Using the SIRAH Force-Field to Model Interactions Between Short DNA Duplexes

Abstract

Background/Objectives: In recent years, short DNA duplexes have been studied as promising self-assembling systems and versatile building blocks for DNA-based nanotechnologies. Numerical simulations of colloidal systems incorporating such components require, as an input ingredient, reliable yet simplified force-fields capable of capturing the essential features of duplex-duplex interactions. Methods: We employed the coarse-grained SIRAH force field under an implicit solvent approximation to investigate the interactions between a pair of short, rigid double-stranded DNA (dsDNA) duplexes. We investigated the effect of duplex size by employing duplexes of 8 and 20 base pairs. Results: Using this realistic coarse-grained model, we obtained detailed insights into how the interaction force depends on the relative positions and orientations of the duplexes, as well as on salt concentration. Conclusions: Our findings provide a foundational step toward the systematic development of simplified, yet qualitatively accurate model potentials for DNA-based colloidal systems. Beyond nanotechnology, the short-range interaction features captured here are also relevant to biological contexts, including chromatin compaction, homologous recombination, and DNA repair.

1. Introduction

Besides its fundamental role as the molecule of life, DNA is a fascinating material in colloidal science [1] due to its programmable nature, which allows the precise design and reliable reproduction of specific sequences of nucleotides. Since the exact alternation of bases modifies its interaction properties, DNA is currently being investigated as a building block to control the self-assembly of supramolecular structures in a rational and predictable manner [2,3,4,5]. The phase diagrams of systems made of short fragments of double-strand DNA (duplexes) have been investigated with experimental and theoretical [6,7,8,9] methods, providing evidence that even short duplexes may display rich and nontrivial phase diagrams. Liquid crystal phases (LC) have been observed for duplexes as short as six base pairs (6 bp) [7]. Moreover, a comprehensive understanding of the interplay between chirality and the formation of chiral mesophases of left- and right-handed oligonucleotides remains a challenge [6].

Understanding the physical interactions between such duplexes also yields crucial insight into diverse physiological processes, particularly those involving higher-order DNA organization and genome maintenance [10,11,12].

In biological contexts, transient duplex–duplex contacts—mediated by base stacking, electrostatic interactions, and sequence-dependent flexibility—can influence chromatin folding [10], homologous recombination [11], and DNA repair mechanisms [12]. For instance, non-contiguous DNA segments within chromatin often engage in stacking-like interactions that contribute to fiber compaction, nucleosome positioning, and phase separation phenomena linked to the organization of chromatin domains [10]. During homologous recombination, strand invasion and D-loop formation require transient pairing between homologous sequences, likely stabilized by stacking forces and ionic conditions [11]. Similarly, the accurate recognition and alignment of homologous regions during double-strand break repair rely on short-range DNA–DNA interactions that ensure fidelity [12].

These interactions—though fleeting and challenging to capture experimentally—are critical for maintaining genome stability and orchestrating the cellular response to DNA damage. Beyond recombination, DNA fragment interactions are involved in a wide array of repair processes, including non-homologous end joining (NHEJ), base excision repair (BER), and nucleotide excision repair (NER), where the recognition, alignment, or bridging of DNA ends or damaged regions are essential.

A theoretical understanding of such complex behavior through numerical methods requires realistic models of the interactions between dsDNA fragments. Fully atomistic simulations with an explicit aqueous solvent, repeated across many concentrations and thermodynamic states, remain computationally prohibitive. Nevertheless, some all-atom studies have examined interactions for short (4 bp) dsDNA [13] and dsRNA [14] oligomers.

Coarse-grained (CG) interaction models with an explicit solvent partially reduce computational costs, but the extensive sampling of the thermodynamic phase space is limited by the very slow dynamics of counterions. Implicit solvent versions of CG models provide an efficient alternative, allowing the development of force-fields that go beyond the simplest models containing only a cylindric excluded-volume effect and isotropic short-range end-to-end attractions.

