Strengthened cooperativity of DNA-based cyclic hydrogen-bonded rosettes by subtle functionalization

Abstract

Cooperative effects cause extra stabilization of hydrogen-bonded supramolecular systems. In this work we have designed hydrogen-bonded rosettes derived from a guanine–cytosine Janus-type motif with the aim of finding a monomer that enhances the synergy of supramolecular systems. For this, relativistic dispersion-corrected density functional theory computations have been performed. Our proposal involves a monomer with three hydrogen-bonds pointing in the same direction, which translates into shorter bonds, stronger donor–acceptor interactions, and more attractive electrostatic interactions, thus giving rise to rosettes with strengthened cooperativity. This newly designed rosette has triple the cooperativity found for the naturally occurring guanine quadruplex.

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Introduction

Supramolecular chemistry is growing considerably due to its promising role and applications in materials science, specifically focusing on novel nanostructures and nanoelectronics. The selection and design of appropriate building blocks by considering their molecular recognition capabilities, self-assembly and self-organization becomes a determinant step. An interesting functionalization at the supramolecular level is the capability of cooperativity between hydrogen-bonded structures.^1–5

Taking into consideration the spatial disposition of cooperative molecules, mainly there are two different kinds of studied hydrogen-bonded systems with specific capabilities or properties related to their arrangement, thus being either linearly^6–10 or cyclically cooperative.^1,11–13 With respect to the latter, lately the so-called rosette structures or cyclic hexamers have gained interest.^14–16 These are hydrogen-bonded cyclic complexes of relatively small organic compounds, or even derived or inspired from DNA nucleobases. In particular, the guanine (G) nucleobase has become an important building block both experimentally and theoretically, like in guanine quartet structures (G₄) that are of high significance in quadruplex structures of DNA.^17–19 G₄ has been proven to experience a large synergistic effect due to charge separation through donor–acceptor interactions in the σ-electron system.^14–16

Of high importance is the Janus-type molecule, i.e., presenting two different hydrogen-bond patterns, synthesized and characterized by Lehn and coworkers,^20,21 designed to self-assemble uniquely into a supramolecular cyclic entity. This was derived from the guanine–cytosine (G–C) base pair, with the ability to hydrogen bond to G and C simultaneously (Scheme 1). In addition, with G₄ in mind and inspired by guanine and cytosine structures, some hydrogen-bonded cyclic rosettes have been recently synthesized with significant stability, as complexes with Janus-type rigid monomer molecules where two six-membered heterocycles are fused together and oriented at a 60° angle with low conformational freedom (Fig. 1).^14,15,22,23 Importantly, in this kind of hydrogen-bonded system, cooperativity becomes a determinant for the adequate thermodynamic stability of the supramolecular system.^14,15,22,23

Scheme 1 Schematic representation of the design of the Janus-type monomer AAD from the G–C base pair. Front atoms of guanine (G) are shown in red, front atoms from cytosine (C) are shown in blue, and the bond that drives fusion is shown in green.

Fig. 1 Structure of a G–C Janus-type monomer, referred to as AAD in the present study (left), and the schematic structure of the rosette derived from the AAD monomer (right). A (red) and D (blue) refer to hydrogen-bond acceptor and donor atoms, respectively.

In this work, the G–C Janus-type motif for rosettes will be further analyzed and used as a departing structure for the design of other monomeric structures with the aim of synthesizing hexamers with strengthened synergy. Thus, by means of a quantitative Kohn–Sham molecular orbital analysis combined with an energy decomposition analysis, we have unveiled how a slightly modified monomer derived from initial AAD (Fig. 1) can largely improve cooperativity in the corresponding rosette. In particular, the three hydrogen-bonds must point in the same direction, instead of two hydrogen-bond acceptors and one hydrogen-bond donor as in the previously synthesized AAD. Having all hydrogen bonds pointing in the same direction translates into shorter bonds, stronger donor–acceptor interactions, and more attractive electrostatic interactions, thus giving rise to rosettes with strengthened cooperativity.

