Resolving DNA origami structural integrity and pharmacokinetics in vivo

TL;DR

A new method called PLASTIQ allows researchers to track DNA origami structures in the body with high precision, revealing how they degrade and how modifications like PEGylation can slow this process.

Contribution

The introduction of PLASTIQ, a label-free proximity ligation assay for quantifying DNA origami structural integrity in vivo with high sensitivity and single-helix resolution.

Findings

PLASTIQ can detect DNA origami structures in as little as 1 µl of blood with a detection limit of 0.01 fM.

PEGylation significantly slows the degradation of DNA origami in a murine model.

Internal DNA helices in a double-layered origami structure degrade more slowly than outer helices.

Abstract

DNA origami holds great potential for advancing therapeutics, but the lack of methods for the precise assessment of structural integrity in vivo prevents its translation. Here we introduce proximity ligation assay for structural tracking and integrity quantification (PLASTIQ) for resolving origami structural integrity with only 1 µl of blood sample and with a detection limit of 0.01 fM. Through PLASTIQ, we could observe and quantify the dynamics of DNA origami degradation during blood circulation and evaluate the effectiveness of PEGylation for slowing this process in a murine model. Additionally, by using a double-layered barrel-like origami structure, we found distinct degradation kinetics of DNA helices depending on their specific location, revealing the slower degradation of internal helices compared with the outer ones. Our results suggest that PLASTIQ offers a quantitative approach for assessing DNA origami integrity in vivo by longitudinal sampling, providing dynamic pharmaceutical-level insights for accelerating the development of DNA-nanostructure-based therapeutic molecules and drugs.

A label-free, DNA-based proximity ligation assay that uses ligatable staple pairs enables the longitudinal quantification of DNA origami structural stability dynamics in vivo, with single-helix resolution for both wireframe and lattice designs.

Figures

Schematic of the PLASTIQ workflow for assessing DNA origami integrity using 1 µl of blood.The nanostructure of interest is designed to contain a set of LSPs, consisting of two contiguous staples that can be ligated due to the presence of a 5′-phosphate group (represented as the circled P) on one of them. Ligation of the LSPs occurs only when they are held in proximity by the scaffold in an intact origami structure. This is followed by amplification for quantification, thereby assessing the structural integrity of the DNA origami.

In vitro proof of concept to assess DNA origami integrity with PLASTIQ.a, PLASTIQ workflow in vitro. LSPs consisting of two contiguous staples with the 5′-end breakpoint containing a phosphate group for ligation and flanked by a protruding primer targeting region (pink and blue) for pooled PCR. After ligation and PCR, the products are resolved by PAGE. b, Representative cyro-electron microscopy image of the ^W^rod origami (left). Scale bar, 100 nm. TEM micrographs of the ^L^rod (right). Scale bar, 50 nm. c, Location of the LSPs in ^W^rod. d, Products of ligated and amplified LSPs on PAGE gel f

Tracking of DNA origami in vivo integrity using PLASTIQ.a, Experimental workflow for i.v. or i.p. injection of the origami into mice, collection of blood samples from the same subject animal at different time points, PLASTIQ protocol processing, pooled PCR amplification and gel assay or sequencing analysis. b,c, Gel assays including PAGE (b) and intensity (c) analyses of products from the pooled PCR for the amplification of ligated LSPs from the blood of mice injected with origami via i.v. administration. The different lanes correspond to blood samples collected at different time points. The d

In vivo quantification of DNA origami integrity using PLASTIQ followed by qPCR.a, PLASTIQ workflow applied to blood samples, followed by qPCR analysis. b,c, Time-dependent changes in origami integrity following i.v. (b) or i.p. (c) injection across multiple mice. *n* = 3. d–g, Representative graphs showing the quantification of individual LSPs for one individual mouse resulting in the averages in b and c. The blood concentrations of each ligated LSP were determined by qPCR following i.v. (d and f) or i.p. (e and g) injection of bare ^W^rod (d and e) and PEGylated (f and g) ^PEG-W^rod. The over

