Quantifying replication fidelity of unnatural base pairs using nanopore sequencing

Abstract

Expanded genetic alphabets built from unnatural base pairs (UBPs) are part of an emerging frontier in biotechnology. However, their wider adoption is constrained by lower replication fidelity relative to standard DNA bases. To address this challenge, we develop a method to rapidly assess UBP replication fidelity using nanopore sequencing. We train post hoc machine-learning classifiers to detect UBPs in sequencing data, then use these models to extract fidelity measurements from PCR-amplified datasets. This approach provides a general route to assess the replication fidelity of diverse UBPs, enabling optimization across chemistries, enzymes, and reaction conditions. In this work, we apply this strategy to three distinct UBP systems, demonstrating: (i) rapid screening of reaction conditions that yields > 98.6% per-cycle replication fidelity for the B ≡ S base pair, (ii) single-molecule tracking of replication outcomes in an 8-letter UBP system (ATGCBSPZ), and (iii) quantitative decomposition of multiple error pathways for the hydrophobic Ds:Diol-Px system.

Expanded DNA alphabets with more than 4 letters can be replicated by polymerases, but with higher error rates than standard DNA. Here the authors develop a high-throughput sequencing approach to quantify the replication fidelity of unnatural base pairs.

Introduction

Modern molecular biology widely operates on infrastructure implicitly optimized for a 4-letter genetic alphabet (A, T/U, G, C). Core operations such as sequencing, synthesis, and amplification are highly optimized and routinely performed at scale. Over the past several decades, however, structurally modified nucleotides have shown transformative potential across biotechnology, spanning therapeutic aptamers^1–3, enhanced diagnostic tests^4,5, and biomanufacturing of biologics^6,7. This growing interest has motivated the synthesis and characterization of hundreds of nucleotide analogs, many of which are now commercially available as phosphoramidite or triphosphate monomers^8–10.

Within this broader landscape of non-standard nucleic acids, a subset of nucleotides are capable of supporting an expanded genetic alphabet. Unnatural base pairs, or UBPs, are synthetic base-modified xenonucleic acids (XNAs) that are specifically designed to expand the chemical rules that underlie genetic information storage and transmission⁸. UBPs introduce new functionality through orthogonal base-pairing rules, allowing us to extend alphabets beyond the 4-letter limit (A = T, G ≡ C). Here, hydrogen-bonding UBPs achieve orthogonality by adopting distinct donor–acceptor patterns at the purine–pyrimidine interface, while non-hydrogen-bonding systems rely instead on steric complementarity and entropic exclusion to maintain pairing selectivity (Fig. 1)^11–13.

Fig. 1. Nucleobase structures and mutation modes of unnatural base pairs (UBPs).

a Nucleobase structures of the standard DNA base pairs (G ≡ C, A = T). Dashed arrows indicate functional groups that participate in hydrogen bonding, drawn from the hydrogen-bond donor to the acceptor. b Nucleobase structures of two hydrogen-bonding UBPs (B ≡ S, P ≡ Z) studied in this work. The structure of S shown is Sⁿ (5-methyl-isocytosine). Putative replication error modes of each UBP are shown by red equilibrium arrows. During replication, keto-enol tautomerization (Taut.) of B can rearrange the H-bonding patterns (shown in red), leading to a Watson-Crick-Franklin mismatch with T, resulting in B → A and S → T DNA transitions. Similarly, deprotonation of the Z nucleobase can lead to a mismatch with G, resulting in P → G and Z → C DNA transitions. c Nucleobase structures of the non-hydrogen-bonding UBP, Ds:Diol-Px. Self-pairing of the Ds base can lead to UBP strand inversions (i.e, Ds→Diol-Px and Diol-Px→ Ds).

Despite their substantial structural divergence from canonical nucleotides, hydrogen-bonding and non-hydrogen-bonding UBPs have been shown to be faithfully incorporated by polymerases¹⁴. Yet even with biochemical compatibility, replication fidelity of UBPs is measurably lower than that of standard DNA (in vitro: 10⁻⁴ to 10⁻⁷; in vivo: 10⁻⁹ to 10⁻¹⁰ errors per nucleotide replicated). Notably, estimates of in vitro UBP replication fidelity have been reported to be as low as ≈ 85% (for the B ≡ Sⁿ pair). On the high end, replication fidelity for UBPs can exceed 98% for certain pairs ( > 99.97% Ds:Px^15,16, ≈ 99.98% dNaM:dTPT3¹⁷, 99.7% P ≡ 2-F-Z(CONH₂)¹⁸. Far less is known about the in vivo replication fidelity of UBPs, with estimates reported only for dNaM:d5SICS and dNaM:dTPT3, reaching as high as 99.6% retention/doubling in certain sequence contexts using an engineered E. coli strain^19,20. The low replication fidelity observed in expanded alphabets poses a significant challenge for integrating UBPs into molecular biology workflows and hinders the prospect of their usage for long-term biological information storage.

Prior research efforts have directly explored the molecular basis of UBP replication error. Error modes have been attributed to structural features that allow mismatches in the pre-insertion complex during replication. One of the most well-studied examples is the error associated with template-B replication. Though the keto-B tautomer is commonly depicted in the B ≡ S base pair, B is also known to exhibit various minor tautomers, of which the enol-B tautomer (Fig. 1b) is proposed to form a Watson-Crick-Franklin pair with T^21–23. The resulting enol-B ≡ T pair leads to a B → A, S → T transition. Similarly, the H(1 N) position in amino-5-nitro-(1H)-pyridin-2-one (Z) has a relatively low pK_a ( ≈ 7.8), which leads to a Z(-H) ≡ G mismatch and P → G, Z → C transition when deprotonated^24–28. Finally, for the hydrophobic Ds:Px system, Ds:Ds self-pairs (Fig. 1c) have been observed, which may lead to inversions during PCR (i.e., Ds → Px, Px → Ds)^29,30. Lesser-known sources of error in the Ds:Px system, including Ds:A, Ds:T, Ds:C, and Px:T mismatches, have also been observed, with their relative frequencies thought to depend on the surrounding sequence context^12,15,29,31.

Understanding the origin of UBP replication errors, including a mechanistic understanding of error modes, can help us improve UBP replication fidelity. For example, lowering reaction pH and optimizing nucleotide concentrations effectively reduces Z(-H) ≡ G mismatching^24,32. Alternatively, structural modifications have been used to discourage common error modes in various pairing systems (e.g., Px > Pa, 2-F-Z(CONH₂) > Z)^12,18. For the B ≡ S pair, modifications to the B heterocycle, including 7-deaza-isoguanosine, 8-aza-7-deaza-isoguanosine, and 8-aza-isoguanosine, have also been proposed or shown to reduce mismatching by favoring the keto form^23,33–36. Substituting T with 2-thio-T in PCR introduces steric clashes with enol-B and also decreases replication error³⁷. Despite these improvements, UBP replication fidelity still falls below desired thresholds for reliable amplification.

Although substantial progress has been made in the field, the fidelity landscape of UBP replication remains poorly characterized, creating barriers to adoption by the wider scientific community. Sequence context effects on fidelity are known but incompletely characterized^15,32,38. Various other error modes, including standard DNA → UB forward mutations and UB → UB transversions, have been proposed but sparsely measured. UBP replication fidelity is also further modulated by poorly understood factors such as transient polymerase stalling, polymerase active-site microenvironment, identity of divalent cation loaded in polymerase active site, and reaction conditions (including temperature, pH, buffer composition). New UBP structures address some of the replication failure modes, but themselves remain incompletely characterized or commercially inaccessible. Efforts to consolidate these knowledge gaps face additional hurdles. Existing methods for measuring replication fidelity are bespoke and depend entirely on the UBP system being studied. Additionally, prior work has primarily used low-throughput techniques (e.g., gel-based assays, mass spectrometry quantification, and Sanger sequencing-style di-deoxynucleotide termination assays) that are difficult to reproduce and have high margins of error^{15,18,19,39,40}. Finally, the field lacks a unified mathematical descriptor of replication fidelity, which makes comparisons of reported values non-generalizable. Standardized, high-throughput fidelity-measurement strategies are needed to enable quantitative, unified benchmarking across UBP systems and to accelerate further optimization of base structure, polymerase choice, and other reaction conditions.

In this work, we introduce a nanopore sequencing-based strategy that uses deep learning to quantify UBP retention at a single-molecule resolution. Although nanopore reads exhibit modest de novo basecalling accuracy ( ≈ 90–95%), post hoc RNN classifiers trained directly on specific sequences can detect modified bases with high accuracy ( > 98%). Here, we train and benchmark 33 models spanning three UBP systems (BS: B ≡ Sⁿ, PZ: P ≡ Z, and DsPx: Ds:Diol-Px), demonstrating that this approach measures per-cycle UBP retention during PCR and resolves strand-specific replication error signatures. We further benchmark the method against experimental conditions and published values, proposing a unified analytical framework for UBP polymerase fidelity measurements (Supplementary Table 1). Through a series of experimental vignettes, we use this high-throughput method to identify higher fidelity conditions for BS replication, quantitatively track formation of various molecular species in an 8-letter PCR system (B, S, P, Z), and provide robust evidence for unique error modes that appear under certain conditions in a hydrophobic UBP system (DsPx).

Results

Training and testing comparative basecalling models for UBPs

Nanopore sequencing is one of the few platforms capable of detecting modified and non-canonical nucleotides. In nanopore sequencing, a helicase protein unwinds dsDNA and an applied voltage drives single DNA molecules through a membrane-embedded pore protein while the ionic current is measured. The mobility of ions through the pore is modulated by the identity of the nucleotides occupying the pore volume, resulting in an ionic current signal that can be mapped to the underlying DNA sequence. Commercial platforms for nanopore sequencing (Oxford Nanopore Technologies, ONT) pair a highly processive motor protein with a pore protein that typically interrogates a 9–10 nt sequence window (r10.4.1 chemistry). Prior studies have shown that ONT’s motor proteins (in both r9.4.1 and r10.4.1 chemistries) can translocate a wide range of modified nucleotides, including epigenetic marks and UBPs^41,42. Although ONT’s default basecalling models are trained exclusively on canonical DNA (A, T, G, C), secondary analysis of the raw ionic current signal can be used to detect deviations from that of the canonical bases. One of the most sensitive approaches for modified base detection uses deep learning to train comparative basecalling models, in which neural networks learn to distinguish modified from unmodified DNA based on raw current trajectories. When trained using a defined sequence context, comparative basecalling models can achieve high-accuracy classification^43–45.