Computational methods

All geometry optimizations and energies were computed using the Amsterdam Density Functional (ADF2021.101) program at the dispersion-corrected relativistic density functional theory (DFT) ZORA-BLYP-D3(BJ)/TZ2P level of theory.²⁴ Previous studies have proved the reliability of this level of theory for the evaluation of the hydrogen bonding interaction mechanism within weakly-bound complexes.^25–27

The bonding energies of the hexamers, as well as their subunits, i.e., dimers, trimers, tetramers and pentamers, were computed using eqn (1):

ΔEⁿ_bond = E_mn − n × E_m (1)

Here, n is the number of monomers, m is the monomer under analysis (Fig. 1), E_mn is the energy of the optimized complex, and E_m is the energy of the isolated optimized monomer. Then, the overall bond energy of every hexamer ΔE_bond is computed as follows:

ΔE_bond = E_rosette − 6 × E_monomer (2)

And this overall bond energy can be split as shown in eqn (3):

ΔE_bond = ΔE_strain + ΔE_int (3)

Here, the strain energy ΔE_strain is the energy needed to deform the isolated monomers into the geometry they adopt within the complex and the interaction energy ΔE_int is the actual energy change when the deformed monomers are combined to form the interacting hexamer. The latter can be further decomposed into physically meaningful terms within the framework of the Kohn–Sham molecular orbital theory using a quantitative energy decomposition analysis (EDA):^28,29

ΔE_int = ΔE_Pauli + ΔV_elstat + ΔE_oi + ΔE_disp (4)

Here, ΔE_Pauli is the Pauli repulsion that comprises the destabilizing interactions between occupied orbitals and is responsible for steric repulsions. ΔV_elstat corresponds to the classical electrostatic interactions between the unperturbed charge distributions of the deformed monomers and is usually attractive. ΔE_oi is the so-called orbital interaction that accounts for donor–acceptor interactions between occupied orbitals on one moiety and unoccupied orbitals of the other, including the HOMO–LUMO interaction, and the polarization that accounts for empty/occupied orbital mixing due to the presence of another monomer. The term ΔE_disp accounts for the dispersion correction. The orbital interaction energy ΔE_oi can be even further decomposed into contributions from each irreducible representation Γ of the interacting system. In our case, as all systems possess C_s symmetry, it has been split into σ and π contributions in eqn (5):

ΔE_oi = ΔE^σ_oi + ΔE^π_oi (5)

The electron charge distribution has been analyzed within the Voronoi Deformation Density (VDD) analysis.^4,30

Results and discussion

We have studied four systems that can form hydrogen-bonded rosettes derived from a G–C Janus-type monomer,^20,21 with two proton acceptor and one proton donor groups. The three new monomers maintain the overall structure of the original monomer (Fig. 1), while different subtle functional modifications have been introduced with the aim of strengthening the cooperativity of the formed rosettes. From the AAD system, with two hydrogen bond acceptors (A, red arrow in Fig. 2) and one hydrogen bond donor (D, blue arrow in Fig. 2), we have systematically analyzed AA, AAA and AAA^OH monomers (Cartesian coordinates of the systems under study are given in Tables S2–S7 of the ESI†). AA is introduced to understand the effect of one hydrogen-bond donor in AAD, that is, the effect of one hydrogen bond pointing in the opposite direction. Next, AAA involves changing the hydrogen bond donor (D) in AAD into a hydrogen bond acceptor (A), such that all hydrogen bonds point in the same direction. AAA^OH is proposed to improve the synergy further. The hexamers formed by these monomers have different hydrogen bond interactions (Fig. 2): the hydrogen bond donor can be an amine group or a secondary amine group (N–H) and the hydrogen bond acceptor can be an endocyclic N atom or the oxygen atom of a carbonyl or hydroxyl group.

Fig. 2 Structures of AAD, AA, AAA, and AAA^OH monomers. Red and blue arrows indicate the hydrogen bond acceptors and donors, respectively.