Although CG models for biomolecular interactions have been developed over many years, specific CG models for DNA have emerged only in recent decades [15,16,17,18,19,20,21] (see a recent review for a comprehensive list [22]). Most of the existing tests and applications focus on intramolecular interactions, necessary to study phenomena like pairing between complementary single strands or intramolecular defects. Much less is known about the capabilities of these force-fields to describe inter-duplex interactions, which are critical for modeling recently proposed DNA-designed colloidal systems. On the one hand, LC phases strongly depend on the effective interactions between duplexes; conversely, recent experiments [23,24] highlight the need for more accurate force-fields beyond simple models like hard rods decorated with attractive sites [15].

A first successful and accurate CG model for DNA was proposed by Pantano and coworkers [19], named the SIRAH (South-American Initiative for a Rapid and Accurate Hamiltonian) force-field. More recently, other CG models have been introduced [16,17,18], differing in levels of coarse-graining, accuracy in reproducing physical properties, or practical considerations regarding integration with molecular dynamics packages or other force-fields.

In the present paper, we study the energy landscape and resulting forces between two short DNA duplexes described by the SIRAH force-field. We calculated the energy and force of 8 bp and 20 bp duplexes across a representative set of configurations in the implicit solvent approach, where the effect of the ionic solution is fully absorbed into modifications of the bare DNA–DNA interactions. For a small subset of configurations, we also performed limited explicit solvent calculations, in which water and salt ions were treated at the same coarse-grained level as DNA. These calculations have the limited scope of providing a first assessment of the spatial modulation of solvent density around the duplexes. In the present work, we did not pursue the more ambitious goal of comparing inter-duplex forces obtained with implicit and explicit solvents. We will discuss the reasons for this choice when presenting the results for the solvent density around the duplexes.

The present results lay the groundwork for developing new rigid duplex–duplex interaction models, suitable for extensive numerical simulations of phase diagrams.

The paper is organized as follows. Section 2 briefly describes the force-field model and its application in our calculations. Section 3 presents a detailed analysis of the energy landscape and forces. In the final section, we provide a concise summary and a discussion of the results.

2. Methods

The numerical simulation of DNA is a particularly challenging task. Spatial scales range from inter-atomic distances within constituent molecules to macroscopic lengths (of the order of one meter) for the unswollen double helix of human DNA [19]. Similarly, timescales of all the possible dynamical processes span more than twenty orders of magnitude. Thus, rather than a single modeling strategy, it is useful to develop several complementary methods, each adapted to a particular resolution level, ranging from quantum chemistry accuracy (molecular level) to elastic mesoscopic models, passing through Quantum Mechanics/Molecular Mechanics (QM/MM) and atomistic and coarse-grained levels of description.

Particle-based coarse-grained (CG) models replace groups of atoms with effective beads, designed to maintain the geometry of the original groups (see ref. [25] for a comprehensive review). Models differ in the number of atoms represented by a single bead. When combined with coarse-grained solvent representations, particle-based CG models strongly reduce the number of independent degrees of freedom while retaining good accuracy in describing geometry and energy. DNA is particularly suitable for CG modeling, and various research groups have developed CG models for numerical simulations [26]. Among these, the SIRAH force-field [19] represents a flexible and accurate model, applicable with explicit or implicit solvent descriptions and suitable as a benchmark for more approximate Hamiltonians.

The SIRAH force-field for DNA uses six beads per nucleic base. Each bead is positioned at the location of a corresponding atom in the atomistic reference structure, allowing the straightforward reconstruction of atomic positions if needed. Partial electrostatic charges are assigned to the beads so that each nucleotide carries a unit negative charge, ensuring Watson–Crick electrostatic recognition. Moreover, the resulting electric dipole distribution is compatible with all-atom models [19]. The model preserves the identity of minor and major grooves, as well as the 5′ to 3′ directionality of DNA helices. In addition to the electrostatic term, bead–bead interactions include [19] (i) harmonic bond stretching, (ii) harmonic angle bending, (iii) dihedral torsional barriers, and (iv) effective 12−6 Lennard-Jones interactions, which primarily account for bead–bead excluded volume effects through their repulsive part. Parameters for bead–bead interactions are listed in the original paper [19].

