depend on the macromolecular geometrical arrangement. The induction of a non zero ECD by supramolecular arrangement can be easily understood and computed thanks to the use of the so called Frenkel exciton. Consider for the sake of simplicity a system composed by two interacting chromophores A and B. Upon excitation the global system wavefunction |Ψ± i may be obtained as a linear combination of excitations centered on monomer A or B respectively:

± 0 ∗ ∗ 0 |Ψ± i = c± A |φA φB i ± cB |φA φB i

(1)

where |φ∗A φ0B i is the wavefunction representing an excitation of the monomer A while 7



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B is in its electronic ground state. Already from equation 1 it is evident that the effect of the Frenkel expression is to mix the wavefunctions of A and B and as a consequence eventually lead to the splitting of the excited states degeneracy. The extension to the case of a multichromophoric system is straightforward and the total wavefunction will again be expresses as a linear combination of excitation centered on individual monomers. As a consequence, in order to obtain the Frenkel energy spectrum one should resort to an effective two-body Hamiltonian coupling excitations on different monomers.

A ˆ B ˆ ijAA = εA ˆ AB H i δij ; Hij = hΦi |H|Φj i

(2)

th In Equation 2 εA excitation energy of the monomer A and δij is the Kronecker i is the i

ˆ B delta, while hΦA i |H|Φj i represents the coupling between excited states centered on monomers A and B, respectively. The diagonalization of the associated secular equation will provide eigenvalues (E), i.e. the Frenkel excitation energies, and eigenvectors (U) representing the Frenkel wavefunction.

H·U=E·U

(3)

In the simplest approach the effective hamiltonian elements may be approximated knowing the monomers’ transition dipole moments following the equation

ˆ AB = H ij

B B (µA µA i · RAB )(µj · RAB ) i · µj − 3 |RAB |3 |RAB |5

(4)

th where µA i is the transition dipole moment of the i excited state centered on the monomer

A, and RAB is the vector distance connecting the center of charges of two monomers A and B. Once the Frenkel energies (E) and the eigenvectors (U) have been obtained for each transition k one can easily calculate the oscillator strenght f for absorption, and the rotatory strengths for ECD intensities

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fk =

X

(µi · µj )Uik Ujk

(5)

Ek [Rij (µi · µj )] Uik Ujk

(6)

i,j

rk =

X i,j

Note that to have ECD in homogeneous media (solution) the vector rk has to be averaged over the three cartesian components. Different and more elaborate strategies have been proposed and used in order to estimate the effective hamiltonian components. In particular Mennucci and coworkers have relied on the use of rather sophisticated techniques taking into account the coupling between the ground and excited state densities of the different monomers. 48,49 Their approach provides good agreement with higher level calculations and is able to solve some of the problems arising for the simpler dipole approaches in particular in the case of strongly coupled chromophores. 48 However, even if somehow crude the dipole approach has the advantage to be straightforward, fast to calculate and easy to implement. Moreover, as shown below it is able to provide a generally good agreement with the experimental ECD band shapes.

Computational Protocol G-quadruplex conformations, parallel (pdb id: 1KF1), hybrid (2HY9) and antiparallel (143D) were taken from the Protein Data Bank. For each conformations Molecular Dynamics (MD) simulations were performed with the AMBER software, 50 using the AMBER99 force field with the bsc0 correction. 51 First, the two stabilizing K+ (in the case of hybrid type) and Na+ (in the case of antiparallel type), absent in the pdb data file, were added manually between each G-quadruplex planes. Then oligonucleotides were solvated in a truncated octahedron box with edges of approximately 76 ˚ A. A TIP3P water model was used and K+ or Na+ (in the case of the antiparallel) were added to neutralize the systems. Particle Mesh Ewald (PME) and periodic boundary conditions were used throughout. 9




