Abstract
In this work, we investigate the dependence of the melting temperature of low-valency DNA constructs on the length of non-inert dangling ends, controlling their sequence composition. We compare two computational models to evaluate their effectiveness and limitations in predicting the melting behavior of DNA oligomers (bivalent linkers) and more complex structures (trivalent nanostars), benchmarking the results against experimental spectroscopic data. Our results suggest that the length of non-inert dangling ends has minimal impact on the melting point of the DNA duplex for the duplexes we studied, informing the future design of DNA supramolecular constructs.
1 Introduction
Beyond its primary use as genetic material, DNA has been exploited as a building block for nanoscale technological applications for almost 40 years (; ). DNA nanotechnology employs the same physics and chemistry as DNA’s biological function, using Watson-Crick base-pairing rules of complementarity to achieve high-yield self-assembly of complex structures (; ; ). As practical applications for DNA-based nanosystems are explored, precise thermodynamic control over the hierarchical self-assembly of complex higher-order structures is paramount (; ; ; ; ; ). A deep understanding of structure-property relationships is critical for the advancement of DNA-based nanotechnology, enabling innovative applications, such as environmental monitoring, biomolecular interactions detection and identification of pathogenic biomarkers (; ; ).
The supramolecular assembly of DNA hydrogels and other high-order DNA materials follows a hierarchical, step-by-step strategy, based on complex DNA “building blocks”, constructs that are rather stable at intermediate temperatures and that bind together through short complementary single-stranded sequences called “sticky ends”. This strategy exploits the dependence of the melting temperature on the duplex length: the design allows the building blocks to remain stable in a target thermodynamic region where dynamic formation and breaking of bonds is taken into account, shaping the overall phase diagram (; ; ; ; ).
However, the presence of unpaired bases also influences the stability of the construct. As previously reported (), a moderate increase in melting temperature is observed upon adding a single unpaired base to a short duplex. Increasing the length of the resulting dangling end with identical bases, e.g., a series of thymines that acts as a free joint, creates an inert tail and induces a monotonic decrease of ; the melting temperature becomes constant for larger than a few nucleotides, with a plateau value either matching or deviating from the melting temperature of the original duplex , depending on the ionic strength or the detailed design of the construct. This monotonic decrease is driven by electrostatic interactions: after an initial free energy gain due to residual stacking contributions, the presence of residual charges on the single strand may compensate or even overcome the initial rise in .
Here we obtain the melting temperatures as a function of for similar systems (Figure 1), i.e., simple bivalent or trivalent DNA constructs, with heterogeneous sequences and non-inert tails. The melting temperature reflects the interplay between energy and entropy, serving as a key indicator for assessing the stability and functionality of complex DNA nanostructures. Computational implementations of physical models are often employed to provide estimates of thermodynamic properties, aiming to guide experimental efforts. However, even for relatively simple tasks, widely used software faces challenges related to accurate modelling of experimental conditions and arriving at the required statistics. Here we consider how the melting temperature of a duplex with non-inert tails is affected by . We tackle the problem experimentally and computationally, using a selection of two popular computational approaches and focusing on the ones of highest practical relevance. We show experimentally that the melting temperature is independent of ; notably, only one numerical method predicts the experimental trend.
FIGURE 1
In the following text, we give information on the short DNA constructs employed in this study, specifically bivalent “linkers” (L, Figures 1a,b) and trivalent “Y-shapes” (Y, Figure 1c). We start by briefly presenting experimental methods and theoretical models, NUPACK and oxDNA. We then discuss the experimental ground truth and expose a limitation of NUPACK that, upon inclusion of sticky ends, shows a qualitative discrepancy with experiments, which however can be corrected by using melting curve normalization or a method based on first derivatives to extract melting temperature values (cf.Supplementary Figure S4). Instead, results of direct sampling from Molecular Dynamics simulations with the oxDNA model qualitatively reproduce both the literature results () and the experimental data (). We conclude with a discussion of our results from a thermodynamic standpoint, critically reviewing and pointing to specific strengths and limitations of each approach.
2 Methods
2.1 System description
Linkers are bivalent constructs consisting of a 26-base-long double-stranded DNA (dsDNA) core with single-stranded DNA (ssDNA) ends (dangling ends or tails) on both sides. The length of the tails ranges from 0 to 12 bases at both ends (Figures 1a,b shows ); we employ the nomenclature LS, with denoting the number of bases in the sticky end). Y-shapes are trivalent nanostars (or trimers) with three interconnected duplex arms that meet in a central core (Figure 1c); each arm of the Y-shape has a 12-base-pair non-inert dangling tail.
Finally, to facilitate comparison with thermodynamic information on shorter oligos, we included in our analysis dimers used in a preceding work () (see SI).