Building on this premise, we set out to develop a comparative basecalling framework to quantify UBP replication fidelity. To generate training inputs, we designed and sequenced synthetic DNA oligos (Supplementary Data 1, Supplementary Tables 2–4) that contained a site-specific UBP substitution for six unnatural bases: B, S (S = Sⁿ variant), P, Z (Z = nitro-Z variant), Ds, Px (Px = Diol-Px variant). For each UB-containing oligo, we also generated and sequenced the corresponding standard DNA oligos where the unnatural base was substituted with the DNA base that would result from likely modes of replication error (B → A; S → T; P → G; Z → C). Since the error modes of the Ds:Diol-Px base pair are less well defined, standard DNA-version oligos were generated that contained a mixture of all four standard bases at the UB position (Ds → N, Px → N). Example normalized and segmented ionic-current traces for all six comparative datasets (Fig. 2a, Supplementary Figs. 1–4) show clear, localized differences within ≈ 2-3 nt of the UB substitution, with the magnitude and spatial extent of these perturbations varying across bases and sequence contexts.

Fig. 2. Sequencing, training, and benchmarking comparative basecalling models.

a Segmented and normalized (norm.) nanopore signal traces for DNA sequences containing UBs (blue: B, S; orange: P, Z; red: Ds (D), Diol-Px (X)) compared with identical sequences containing only standard bases (black traces). The colored shade highlights the UB position in the sequence. The median signal is plotted (n = 500 reads per class). b Overview of comparative basecalling model architecture. c Confusion matrices generated from benchmarking comparative models (BA1, ST1) to detect BS error modes in the 5′-GBC-3′ context (left: B vs A; n = 10,000 reads per class, right: S vs T; n = 10,000 reads per class). The quantified UB fraction B ($f_B$; blue) and fraction S ($f_S$; gray) when the same models are applied to demultiplexed synthetic DNA standards containing an AT (BA1:ST1) or BS (B1:S1) base pair across five independent sequencing experiments. The mean ± SD of experimental replicates (n = 5) is plotted with replicate values overlaid as points. d Specificity (TNR; true negative rate) versus recall (TPR; true positive rate) for all comparative basecalling models generated in this work. Colors correspond to the UB each model is trained to detect (blue: B; light blue: S; orange: P; light orange: Z; red: Ds; light red: Px). Dashed lines show 98% thresholds for recall and specificity. Raw data are tabulated in the Source Data file.

For each comparative set, we trained deep-learning classifiers based on Long Short-Term Memory recurrent neural networks (LSTM RNNs) using a modified implementation of Remora (Oxford Nanopore Technologies)⁴⁶. In this architecture, raw normalized ionic-current traces centered on the target position are first processed through a stack of one-dimensional convolutional layers to extract local signal features. In parallel, a one-hot encoded representation of the signal-mapped, aligned reference sequence, expanded into k-mer representation (9-mer), is passed through a separate convolutional stack. The resulting feature sequences are concatenated and fed into two LSTM layers, after which a fully connected head outputs logits and label probabilities. These probabilities correspond to the classification of a canonical (DNA) versus modified (UB) state at the queried position (Fig. 2b). For this type of classification task, we found model training converged rapidly (typically within 20–30 epochs) and required only a modest number of reads ( ≈ 1000 reads per model). Training statistics for all comparative basecalling models generated are summarized in Supplementary Table 5.

Representative confusion matrices and external test results for one set of B → A and S → T classifiers (Fig. 2c) illustrate that this strategy can reproducibly discriminate key replication-error modes with high accuracy. Across the 33 models we trained, most showed > 98% recall and specificity in benchmarking, underscoring their suitability for quantifying UBP retention within defined sequence contexts. For most models, > 95% recall and specificity could be achieved using a signal window size of ± 50 data points (Fig. 2d). However, the P → G classifier showed improved accuracy when the window size was increased to ± 125 data points, suggesting that the required information was embedded in longer-range perturbations for this sequence context (Supplementary Figs. 3, 5).

We evaluated quantitative response in silico by generating synthetic .POD5 files containing controlled mixtures of UBP (BS) and standard DNA (AT) reads. For each mixture, the predicted proportions closely matched the expected values, yielding linear responses with R² ≥ 0.999 (Supplementary Fig. 6). Comprehensive benchmarking statistics for all comparative models are provided in Supplementary Table 6. Together, these results demonstrate that the comparative basecalling models are both accurate and generalizable within their training scope. We next applied these models to quantify PCR replication fidelity, first focusing on the B ≡ S pair, which is known to exhibit a high error rate attributed to the keto-enol tautomerization of B.

Quantifying replication fidelity of the BS base pair in PCR

We first needed to establish the experimental and theoretical basis for making fidelity measurements from single-molecule reads. First, PCR needs to be performed under conditions where the number of effective doublings, or theoretical doublings, is defined stoichiometrically and is therefore independent of amplification efficiency. This is achieved by running reactions in a primer-limited regime, using the primer-to-template ratio to set the theoretical cycle number $n$ (Supplementary Method 1). Additionally, though fidelity is often estimated using endpoint values, a more robust strategy is to measure the relative loss of UB species as a function of doubling³⁷. Fractional loss is insensitive to absolute yield and initial template abundance, and less sensitive to basecalling model accuracy. Using the comparative basecalling models we measure $f_B\left(n\right)$ and $f_s\left(n\right)$, which are the fraction B and fraction S remaining after $n$ theoretical cycles. In an ideally replicating system, $\log f\left(n\right)$ is linear. These measurements can then be mapped directly to the underlying average fidelity parameter, ${\phi }_{⟨B,S⟩}$ using Supplementary Equations (17-34) (Supplementary Method 2).

Complementary synthetic templates containing the BS base pair (Sequences B1:S1, Supplementary Data 1) were amplified by Taq polymerase in PCR reactions containing equimolar amounts of six nucleoside triphosphates (dATP, dTTP, dGTP, dCTP, dBTP, and dSTP). Each reaction was performed in triplicate, using unique pairs of forward and reverse primers containing 24-mer DNA barcodes (Fig. 3a; Supplementary Table 2 and 3), allowing many samples to be multiplexed on a single nanopore flow cell. Pooled PCR products are sequenced, demultiplexed, and classified by our trained comparative sequencing models to obtain $f_B\left(n\right)$ and $f_s\left(n\right)$ from sequencing data (Supplementary Fig. 7). Individual sequencing runs also contained barcoded synthetic DNA standards (Supplementary Fig. 8), used as internal controls to validate the performance of our comparative basecalling models.

Fig. 3. Replication fidelity quantification and PCR conditions screening for the BS UBP.

a Synthetic template containing the UBP is PCR amplified with primers containing barcode (BC) sequences. b Raw fractions of B ($f_B$ (+); blue) and S ($f_S$ (−); gray) after PCR with Taq polymerase, including internal standards (BS or AT). PCR Step 2 represents a 1000× dilution of products from PCR Step 1. The mean ± SD of experimental replicates (n = 3) is plotted with replicate values overlaid as points. c -Log₂-transformed fraction B (B; blue), fraction S (S; gray), and average fraction ($⟨\mathrm{B},\mathrm{S}⟩$; black), plotted as mean ± SD of experimental replicates (n = 3). The average replication fidelity, ${\phi }_{⟨B,S⟩}$ (95% CI) is calculated from the slope (m) of the regression line (dashed line) using the equation shown. d Fold-change in average UB fraction at a tested experimental versus reference condition ($f_{⟨B,S⟩}/f_{⟨B,S⟩}^{ref}$) after a fixed value of theoretical cycles. Conditions include nucleotide concentration ([dNTP]; sky blue), polymerase (Pol.; purple), sequence context (Seq.; green), divalent cation (DV Cat.; orange), PCR supplements (Suppl.; gray), or pH (pH; blue). P-values are from a two-tailed Welch’s t-test (n = 3 per group). e Average polymerase error rate (${\epsilon }_{⟨B,S⟩}$) for polymerases with (purple) or without (gray) 3′ → 5′ exonuclease activity at two theoretical cycle values (n = 3 per group). Mean values are plotted ± SD (n = 6, replicates pooled). f ${\epsilon }_{⟨B,S⟩}$ in 5 sequence contexts for Taq polymerase (gray) and Q5 polymerase (green). WLS regression-derived estimates of ${\epsilon }_{⟨B,S⟩}$ are plotted (95% CI; n = 3). Estimates of ${\epsilon }_{⟨B,S⟩}$ from independent regression fits to each experimental replicate are overlaid as points. Asterisks denote statistical significance in a two-tailed z-test (** p < 0.01, * p < 0.05). g ${\epsilon }_{⟨B,S⟩}$ for Taq polymerase at varying nucleotide concentration ratios of dBTP/dATP (gray), dSTP/dTTP (sky blue), or both (combined; white). Mean ± SD is plotted with experimental replicate values overlaid (n = 3). h -Log₂-transformed average UB fraction ($f_{⟨B,S⟩}$) in optimized PCR conditions. Mean ± SD is plotted with experimental replicate values overlaid (n = 3). The raw data used to generate each plot and the exact p-values of statistical tests are tabulated in the Source Data file.