Pharmacokinetic modelling of DNA origami in vivo*.*a, i.v. injection model based on linear elimination kinetics. b,c, Fitted ligated LSP blood concentration profiles plotted on top of i.v. injection experimental data for ^W^rod (b) and ^PEG-W^rod (c). The plots for each ligated LSP shown separately are provided in Supplementary Fig. 10. d, Illustration of i.p. injection model based on two compartment kinetics in which an initial peritoneal absorption phase is followed by an elimination phase in blood. e,f, Fitted ligated LSP blood concentration profiles plotted on top of i.p. experimental data

In vivo integrity loss pattern of a double-layered barrel-like DNA origami revealed by PLASTIQ.a, ^W^barrel origami design from different perspectives, displaying the colour-coded LSPs at different locations. b, Representative cyro-electron microscopy image of the ^W^barrel origami. Scale bar, 100 nm. c, PAGE gel analysis of the pooled PCR amplicons, obtained after processing the ^W^barrel through the in vitro PLASTIQ workflow. L, ligated products; NL, non-ligated ^W^barrel origami as a negative control. Right: bands are matched to colour-coded boxes corresponding to the location of the LSPs i

Full text

Main

DNA origami uses DNA base pairing to assemble nanostructures with high spatial precision, enabling novel therapeutic and diagnostic applications^1,2^. Increasingly, these structures are tested in mice for delivering agents against cancer, neuroinflammation, viral infections and autoimmune diseases^3–8^. Its utility lies in the precise positioning of biomolecules to advance drug delivery and vaccine design^9–20^.

However, their functionality depends on maintaining structural integrity. Degradation by nucleases or staple dissociation in low-cation environments can disrupt origami integrity^21^^,22^, reducing functionality and increasing side effects^23,24^. Although stabilization strategies such as polymer or protein coating, ultraviolet (UV) crosslinking, groove binders and enzymatic ligation have been explored^23,25–34^, no robust method exists to assess structural integrity in vivo, which is essential for understanding origami pharmacokinetics and meeting regulatory standards.

Existing tracking approaches, like infrared dye labelling^35^, can overestimate persistence since fluorescence remains after disassembly^23,36^. Scaffold-targeted methods (for example, quantitative polymerase chain reaction (qPCR) or origamiFISH^37,38^) offer higher sensitivity but cannot distinguish intact structures from degraded ones, as they only detect scaffold fragments. Consequently, quantifying intact DNA origami in vivo remains unaddressed.

Here we present proximity ligation assay for structural tracking and integrity quantification (PLASTIQ), a label-free method for measuring DNA origami integrity in vivo. PLASTIQ uses proximity ligation between ligatable staple pairs (LSPs)—two contiguous staples bridged by the scaffold—to report whether local helices remain intact^39–41^. Distributed LSPs provide single-helix resolution, and ligated products are amplified for sequencing or qPCR, enabling accurate quantification from as little as 1 µl of blood (Fig. 1). This approach supports longitudinal monitoring within the same animal, revealing origami pharmacokinetics and guiding the design of next-generation nanotherapeutics.Fig. 1. Schematic of the PLASTIQ workflow for assessing DNA origami integrity using 1 µl of blood.The nanostructure of interest is designed to contain a set of LSPs, consisting of two contiguous staples that can be ligated due to the presence of a 5′-phosphate group (represented as the circled P) on one of them. Ligation of the LSPs occurs only when they are held in proximity by the scaffold in an intact origami structure. This is followed by amplification for quantification, thereby assessing the structural integrity of the DNA origami.