Within the SIRAH model, the solvent can be treated at two levels. The implicit solvent model [19] captures hydration and ionic effects via the Generalized Born model [27], while the explicit solvent model restores solvent and ionic degrees of freedom through a coarse-grained description of water molecules (WAT FOUR, WT4) [28] and hydrated ions. In WT4, groups of 11 water molecules are represented by four tetrahedrally interconnected beads, each carrying an explicit partial charge, thereby generating its own dielectric permittivity without imposing a uniform dielectric medium. The model reproduces several key properties of liquid water and simple electrolyte solutions [28]. Similarly, cations (Na⁺, K⁺, Ca⁺⁺) plus their hydration spheres are modeled as coarse-grained molecules. A complete parameter list is provided in ref. [28]. The CG model for the solvent was extensively tested by its authors. Despite the simplifications inherent to representing 11 water molecules as a single bead, the model provides a satisfactory description of water properties, comparable with the results from well-established atomic models (TIP4P, SPC) [28].

Solvated ions are represented by CG particles corresponding to a central ion surrounded by six water molecules, roughly representing the first solvation shell. Their masses are the sum of the ion plus six water molecules, with partial charges set to unitary values. Van der Waals radii are adapted to match the first minima of the radial distribution function (RDF, g(r)) of hydrated ions from neutron diffraction experiments. Well depths are the same as those for WT4 beads, ensuring proper interaction between CG ions and WT4 molecules, implicitly accounting for the first solvation shell.

All calculations were performed for isolated pairs of duplexes, considered in two lengths: 20 bp and 8 bp. Figure 1 illustrates the SIRAH coarse-grained representation of the two duplex fragments.

The 20-mer duplex is based on the sequence 5′-(C₁A₂T₃G₄C₅A₆T₇G₈C₉A₁₀T₁₁G₁₂C₁₃A₁₄-T₁₅G₁₆C₁₇A₁₈T₁₉G₂₀)-3′, indicated as SAA₂ by Machado et al. [20]. The shorter 8 bp duplex corresponds to the first 8 nucleotides of the 20-mer, chosen to have identical terminal bases at both ends of the double strand. In all cases, the model building procedure starts from the Cartesian coordinates of all-atom structures, constructed in canonical B-form using the NAB utility of AMBER [29,30] and then mapped to the SIRAH coarse-grained representation by removing and renaming the corresponding atoms. For completeness and transparency, these coarse-grained coordinates of the initial duplexes (20-mer and 8-mer) are included in the Supplementary Materials and serve as the starting point for all analyses.

All bonding parameters used in the model are contained in Tables 1 and 2 of the original SIRAH force-field description [19].

As noted in the introduction, the main aim of this study is to characterize the implicit solvent SIRAH energy landscape of duplex–duplex interactions for two isolated duplexes at a fixed internal configuration. This constraint is artificial, as a real duplex interaction involves atomic relaxations, but our focus is on the deviations from a rigid cylindric model due to the 3D structure of the helix. For this purpose, a rigid double helix model is sufficient.

To assess solvent perturbation induced by the duplexes, we also performed a limited set of explicit solvent calculations, using CG water molecules and hydrated CG ions to simulate a 1 M aqueous NaCl solution. The simulation cell was a truncated octahedron to optimize the number of solvent particles [31], with a total volume of 426.1 nm³. For the two 20-mer duplexes, the simulation box contained 6036 coarse-grained particles, including the duplexes, 1431 CG water molecules groups, 76 hydrated sodium ions, and 48 hydrated chloride ions. CG water molecules were described by the so-called WAT FOUR model [28].

The primary methodological framework is based on implicit solvent simulations, enabling an efficient exploration of duplex–duplex configurations and salt concentrations. To complement these results, a small number of explicit solvent simulations were performed, primarily to examine how solvent density is modulated around the duplexes. Molecular dynamics calculations were performed using the GROMACS package [32].