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base, and the dangling bond was treated with the link atom scheme. Time-dependent density functional theory (TDDFT) with the M06-2X functional 53 and 6-31G(d,p) basis set is used to describe the different excited states. Meta-GGA M06-2X has been chosen for its capacity in reproducing π-stacked systems and for its good performance with charge-transfer states that may be artificially overstabilized by hybrid functionals for coupled chromophores. The excitation energy of the first twelve excited states of each QM unit were determined together with their electronic transition dipole moments. Test cases performed calculating twelve or twenty excitations per monomers showed no significant deviations. Excitation energies and transition dipole moments were used to build the Frenkel Hamiltonian and simulate the electronic circular dichroism spectra of the different quadruplex structures. QM/MM calculations were performed using a modified version 36,54 of Gaussian 09, 55 coupled with Tinker. 56 Spectral band shapes have been obtained convoluting each snapshot with a Gaussian function of full width at half-length of 0.3 eV. Note that excitation energies, dipole moments and Frenkel energies and rotatory strengths have been individually calculated for each snapshot and the resulting ECD vertical transitions have been convoluted to obtain the final spectrum. Frenkel ECD transitions have been calculated using a code developed at the University of Lorraine to post-process Gaussian 09 outputs. 42

Electronic Circular Dichroism Spectra Circular dichroism spectra were recorded on a Jasco J- 715 spectropolarimeter, using 1 cm path-length quartz cells. The telomeric sequences 5’-AGGGTTAGGGTTAGGGTTAGGG3’ (hTelo) and 5’-AAAGGGTTAGGGTTAGGGTTAGGGAA-3 (hTelo-2HY9) were purchased from IDT (Integrated DNA Technologies, Belgium) in HPLC purity grade. The lyophilized strand was firstly diluted in MilliQ water to obtain 100 µM stock solution. This was then diluted to the desired concentration and the experiments were carried out in buffer (pH 7.4) containing 50 mM Tris-HCl, 100 mM salt (KCl or NaCl) in the absence or pres-

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ence of PEG 200 as indicated. The oligonucleotides were folded into their G-quadruplex conformation by heating the solutions up to 90 ◦ C for 5 min and then by slowly cooling at room temperature. The exact concentration of the samples was checked measuring the absorbance at 260 nm and using the appropriate extinction coefficient value provided by the manufacturer (228500 for hTelo and 278200 M-1 cm-1 for hTelo-2HY9). The antiparallel structure, characterized by a negative peak near 260 nm and a positive peak near 295 nm, was obtained annealing the hTelo sequence in 100 mM NaCl buffered solutions; the hybrid (mixed parallel/antiparallel) structure, characterized by a negative peak near 240 nm and a positive peak near 290 nm with a shoulder at 270 nm, was obtained using hTelo-2HY9 in 100 mM KCl buffered solutions; finally, the all parallel structure, showing a negative peak near 240 nm and a positive peak near 265 nm, was obtained using hTelo in 100 mM KCl buffered solution with 40% (w/v) of the crowding agent PEG 200. Solvents and reagents were all commercial and used without further purification.

Results and Discussion 4

4

Full Core

3.5

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3.5

A)

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RMSD (Å)

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40 60 Time (ns)

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0

20

40 60 Time (ns)

80

100

0

0

20

40 60 Time (ns)

80

Figure 4: Time series of the root mean square deviation (RMSD) from the average structure for the three G4 conformations: A) Parallel, B) Hybrid and C) Antiparallel. Full RMSD in reported in red while the RMSD relative to the core guanines only is in blue.

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G4 Structural Parameters The G-rich strand of human telomere DNA 5’-AGGGTTAGGGTTAGGGTTAGGG-3’ adopts three different conformations, with typical CD signals, depending on the environment. 24 Significant structural parameters for the three conformations (parallel, hybrid, and antiparrallel) have been extracted from the MD trajectories. A global stability all along the trajectory can be evidenced for each system, in particular, as expected for G4, the guanine core region is quite rigid while a much greater mobility is observed for the flanking bases that may in certain cases form more labile π-stacking interaction with the G4 core. This aspect can be easily inferred by the root mean square deviations (RMSD) reported in Figure 4, in particular we may see that the core region has RMSD close to, or even lower than 1.00 ˚ A, on the other hand the global RMSD may reach value of 3.00 ˚ A. Antiparallel conformation (Figure 4 C) is a partial expception, indeed in this case the flanking bases are much less flexible resulting in a very low total RMSD. 600