PLASTIQ validation in vitro

To validate the PLASTIQ concept, we designed two rod-shaped DNA origami structures: a wireframe structure (^W^rod) and a lattice-based structure (^L^rod) (Fig. 2a,b and Supplementary Figs. 1 and 2). Each contained nine (^W^rod) or eight (^L^rod) LSPs with unique sequence, length and positions (Fig. 2c,f), or only one LSP as controls. Each LSP featured a 5′-phosphate at its breakpoint and flanking primer sites for pooled PCR amplification (Fig. 2a).Fig. 2. In vitro proof of concept to assess DNA origami integrity with PLASTIQ.a, PLASTIQ workflow in vitro. LSPs consisting of two contiguous staples with the 5′-end breakpoint containing a phosphate group for ligation and flanked by a protruding primer targeting region (pink and blue) for pooled PCR. After ligation and PCR, the products are resolved by PAGE. b, Representative cyro-electron microscopy image of the ^W^rod origami (left). Scale bar, 100 nm. TEM micrographs of the ^L^rod (right). Scale bar, 50 nm. c, Location of the LSPs in ^W^rod. d, Products of ligated and amplified LSPs on PAGE gel from the ^W^rod origami containing either all nine LSPs pairs (all) or only one LSP (numbered 1–9) to resolve the bands from the pooled PCR with all LSPs. Data are representative of three independent experiments with similar results. e, PAGE gel visualization of PCR amplification with primers targeting the scaffold or an LSP from either non-denatured (ND) or denatured (D) ^W^rod sample. Data are representative of three independent experiments with similar results. f, Location of the LSPs in the ^L^rod. g, Products of ligated and amplified LSPs on PAGE gel from the ^L^rod origami containing either all eight LSPs pairs (all) or only one LSP (numbered 1–8) to resolve the bands from the pooled PCR with all LSPs. h, PAGE gel visualization of PCR amplification with primers targeting the scaffold or LSPs from either ND or D ^L^rod.Source data

Using origami samples in test tubes, we sequentially performed ligation, PCR and polyacrylamide gel electrophoresis (PAGE; Fig. 2a). For both ^W^rod and ^L^rod, amplification bands appeared only after ligation (Supplementary Fig. 3) and matched the sizes of single-LSP controls (Fig. 2d,g). When the origami was heat denatured before ligation, no LSP bands were detected (Fig. 2e,h), confirming that proximity ligation requires intact structures. By contrast, we showed that scaffold-targeted qPCR or origamiFISH assays^37,38^ still detected DNA regardless of the structural state (Fig. 2e,h), emphasizing their inability to distinguish intact origami from degraded origami.

Previous studies have shown that the coating of DNA nanostructures with the oligolysine-PEG polymer can protect them against nucleases and denaturation in low-salt environments, potentially increasing their stability in vivo^23^. Since PEGylation confers a physical barrier for the interaction of enzymes with DNA helices, we hypothesized that the ligase might also have decreased accessibility to PEGylated origamis. However, our in vitro experiments with PEGylated ^PEG-L^rod showed comparable ligation and amplification efficiencies to the bare ^L^rod (Supplementary Fig. 4). Another approach to enhance lattice-based origami stability in low-salt buffers and improved resistance to nucleases is sequence-specific covalent UV crosslinking^26^. We tested the application of the PLASTIQ protocol to a crosslinked version of the ^L^rod (^UV-L^rod) with the same LSPs as ^L^rod. We observed a similar amplification pattern when compared to the non-crosslinked ^L^rod after PAGE electrophoresis of the pooled PCR-amplified LSPs (Extended Data Fig. 1).

Together, these results demonstrate that PLASTIQ reliably detects DNA origami integrity at the single-helix level for both wireframe and lattice designs, and that it is compatible with PEGylated or UV-crosslinked nanostructures.

PLASTIQ tracks DNA origami integrity in vivo

Blood proteins rapidly adsorb onto nanoparticles in circulation, forming a corona that can alter their pharmacokinetics and cellular interactions^42^. Given their negatively charged surfaces, DNA origamis may similarly acquire a protein corona, potentially hindering ligase access to LSPs in blood. To evaluate this, we incubated the ^W^rod and its PEGylated variant (^PEG-W^rod; Supplementary Fig. 5) in serum (Supplementary Fig. 6a). PCR and PAGE analyses revealed nearly identical amplification patterns for both constructs compared with phosphate-buffered saline (PBS) controls across all time points (Supplementary Fig. 6b). Repeating the experiment in 80 mg ml^−1^ of serum, approximating the blood protein concentration in mice^43^, and using LSP-specific qPCR primers, yielded similar amplification profiles (Supplementary Fig. 6c). These results indicate that possible corona formation on DNA origami does not impede ligation during PLASTIQ.