2.2 Experimental methods
We ordered the custom-made DNA oligonucleotides in Table 1 from biomers.net GmbH. The oligonucleotides were HPLC-purified, freeze-dried and subsequently dissolved in 10 mM phosphate buffer saline (PBS) supplemented with 100 mM NaCl (pH 7.6), following an established protocol (; ). All oligo concentrations were then measured using NanoDrop 1000 and the hybridisation behaviour verified using polyacrylamide gel electrophoresis and UV-visible spectroscopy. Y-shaped (trivalent) nanostars are formed by the designed single strands Y1, Y2 and Y3, while bivalent DNA linkers are formed by linker strands LS-1 and LS-2. The linkers LS investigated experimentally are reported in Table 1, where the sticky ends are highlighted with different colours. All samples were stored at and equilibrated to room temperature prior to spectroscopic experiments.
TABLE 1
 |
DNA strands comprising Y-shapes and linkers, with labelled sticky ends (black-green) and hybridising segments between Y1 and Y2, Y1 and Y3, Y2 and Y3 (shades of grey), LSX-1 and LSX-2 (matching colour). All synthesised DNA strands were purified via HPLC before use.
UV-visible absorption spectra were then recorded at a wavelength of 260 nm by Cary 3,500 Multicell Peltier UV-visible spectrophotometer (Agilent Technologies). At this wavelength, we used the differential absorbance of ssDNA and dsDNA to confirm the formation of the Y-shapes and linkers, alongside obtaining information about their melting temperatures. All temperature ramps (heating and cooling) were performed between and at a controlled rate of that minimised hysteretic effects. The oligo concentration in each case was close to 1 M, ensuring absorbance values within the specified range of operation of Cary 3,500. The melting temperature was determined as the mid-point of the sigmoidal melting curve, where on average half of all hydrogen bonds were broken (heating) or formed (cooling). The uncertainties in the melting temperatures were identified as the differences between the values measured in heating and cooling ramps.
2.3 Statistical mechanics approach: NUPACK
The NUPACK tool (Zadeh et al., 2011) was designed to construct and analyse nucleic acid systems, predicting DNA secondary structure from the sequences, i.e., the base-pairs of a set of DNA strands. For each candidate secondary structure, NUPACK algorithms add an empirical estimate of the free energy parameters (), with a strand association penalty energy and stacking contributions (). The tool allows identification of the Minimum Free Energy (MFE) structure under given conditions, viz., temperature, salt concentration and other thermodynamic parameters. NUPACK advantages include open accessibility, ease of use, and the ability to provide estimates of equilibrium and thermodynamic properties, such as melting profiles, even for systems involving multiple interacting strands (Zadeh et al., 2011). On the other hand, the tool is limited in the properties it can predict for small constructs and may propose highly improbable configurations in the presence of dangling ends (). Another issue stems from NUPACK’s inability to distinguish between broken base pairs and single bases belonging to tails, which leads to severe underestimation of bonded fractions at low temperatures for short oligomers. In this analysis, we used the energy parameter set “dna04”, with 100 mM ] and 1 M DNA strand concentration.
2.4 Computational approach with oxDNA
OxDNA (; ; ) is a widely used physical model that enables in-silico studies of DNA origami and other types of all-DNA fluids, including their self-assembly kinetics. In addition to its effectiveness in reproducing the mechanics and thermodynamics of DNA constructs (; ; , oxDNA is arguably the most accessible simulation code for DNA, providing introductory material (; ), supporting a number of web tools (; ; ; ) and allowing extensions ().
In a nutshell, oxDNA is a top-down, nucleotide-level coarse-grained model that accounts for different potential energy contributions between base pairs (Figure 1d) (). The oxDNA code supports both Monte Carlo (MC), with native support for Umbrella Sampling (US), and Molecular Dynamics (MD) simulations. Notable for our work is the GPU acceleration of oxDNA, which enables scaling up in simulations of larger systems ().