We first focus on the geometries and energies of the dimers formed from the four monomers. Optimized geometries of the dimers with C_s symmetry are shown in Fig. 3 with their hydrogen bond lengths and bonding energies. The reference AAD system presents the strongest stabilization energy (−29.2 kcal mol⁻¹) and also the shortest O⋯N distances of the two outer hydrogen bonds (2.81 and 2.86 Å). The N⋯N distance amounts to 2.91 Å in the case of [AAD]₂ and is shorter only for the [AA]₂ dimer (2.86 Å). The bond energy is less stabilizing when only hydrogen-bond donor groups are present on one monomer and hydrogen-bond acceptors on the other monomer to form the interaction. ΔE increases only slightly from [AA]₂ to [AAA]₂ and to [AAA^OH]₂ (from −21.0 to −22.2 and to −24.0 kcal mol⁻¹, respectively). As AAA^OH has the possibility of tautomerization, we have also investigated by substituting –OCH₃ instead of –OH (see Fig. S1 in the ESI†), which showed almost identical hydrogen bond lengths and bonding energies.

Fig. 3 Optimized structures of hydrogen-bonded dimers with C_s symmetry computed at the ZORA-BLYP-D3(BJ)/TZ2P level. Bond lengths (in Å) and bonding energies (between brackets, in kcal mol⁻¹, computed with monomers in C₁ symmetry) are included. For comparison, bonding Gibbs free energies are −13.2, −6.1, −9.8 and −12–7 kcal mol⁻¹ for [AAD]₂, [AA]₂, [AAA]₂ and [AAA^OH]₂, respectively, in C₁ symmetry.

The geometries and hydrogen bond energies of the rosettes [AAD]₆, [AA]₆, [AAA]₆ and [AAA^OH]₆ are shown in Fig. 4. We have focused our analyses on the C_s symmetry structures, as experimentally these systems are either on the surface or stacked on top of each other.^31–33 Nonetheless the non-planar dimers and rosettes have also been computed (Tables S2–S7 in the ESI†), which are only up to −1.6 and −2.7 kcal mol⁻¹ more stable than their C_s counterparts, mainly due to the pyramidalization of the amino groups. The strongest bound rosettes are [AAA]₆ and [AAA^OH]₆ with three hydrogen bonds pointing in the same direction (−209.8 kcal mol⁻¹ and −227.9 kcal mol⁻¹, respectively). The bonding energy for [AAD]₆ only amounts to −191.4 kcal mol⁻¹ despite that in the case of the dimer [AAD]₂ is the strongest.

Fig. 4 Optimized structures of hydrogen-bonded rosettes with C_s symmetry computed at the ZORA-BLYP-D3(BJ)/TZ2P level. Bond lengths (in Å) and bonding energies (between brackets, in kcal mol⁻¹, computed with monomers in C₁ symmetry) are included.

The hexamers with all hydrogen bonds pointing in the same direction have been shown to experience cooperativity.^1,12,16 This cooperativity or synergy, ΔE_syn, can be computed by comparing the interaction energy ΔE_int of the rosette with the summation ΔE_sum of the individual pairwise interactions for all possible pairs of units in the rosettes (eqn (6)). In particular, ΔE_sum includes the interaction energy between the two hydrogen-bonded molecules (ΔE_pair, green in Fig. 5), the interaction energy between the two mutually diagonally oriented molecules (ΔE_diag, blue in Fig. 5), and the interaction energy between the two frontal molecules (ΔE_front, red in Fig. 5). In the case of the rosette, we have 6 pairwise-, 6 diagonal-, and 3 frontal-interaction energies (eqn (7)).

ΔE_syn = ΔE_int − ΔE_sum (6)

ΔE_sum = 6·ΔE_pair + 6·ΔE_diag + 3·ΔE_front (7)

Fig. 5 Definition of ΔE_pair, ΔE_diag, and ΔE_front interaction energy terms in a rosette.