We next applied PLASTIQ in vivo to monitor the structural integrity of ^W^rod in mice. After an intravenous (i.v.) or intraperitoneal (i.p.) injection of ^W^rod containing nine LSPs, we collected 1 µl of blood at defined intervals for immediate ligation, denaturation and centrifugation, followed by PCR and PAGE analyses (Fig. 3a and Supplementary Fig. 7). In parallel, ^PEG-W^rod was evaluated following the same procedure (Supplementary Fig. 5). For i.v. injections, ligated LSP bands appeared in both ^W^rod and ^PEG-W^rod at 5 min but declined rapidly (Fig. 3b). By 20 min, ^PEG-W^rod retained a faint signal, whereas ^W^rod became undetectable, suggesting that PEGylation moderately prolonged the circulation half-life (Fig. 3c). Both constructs exhibited concentration peaks immediately after injection, followed by rapid clearance, consistent with typical i.v. pharmacokinetics.Fig. 3. Tracking of DNA origami in vivo integrity using PLASTIQ.a, Experimental workflow for i.v. or i.p. injection of the origami into mice, collection of blood samples from the same subject animal at different time points, PLASTIQ protocol processing, pooled PCR amplification and gel assay or sequencing analysis. b,c, Gel assays including PAGE (b) and intensity (c) analyses of products from the pooled PCR for the amplification of ligated LSPs from the blood of mice injected with origami via i.v. administration. The different lanes correspond to blood samples collected at different time points. The dots represent the two biological replicates. Ctrl, control corresponding to a blood sample collected 5 min post-injection without the ligation step. d,e, Gel assays including PAGE (d) and intensity (e) analyses of the products from the PCR amplification of ligated LSPs from blood of mice injected with origami via i.p. administration. The different lanes correspond to blood samples collected at different time points. The dots represent the two biological replicates. Ctrl, control corresponding to a blood sample collected 5 min post-injection without the ligation step. f, Fluorescence imaging of blood samples collected at different time points after injecting mice with Alexa 750 dye or dye-labelled nanostructures. g, Alexa 750 fluorescence-based blood pharmacokinetic curves. h, Fluorescence imaging of live mice at 1- and 2-h post-injection. I, dye; II, dye-labelled origami; III, dye-labelled PEGylated origami.Source data

After i.p. injection, ligated LSP bands persisted for up to 1 h (Fig. 3d,e), markedly longer than with i.v. delivery. The PLASTIQ profiles revealed pharmacokinetics typical of i.p. absorption, with blood origami levels rising during the initial 20 min, peaking at around 30 min, and subsequently declining. ^PEG-W^rod exhibited slightly higher early phase signals, consistent with enhanced absorption from the peritoneal cavity into circulation.

To compare with fluorescence-based tracking, we incorporated Alexa 750-modified staples into ^W^rod. After i.v. injections, blood samples were collected at multiple time points for imaging (Fig. 3f). Although the fluorescence signal from the dye-labelled origami showed a similar trend from 0 to 20 min as our PLASTIQ method, it never reached a nadir, and the dye alone exhibited a comparable signal pattern—raising concerns about the reliability of fluorescence-based tracking for evaluating DNA origami pharmacokinetics (Fig. 3g). Regarding biodistribution, although the fluorescence signal from ^PEG-W^rod appeared more broadly distributed throughout the body, the dye alone and ^W^rod showed similar patterns 1 h post-injection, with signals predominantly localized in the bladder and minimal signals elsewhere, suggesting urinary excretion (Fig. 3h). The broader distribution observed in ^PEG-W^rod-treated mice probably reflects transient PEG-induced alterations or residual dye dissociated from degraded origamis. The persistence of fluorescence when no intact origami was detected by PLASTIQ highlights the limitations of dye-based approaches for quantitative pharmacokinetic assessment.

Following pooled PCR amplification, all PLASTIQ products were sequenced. Ligated LSPs were identified across all samples, with fewer than 10% of the reads unmapped (Extended Data Fig. 2). Although the overall read counts did not strictly correlate with qPCR or PAGE results—probably due to biases introduced during library preparation—the relative abundance of specific LSPs (particularly LSP4, LSP5, LSP8 and LSP9) was slightly higher in post-injection samples, suggesting that these regions were more stable or more accessible for ligation and amplification.

These results collectively support the applicability of PLASTIQ as a sequence-based method for resolving DNA origami integrity and analysing the pharmacokinetics patterns of DNA origami structures in vivo.