We performed standard MD simulations, also termed here “unbiased sampling”, and MC simulations with Umbrella Sampling (cf. SI). We employed the oxDNA2 model (), which explicitly includes the effect of screened electrostatic interactions, and set the Na+ concentration to mM, to directly compare with experiments; we performed simulations in bulk using periodic boundary conditions. In MD simulations, we employed an Anderson-like thermostat (“Brownian” in oxDNA), with a damping time of 100 time steps; we set an elementary time step oxDNA time units. With very short duplexes, we ran independent replicas of single-molecule simulations, i.e., we simulated a single molecule in a sufficiently large box; for the longer duplexes and the Y-shape, we leveraged oxDNA’s GPU-enabled code, simulating 40 linkers or 30 Y-shapes in a much larger box. In both cases, we started from a low temperature [C for oligomers in Table 1, C for validation of strands from ] and let the simulation run for number of steps (cf. SI), ensuring that the hydrogen bond contribution to the potential energy reached a plateau. We then sampled the number of hydrogen bonds and computed the fraction of observed hydrogen bonds with respect to a reference maximum value, corresponding to the fully formed duplex state. To construct the melting curve, we then increased the temperature and repeated the procedure, starting from the previous configuration state; we simulated up to C for oligomers in Table 1 (up to C for strands from ()). In both cases, we applied the bulk extrapolation correction (); for multiple DNA constructs in the same box, the large size of the box significantly reduced the probability for strands to meet and recombine. Indeed, the latter never occurred in our simulations and hence the results of the two simulation approaches were considered comparable.
3 Results and discussion
3.1 Validation on reference system
First, we briefly validated our chosen numerical methods on a reference system () (details in the SI). We observed that both unbiased MD and US with oxDNA qualitatively retrieve the reported results. Notably, while we reliably captured a difference in melting temperature C, associated with the first non-paired base in the dangling end (guanine), we found only incremental changes to the melting curves on further addition of bases to the dangling ends. This we interpreted as a limitation of the oxDNA model and other proposed approaches: US convergence is slow, and classical MD visits uniformly phase space, whereas sampling within the melting region is expected to benefit from advanced sampling techniques. Moreover, short duplexes are highly susceptible to thermal fluctuations close to the melting region, which may push the system towards complete melting. In our scheme, premature melting affects simulations from a certain temperature onwards, as recombination would happen over much longer timescales. For our target bivalent and trivalent constructs, we resorted to unbiased sampling, due to the higher computational cost of the US approach. Validation with NUPACK was considered unsuitable for our short sequences () and was therefore not performed.
3.2 Experimental results
Next, we investigated experimentally through UV-visible spectroscopy a set of duplexes with non-inert tails (Section 2.1), thereby providing ground truth for comparison with the two in-silico approaches we selected. We show normalised transmittance at 260 nm in Figure 2a. At this wavelength, single-stranded DNA absorbs more strongly than double-stranded DNA, which yields a sigmoidal curve. The mid-point of the sigmoidal curve–equivalent to the temperature at which the fraction of bonded bases equals 0.5 (a value that closely matches the temperature corresponding to the maximum of the first derivative, as shown in Supplementary Figure S3)–represents a transient dynamic state between a fully assembled and fully dissociated duplex, where on average half of all hydrogen bonds are formed (during cooling) or broken (during heating). Notably, the melting temperature displays little to no variation as we deleted bases from the sticky ends of the double-stranded linkers. However, the Y-shapes display a notably different melting temperature from the linkers, with C, informing on the hierarchical step-by-step assembly of higher-order systems based on the linking between bivalent linkers and trivalent nanostars.
FIGURE 2
In Figure 3, we included a summary of these experimental melting-temperature results, shown as square symbols, where we indeed observed that is roughly constant with .
FIGURE 3
3.3 NUPACK predictions
For the same oligomers, we computed a prediction of the melting temperature using NUPACK. Figure 2b shows melting curves for different lengths of the dangling ends, . According to NUPACK, the melting temperature generally shifts down for linkers with longer sticky ends. This prediction seemingly contradicts the experimental evidence for relatively constant melting temperature, since with NUPACK we observe a monotonic decrease with increasing , without ever reaching a plateau (cf. triangles in Figure 3). While NUPACK calculations yield an accurate estimate of for short oligos with , they qualitatively fail to reproduce the experimental trends on increasing . A possible explanation to this observation could be the NUPACK treatment of free bases in the dangling ends, which are included in the total count of non-hybridised bases, precluding the accurate determination of . The limitations of NUPACK also originate from the fact that it is a nearest-neighbour model; this suggests lower accuracy in melting temperature estimation, as evidenced by a recent attempt to improve NUPACK’s prediction of secondary structures ().
3.4 oxDNA results
Approaching the melting-point determination task using unbiased MD with the oxDNA model leads to the results reported in Figure 2c, where we again provide the curves for different values of ; error bars represent standard deviation of the fraction of bonded bases, recorded every 1.515 ns in equilibrium simulations. The corresponding values as a function of are represented by circles in Figure 3. While we observe a systematic offset compared to the experimental baseline (C), the independence of on is retrieved. This suggests that oxDNA captures more reliably the hybridisation dynamics between DNA filaments with long dangling ends compared to NUPACK. Finally, we note that for relatively long oligomers (40–50 bases), melting events due to statistical fluctuations at are highly improbable. We suggest that the discrepancy between melting temperatures forecast by oxDNA model and those measured in experiments is due to inherent limitations of oxDNA. As NUPACK, it is a nearest-neighbour model, which implies that long-range interactions are not considered, possibly accounting for discrepancies with experiments. Moreover, the oxDNA model is well-suited to reproduce melting properties in bulk, similarly to the SantaLucia model (); bulk extrapolation then only partially corrects for systems that significantly deviate from the expected bulk conditions.