600

Plane1 − plane2 Plane2 − plane3

600


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3.3

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C)

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3.4


3.7

3.8

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0

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3.3

3.4


3.7

3.8

Figure 5: Distribution of the distances between consecutive G4 planes as extracted from the MD trajectory. Note that planes are numbered sequentially from the top, see SI for details. A) Parallel, B) Hybrid and C) Antiparallel. In Figure 5 we report the distribution of the distance between the G4 core planes in the three different conformation. As expected, also due to the rigidity of the G4 core, the distributions have an almost ideal Gaussian shape and are relatively sharp and peaked. The average distance value is around 3.5 ˚ Afor parallel and hybrid conformer, while the antiparallel 13


3.9



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Another important feature related to the G4 structure is the occurrence of Hoogsteen hydrogen bonds, determining the formation and the stability of the core planes. The average distribution of the O−H distances per plane along the MD trajectory is reported in Figure 6. Although once again the stability of the different conformations is confirmed, a rather different behavior may now be evidenced. In particular a larger deviation between the edge and the central planes is now clearly visible. Indeed the distribution of the hydrogen bond distances in the central plane is constantly broader for the three conformations. Furthermore, the distribution for the central plane also peaks at 0.2 ˚ A larger distance than the edge units. This larger variability, that seems correlated to a sort of larger breathing of the central plane (see also the distances involving the central cation in SI) is due to a larger mobility of the backbone allowing larger vibrational motions, as well as to the influence of the single strand terminal bases. However, all the distances remain well representative of persistent hydrogen bonds and occur in between 2.0 and 2.3 ˚ A. Moreover, their behavior is extremely similar for the three conformers, the only small difference occurring for the central plane of the antiparallell structure that presents a maximum shifted of 0.1 ˚ A compared to the other two conformers. From the structural analysis we may safely conclude that MD is able to correctly reproduce stable and coherent structures and behavior of the different G4 conformers.

G4 ECD Spectra The comparison between the calculated and measured ECD spectra for the human telomere region in different configuration and in the region above 250 nm is reported in Figure 7. First of all we may notice that the three different conformers present a specific spectroscopic signature that allows the straightforward identification of the different structures. In particular the parallel conformation (Figure 7A) presents a very well resolved and rather narrow positive band peaking at about 260 nm. On the other hand, the other conformers show more complex spectral features. This is somehow expected for the hybrid structure (Figure 7 B) since in that case the variability is larger compared to the rather uniform parallel one. 15



The ECD band is now quite broad covering a large spectral domain going from 265 to 295 nm. Finally the antiparallel configuration (Figure 7C) shows a pretty distinctive signature with a narrower positive band at around 300 nm followed by a poorly resolved shoulder at around 270 nm and a negative less intense band at 260 nm. In Supplementary Information we also report the spectra calculated and measured for lower wavelengths. However, in the higher energy domain the interpretation becomes much more cumbersome due to the higher density of signals.

Parallel, 0.3 eV shift

Hybrid, 2HY9, 0.45 eV shift Theo. Exp.

CD

Theo. Exp.

CD

!"## 250

260

270

280

%"##

290 300 310 Wavelength (nm)

320

330

340

250

260

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320

330

340

Antiparallel, 143D, 0.75 eV shift Theo. Exp.

CD

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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$"## 250

260

270

280


320

330

340

Figure 7: Computed (red) and experimental (blue) spectra for the three G4 conformers. The theoretical spectra have been shifted in order to better reproduce the maxima wavelengths. A) Parallel B) Hybrid C) Antiparallel

Although the theoretical excitation energies need to be shifted by values comprised between 0.30 and 0.75 eV to match the correct experimental maxima, a procedure commonly 16