For implicit solvent calculations, an extensive sampling of configurations was performed, varying distance, mutual orientation, and salt concentration. Hydration and ionic strength effects were implicitly incorporated through electrostatic interactions using the Generalized Born (GB) model [27] as implemented in AMBER [29,30]. Born effective radii were fixed at 0.15 nm for all superatoms, and the maximum atom pair distance considered for calculating effective Born radii was set to 1 nm. Non-bonded interactions were calculated up to a cutoff of 8.6 nm within the GB approximation, with salt concentrations ranging from 0.15 M to 2.0 M.

The chosen salt concentrations span from physiological conditions (0.15 M) to high-salt regimes that are experimentally underexplored, allowing for a direct comparison with previous studies, such as those by Podgornik et al. [33] (typically up to ~0.6 M), while also reaching regions where theoretical models (e.g., Kornyshev & Leikin [34,35]) and CG simulations [36,37,38] predict nontrivial interaction regimes under strong screening. Recently, Zhang et al. [39] reported the destabilization of DNA and RNA duplexes at high monovalent salt concentrations, further motivating exploration beyond 1 M.

Tests on cutoff dependence (see Supplementary Data, Tables S1–S4) show that a cutoff of 4.8 nm is close to numerical convergence, with full convergence achieved at 6.4 nm. This cutoff ensures smooth force behavior across all configurations. Convergence was verified for dsDNA_20 bp, and shorter duplexes such as dsDNA_8 bp converged even faster due to the reduced charge distribution. At higher salt concentrations, electrostatic screening further reduces long-range contributions, so convergence at 6.4 nm is expected to hold a fortiori.

3. Results

3.1. Duplex–Duplex Interaction

Calculations with the implicit solvent model are straightforward and computationally efficient. Among the many configurations studied, we discuss a representative subset to illustrate the main features of the inter-duplex interactions.

In Figure 2, the variation in the inter-duplex total force is shown for two 20 bp (left panel) and two 8 bp (right panel) dsDNA helices at salt concentrations ranging from 0.15 M to 2.0 M.

As expected, increasing the salt concentration enhances the screening of Coulomb interactions, significantly reducing both the strength and the range of repulsion. Repulsions are generally short-range, and even at 0.15 M they become negligible beyond ~5.5 nm. More importantly, at 2 M, a small attractive component emerges for both duplexes, as shown in the insets of Figure 2.

In the presence of multivalent ions in solution, the possibility of such attractive interactions is well established in experiments and computer simulations [40,41,42]. Less is known about the case of monovalent ions. Experiments on DNA interactions at high NaCl concentrations could provide a direct test of this prediction.

At NaCl concentrations up to 0.6 M, where experimental data are available, an analysis of the force in the logarithmic scale (see Figure 3) allows for a comparison with the experimental data of Podgornik et al. [33] for similar distance ranges. Their main conclusion was that interactions below 3 nm are influenced by solvent layering, while, at distances up to 3.5 nm, the repulsion approaches an exponential decay.

In the implicit solvent model, there is no explicit solvent, yet we observe a reasonably accurate exponential decay starting at around 2.5 nm. The implicit solvent parameters capture the effect of salt concentration, producing a concentration-dependent repulsion with a screening length comparable to values obtained by Podgornik et al. [33]. Specifically, for salt concentrations between 0.15 M and 0.5 M, we find decay lengths ranging from 1.63 nm to 1.23 nm, while Podgornik et al. report 1.32 nm at 0.2 M to 0.76 nm at 0.6 M.

We evaluated the anisotropy of side-by-side interactions between two parallel duplexes. Consistent with “primitive model” calculations [43] and the theoretical predictions of Kornyshev and Leikin [34,35], we observe a rapidly decaying dependence of the interaction energy on the difference of the azimuthal angle (Δϕ). According to Kornyshev and Leikin [34,35], the dominant angular dependence can be expressed as follows:

E = E₀(1+ α cos(𝝙𝞍)).

(1)

Already at an inter-duplex distance of 2.4 nm, this form accurately captures the angular modulation, with α ≈ 0.04, decreasing to 0.01 at 4.0 nm, and becoming negligible at 7.0 nm.