Plots for $f_B\left(n\right)$ and $f_s\left(n\right)$ show exponential decay of B and S is maintained across 29 theoretical cycles, or 5 ×10⁸-fold amplification (Fig. 3b, Supplementary Fig. 9). Notably, the measurements of $f_B\left(n\right)$ and $f_s\left(n\right)$ are strand-resolved and show slight disagreement, which is consistent with asymmetric polymerase fidelities on templates B and S. We can show how this effect arises when the primary error mode is mediated through B ≡ T mismatching by modeling the ODEs that govern this system (Supplementary Fig. 10, Supplementary Method 3, Supplementary Equations (39-40)). While the individual polymerase fidelities on template B (${\phi }_B$) and S (${\phi }_S$) cannot be decoupled without an estimate for either ${\phi }_B$ or ${\phi }_S$, the average replication fidelity, ${\phi }_{⟨B,S⟩}$, can be extracted from the slope of the log-transformed average fraction data. Under our baseline conditions with Taq polymerase, we estimate ${\phi }_{⟨B,S⟩}$ = 89.0 ± 0.4% (95% CI) per theoretical cycle (Fig. 3c, Supplementary Table 7). ${\phi }_B$ can be estimated directly from ${\phi }_{⟨B,S⟩}$ measurements (${\phi }_B$ = ${\phi }_{⟨B,S⟩}^2$) if we assume template-B replication errors are the primary source of mutations (i.e., ${\phi }_S$ ≈ 1). Under these assumptions, we place our own baseline estimate of ${\phi }_B$ ≈ 79% per theoretical cycle.

Taken together, these results demonstrate that $f_B\left(n\right)$ and $f_S\left(n\right)$ can be measured independently and jointly used to derive ${\phi }_{⟨B,S⟩}$ with high internal consistency. Moreover, these measurements exhibit negligible flow cell-to-flow cell variability, indicating that the inferred quantities are robust to experimental replication (Supplementary Fig. 11). The resulting UB fraction trajectories agree closely with the expected theoretical behavior and are obtained under an experimental design that minimizes confounding sources of error (Supplementary Figs. 10 and 12). As such, deviations from linearity in the log-transformed traces can provide an early indication if model assumptions are being violated. Notably, the strand-resolved nature of the method eliminates the need for a correctly paired UBP duplex, which can become minor products (BT + AS > BS) due to strand-swapping as primers are consumed (Supplementary Fig. 13). These findings underscore the need for caution when interpreting fidelity measurements that only use an endpoint measurement, or methods that require intact UBP duplexes (e.g., restriction digests), as such approaches may obscure the true replication dynamics of the system.

High-throughput optimization of BS replication fidelity

Having validated this approach, we next took advantage of the high-throughput capacity of this strategy to improve the replication fidelity of the B ≡ S base pair in PCR. Though the B ≡ S pair (here, S = iso-cytosine) was first reported over 30 years ago, few prior efforts have investigated improving replication fidelity during PCR. As previously mentioned, replication errors of B ≡ S base pairs have largely been attributed to base pairing between the B enol tautomer and T (B-enol ≡ T), with upper bound estimates of this tautomeric equilibrium constant being ≈ 10 ([keto]/[enol]), or 10% in neutral pH water^23,35,47. During PCR, various types of additional interactions could play a major role in either shifting this equilibrium or modulating rates of dTTP extension on template B-enol strands, including interactions with residues in the polymerase active site, stacking interactions from adjacent nucleotides, microenvironment pH, and divalent cation (M²⁺) loaded in polymerase.

We started this fidelity optimization campaign using the previously measured baseline conditions (Taq polymerase, equimolar dNTPs). In an initial condition screen, we performed endpoint-based fidelity measurements (12-16 theoretical cycles, Fig. 3d, Supplementary Table 8 and 9, Supplementary Figs. 14-18) on the same annealed BS template (B1:S1, Supplementary Data 1) varying polymerase (A-family, B-family, and engineered variants), divalent cation (Mn²⁺, Mg²⁺, Co²⁺), buffer pH (7.75-9.25), and buffer additives (betaine, DMSO). In a screen of 10 polymerases (Fig. 3e), we found Q5 had the highest end-point average fidelity (Q5: ${\phi }_{⟨B,S⟩}$ ≈ 96.4%, or 3.6% error rate) compared to Taq polymerase in the same screen (Taq: ${\phi }_{⟨B,S⟩}$ ≈ 87.6%). No clear trends emerged for polymerase family (A vs B) or proofreading activity ( ± 3′→5′ exo). However, Deep Vent polymerase (DV exo+; ${\phi }_{⟨B,S⟩}$≈ 92.1%) outperformed the variant Deep Vent polymerase (DV exo-: ${\phi }_{⟨B,S⟩}$ ≈ 87.7%) suggesting that 3′→5′ exonuclease activity could play a role in improving net fidelity.

The nucleotide identity 3′ to the template UB has previously been shown to significantly impact the relative incorporation efficiency of dSTP opposite template-B by Taq polymerase. This prior work proposed that 3′ neighboring nucleotide could be altering the B keto-enol tautomer equilibrium, with varying degrees of effect (3′-C > 3′-G > 3′-T favoring enol-B)³⁸. However, the investigation was purely kinetic, and replication fidelity was never measured. Based on these prior findings, we measured the influence of sequence context (templates 5′-GBT-3′, 5′-GBC-3′, 5′-GBA-3′, 5′-GBG-3′, and 5′-CBG-3′) on BS replication fidelity for both Taq and Q5 polymerase (Fig. 3f, Supplementary Figs. 19-21). For Taq polymerase, we observed ${\phi }_{⟨B,S⟩}$ trends consistent with previously reported kinetics regarding the adjacent 3′-nt (C > A = G > T). Also consistent with prior kinetic studies, we observed no significant dependence on the tested 5′-nt (G vs C). This result is mechanistically consistent with extension, in which the 5′-nucleotide is flipped out of the stacking arrangement³⁸. The effects of 3′-nt were less pronounced for Q5 replication, with only slightly reduced ${\phi }_{⟨B,S⟩}$ observed for 3′-G.

Some of the largest fidelity improvements in the B ≡ S system have previously been achieved by tuning nucleoside triphosphate ratios in PCR. To systematically evaluate these effects, we performed a screen using Taq polymerase in which the relative amounts of dBTP/dATP and dSTP/dTTP were varied to favor formation of B ≡ S pairs and disfavor B ≡ T mismatches (Fig. 3g, Supplementary Fig. 22). The strongest gains in fidelity were obtained by increasing the dSTP/dTTP ratio, consistent with B ≡ T mismatching as the dominant error pathway. Simultaneous increases to both dSTP/dTTP and dBTP/dATP did not yield significant improvements in fidelity beyond those achieved by elevating dSTP/dTTP alone. Similar improvements were observed with both Taq and Q5 polymerases in a different sequence context (B2:S2; Supplementary Figs. 23 and 24). While significantly improving retention of an error-prone UBP, manipulating nucleotide ratios may also increase the prevalence of UB misincorporations throughout the amplifying template. Analyzing the positional error rate of the standard basecaller suggests elevated UB misincorporation, which we attribute to the depletion of the reduced (50 μM) dATP or dTTP pool at high nucleotide ratios (Supplementary Table 9, Supplementary Figs. 22 and 24).

By combining optimal conditions for polymerase choice, sequence context, and nucleotide composition, we achieved the highest B ≡ S replication fidelity reported to date (Supplementary Table 1, Supplementary Figs. 25–27). Q5 polymerase in the 5′-GBT-3′ sequence context with a 6× dSTP/dTTP ratio produced a log-linear decay corresponding to φ_〈B,S〉 = 98.3 ± 0.2% (95% CI, Fig. 3h), consistent with > 90% B ≡ S retention over a 1000-fold amplification (≈ 10 theoretical cycles). Additional fidelity improvements were observed at higher nucleotide skews, with ${\phi }_{⟨B,S⟩}$ = 99.2 ± 1.5% (95% CI) when using 10× dSTP/dTTP and dBTP/dATP. However, agarose gel electrophoresis and basecaller error rate analysis for these reactions revealed substantial side-product formation and UB misincorporation events (Supplementary Fig. 27d-g), indicating diminishing returns and practical limits on amplification at extreme nucleotide ratios.

Tracing PCR optimization of PZ replication

One of the strengths of this strategy is its generalizability to different UBP systems. A recent study by Wang et al. (2024) reported replication-fidelity optimization for the P ≡ Z base pair. In their work, an enzyme-assisted sequencing strategy was developed to quantify the UBP fraction after amplification using short read (Illumina) sequencing. To reduce replication errors due to Z deprotonation (Fig. 1b), they found that lowering the buffer pH to 8.0 and increasing dPTP concentration improved P ≡ Z replication fidelity to an optimized ${\phi }_{⟨P,Z⟩}$  = 98.68% (value calculated from the reported decay rate: $\left(1-{\delta }_{⟨P,Z⟩}\right)$ = 99.34%)³².

In a single set of experiments, we were able to re-trace this prior fidelity optimization and provide an updated ${\phi }_{⟨P,Z⟩}$ estimate with higher precision and accuracy (Fig. 4a-c). Starting from high pH (8.8) conditions, we amplified P ≡ Z template (P1:Z1, Supplementary Data 1, Supplementary Fig. 28) using Takara Taq polymerase, which was previously found to replicate the PZ base pair with high fidelity and amplification efficiency³². Consistent with the expected error mode, at this high pH we measured a low fidelity, ${\phi }_{⟨P,Z⟩}$ ≈ 94.9%, or a 1 in 20 error rate. At pH 8.0, we observe the error rate decreases by half to a 1 in 40 error (${\phi }_{⟨P,Z⟩}$≈ 97.4%). Finally, optimization of dPTP concentration shows further improvement to ${\phi }_{⟨P,Z⟩}$ = 97.9 ± 0.4% (95% CI). This corresponds to a decay rate of ${\delta }_{⟨P,Z⟩}$ = 98.95%, which is consistent with the previously reported value³². Though the original estimate for ${\phi }_{⟨P,Z⟩}$ is comparable to our own measurement, the uncertainty of endpoint-based measurements is markedly larger and often not quantified (Supplementary Table 1). Since accurate fidelity quantification becomes increasingly challenging as replication error rates decrease, this approach can provide the resolution needed to distinguish small, but consequential, changes in replication fidelity. High precision will inevitably be required to guide the future engineering of high-fidelity UBP systems.