Pharmacokinetics of DNA origami after different injection routes

To quantify DNA origami integrity in vivo, we incorporated qPCR analysis for each ligated LSP as an additional end-point in the PLASTIQ workflow (Fig. 4a). Measuring multiple LSPs enabled the dynamic profiling of structural integrity over time. Each LSP was amplified using a unique primer pair, and DNA concentrations were calculated from individual standard curves generated through serial dilutions of the ^W^rod template (Supplementary Figs. 8 and 9), thereby accounting for differences in amplicon length, GC-content and secondary structure between LSPs. The calculated in vitro detection limit was 0.01 fM (Supplementary Figs. 8 and 9).Fig. 4. In vivo quantification of DNA origami integrity using PLASTIQ followed by qPCR.a, PLASTIQ workflow applied to blood samples, followed by qPCR analysis. b,c, Time-dependent changes in origami integrity following i.v. (b) or i.p. (c) injection across multiple mice. n = 3. d–g, Representative graphs showing the quantification of individual LSPs for one individual mouse resulting in the averages in b and c. The blood concentrations of each ligated LSP were determined by qPCR following i.v. (d and f) or i.p. (e and g) injection of bare ^W^rod (d and e) and PEGylated (f and g) ^PEG-W^rod. The overall origami integrity curve is generated by averaging the signals from all ligated LSPs.Source data

The qPCR results showed time-dependent changes in blood concentration for each ligated LSP, with minor regional differences reflecting the local degradation rates (Fig. 4d–g). However, all LSPs followed the same global trend governed by the injection route (Fig. 4b,c). The average weighted concentration of all ligated LSPs at each time point was used to define the overall origami integrity. For both ^W^rod or ^PEG-W^rod, the concentration profiles followed administration-specific kinetics: a sharp initial peak followed by rapid decay after i.v. injection (Fig. 4b,d,f) and a biphasic trend after i.p. injection (Fig. 4c,e,g).

Following i.v. administration, origamis directly entered the systemic circulation (Fig. 4b). ^PEG-W^rod showed a lower early signal than ^W^rod, probably reflecting faster systemic clearance. PEGylation increases the hydrodynamic size and masks DNA’s negative charge, reducing non-specific interactions with serum proteins and promoting renal or hepatic elimination. By contrast, unmodified origami—with stronger electrostatic interactions—persisted slightly longer. By 20 min, however, both constructs dropped to near-background levels, indicating extensive degradation or clearance within this period.

After i.p. injection, the trend reversed: ^PEG-W^rod origami exhibited higher blood levels than ^W^rod at early time points (Fig. 4c,e), probably due to enhanced absorption across the peritoneal barrier. The PEG coating provides a hydrophilic shell that protects against nuclease degradation, minimizes protein adsorption and reduces immune clearance, collectively facilitating diffusion and entry into systemic circulation. Unmodified origami probably experiences partial degradation or retention in the peritoneal cavity, resulting in lower initial levels. Nonetheless, ^PEG-W^rod concentrations declined more rapidly at later time points, falling below ^W^rod by 2 h post-injection—consistent with accelerated systemic clearance also seen in the i.v. route.

The influence of PEGylation on nanoparticle circulation varies with the PEG density, molecular weight and nanoparticle composition, resulting in either longer or shorter half-lives^44–46^. In our case, PEGylation enhanced early absorption following i.p. delivery but also promoted faster elimination once in circulation, whether injected by i.p. or i.v. routes.

To further examine PLASTIQ’s versatility for different administration pathways, ^PEG-W^rod was also delivered via intramuscular and subcutaneous injections (Extended Data Fig. 3). Measurable amounts were observed in all mice, with peak signals occurring 25–75 min post-injection. This delay aligns with the slower systemic absorption typical of intramuscular and subcutaneous delivery, contrasting with the rapid appearance and clearance characteristic of i.v. injection.