Figure 4 illustrates the strong angular dependence of end-to-end attraction, which is significantly reduced at certain azimuthal angles. Here, and in the following two figures, the continuous lines were employed exclusively to connect the underlying data for visual clarity, with data point markers omitted. No smoothing, interpolation, or curve fitting was applied. These results indicate that simplified cylindrical models can only approximate real 3D interactions at a coarse level, and an explicit consideration of geometry is necessary for accurate predictions.

Figure 5 shows the variation in the head–tail force between two aligned 20 pb duplexes as a function of salt concentration. Increasing the salt from 0.15 M to 2 M results in a consistent enhancement of the attractive force by approximately 40%.

The head–tail interaction strongly influences the phase behavior of short duplex systems [6]. Compared to side-by-side interactions, end-to-end DNA association has been less extensively studied. Depending on the presence or absence of head–tail attraction, liquid crystal phases or reversible duplex chaining may be favored [7]. Furthermore, numerical simulations [36] predict a weak end-to-end attraction in NaCl solutions at concentrations above 1 M, with only a minor dependence on ionic strength. Interestingly, our implicit solvent approach reproduces this behavior.

Figure 6 demonstrates the dependence of the interaction energy on the axial displacement (∆x) between two 20 bp duplexes in a head–tail alignment. ∆x = 0 corresponds to a perfect alignment. The curves show that even slight deviations from axial alignment lead to a substantial reduction in the attractive force.

These interaction features can be interpreted in terms of known biochemical forces. In particular, the strong axial dependence of the head-to-tail association may reflect contributions from base stacking interactions between exposed termini.

Furthermore, the angular dependence observed in both lateral and axial geometries is consistent with the anisotropic electrostatic potential generated by the helical charge distribution, especially the alignment (or misalignment) of major and minor grooves. This azimuthal sensitivity is in good agreement with theoretical models that describe electrostatic groove recognition and directional specificity in DNA–DNA interactions [34,35].

3.2. Effects of Solvent Density

To explicitly evaluate how the solvent density is perturbed by the presence of the duplexes, we performed a limited set of explicit solvent simulations. System averages were taken over times exceeding 300 ns, reaching up to 1 μs in a few cases. Although solvent equilibration was satisfactory, counterion equilibration proved challenging. In the experiments, sodium cations tend to localize in the major grooves, and the coarse-grained hydrated sodium ions in the SIRAH model faithfully reproduce this behavior. However, their strong interaction results in long residence times, exceeding 300 ns. Consequently, even 1 µs runs provide a limited sampling of the ionic configurations. While averaging over independent initial counterion configurations might alleviate the problem, preliminary evidence suggests that attaining a sufficient accuracy in explicit solvent calculations would demand an impractically large number of independent runs.

Despite these sampling limitations, the qualitative trends are consistent with the implicit solvent results. The averages obtained for solvent density profiles were robust and showed a clear modulation around the duplexes, supporting the qualitative expectations from the implicit model.

We present in Figure 7 the average density of CG water molecules in a slab of 2 nm perpendicular to the axes of two parallel 8 bp duplexes. The density values are represented using a gray-scale code (darker gray corresponds to higher density) for three inter-duplex distances. These results qualitatively illustrate the layering of water around the duplexes.

A clear modulation of the CG water profile is visible, extending around each duplex on a radial length scale of about 1 nm. The absence of density fluctuations far from the two duplexes is a measure of the good equilibration of the pure solvent. Although the previously mentioned issues related to the counterion dynamics make it difficult to obtain a direct and a fully reliable quantitative estimate of their contribution to duplex–duplex interactions, it is reasonable to expect that such solvent modulation could have qualitative effects on the DNA–DNA interactions that are not presently captured by the current implicit solvent interaction models. This suggests that solvent-structuring effects may contribute to short-range interactions and represent an interesting direction for future investigations.

The density modulations observed in the explicit solvent simulations are qualitatively compatible with the hydration structuring effects previously reported in atomistic simulations and scattering studies [41]. In particular, water layers confined in the minor and major grooves of DNA show slow relaxation dynamics, which may influence duplex–duplex interactions at a short range.