Fig. 4. Quantifying replication fidelity for 6-letter (PZ) and 8-letter (PZBS) PCR.

a Synthetic template containing the PZ UBP is PCR amplified at pH 8.0 or pH 8.8. b UB fractions for P ($f_P$; darker shades) and Z ($f_Z$; lighter shades), following PCR amplification with Takara Taq polymerase at pH 8.0 (orange) or pH 8.8 (gray). UB fractions measured for demultiplexed internal standards (PZ, GC) are shown in orange. c -Log₂-transformed, normalized average UB fractions ($f_{⟨P,Z⟩}$), plotted as mean ± SD of experimental replicates (n = 3). Data series include reaction pH 8.8 (gray) and pH 8.0 (orange), at either standard dPTP concentration (0.2 mM; circles) or optimized (opt) dPTP concentration (0.5 mM; diamonds). WLS linear regression fits are shown using a dashed line. The average replication fidelity, ${\phi }_{⟨P,Z⟩}$ (95% CI; n = 3) for each condition is displayed on the plot. d 8-letter PCR performed on 6-letter DNA (ATGCBP) ssDNA template. e Normalized species fractions for the various 4-letter (gray; $f_{GA}$, $f_{TC}$), 5-letter (blue: $f_{GB}$, $f_{SC}$; orange: $f_{PA}$, $f_{TZ}$), and 6-letter (purple: $f_{PB}$, $f_{SZ}$) DNA molecular species. Darker shades represent sense-strand (+) species, and lighter shades represent antisense-strand (-) species. Mean ± SD is plotted with experimental replicate values overlaid as points (n = 3). Modeled species fractions (Supplementary Equation (41)) are plotted using dashed lines, with the fidelities used to constrain the model (${\phi }_{⟨B,S⟩}$ and ${\phi }_{⟨P,Z⟩}$) included on the plot. f -Log₂-transformed average fraction of 6-letter species ($f_{⟨PB,SZ⟩}$). Mean ± SD is plotted with experimental replicate values overlaid (n = 3). The average joint replication fidelity for the 8-letter species, ${\phi }_{⟨B,S\mid P,Z⟩}$ (95% CI; n = 3) is shown on the plot. Average replication fidelities for each individual UBP, ${\phi }_{⟨B,S⟩}$ and ${\phi }_{⟨P,Z⟩}$  (95% CI; n = 3) are also shown (gray font). The raw data used to generate these plots are tabulated in the Source Data file.

Measuring replication fidelity in 8-letter PCR

At the upper end of UBP complexity are genetic alphabets composed of 8 distinct nucleotides. The Hachimoji (8-letter) DNA system, consisting of the canonical bases (A, T, G, C) and four unnatural bases (B, S, P, Z), was previously shown to support both replication by DNA polymerases and transcription by a T7 RNA polymerase mutant¹¹. A central challenge for such 8-letter systems is the simultaneous optimization of replication fidelity across multiple unnatural base pairs; conditions that favor high-fidelity replication of one UBP may compromise replication fidelity of the other. Prior approaches for measuring UB fraction are unable to measure heterogeneous populations. Nanopore sequencing, by contrast, allows us to observe changes with single-molecule resolution and provides us a general means for tracking the decay, emergence, and interconversion of various species in an 8-letter system.

To explore this capability, we performed 8-letter PCR (Fig. 4d) on a 6-letter starting template (PB1, Supplementary Data 1, Supplementary Figs. 29–36) to generate a Hachimoji DNA-like product. In this implementation, the S nucleotide supplied was the N-nucleoside, 5-Me-isocytosine (Sⁿ), rather than the originally reported C-nucleoside¹¹. We trained four comparative sequencing models (B, S, P, Z) to monitor the mutation of each UBP to a standard DNA counterpart (B → N, S → N, P → G, Z → N) in the PB1 template (Supplementary Tables 5 and 6, Supplementary Fig. 35). Applying these models to both UBP positions (BS and PZ) within an individual read revealed the progressive decay of 8-letter DNA (BSPZ) and appearance of both the 6-letter (BS or PZ) and 4-letter (ATGC-only) products (Fig. 4e). The UB fraction estimates derived from the purine-containing (BP → AG) sense and pyrimidine-containing (SZ → TC) antisense strand showed strong agreement, supporting internal consistency in this approach (Supplementary Fig. 31). Under the tested conditions with Taq polymerase, we estimate an effective fidelity for joint retention of both UBPs to be ${\phi }_{⟨B,S\mid P,Z⟩}$  = 88.8 ± 1.6% (95% CI) per theoretical cycle (Fig. 4f). Average replication fidelities for the individual base pairs were also calculated, with ${\phi }_{⟨B,S⟩}$  = 93.0 ± 0.7% and ${\phi }_{⟨P,Z⟩}$  = 95.6 ± 0.8% per theoretical cycle (95% CI; Supplementary Fig. 30). While ${\phi }_{⟨P,Z⟩}$ was consistent between PCR reactions containing six (ATGCPZ) or eight (ATGCBSPZ) nucleoside triphosphates, ${\phi }_{⟨B,S⟩}$ was reduced by ≈ 2% upon the addition of dPTP and dZTP (Supplementary Fig. 33). Analysis of the canonical basecalls for reads classified as N by mutation-agnostic comparative models (BN2, SN2, ZN1; Supplementary Table 5) does not suggest the presence of DNA transversions indicative of purine-purine (B ≡ P) UB mismatches during the initial extension of template PB1 (Supplementary Fig. 33)⁴⁸. Using Takara Taq polymerase for 8-letter PCR, we observed consistent ${\phi }_{⟨B,S⟩}$ (93.0 ± 2.4%) and improved ${\phi }_{⟨P,Z⟩}$ (96.8 ± 0.5%), resulting in an increased average joint fidelity of ${\phi }_{⟨B,S\mid P,Z⟩}$  = 90.4 ± 2.4% (95% CI, Supplementary Fig. 32c). Although the PCR conditions were not further optimized for maximum fidelity, these results demonstrate that position-resolved basecalling can quantitatively trace decay pathways for multiple molecular species, providing a practical framework to guide future analysis and optimization of increasingly complex expanded-alphabet systems.

Distinguishing between error modes of the hydrophobic DsPx pair

Hydrophobic UBPs exhibit among the highest replication fidelities for expanded genetic alphabets. For example, prior works have reported replication fidelities for hydrophobic bases > 99.9% retention per cycle in PCR experiments (Supplementary Table 1)^15,16. Despite their high fidelity, hydrophobic UBPs are associated with a wider diversity of replication error modes^29,40,49. In particular, several hydrophobic pairs display marked sensitivity to local sequence context. For the DsPx pair, both the replication fidelity and amplification efficiency have been shown to depend on the 5′ and 3′ flanking nucleotides, with reduced fidelity and/or amplification efficiency reported for purine-rich contexts, such as 5′-Pu-Ds-Pu-3′ (Pu = Purine)^15,16,31. In addition to UB → DNA transversions, hydrophobic UBPs have been reported to self-pair (e.g., Ds:Ds, rate unknown), leading to inversion-type errors in which the unnatural base pair is retained but the strand is inverted. Similar types of inversion errors have been observed in another hydrophobic UBP system (dNaM:dTPT3), though inversion rates were not quantified⁴⁰. One prior challenge is that quantifying these inversion-type errors requires accurate identification of strand-specific products, which our strategy can directly address.

In our experimental system for DsPx, we used Px = Diol-Px, a structural variant reported to display similar or higher replication fidelity than the originally-reported NH₂-hx-Px¹². Due to the multiple possible error modes in the Ds:Diol-Px system, we developed a multiclassification approach to discriminate between transversions, inversions, and correct incorporations by combining the outputs of three binary classification models. First, we trained generalized Ds → N and Diol-Px → N models to capture all standard DNA transversion routes by sampling all possible canonical bases at the UB position (Models DN1/2, XN1/2, Supplementary Tables 5 and 6). To classify inversion events, we trained Ds → Diol-Px and Diol-Px → Ds models using DNA sequences in which the UBP was inverted at the focus position (Models XD1/2, DX1/2). Finally, we trained additional Ds → N and Diol-Px → N models against the inverted sequences (Models I-DN1/2, I-XN1/2). All three classes of models demonstrated high accuracy in training and benchmarking (Supplementary Tables 5 and 6). To obtain strand-specific measurements of both UB → DNA transversions and UBP inversions, we enumerate the three model outputs corresponding to each read using predefined mapping rules defined in Supplementary Table 10. Per-class multiclassification benchmarking statistics are shown in Supplementary Table 11 and Supplementary Fig. 37.

We PCR-amplified ssDNA templates containing Ds embedded in previously-reported high-fidelity (D1, 5′-CDsT-3′) and low-fidelity (D2, 5′-GDsA-3′) sequence contexts (Fig. 5a, Supplementary Data 1, Supplementary Fig. 38)¹⁵. Applying our multiclassification logic, we first estimate the average UB → DNA transversion fidelity using the inversion-agnostic UB fraction, defined as the fraction of reads in which the unnatural base was either retained or inverted. This allows us to calculate the average transversion fidelity, ${\phi }_{⟨Ds,Px⟩}^{\mathrm{trnv}}$, decoupled from inversion events. To infer the UBP inversion error terms, we fit a state-space model to the residual UBP decay (Fig. 5b, Supplementary Method 4, Supplementary Equations (47-50)). Consistent with prior reports, we observe high retention of DsPx pair in the high-fidelity context and a more rapid decay in the low-fidelity context (Fig. 5c-d). Notably, UBP inversion events are negligible in the high-fidelity context, whereas in the low-fidelity context, UBP inversions are the dominant decay product.