To better understand the dynamic concentration profile observed, we modelled the in vivo pharmacokinetics of DNA origami using an exponential decay for the i.v. injection, and a two-compartment model consisting of a peritoneal cavity and blood compartment for the i.p. injection. The decision to use a two-compartment model was based on the need to capture the absorption of DNA from the peritoneal cavity into the blood and its subsequent elimination from the bloodstream. The dynamic model is governed by the following differential equation for the i.v. case:

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{{\rm{d}}{C}_{\mathrm{blood}}}{{\rm{d}}t}=-{k}_{{\rm{e}}}{C}_{\mathrm{blood}},$$\end{document}

and for the i.p. case,

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{{\rm{d}}{C}_{{\rm{peri}}}}{{\rm{d}}{t}}=-{k}_{{\rm{a}}}{C}_{{\rm{peri}}}$$\end{document}

and

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{{\rm{d}}{C}_{{\rm{blood}}}}{{\rm{d}}{t}}={k}_{{\rm{a}}}\left(\frac{{V}_{{\rm{peri}}}}{{V}_{{\rm{blood}}}}\right){C}_{{\rm{peri}}}-{k}_{{\rm{e}}}{C}_{{\rm{blood}}},$$\end{document}

where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${C}_{{\rm{peri}}}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${C}_{{\rm{blood}}}$$\end{document} are the molar concentrations of DNA origami in the peritoneal cavity and blood compartment, respectively; \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${k}_{{\rm{a}}}$$\end{document} is the absorption rate constant; \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${k}_{{\rm{e}}}$$\end{document} is the elimination rate constant; and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${V}_{{\rm{peri}}}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${V}_{{\rm{blood}}}$$\end{document} are the estimated volumes of the peritoneal cavity and blood compartment, respectively. The model was parameterized for each LSP trajectory independently of others by minimizing residuals between the model and trajectory data, with fits capturing the decay and peaked shapes of the i.v. (Fig. 5a–c) and i.p. (Fig. 5d–f) curves, respectively, yielding values for the absorption and elimination rate constants, as well as the initial concentrations (Supplementary Table 1). The resulting two-compartment model, fitted to the observed blood concentration, enabled us to infer the unobservable concentration of DNA origami in the peritoneal cavity for i.p. injections, revealing a biphasic pattern of initially increasing DNA origami concentration in blood characterized by the exponentially decaying concentration in the peritoneal cavity, followed by an elimination phase as blood concentration drops back towards zero. We obtained the absorption and elimination parameters (Fig. 5h) by fitting each LSP to the pharmacokinetic model for both non-PEGylated and PEGylated conditions. Here we observed a distribution of parameters over the LSPs, suggesting variation in the individual kinetics of each LSP, but differences between the population of non-PEGylated and PEGylated LSPs were not significant.Fig. 5. Pharmacokinetic modelling of DNA origami in vivo*.*a, i.v. injection model based on linear elimination kinetics. b,c, Fitted ligated LSP blood concentration profiles plotted on top of i.v. injection experimental data for ^W^rod (b) and ^PEG-W^rod (c). The plots for each ligated LSP shown separately are provided in Supplementary Fig. 10. d, Illustration of i.p. injection model based on two compartment kinetics in which an initial peritoneal absorption phase is followed by an elimination phase in blood. e,f, Fitted ligated LSP blood concentration profiles plotted on top of i.p. experimental data for ^W^rod (e) and ^PEG-W^rod (f). The plots for each ligated LSP shown separately are provided in Supplementary Fig. 11. Smooth model curves for observable blood concentration and hidden inferred peritoneal concentration for i.p. injection samples are shown in Supplementary Fig. 12. g, Artificially generated kinetic profile for a repeated dose with 30-min interval, plotted using mean fitted parameter values for i.p. injection of ^PEG-W^rod. Artificially generated kinetic profiles with 60- and 120-min intervals are provided in Supplementary Fig. 13. h, Swarm plots of parameter values (absorption and elimination rate constants, as well as the initial concentration Qo) fitted according to their respective models (two compartment or single compartment) using nonlinear least squares optimization for the i.v., i.p., ^PEG-W^rod and ^W^rod conditions, with each point representing an independently fitted LSP. The spread, thus, captures the variability between individual LSPs. The statistical results are shown in Supplementary Table 1.Source data

The parameterized model enables the simulation of profiles under artificial or speculative conditions. To show how the concentration of the administered structures fluctuates over time between the peritoneal cavity and the bloodstream, we simulated timed repeated deliveries, such as with a 30-min injection interval (Fig. 5g). The peritoneal concentration (dashed line) increases rapidly with each injection before declining due to absorption into the bloodstream (solid line), and the profile gradually stabilizes within a repeating pattern of peaks and troughs as absorption and elimination reach dynamic equilibrium. The simulation represents how a hypothetical regimen would maintain blood concentration within a particular range, for example, to ensure that drug concentration remains within a therapeutic window that is high enough for efficacy but low enough to avoid toxicity.