Our model also captures the strong binding of Na⁺ ions within the major groove, with residence times exceeding 300 ns. This behavior is consistent with the experimental and computational evidence for long-lived cation localization near phosphate and groove regions [42].

4. Discussion

We have presented a numerical study of the SIRAH CG model energy landscape for the interaction of two short DNA duplexes under implicit solvation. The main aim of the present study was to use a refined CG model to go beyond the simplest decorated hard-cylinder models traditionally employed to study condensed phases of DNA double strands and DNA-based colloids. Our results highlight features that are absent from cruder models and provide a physical intuition useful for future coarse-grained developments. Overall, the observed trends are consistent with the theoretical understanding of DNA–DNA interactions [33].

The implicit solvent calculations presented here provide detailed information on the characteristics of duplex–duplex interactions, clarifying how far rigid, cylindrically symmetric force-fields can be safely pushed and where they fail. We find a pronounced dependence on salt concentration, including indications of a possible lateral attraction above 2 M. The dependence on azimuthal rotation in parallel configurations agrees with theoretical predictions and, due to its repulsive nature, implies that angular averaging would result in an effectively larger duplex diameter. Head–tail interactions—critical for the emergence of LC phases—are strongly localized along the molecular axis and highly sensitive to the relative azimuthal angle. This implies that, once a chain of duplexes forms, rotational flexibility is strongly suppressed, whereas angular dependence may act as an additional kinetic constraint during chain formation.

Salt concentration plays a major role, with indications of a weak lateral attraction emerging at the highest concentrations. These trends are consistent with earlier theoretical predictions and with recent experimental evidence of duplex destabilization at high monovalent salt concentrations reported by Zhang et al. [39], suggesting that nontrivial interaction regimes arise beyond ~1 M, where screening and overcharging reshape DNA behavior. In addition, although Ref. [7] focuses on duplex concentration rather than ionic strength, our analysis provides a complementary perspective by showing that salt-dependent screening only weakly modulates the stacking tendencies relevant to LC-phase formation, even for very short duplexes.

The implicit solvent model we have used efficiently incorporates salt effects and provides a consistent description of duplex–duplex interactions. However, the local solvent-structuring is not explicitly represented. The clear layering pattern observed in explicit solvent density maps thus suggests that solvent-structuring effects may contribute to short-range interactions in ways not captured by the current implicit solvent models. This motivates future work on efficient methods to perform more extensive explicit solvent simulations, not only to quantify solvent-structuring contributions but also to directly test the possible emergence of lateral attraction at high salt concentrations, consistent with the observations of Zhang et al. [39]. However, the implicit solvent framework adopted in this work allowed us to sample a large number of configurations and achieve a description of force and energy curves much more accurate than primitive models based on decorated hard cylinders within feasible computational timescales. In particular, the possible emergence of lateral attraction at high salt concentrations should be viewed as a qualitative prediction awaiting experimental verification.

From our calculations, we can also draw some conclusions about the SIRAH force-field. The observed screening lengths in the implicit model align with experimental osmotic stress data on DNA–DNA repulsion [41], and the anisotropic interaction profiles agree with theoretical predictions [42,43]. Furthermore, hydration shell structuring and slow water dynamics—characterized in atomistic simulations [44]—are qualitatively consistent with the solvent density modulations we observe in the explicit simulations.

Also, the long-lived localization of Na⁺ ions in the grooves, seen in our coarse-grained runs, matches with NMR and crystallographic studies showing strong electrostatic stabilization effects [45].

These parallels suggest that SIRAH-based calculations capture not only the structural geometry but also the essential physicochemical mechanisms governing DNA–DNA association, in line with ion-distribution measurements reported in scattering studies [46].

The picture obtained from our analysis aims to be a solid foundation for the development of simplified, yet physically meaningful interaction models aimed at the described condensed phases of short duplexes and DNA-coated colloids. These findings are expected to guide the development of new generations of model potentials and to stimulate experimental tests in the high-salt regime, where distinctive DNA–DNA interaction features are predicted, with potential implications for DNA compaction and molecular recognition.