Fig. 5. Quantifying replication fidelity and strand inversion for the hydrophobic Ds:Diol-Px base pair in PCR.

a Synthetic ssDNA template containing the Ds base is PCR amplified using AccuPrime Pfx polymerase, resulting in products that may contain DNA transversions or UBP inversions. b Schematic of the DsPx (Px = Diol-Px) PCR model (Supplementary Equation (46)), with arrows representing replication events drawn from the template to the inserted base. Included are UB → N transversion errors (gray), UBP inversion errors (red), and correct UB incorporations (black). Epsilon ($\epsilon$) is the error rate and mu ($\mu$) is the correct UB incorporation rate, with the superscript sign denoting the template strand ( + for sense, - for antisense). Normalized fraction of Ds ($f_{Ds}$), Px ($f_{Px}$), and N ($f_N$; N = A,T,G,C) located on the sense (+, lighter shades) or antisense (-, darker shades) strands are shown following PCR amplification of ssDNA templates c D1 or d D2. Retained UBs (Sense: Ds; Antisense: Px) are shown in blue, inverted UBs (Sense: Px; Antisense: Ds) are shown in red, and DNA transversions (N; either strand) are shown in gray. On each plot, the mean value ± SD is plotted with experimental replicate values overlaid as points (n = 3). e -Log₂-linear transform of the fraction of UB-containing (inversion-agnostic) species ($f_{Ds}$ + $f_{Px}$), averaged across strands ($f_{⟨Ds+Px,Px+Ds⟩}$) for templates D1 (blue) and D2 (black). The mean value ± SD of experimental replicates is plotted (n = 3). The DNA transversion fidelities (${\phi }_{⟨Ds,Px⟩}^{\mathrm{trnv}}$) for PCR amplification of templates D1 and D2 are shown on the plot (95% CI). f Fraction Ds ($f_{Ds}$) relative to the fraction of the UB-containing species ($f_{Ds}$ + $f_{Px}$) on sense (+, black) and antisense (-, red) strands for template D2. The mean value ± SD is plotted with experimental replicate values overlaid as points (n = 3). The dashed lines represent the nonlinear fit of a reduced (${\epsilon }_{YY}^{+}={\epsilon }_{XX}^{-}=0$) state-transition model for the effective inversion rate (${\epsilon }_{inv}={\epsilon }_{XX}^{+}={\epsilon }_{YY}^{-}$) on the sense (black) and antisense (red) strands. The root-mean-square error (RMSE) of the nonlinear model fit is shown. Plotted values are the mean of experimental triplicates ± standard deviation (n = 3). The raw data used to generate each plot are tabulated in the Source Data file.

Fitting observations of the total fractional UBP loss, we measured an average transversion fidelity of ${\phi }_{⟨Ds,Px⟩}^{trnv}$ = 99.3 ± 0.3% (95% CI) for the high-fidelity (D1, 5′-CDsT-3′) context and ${\phi }_{⟨Ds,Px⟩}^{trnv}$ = 97.4 ± 1.1% (95% CI) for the low-fidelity context (D2, 5′-GDsA-3′) (Fig. 5e). These fidelity values correspond to UBP decay rates of ${\delta }_{⟨Ds,Px⟩}^{trnv}$ = 99.7% for the high-fidelity context and ${\delta }_{⟨Ds,Px⟩}^{trnv}$ = 98.7% for the low-fidelity context, which are consistent with previously-reported values under similar PCR conditions (Supplementary Table 1)¹⁵.

Fitting observations to an unconstrained state-transition model (Fig. 5b) revealed that inversion errors are context-dependent, resulting in a directional shift from the inversion-prone context (D2, 5′-GDsA-3′) to a more stable, pyrimidine-rich context (5′-TDsC-3′). To quantify this inversion rate, we parameterized a four-state model using an effective inversion error rate (${\epsilon }_{\mathrm{inv}}={\epsilon }_{XX}^{+}={\epsilon }_{YY}^{-}$) and directionality constraints (${\epsilon }_{XX}^{-}={\epsilon }_{YY}^{+}=0$), yielding an effective inversion rate of ${\epsilon }_{inv}$ = 4.1 ± 0.1% (95% CI) per theoretical cycle (Fig. 5f). This effective error rate is the average of the strand-specific inversion rates (${ϵ}_{XX}^{+}$ and ${ϵ}_{YY}^{-}$), which are coupled in PCR and cannot be independently resolved. Modeled as an inversion-type decay of dsDNA species (i.e., Ds:Px → Px:Ds), we estimate an inversion rate of ${\delta }_{\mathrm{inv}}$ = 2.0% per theoretical cycle. Taken together, these findings demonstrate an approach to quantitatively decompose multiple error pathways, providing a mechanistically resolved estimate of hydrophobic UBP replication fidelity. Understanding replication error modes at this level of detail will help clarify the stability of these systems and guide the discovery or engineering of polymerases that avoid the same classes of errors.

Discussion

Despite substantial progress, replication of expanded genetic alphabets remains an active area of investigation, with current state-of-the-art systems still far from matching the fidelity of the canonical DNA alphabet. Without selective pressure, expanded alphabet bases are progressively lost over successive replication cycles. This progressive genetic erasure provides an intrinsic form of containment, operating both temporally, through loss across successive generations as a function of replication fidelity, and spatially, through dependence on access to engineered polymerases and synthetic nucleotide building blocks. While this intrinsic containment increases the biosafety of the controlled use of biological systems with expanded DNA alphabets, the use of these systems will simultaneously raise biosafety concerns, particularly regarding potential escape. While these are valid concerns in the context of engineering DNA, our work shows that the technology offers enhanced biosafety features, both in controlled settings and in the case of escape. It should be noted that either in the event of escape or in the absence of unnatural building blocks, the information encoded by UBPs will ultimately be erased. This intrinsically obviates the requirement of a precautionary approach and mitigates potential ethical concerns regarding broader application. However, as high-throughput optimization strategies, such as the approach described here, further improve the efficiency of UBP integration into biological systems, it will become increasingly important to understand the long-term behavior, stability, and evolutionary persistence of expanded genetic alphabets.

Our work demonstrates that post hoc analysis of single-molecule nanopore reads can faithfully capture the fractional loss of structurally diverse UBP species during replication. Under a set of assumptions, replication fidelity can be directly measured from the observed transitions between UB and DNA states across successive replication cycles. For the broader field, the presented strategy enables high-throughput measurement of replication fidelity, systematic screening of reaction space, evaluation of polymerase variants, and rapid optimization of replication conditions for newly synthesized nucleotide structures. Additionally, since observations are strand-resolved, replication fidelity can be quantified with greater robustness and sensitivity while allowing direct decomposition of replication error modes. As expanded genetic systems approach the fidelity thresholds required for reliable amplification and information storage, such single-molecule, high-throughput strategies provide a common quantitative framework for guiding chemical and enzymatic optimization across diverse nucleotide chemistries and replication systems.

More broadly, this work illustrates how quantitative observables can be extracted from single-molecule sequencing data using widely accessible, commercial platforms. While replication fidelity is a critical metric for expanded genetic alphabets, the same measurement paradigm applies to a wide range of molecular processes in which heterogeneity, rare events, and context dependence are central. Important processes, such as installation/removal of epigenetic modifications in disease models or chemically induced damage of DNA from environmental exposures, will not only be observable but also quantifiable. As single-molecule sequencing technologies continue to mature, such approaches are expected to extend to a wider range of biochemical and biophysical measurements that are poorly captured by ensemble averages.

Methods

Commercial materials

Agarose (0710-500 G; electrophoresis grade) and AMPure XP purification beads (NC9959336) were purchased from Thermo Fisher Scientific (Waltham, MA). Tris base (10708976001), 5 M betaine solution (B0300-1VL), 6 N hydrochloric acid (1430071000), GelGreen (SCT124), premixed TBE buffer (10×, 11666703001), potassium chloride (P3911-500G), potassium acetate (P1190-100G), bovine serum albumin (A7030-10G), dimethyl sulfoxide (DMSO; D8418-250ML), magnesium chloride hexahydrate (63068-250 G), TritonTM X-100 (X100-500ML), and sodium chloride (S3014-5KG) were purchased from Sigma-Aldrich (St. Louis, MO). Restriction enzymes, Exo III (M0206L), thermolabile Exo I (M0568L), Exo I (M0293L), Exo VIII (truncated; M0545S), NEBNext Ultra^TM II End Repair/dA-Tailing Module (E7546S), NEBNext Ultra^TM II Ligation Module (E7595S), Salt T4 DNA Ligase (M0467S), 50 bp DNA ladder (N3236S), and 2′-Deoxynucleoside triphosphate solution mix (dNTP; N = A, T, G, C; N0446S) and 2′-Deoxynucleoside triphosphate solution set (dATP, dTTP, dGTP, dCTP; N0446S) were purchased from New England Biolabs (Ipswich, MA). GeneRuler 1 kb plus DNA ladder (SM1331) was purchased from Invitrogen (Carlsbad, CA). Thermostable polymerases Q5 (M0491L), Phusion (M0530S), DeepVent (M0258S), DeepVent (exo-) (M0259S), and OneTaq (M0480S) were purchased from New England Biolabs (Ipswich, MA). Thermostable polymerases Taq (50-103-7174), Titanium Taq (NC9806143), AccuPrime Pfx (12344024), Tth (NC1894531), SD (501685638), Pfu (501036614), KlenTaq1 (NC9707348), and Takara Taq (50443948) were purchased from Thermo Fisher Scientific (Waltham, MA). Deoxyoligonucleotide (oligo) sequences are included in Supplementary Data 1 and Supplementary Tables 2 and 4. Oligos containing only standard bases, in addition to oligos B1-5 (/iisodG/) and oligos S1-5 (/iMe-isodC/) were purchased from Integrated DNA Technologies (IDT; Coralville, IA). Oligos P1, Z1, and PB1 were purchased from Firebird Biomolecular Sciences LLC (Alachua, FL), and oligos D1-4 were purchased from Xenolis Pte. Ltd (Singapore). Upon receipt, all oligos were resuspended in elution buffer (10 mM Tris-HCl, pH = 8.2) at a stock concentration of 100 μM and stored at either 4 °C for immediate usage or −20 °C for long-term storage. Xeno nucleoside triphosphates dPTP, dZTP, dBTP (dPTP-201, dZTP-101, dBTP-301P) were purchased from FireBird Biomolecular Sciences LLC (Alachua, FL). Xeno nucleoside triphosphate dSⁿTP (C-001) was purchased from TriLink BioTechnologies (San Diego, CA). Xeno nucleoside triphosphates dDsTP and dDiol-dPxTP (XTP-0100, XTP-0101) were purchased from Xenolis Pte. Ltd (Singapore). DNA purification kits (ZD4034, ZD7011) were purchased from Zymo Research (Irvine, CA). MinION sequencing devices (MIN-101B), Flongle Adapters, Flongle Flow Cells (FLO-FLG114), Ligation Sequencing kits (SQK-LSK114), and Flongle Sequencing Expansion kits (EXP-FSE002) were purchased from Oxford Nanopore Technologies (ONT; Oxford, United Kingdom). Unless otherwise specified, other commodity chemicals were purchased from major domestic distributors (Sigma-Aldrich, St. Louis, MO; Thermo Fisher Scientific, Waltham, MA).