PLASTIQ reveals localized integrity loss in individual DNA origami

The variability among ligated LSPs in the ^W^rod experiments suggested differing in vivo integrity loss dynamics across origami regions. This indicated that PLASTIQ could reveal detailed integrity differences not only among distinct origami structures but also within a single origami particle. However, confirming the exact cause of these discrepancies is challenging. There were no indications in the experiments of PCR bias, as the results sorted by amplicon (ligated LSPs) length did not explain the variability in signal, and the GC-content was similar across LSPs. We, therefore, hypothesized that signal heterogeneity could be explained by differential degradation due to location in the origami structure, which we subsequently tested.

To investigate this hypothesis, we engineered a double-layered barrel-like wireframe origami structure, ^W^barrel, with more- and less-exposed regions (Fig. 6a and Supplementary Fig. 14). This barrel design includes a hinge area, three locking points between the outer layers and three closing helper strands between the internal layers. Interconnecting staple strands traverse between the inner and outer layers, securing the structure. The resulting barrel has an internal diameter of about 30 nm, a length of 39 nm and a thickness of around 9 nm. For a detailed analysis, we segmented the ^W^barrel origami into four regions: top, bottom, outer surface and inner surface. Within each region, we designed three LSPs to conduct PLASTIQ, allowing for the precise examination of structural integrity across distinct regions of the origami (Fig. 6a).Fig. 6. In vivo integrity loss pattern of a double-layered barrel-like DNA origami revealed by PLASTIQ.a, ^W^barrel origami design from different perspectives, displaying the colour-coded LSPs at different locations. b, Representative cyro-electron microscopy image of the ^W^barrel origami. Scale bar, 100 nm. c, PAGE gel analysis of the pooled PCR amplicons, obtained after processing the ^W^barrel through the in vitro PLASTIQ workflow. L, ligated products; NL, non-ligated ^W^barrel origami as a negative control. Right: bands are matched to colour-coded boxes corresponding to the location of the LSPs in ^W^barrel, with the amplicon length in base pairs. Data are representative of three independent experiments with similar results. d, Workflow of the ^W^barrel origami in vivo, including administration via i.p. injection, blood collection at different time points and PLASTIQ processing by qPCR amplification. Each LSP contained unique protrusions for primer targeting during qPCR. e, Concentration of ligated staples from ^W^barrel in blood at the indicated time points, analysed via PLASTIQ followed by qPCR. Each point corresponds to the concentration of origami in blood measured as the qPCR amplification of a different LSP (n = 3). The bars represent the average concentration from the three LSPs of each ^W^barrel region shown in the legend. One-way ANOVA followed by Dunnett’s test was used for statistical analysis (P = 0.0481).Source data

We utilized the ^W^barrel to conduct PLASTIQ in vitro followed by PCR. PAGE gel electrophoresis revealed that all 12 ligated LSPs displayed correct lengths, confirming the success of the reactions (Fig. 6c). For in vivo experiments, the ^W^barrel origami was administered to mice by i.p. injection, and the blood samples were processed by PLASTIQ with qPCR analysis (Fig. 6d). At time points of 30 min post-injection, quantities of ligated LSPs in the top, bottom and outer surface regions of the origami were statistically significantly lower than those in the inner surface (Fig. 6e). This discrepancy probably stems from the inner surface experiencing relatively fewer interactions with DNase in the bloodstream, resulting in prolonged DNA stability. This underscores the capability of PLASTIQ to meticulously analyse integrity-loss dynamics within a single DNA origami structure.

Conclusion

In this study, we established PLASTIQ as a label-free method for assessing the structural integrity of DNA origami in vivo with single-helix resolution. The approach relies on proximity ligation between adjacent staples, which occurs only when the scaffold holds them together in close contact, allowing a quantitative evaluation of intact regions through qPCR or sequencing. With a detection limit as low as 0.01 fM from only 1 µl of blood, PLASTIQ enables the longitudinal tracking of origami integrity in the same animal, minimizing experimental variability and animal distress.