Then, if |ΔE_int| > |ΔE_sum| in eqn (6) we have positive cooperativity, which means that the average energy of the hydrogen bonds in the rosette is reinforced with respect to their isolated counterparts.^1,12,16

Table 1 includes the bond energy, the interaction energy, the sum of pairwise interactions and the synergy for the four rosettes. ΔE_syn clearly increases from [ADD]₆ to [AA]₆ to [AAA]₆ and to [AAA^OH]₆ from −12.7 to −32.1 to −61.2 and to −66.2 kcal mol⁻¹. Thus, our goal of designing a macromolecular hexamer with strengthened cooperativity is achieved. It should be noted that the synergy of either AAA or AAA^OH hexamers is almost triple the value previously obtained for G₄, which amounted to −20.9 kcal mol⁻¹.¹ This strengthening of the hydrogen bonds due to cooperativity effects is also verified from the comparison of the dimerization energies between the hexamers and the dimers. For instance, in the case of ADD, ΔE_bond increases from −29.2 to −31.9 kcal mol⁻¹ from the optimized dimer to the equivalent average dimer within the rosette (computed as ΔE_bond/6, Table 1). More importantly, such an increase due to cooperativity is much more pronounced for AAA (ΔE_bond increases from −22.2 to −35.0 kcal mol⁻¹ from the dimer to the hexamer) than for AA (from −21.0 to −26.4 kcal mol⁻¹) because of the third hydrogen bond in the former. Thus, from these data, it is shown how stronger hydrogen bonds also give rise to more cooperativity. Furthermore, as stated above, the strongest reinforcement by cooperativity is found for AAA^OH with ΔE_bond increasing from −24.0 to −38.0 kcal mol⁻¹, which means that the pair of hydrogen bonds within the rosette becomes 58% stronger than the isolated interactions. Such synergy arising from the formation of the hexamer causes the hydrogen-bond lengths to be clearly shortened (Fig. 4), a trend that is more pronounced when all hydrogen bonds point in the same direction. For instance, in the case of AAA^OH, hydrogen-bond lengths in the dimer, 3.09 (O⋯N), 3.07 (O⋯N), and 2.94 Å (O⋯N), are shortened to 2.96, 2.92, and 2.74 Å, respectively.

Table 1 Bonding, interaction, and synergy energies (in kcal mol⁻¹) of hexamers, computed at the ZORA-BLYP-D3(BJ)/TZ2P level

Hexamer	ΔEbond	ΔEbond/6	ΔEint	ΔEsum	ΔEsyn
AAD	−191.4	−31.9	−218.5	−205.8	−12.7
AA	−158.2	−26.4	−179.9	−147.8	−32.1
AAA	−209.8	−35.0	−239.9	−178.7	−61.2
AAA^OH	−227.9	−38.0	−260.5	−194.3	−66.2

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Now that we have demonstrated that the hydrogen bonds in these series of rosettes can be strengthened by synergy, we will analyze how this synergy develops when we go from initial AAD to AA, with only two hydrogen-bonds pointing in the same direction, and then to the strongest cooperative AAA and AAA^OH systems, with three hydrogen-bonds pointing in the same direction. For this, we will analyze the construction of the hydrogen-bonded rosette by adding one monomer at a time, that is, a stepwise procedure in which an incoming monomer is added to the former one until the hexamer is formed (Fig. 6).^12,16 For each step the interaction energy is decomposed by means of an energy decomposition analysis (see eqn (4)), and the synergy of the EDA components (either interaction, electrostatic, Pauli, orbital or dispersion) within the hexamers is also computed.^28,29,34 These are computed as follows:

Fig. 6 Representation of molecular fragments in the formation of the rosette structures by a stepwise addition of monomers in a one-way direction. Grey hexagons represent the incoming monomer.

It is the difference between the sum over the gradual formation of the hexamer and the sum of the pairwise interactions. The acquisition of the EDA components for the formation of the hexamer by the addition of a monomer to the previously formed complex is shown in Fig. 7. The sum of pairwise interactions, ΔV_sum,elstat, ΔE_sum,Pauli, ΔE_sum,oi, and ΔE_sum,disp, is computed using eqn (7), for each component, that is, for the electrostatic, Pauli, orbital interaction and dispersion component, respectively (see all data in Table S1 in the ESI†).