4 Conclusion
We investigated the effect of adding non-inert nucleotides to the sticky end attached to a duplex core in DNA constructs. We compared NUPACK and oxDNA models with an experimental reference; oxDNA was used in the context of Molecular Dynamics simulations, both unbiased and with Umbrella Sampling. In the SI, we summarise additional attempts at using advanced sampling techniques, discussing the challenges and potential pitfalls one encounters along the way. US promotes quicker convergence, but becomes impractical for strands containing even a few tens of bases since the required simulation time increases significantly and it becomes non-trivial to estimate the bias weights. Unbiased MD is cheaper to run and capable of handling larger systems, even with tens of molecules owing to GPU-acceleration; on the other hand, its uniform exploration of states in the melting region implies longer simulation times, since fluctuations become large and the system requires more time to reach steady state. One significant disadvantage of explicit counting of hydrogen bonds in unbiased MD is that it requires careful handling of statistical results by running multiple independent simulations for extended periods. For the long duplexes, the equilibration time was estimated to be approximately steps (roughly twice as long close to ). The estimation of can be improved by running multiple independent simulations and tuning the integration time step. However, oxDNA captures the experimental trend in contrast with NUPACK, showing that is independent of for non-inert bases. In this setting, the thermodynamics of the DNA duplex is largely unaffected by the presence of the dangling ends; this finding complements previous results (), considering the effect of inert tails. Moreover, the data support the physical interpretation that sticky ends serve as primary stabilising elements in DNA duplexes. Complex multivalent motifs, such as Y-shapes, exhibit reduced thermal stability due to steric and entropic constraints. As such, this study analyses the advantages and pitfalls of simple, direct approaches for the estimation of the melting temperature in-silico, showing that MD unbiased simulations within oxDNA may be used to obtain melting-temperature estimates that are within a few degrees from experimental values. To conclude, the approach outlined here enables the study of linkers with larger values, or even of more complex structures, such as molecules made by an arbitrary number of Y-shapes and linkers, whose melting curves may otherwise be challenging to tackle with advanced sampling techniques.
Statements
Data availability statement
The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.
Author contributions
AS: Writing – review and editing, Methodology, Formal Analysis, Software, Writing – original draft, Investigation, Visualization. FM: Writing – original draft, Formal Analysis, Software, Visualization, Resources, Methodology, Investigation, Writing – review and editing, Validation. EL: Writing – original draft, Writing – review and editing, Software, Formal Analysis, Investigation, Validation, Methodology. IS: Writing – review and editing, Validation, Funding acquisition, Project administration, Supervision, Data curation, Writing – original draft, Resources, Conceptualization, Investigation.
Funding
The author(s) declare that financial support was received for the research and/or publication of this article. AS and IDS kindly acknowledge financial help from the Karlsruhe Institute of Technology Excellence Strategy via the Young Investigator Group Preparation Program. We acknowledge funding by the Carl-Zeiss-Foundation through the Seed Funding Program of the Center for Synthetic Genomics.
Acknowledgments
FM acknowledges CINECA through ISCRA initiative, in detail IsCc4 project (ID: HP10CSR1I8). FM also gratefully acknowledges the Data Science and Computation Facility and its Support Team for their support and assistance on the IIT High Performance Computing Infrastructure.
Conflict of interest
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Generative AI statement
The author(s) declare that no Generative AI was used in the creation of this manuscript.
Publisher’s note
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.
Supplementary material
The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fmolb.2025.1646428/full#supplementary-material
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Summary
Keywords
DNA nanotechnology, melting curves, oxDNA, NUPACK, molecular dynamics, umbrella sampling
Citation
Soto A, Mambretti F, Locatelli E and Stoev ID (2025) Modelling the melting of DNA oligomers with non-inert dangling ends. Front. Mol. Biosci. 12:1646428. doi: 10.3389/fmolb.2025.1646428
Received
13 June 2025
Accepted
28 July 2025
Published
13 August 2025
Volume
12 - 2025
Edited by
Li-Tang Yan, Tsinghua University, China
Updates
Copyright
© 2025 Soto, Mambretti, Locatelli and Stoev.
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*Correspondence: Iliya D. Stoev, iliya.stoev@kit.edu
Disclaimer
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.