Preparation of DNA for model training and benchmarking

Canonical and UB-containing DNA oligos used to train comparative basecalling models were designed to differ only at the UB position. For a given replication error mode, UB position variations were selected to include the expected mutation. For unknown error modes, the UB position was replaced with a randomized base (A, T, G, or C). Synthetic DNA sequences used to train comparative basecalling models are tabulated in Supplementary Data 1. All training sequencing data were generated using Flongle flow cells from Oxford Nanopore Technologies (R10.4.1).

To prepare training sequences for B and S (B: isoguanine; S: 5-Me-isocytosine), complementary 90-mer oligos containing the UB (B1-B5, S1-S5) were combined in an equimolar ratio with 100 mM NaCl and annealed by heating to 95 °C and slowly cooling to 20 °C (0.1 °C /s) using a thermocycler. The annealed oligos were then purified using the Zymo DNA Clean & Concentrator kit and prepared for nanopore sequencing as described in the “Nanopore sequencing sample preparation and data acquisition” subsection. Corresponding canonical training sequences containing only standard DNA bases were generated by PCR amplification of oligos containing a standard base at the UB position (BA1-5, SA1-5, BN2, SN2) using a high-fidelity polymerase (Phusion Polymerase in HF Buffer or Q5 polymerase in Q5 reaction buffer) at a dNTP concentration of 200 μM. Forward and reverse PCR primers contained 24-mer barcodes (Supplementary Table 2 and 3), enabling multiplexing of multiple canonical training sequences on a single flow cell. Before training, multiplexed reads were demultiplexed using CutAdapt (v: 4.9).

To prepare training sequences for P and Z (P: (2-amino-8-(1′-β-d-2′-deoxyribofuranosyl); Z: (6-amino-5-nitro-3-(1′-β-d-2′-deoxyribofuranosyl)−2(1H)pyridine)), complementary 71-mer oligos containing P and Z (P1, Z1) were annealed and then lengthened by TA ligation with barcoded DNA hairpin sequences (Supplementary Table 4, Supplementary Fig. 8), as described in the “Preparation of synthetic DNA controls” subsection. The ligation products were then digested with ScaI-HF to remove the outer hairpins, purified by AMPure XP, and prepared for sequencing according to standard methods. Canonical DNA sequences containing the G ≡ C pair substituting the P ≡ Z position were prepared by PCR amplification of identical 71-mer oligos containing a G at the P position (PG1), and a C at the Z position (ZG1) using a high-fidelity DNA polymerase.

For 8-letter (BSPZ) training, sequence PB1 (containing P and B, Supplementary Data 1) was designed to maintain compatibility with previously trained models and minimize potential signal interference between the two unnatural bases. For the R10.4.1 flow cell chemistry (ONT), the surrounding 9 bases can have a measurable effect on the measured current signal. Therefore, the $\pm$10 bases flanking B and P in sequence PB1 were chosen to match the flanking regions in sequences B2 and P1, respectively; the two UB positions are 20 nt apart. To prepare 8-letter training sequences, the ssDNA template containing P and B (PB1) was annealed with primer R_14 (Supplementary Table 2) and extended using Q5 polymerase at 72 °C for 15 min in Q5 Reaction Buffer (1×). dNTP stocks were added at the following final concentrations: dATP (0.2 mM), dGTP (0.2 mM), dCTP (0.2 mM), dTTP (0.2 mM), dSTP (0.6 mM), and dZTP (0.2 mM) during the extension reaction.

To prepare training sequences for the Ds:Diol-Px pair, 60-mer ssDNA templates containing Ds (D1-4) were annealed with a complementary primer (D1-2: Ext_D1-2_30; D3-4: Ext_D3-4_25; Supplementary Table 2). Primer extensions were performed using AccuPrime Pfx polymerase at 68 °C for 60 min. Deoxynucleoside triphosphate stocks were added at the following final concentrations: dATP (0.4 mM), dGTP (0.4 mM), dCTP (0.4 mM), dTTP (0.4 mM), and dDiol-PxTP (0.05 mM).

Nanopore sequencing sample preparation and data acquisition

Samples were prepared for nanopore sequencing using the Ligation Sequencing Kit V14 from Oxford Nanopore Technologies. 500 ng of DNA was prepared for adapter ligation using the NEBNext Ultra II End Repair/dA-Tailing module, followed by an AMPure XP cleanup using a 1.8-3.0× bead ratio, using higher ratios for shorter sequences. Beads were washed twice using freshly prepared 70% ethanol and clean samples were ligated with ligation adapters (LA) in ligation buffer (LNB) using either Quick T4 DNA Ligase (NEB) or Salt T4 DNA Ligase (NEB). Ligations were purified using AMPure XP and washed twice with the ONT short fragment buffer (SFB) prior to elution using ONT elution buffer (EB). Flongle flow cells were flushed with flow cell flush (FCF) containing flow cell tether (FCT). DNA prep quality was assessed by A₂₆₀ before loading flow cell with library beads (LIB), sequencing buffer (SB) and the full DNA sample. Data acquisition for nanopore sequencing was performed using MinKNOW (v:23.11.7, ONT).

Model training, basecalling, and classification

Comparative UB basecalling models were trained using sequencing data generated from prepared sequences (Supplementary Data 1). Raw nanopore sequencing data (.POD5 file format) were first basecalled using the Dorado basecaller (ONT, v: 0.8.0) using a high accuracy model (hac; dna_r10.4.1_e8.2_400bps_hac@v5.0.0) with a q-score filtering threshold (5) and move table output. Output sequences were aligned to the canonical base-containing reference using minimap2 (v: 2.17-r941) with the following parameters: -y, -ax map-ont, -k8, -w5, and -s 80. The UB position was specified using a BED file, which was used to extract signal training chunks using Remora (ONT, v: 2.1.3) dataset prepare command. Separate chunk files were generated for modified and canonical data, then merged into a balanced training set. All models were trained using remora model train with the following parameters unless otherwise noted: kmer context = (4,4); chunk context = (50 50), reference anchor = True. The default REMORA PyTorch model (LSTM with reference) was used for training. Training was allowed to proceed until convergence, using a default minimum of 5 epochs. 20% of the training reads were held for internal validation. Training set sizes and performance statistics for each model are shown in Supplementary Table 5.

Model testing and benchmarking

Models were tested using raw data (.POD5 files) withheld from model training and validation. Individual .POD5 files for UB-containing or canonical base sequences were basecalled first using Dorado, then classified using a comparative basecalling model as input to Remora. Results from output per-read modifications files for each aligned sequence were analyzed to calculate true positive (TP), true negative (TN), false positive (FP), and false negative (FN) counts for 10,000 basecalled reads from each dataset. In certain cases, this threshold was reduced if the testing dataset size was smaller than 10,000 reads. Equations (1–4) were used for the benchmarking calculations tabulated in Supplementary Table 6.

$$\text{Recall }\left(\text{TPR}\right)=\frac{\text{TP}}{\text{TP}+\text{FN}}$$ 1

$$\text{Specificity }\left(\text{TNR}\right)=\frac{\text{TN}}{\text{TN}+\text{FP}}$$ 2

$$\text{Precision}=\frac{\text{TP}}{\text{TP}+\text{FP}}$$ 3

$$\text{F1 Score}=2\cdot \frac{\text{Precision}\cdot \text{Recall}}{\text{Precision}+\text{Recall}}$$ 4

To benchmark DsPx multiclassification models, final multiclass predictions were generated by applying a rule-based decision mapping (Supplementary Table 10) to the outputs of three independent binary classifiers. Each read was assigned to one of three outcome classes: UB retained, UB inverted, or DNA transversion. Benchmarking was performed after this final mapping step, in addition to the individual binary classifier outputs alone. Reads were randomly sampled from each ground-truth dataset to ensure equal numbers of reads per class. Per-class recall, specificity, precision, and F1 score were then calculated from the resulting multiclass confusion matrix using a one-vs-rest framework. Ambiguous states arising from conflicting classifier outputs were rare but assigned to the DNA transversion class according to the predefined mapping rules. Multiclass benchmarking statistics are tabulated in Supplementary Table 11.

To validate a model’s quantitative response on mixed datasets, raw reads (.POD5) with a known ground truth were mixed in predefined ratios, and classification models were used to estimate the UB fraction. A graphical overview of this process is shown in Supplementary Fig. 6a. Two 90-bp synthetic DNA constructs, identical except at the UB position (BS: B1:S1 or AT: BA1:ST1), were sequenced separately. Raw sequencing reads (.POD5 format) were randomly sampled and merged using the pod5 package at defined B/A and S/T ratios, ranging from 0 to 1 in increments of 0.1. Each of these merged .POD5 files (200,000 total reads) was basecalled, aligned, and classified using comparative basecalling models BA1 and ST1 (Supplementary Table 5).