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employed in the calculation of ECD spectra of similar systems, 42,48 the global band shape is quite well reproduced for the three different cases. Since we are here dealing with different arrangements of the same molecular building blocks it appears most probable that the necessity to use different energy shifts should be ascribed to the simplifications made in the Frenkel Hamiltonian rather than to TDDFT deficiencies in catching the electronic nature of the individual excited states. Remarkably, the shape of the parallel systems almost perfectly matches the experimental one while slightly larger differences are observed for hybrid and antiparallel configurations. In particular, the double maximum of the hybrid systems is less well resolved in the simulated spectrum, while the intensity of the negative peak of the antiparallel G4 is overestimated. However, the reproduction of the experimental spectra allows to unambiguously assign the configurations on the basis of the sampling performed by MD. This is particularly important since it validates the possibility to use a combination of QM/MM and MD to retrieve structural informations on non-canonical DNA structures and to compare the obtained results with straightforward experimental measurements. On the other hand the combination of theoretical and computational results confirms that the inclusion of crowding agents induces a transition of the human telomere from a hybrid to a parallel structure. The larger deviations from the experiment observed for hybrid and antiparallel configurations is presumably due to the presence of K+ cations that, compared to Na+ , induce larger deviations in the G4 structure. It is also to be noted that the main characteristic of the ECD bands are due to the Guanines planes organization and not to the effect of the flanking bases, indeed their inclusion on the Frenkel procedure produces only a totally negligible change in the spectroscopical features. By inspecting the results reported in the Supplementary Information it also appears evident that the higher energy (lower wavelengths) part of the spectrum is less well reproduced. This can be related to the inherent difficulty of TDDFT to reproduce higher energy excited states but also to the fact that the final ECD spectra being constituted by the delicate equilibrium between positive and negative transitions the truncation of the excitation manifold based on the number of

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computed states can have a rather strong border effect on the limiting part of the spectrum. On the same spirit we also report in the Supplementary Information the ECD spectra obtained with different width of the convoluting Gaussians, in particular for the hybrid configuration, evidencing how the double band structure can be recovered by tuning the convolution parameters, i.e. adjusting the resolution of the simulation to the one of the experiment. Finally the comparison of the calculated absorption maxima of guanine alone (240 nm) compared to the G4’s one (274 nm), allows us to give an estimation of the average strength of the excitonic coupling in G4 structures that amounts at about 0.65 eV.

Conclusions The combination of spectroscopy and molecular modeling is now becoming an invaluable tool in chemical and molecular biology in order to unravel all the fine mechanisms of biological processes, including drug actions. Thanks to a combined experimental and theoretical approach we have proven that it is possible to link the macroscopic ECD spectra to the all atom structure and dynamics of important and complex aggregates such as G4 from human telomeres. In particular we have been able to identify and assign the corresponding spectroscopic signatures of all the different conformations presented by the poly-nucleotides. It is noteworthy that our relatively easy and fast protocol allows to disentangle the rich density of information embedded in the ECD spectra, and hence participating in straightforward and much more powerful structural resolution processes. In particular it will be important to extend the protocol to the study of the interaction between G4, in different conformations, and interacting drugs. In particular, the analysis of the native and induced circular dichroism mapped with the structures obtained from MD trajectories will allow to discriminate between different binding modes and configurations. This in turn will be helpful in the rational design of novel G4 based anticancer drugs. In the future we plan to expand the study determining ECD of DNA interacting with different compounds, both organic and

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inorganic, also comparing non canonical structures, like G4, and B-DNA.

Acknowledgement The COST in Chemistry Action CM1201 ’Biomimetic Radical Chemistry’ is gratefully acknowledged, also for funding AS’ visit to Nancy laboratory. AT received funding from Mahlke-Obermann Stiftung and the European Union’s Seventh Framework Programme for research, technological development and demonstration under grant agreement no 609431. AM also thanks the French ANR Femto2D for partial funding.

Supporting Information Available ECD spectra obtained with different QM partition schemes and their definition. Effect of the polarizable environment on the ECD spectra. Effect of the Gaussian convolution width on the ECD spectra. ECD spectra including the high energy transition. Distribution of the distance between guanine’s center of mass and central G4 ions.

This material is available

free of charge via the Internet at http://pubs.acs.org/.

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Circular Dichroism of DNA G-Quadruplexes: Combining Modeling and

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