Fig. 7 Schematic representation of the energy decomposition analysis (in kcal mol⁻¹) for the formation of AAD, AA, AAA, and AAA^OH rosettes in a stepwise one-way direction, computed at the ZORA-BLYP-D3(BJ)/TZ2P level. See also Fig. S2 and S3 in the ESI for further data.†

First, the removal of one hydrogen-bond from AAD to AA causes weakening of the interaction ΔE_int, as observed above for the dimers, but there is an increase in cooperativity in the AA rosette compared to the AAD rosette (see the larger slope of ΔE_int for AA in Fig. 7). Although for AAD the interaction energy amounts to −33.6 kcal mol⁻¹ for M₁ + M₁ (that is, the formation of M₂) and −35.7 kcal mol⁻¹ for M₂ + M (that is, the formation of M₃), the increase of the interaction energy from M₂ to M₃ is twice as large as that for AA (from −24.2 kcal mol⁻¹ for M₂ and −28.2 kcal mol⁻¹ for M₃). The stabilization of 2.1 kcal mol⁻¹ for AAD from M₂ to M₃ can be attributed mainly to 1.1 kcal mol⁻¹ of electrostatic and 0.6 kcal mol⁻¹ of orbital interactions, whereas the stabilization of 4.0 kcal mol⁻¹ for AA from M₂ to M₃ can be attributed to 2.0 kcal mol⁻¹ of ΔV_elstat and 1.5 kcal mol⁻¹ of ΔE_oi.

The addition of an extra hydrogen bond to the AA rosette in the same direction as that of the other two hydrogen bonds forming the AAA and AAA^OH rosettes shows an even steeper increase of the interaction energy (see Fig. 7). In particular, for AAA, ΔE_int increases from −26.7 to −35.9 kcal mol⁻¹ from M₂ to M₃, i.e., a 9.2 kcal mol⁻¹ difference! This increase can be mainly attributed to the electrostatic interaction (5.3 kcal mol⁻¹) and the orbital interaction (2.8 kcal mol⁻¹).

Further insight into the cooperativity in the hydrogen bonds of the rosettes can be gained if we analyze the synergy in different energy terms of the EDA (Table 2). Already from ADD to AA, synergy is almost tripled from −12.7 to −32.1 kcal mol⁻¹ due to more attractive σ and π orbital interactions as well as electrostatic interactions, whereas Pauli repulsion remains constant. But more noticeably, from AA to either AAA or AAA^OH the synergy is almost doubled (from −32.1 to −61.2 or −66.2 kcal mol⁻¹). In all cases, the largest contribution to the synergy comes from the electrostatic and orbital interactions. And, with respect to the latter, the σ electronic system contributes more than the π electronic system. For instance, for AAA ΔE^σ_syn,oi amounts to −17.1 and ΔE^π_syn,oi to −12.0 kcal mol⁻¹ (Table 2).

Table 2 Energy decomposition analysis (in kcal mol⁻¹) of the synergy term (ΔE_syn) of the rosettes, computed at the ZORA-BLYP-D3(BJ)/TZ2P level^a

Synergy	[AAD]6	[AA]6	[AAA]6	[AAA^OH]6
a See eqn (8)–(11) for the definition of the terms.
ΔEsyn	−12.7	−32.1	−61.2	−66.2
ΔVsyn,elstat	−5.2	−13.7	−27.0	−28.6
ΔEsyn,Pauli	−1.0	−1.8	−4.1	−4.7
ΔEsyn,oi	−6.5	−16.6	−30.1	−32.9
ΔE^σsyn,oi	−3.7	−9.4	−17.1	−20.6
ΔE^πsyn,oi	−2.8	−7.2	−12.0	−12.3
ΔEsyn,disp	0.0	0.0	0.0	0.0

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More insight can be obtained by analyzing the charge distribution by means of the computed Voronoi deformation density (VDD) charges. In Fig. 8, we see that in all cases the charge separation gradually increases throughout the stepwise addition of monomers. Thus, the monomers with hydrogen-bond acceptor atoms become more negatively charged in each step (blue hexagons in Fig. 8), whereas the opposite happens for those with hydrogen-bond donor atoms (red hexagons in Fig. 8). In ADD the monomer with hydrogen acceptor atoms experiences only a small gain of −11 milli-electrons from M₂ to M₃ (that is, from −121 to −132 me⁻). However, the largest increase was obtained for AAA^OH, from −312 to −325 me⁻ from M₂ to M₃, due to having all hydrogen bonds pointing in the same direction. This is in line with our previous work on guanine quadruplexes,¹ which showed that the cooperativity originates from the charge separation in the σ electronic systems due to the covalent component in the hydrogen bonds. The charge transfer within the hydrogen bonds then leads to charge separation within the dimer, which enhances the electrostatic interactions and the orbital interactions between the dimer and the third monomer. However, this charge separation converges, i.e., it does not increase much further from M₃ to M₄ to M_5. For instance, for AAA^OH we go from −325 to −352 to −359 me⁻. This convergency of the charge separation was less in the case of G₄.¹