Purification, preparation, and nanopore sequencing of PCR samples

After thermocycling, completed PCR reactions were held at 4 °C then stored at −20 °C until purification. To assess reaction completion and verify product length, 5 μL of each individual replicate was analyzed by gel electrophoresis (1× TBE buffer, 2% agarose, 1× GelGreen stain) and compared against a 50 bp ladder (NEB). After gel verification, barcoded replicates were pooled (15 μL each) and purified using the Zymo DNA Clean & Concentrator kit. Pooled samples were eluted in 45 μL of Milli-Q water. The concentration of each pooled PCR product was measured at A₂₆₀ using a SpectraMax-QuickDrop Spectrophotometer (Molecular Devices, San Jose, CA, USA). For sequencing, PCR products were pooled equivalently by mass with appropriate synthetic internal control sequences and prepared according to standard procedures. Pooled reaction products were sequenced using Flongle flow cells (Oxford Nanopore Technologies) with R10.4.1 flow cell chemistry. DNA preparation quality was assessed by A₂₆₀ before loading the flow cell. All reads remaining after filtering, alignment, and demultiplexing were used for analysis.

Filtering, demultiplexing, and analysis for PCR sequencing datasets

Nanopore reads were demultiplexed by matching both forward and reverse 24-mer barcode pairs to unique samples. The Natural Barcodes (NB) set from ONT was used (Supplementary Table 3). For each barcode pair, specified forward-reverse and reverse-forward barcode combinations were generated and searched using CutAdapt (v: 4.9) with a minimum overlap requirement of 14 nt and an error tolerance of 20%. For the expected 150 nt product, read lengths were filtered to 120–200 nt. Length filters were adjusted proportionally for shorter products. Reads matching either orientation were combined and deduplicated to form a single .FASTQ file per barcode pair. Next, unique read IDs were extracted from each .FASTQ file and annotated with the corresponding barcode pair. Reads that appeared in multiple barcode files were removed from all files. The resulting read ID list was merged with the per-read modification predictions from Remora (output from remora validate), linking classification results to barcode assignments. The number of reads predicted as modified (class_pred = 1) or unmodified (class_pred = 0) for each barcode pair was written to a summary file for data analysis.

Preparation of synthetic DNA controls

Barcoded, UB-containing synthetic controls were prepared for each template and added to the PCR-amplified sequencing library to serve as internal standards for basecalling and normalization (Supplementary Method 5). For sequences B1-5:S1-5 and P1:Z1, synthetic controls were prepared by TA ligation of annealed oligos to barcoded DNA hairpin sequences (Supplementary Fig. 8). For sequences PB1 and D1-4, synthetic controls were prepared using primer extension as described in the “Preparation of DNA for model training and benchmarking” subsection.

DNA oligos designed to form hairpins (Supplementary Table 4) were ordered from IDT with a 5’-phosphorylation and a 3’-T overhang protected by a phosphorothioate bond. These hairpins contain a 24-mer barcode sequence (Supplementary Table 3) in the annealed region and a ScaI restriction site near the hairpins to generate blunt ends before sequencing. Annealed UB-containing oligos were 5’-phosphorylated and 3’-A-tailed using the NEBNext Ultra II End Repair/dA-tailing Module. End-prepped DNA was immediately ligated with T-tailed hairpins using the NEBNext Ultra II Ligation Module. Ligation products were purified using AMPure XP beads at a 1.8× bead-to-sample ratio. To generate blunt-end products for sequencing, the purified ligation products were digested with ScaI-HF at 37 °C for 3 h and an additional AMPure XP cleanup was performed.

PCR amplification of the BS base pair for fidelity quantification

Complementary oligos containing B or S (B1-B5 and S1-S5, Supplementary Data 1) were combined in a 1:1 molar ratio. A 10-fold serial dilution was prepared 10 μM to 10 pM to serve as templates for PCR reactions. For standard PCR with known template concentration, 1 μL of template was transferred to 25 μL PCR reactions to achieve the desired molar primer-to-template ratio. Reactions contained 0.2 μM of each forward and reverse barcoded PCR primer (Supplementary Table 2). For multi-step PCR, the unpurified PCR product mix from a completed reaction was diluted 1000× into the subsequent PCR reaction as DNA template. Polymerases and buffer were prepared as a 1× mixture. Thermopol Buffer was used for Taq polymerase, and Q5 reaction buffer was used for Q5 polymerase. Nucleoside triphosphates dATP, dGTP, dTTP, dCTP, dBTP, and dSTP were added to the reaction mix at a final concentration of 200 μM unless otherwise specified. PCR thermal cycler conditions were as follows: 2 min at 92 °C followed by 40 cycles of 92 °C for 15 s, 58 °C for 15 s, and 72 °C for 10 s with a final extension at 72 °C for 1 min. Samples were held at 4 °C upon PCR program completion and moved to −20 °C for storage.

PCR amplification of BS for pH, divalent cation, and supplemental additive screening

A 10× concentrated stock of Thermopol buffer without MgSO₄ was prepared, consisting of 100 mM KCl, 100 mM (NH₄)₂SO₄, 200 mM Tris, and 0.1% Triton X-100 (v/v). To screen the buffer pH, buffer aliquots were brought to pH 7.75, 8.00, 8.25, 8.50, 8.80, 9.00, & 9.25 using 1 M HCl. 25 μL PCR reactions were prepared using these buffers (1×) with Taq polymerase (1 U per 25 μL reaction), F/R primers (0.2 μM), dNTP (200 μM), dBTP (200 μM), dSTP (200 μM), and MgSO₄ (2 mM). Annealed template B1:S1 (Supplementary Data 1) was added at 4 pg/μL (11.4 theoretical cycles).

To screen divalent cation supplementation, PCR reactions were supplemented with CoCl₂ or MnSO₄ at final concentrations of either 0.2 mM or 0.6 mM, with and without additional MgSO₄ (0 mM or 2 mM). PCR reaction mixes contained Thermopol buffer (1×, pH 8.80), prepared as described above, Taq polymerase (1 U per 25 μL reaction), F/R primers (0.2 μM), dNTP (200 μM), dBTP (200 μM), and dSTP (200 μM). Annealed template B1:S1 was added at 4 pg/μL (11.4 theoretical cycles).

To screen PCR additive supplementation, DMSO (2-10%) or betaine (100-500 mM) was added to PCR reaction mixes containing Thermopol buffer (1×, pH 8.80) prepared as above, Taq polymerase (1 U per 25 μL reaction), F/R primers (0.2 μM), dNTP (200 μM), dBTP (200 μM), dSTP (200 μM), and MgSO₄ (2 mM). Annealed template B1:S1 (Supplementary Data 1) was added at 4 pg/μL (11.4 theoretical cycles).

The experiments described above were completed with an internal reference condition using Taq polymerase and standard Thermopol buffer (pH = 8.80, 2 mM MgSO₄, no supplement). PCR thermal cycler conditions were as follows: 2 min at 92 °C followed by 40 cycles of 92 °C for 15 s, 58 °C for 15 s, and 72 °C for 10 s with a final extension at 72 °C for 1 min. Samples were held at 4 °C upon PCR program completion and then moved to −20 °C for storage.

PCR amplification of the BS pair for polymerase screening

PCR conditions for each polymerase were first screened using buffers recommended by the supplier, including the recommended supplementation of Mg²⁺. For improved amplification performance with select polymerases, the Mg²⁺ concentration was increased. Buffers and Mg²⁺ concentrations for each polymerase screened are listed in Supplementary Table 8. PCR was performed at two template concentrations to verify the expected loss as a function of theoretical cycles. 25 µL PCR reactions were prepared containing 1× polymerase buffer, polymerase (1 U per 25 µL reaction), dNTPs (200 μM each dNTP, dBTP, and dSTP).

Fidelity was calculated using endpoint UB fraction measurements, which were pooled and averaged across the two template concentrations (n = 6). For Phusion, Deep Vent, Tth, Pfu, Deep Vent (exo-), and SD polymerases, templates B1 & S1 (Supplementary Data 1) were annealed and added at 40 pg/μL and 0.4 pg/uL, corresponding to 8.1 and 14.8 theoretical cycles, respectively. For KlenTaq, Phusion, and AccuPrime Pfx, template B1 & S1 were added at equimolar concentrations (400 pM and 4 pM), corresponding to 9.0 and 15.6 theoretical cycles. Each experimental batch was completed with an internal reference condition performed using Taq polymerase in Thermopol buffer. PCR thermal cycler conditions were as follows: 2 min at 92 °C followed by 40 cycles of 92 °C for 15 s, 58 °C for 15 s, and 72 °C for 10 s with a final extension at 72 °C for 1 min. Samples were held at 4 °C upon PCR program completion and then moved to −20 °C for storage.

PCR amplification of the BS pair for nucleotide optimization

25 μL reactions were prepared containing equimolar amounts of templates B1:S1 or B2:S2 (Supplementary Data 1). Nucleoside triphosphates were added at final concentrations from 0.05 mM to 0.3 mM to achieve desired nucleotide ratios, as listed in Supplementary Table 9. PCR reactions contained either Taq polymerase (1 U per 25 μL) with Thermopol Buffer (1×) or Q5 polymerase (1 U per 25 μL reaction) with Q5 Reaction Buffer (1×). Primers were added to a final concentration of 0.2 μM. For screening experiments where a single endpoint fidelity was measured, DNA template was added to a final concentration of 4 pM (15.6 theoretical cycles). An internal reference condition (200 μM dNTP, dSTP, dBTP) was included to account for batch effects in experiments. PCR thermal cycler conditions were as follows: 2 min at 92 °C, followed by 40 cycles of 92 °C for 15 s, 58 °C for 15 s, and 72 °C for 10 s, with a final extension at 72 °C for 1 min. Samples were held at 4 °C upon PCR program completion and then moved to −20 °C for storage.

Reproducing PCR amplification of the BS pair from literature

The PCR buffer described in Johnson et al. (2004)³⁹ and Karalkar et al. (2016)³⁶ consists of 10 mM Tris-HCl, 40 mM potassium acetate, 2 mM magnesium chloride, and 0.1 mg/mL bovine serum albumin at pH 9.1. A 5× concentrated stock of this buffer was prepared and brought to pH 9.1 using 1 M HCl. To reproduce experiments in Johnson et al. (2004), reactions contained the buffer described above (1×) with Titanium Taq (1 U), dNTPs (25 μM), dBTP (25 μM), dSTP (50 μM), 0.2 μM F/R primers, and equimolar amounts of complementary DNA templates B5 and S5 (200 pM, 20 pM, and 2 pM, 0.2 pM, Supplementary Data 1). To reproduce experiments in Karalkar et al. (2016), reactions contained the buffer described above (1×) with Titanium Taq (1 U), dNTPs (100 μM), dBTP (100 μM), dSTP (100 μM), 0.02 μM F/R primers, and equimolar amounts of complementary templates B2 and S2 (2 nM, 200 pM, 20 pM, and 2 pM) For each set of experiments, thermal cycling conditions used were identical to those reported by the authors.

PCR amplification of the PZ base pair

10× PCR buffers were prepared containing 100 mM Tris-HCl, 500 mM KCl, and 15 mM MgCl₂. The pH was adjusted with 1 M HCl to pH 8.80 and 8.00. PCR reactions contained prepared buffer (1×), Takara Taq polymerase (1.25 U per 25 μL reaction), and deoxynucleoside triphosphates at the following final concentrations: dATP (100 μM), dGTP (100 μM), dCTP (200 μM), dTTP (100 μM), dZTP (100 μM), and dPTP (200 μM). For PCR reactions utilizing optimized dPTP concentrations, dPTP was increased to 500 μM. Complementary oligos containing P and Z (P1 & Z1, Supplementary Data 1) were combined in an equimolar molar ratio and diluted to achieve final template concentrations of 400 pM, 40 pM, 4 pM, and 0.4 pM. PCR reactions contained 0.2 μM of each barcoded PCR primer (Supplementary Table 2). Thermal cycler conditions were 2 min at 92 °C, followed by 30 cycles of 90 °C for 15 s, 58 °C for 15 s, and 72 °C for 60 s, with a final extension of 10 min at 72 °C. Samples were held at 4 °C upon PCR program completion and then moved to −20 °C for storage.

8-letter PCR amplification

For 8-letter PCR with Taq polymerase, reaction mixes were prepared using NEB Thermopol Buffer (1×) and Taq polymerase (1 U per 25 μL reaction). For 8-letter PCR with Takara Taq polymerase, reactions contained 10 mM Tris-HCl (pH 8.80), 50 mM KCl, 1.5 mM MgCl₂, and Takara Taq polymerase (1.25 U per 25 μL reaction). All PCR reactions contained nucleotides at the following final concentrations: dATP (200 μM), dCTP (200 μM), dGTP (100 μM), dTTP (100 μM), dBTP (200 μM), dSTP (200 μM), dZTP (200 μM), and dPTP (200 μM). F/R barcoded PCR primers were added at 0.2 μM (Supplementary Table 2). ssDNA template PB1 (or P1; Supplementary Fig. 34) was added at the following concentrations: 4 nM, 400 pM, 40 pM, and 4 pM. Thermal cycling conditions for all experiments described above were 2 min at 92 °C, followed by 30 cycles of 90 °C for 15 s, 58 °C for 15 s, and 72 °C for 60 s, with a final extension of 10 min at 72 °C. Samples were held at 4 °C upon PCR program completion and then moved to −20 °C for storage.

PCR amplification of the DsPx base pair

Ds-containing oligos (D1 & D2, Supplementary Data 1) were added to 25 µL PCR reactions at the following template concentrations: 4 nM, 1 nM, 400 pM, 100 pM, and 40 pM. F/R barcoded PCR primers were added at 0.2 μM (Supplementary Table 2). AccuPrime Pfx Polymerase and AccuPrime Pfx Reaction Mix were added at concentrations of 1 U per 25 μL reaction and 1×, respectively. The AccuPrime Pfx Reaction Mix contains 0.3 mM dNTPs and 1 mM MgSO₄. Additional dNTPs and MgSO₄ were supplemented to bring the final concentrations to 0.4 mM and 1.5 mM, respectively. Nucleoside triphosphates dDsTP and dDiol-PxTP were added at a final concentration of 50 μM. Thermal cycling conditions were 2 min at 94 °C, 30 cycles of 94 °C for 15 s, 58 °C for 15 s, and 68 °C for 3 min, followed by a final 10 min extension at 68 °C. Samples were held at 4 °C upon PCR program completion then moved to −20 °C for storage.

Statistics and reproducibility

All PCR reactions were performed in experimental triplicate (n = 3). No statistical method was used to predetermine sample size. No data were excluded from the analyses. Experiments were not randomized. The investigators were not blinded to allocation during experiments and outcome assessment.

For each condition, the standard deviation was calculated for each measured UB fraction. The average UB fraction ($f_{⟨X,Y⟩}$) was calculated by averaging measurements of $f_X$ and $f_Y$ for each replicate and was treated as the measured quantity for downstream analyses. Accordingly, variability between $f_X$ and $f_Y$ within a replicate was not propagated into the reported uncertainty of fidelity.

To determine the statistical significance between two groups of measurements, a two-tailed z-test was performed using Eq. (5), where ${\overline{x}}_1$ and ${\overline{x}}_2$ are the means of group 1 and 2, respectively. $s_1$ and $s_2$ are the standard deviations of group 1 and 2, respectively.

$$z=\frac{{\overline{x}}_1-{\overline{x}}_2}{\sqrt{s_1^2+s_2^2}}$$ 5

Standard error of the mean (SEM) of the average UB fraction $\left({\sigma }_{f_{⟨X,Y⟩}}\right)$ is calculated according to Eq. (6), where $n$ is the number of replicates.

$${\sigma }_{f_{⟨X,Y⟩}}=\frac{s}{\sqrt{n}}$$ 6

Standard error of the mean (SEM, $\sigma$) for endpoint fidelity calculations (${\sigma }_{{\phi }_{⟨X,Y⟩}}$) was obtained by propagating the SEM of the average UB fraction (${\sigma }_{f_{⟨X,Y⟩}}$) according to Eq. (7). This equation was derived by taking the derivative $\left(\frac{d{\phi }_{⟨X,Y⟩}}{d{f}_{⟨X,Y⟩}}\right)$ of Supplementary Equation (31).

$${\sigma }_{{\phi }_{⟨X,Y⟩}}=∣2l\cdot \frac{2^{\left({\log }_2{f}_{⟨X,Y⟩}\right)/n}}{n^{*}{f}_{XNA}}∣\cdot {\sigma }_{f_{⟨X,Y⟩}}$$ 7

Similarly, the standard error of the slope (${\sigma }_m$) was propagated to the standard error of the mean of fidelity (${\sigma }_{{\phi }_{⟨X,Y⟩}}$) according to Eq. (8). This equation was derived by taking the derivative $\left(\frac{d{\phi }_{⟨X,Y⟩}}{dm}\right)$ of fidelity (${\phi }_{⟨X,Y⟩}$) with respect to slope ($m\left)\right)$ in Supplementary Equation (34).

$${\sigma }_{{\phi }_{⟨X,Y⟩}}=∣2\mathit{\cdot }\ln 2\cdot 2^{-m}∣\mathit{\cdot }{\sigma }_m$$ 8

For linear regression, slope, y-intercept, coefficient of determination (R²), and slope standard error (Slope SE) were obtained using Weighted Least Squares (WLS) Regression implemented in statsmodels.WLS library (Python) with weights ($w$) defined as $w=1/\mathrm{SE}{\mathrm{M}}^2$, where SEM is the standard error of the mean of experimental replicates. Average fidelity was calculated from the fitted slope using Supplementary Equation (34), and the slope standard error was propagated to the fidelity estimate using Eq. (8). Two-tailed 95% confidence intervals (CI) were calculated using the Student’s t distribution with $n-2$ degrees of freedom, where $n$ is the number of data points used for linear regression. For strand inversion model fitting, parameters were estimated using nonlinear least-squares optimization implemented in scipy.optimize.least_squares (Python).

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Author contributions

Project conceptualization was performed by J.A.M., N.A.K. Methodology for this work was developed by J.A.M., N.A.K., J.R.S. Investigation was performed by N.A.K., J.V.M. Visualization of data and results was performed by N.A.K., J.A.M. Funding for this work was acquired by J.A.M., N.A.K. This project was administered and supervised by J.A.M., J.E.L. Writing of original draft was carried out by J.A.M., J.E.L., N.A.K. Reviewing and editing of the manuscript was performed by N.A.K., J.E.L., J.R.S., J.A.M.

Peer review

Peer review information

Nature Communications thanks Jie Song, Niranjan Nagarajan and the other anonymous reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Funding

This work was supported by National Science Foundation Grant MCB-2419300 (N.A.K., J.E.L., J.A.M.) and by MCB- 2440857 (J.A.M., J.R.S). Material in this work was also supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-2140004 (NAK).

Data availability

The full raw nanopore sequencing dataset (.POD5) generated in this study has been deposited in the Zenodo database under accession code 21630885 (https://zenodo.org/records/21630885). Basecalled nanopore sequencing data (.FASTQ) have been deposited in the Sequence Read Archive (SRA) under Bioproject PRJNA1509986. All processed data generated in this study are provided in the Source Data file. Source data are provided with this paper.

Code availability

The code used for data processing and analysis, including UB quantification models developed in this work, is available in the public xenobiolab/xenoquant repository on GitHub (https://doi.org/10.5281/zenodo.21728091)⁴⁶.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at https://doi.org/10.1038/s41467-026-76964-9.