Fig. 8 VDD charges (in milli-electrons) in the formation of cyclic structures. Values in black are the sum of the atomic charges of the monomer (see also Fig. S4 in the ESI for the changes in the atomic charges of the front atoms†).

The charge separation within the formed complexes also enhances the cooperativity within the orbital interactions. The reason is found in the destabilization of lone pair HOMO orbitals of the hydrogen-bond accepting monomer as the monomer becomes slightly negatively charged when it forms a dimer. At the same time, the antibonding LUMOs of the hydrogen-bond donating monomer are stabilized because the monomer becomes slightly positively charged when it forms a dimer. This gives rise to stronger donor–acceptor interactions as the HOMO–LUMO gap of the interacting moieties decreases upon the gradual formation of the rosette. The effect is even more pronounced for AAA with three hydrogen bonds than for AA with two hydrogen bonds. The HOMO–LUMO gap in AA amounts to 3.9 eV and in [AA]₃ to 2.3 eV, whereas in AAA it amounts to 3.5 eV and in [AAA]₃ to 1.1 eV (Fig. 9). The gap decreases for AAA^OH even to 0.6 eV in the trimer (Fig. S5–S7 in the ESI†).

Fig. 9 N–H unoccupied σ_LUMO orbitals and oxygen and nitrogen lone-pair σ_HOMO orbitals of the front atoms of AA (left) and AAA (right) and their corresponding energies (in eV) for stepwise M₁ and M₃ states, computed at the ZORA-BLYP-D3(BJ)/TZ2P level. The HOMO–LUMO gap (Δ_HL, in eV) is also included.

Thus, the comparison of AA with AAD and AAA shows that for making dimers it is better to have the third hydrogen bond pointing in the opposite direction (see Fig. 3) as that will lead to the strongest dimer, i.e., [AAD]₂ has a bond energy of −29.2 kcal mol⁻¹ compared to [AAA]₂ with −22.2 kcal mol⁻¹. However, if the goal is to obtain stronger rosettes, the additional hydrogen bond should point in the same direction as that of the other two hydrogen bonds. This will lead to stronger donor–acceptor interactions due to more charge transfer within the σ electron system, as observed above.

Conclusions

In this work we have designed hydrogen-bonded supramolecular rosettes with strengthened cooperativity. Our dispersion-corrected DFT computations reveal that stronger cooperativity in rosettes can be achieved by having all hydrogen-bond donors on one side and all hydrogen-bond acceptors on the other side of the hydrogen bonding interaction. This translates into shorter hydrogen-bond lengths between the monomers, with stronger donor–acceptor interactions, and thus more charge transfer within the σ electron system. The overall result is an enhancement of cooperativity due to more pronounced electrostatic attraction and stronger donor–acceptor orbital interactions as proven by our Kohn–Sham molecular orbital analysis together with the quantitative energy decomposition analysis. Noticeably, the two rosettes with all three hydrogen-bonds pointing in the same direction, i.e., AAA and AAA^OH, achieve a cooperative interaction that is triple that previously obtained for the guanine quadruplex (G₄). Overall, the present study opens the door for the design of hydrogen-bonded supramolecular systems with extra gain of cooperativity by modeling the frontal functional groups involved in these interactions.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

We thank the Netherlands Organization for Scientific Research (NWO), the Spanish MINECO (PID-2019-106830GB-I00, PID2022-138861NB-I00 and CEX2021-001202-M) and the Catalan Government (2021SGR442) for financial support.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d3ob01391j

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