For coated DNA origami, the oligolysine-PEG copolymer layer could, in principle, hinder ligase access and lower the ligation yield compared with bare structures^23,47^. However, no significant differences were observed for either wireframe or lattice-based PEGylated origamis, probably because extended reaction times ensured complete ligation. Similarly, PLASTIQ performed robustly on UV-crosslinked origamis stabilized through thymidine covalent bonds^26^, showing comparable in vitro results to non-crosslinked designs. Förster resonance energy transfer can also reflect structural degradation as dye pairs separate^29,48–50^, but it remains semiquantitative and susceptible to background from detached fluorophores, whereas PLASTIQ directly quantifies intact nanostructures in vivo. Although our study focused on circulating origami, some nanostructures may be internalized by innate immune cells such as dendritic cells^51^, which is relevant for cytosine–phosphate–guanine-presenting origamis used in toll-like receptor activation^19,52,53^. As PLASTIQ currently relies on ex vivo ligation, it detects extracellular structures only; but future adaptations incorporating cell or tissue isolation could enable the analysis of internalized DNA nanostructures and provide a more complete pharmacokinetic profile.

Altogether, PLASTIQ provides a sensitive and versatile framework for quantifying DNA origami integrity within living systems. By bridging molecular precision with a biological context, it offers a powerful tool for understanding origami behaviour in physiological environments and guiding the rational design, optimization and regulatory evaluation of next-generation DNA nanotherapeutics.

Methods

DNA origami preparation

The scaffold DNA p7560 was produced using a phage-amplification-in-bacteria protocol described in previous work^54^. Staple oligonucleotides, both with and without the 5′-end phosphate modifications, were sourced from Integrated DNA Technologies (Supplementary Data 1). The ^W^rod and ^W^barrel DNA origami structures were assembled in 100-µl reactions containing final concentrations of 20 nM of p7560 scaffold, 100 nM of each staple strand and 1× PBS. The ^L^rod DNA origami structure was assembled in 100-µl reactions containing final concentrations of 20 nM of p7560 scaffold, 150 nM of each LSP staple, 100 nM of each of the other staple strands, 5 mM of Tris, 1 mM of EDTA and 8 mM of MgCl_2_. The folding reaction for all origamis started with a rapid heat denaturation at 60 °C, and then gradually cooled from 60 °C to 24 °C over 14 h on a PCR thermal cycler. The excess staples were removed by repeated cycles of dilution and centrifugation with 1× PBS for ^W^rod and ^W^barrel, or 1× PBS and 5 mM of MgCl_2_ for ^L^rod, using 100-kDa Amicon Ultra Centrifugal Filters (Millipore) at 14,000g for 1 min. Simultaneously, the samples were concentrated to the needed final concentration, which was determined by UV 260 absorbance using a Nanodrop 2000 spectrophotometer (Thermo Fisher). To coat the DNA origamis with oligolysine (K_10_)-PEG_5K_ copolymer, the structures were incubated with the K_10_-PEG_5K_ copolymer at an N:P ratio of 1:1 for 30 min at room temperature.

UV irradiation

For UV crosslinking the ^L^rod, the samples were irradiated in 1× PBS and 5 mM of MgCl_2_ with a UV light pointer for 2 h on ice using a 300-W xenon light source (MAX-303, Asahi Spectra) with a high-transmission bandpass filter centred at 310 nm (XAQA310, Asahi Spectra).

Gel electrophoresis

The folding quality of the origami structures was assessed with 2% agarose gels in 0.5× Tris-borate-EDTA (TBE) buffer supplemented with 10 mM of MgCl_2_ and 0.5 mg ml^−1^ of ethidium bromide. Gel electrophoresis was conducted at 90 V for 3 h on an ice bath using 0.5× TBE with 10 mM of MgCl_2_ as the running buffer. The gels were imaged using a GE LAS 4000 imager.

Origami imaging with cyro-electron microscopy

The cryogenic specimens were prepared using a Vitrobot Mk4 and a glow-discharged Quantifoil R 1.2/1.3 gold grid. We applied 3 µl of concentrated (>500 nM) DNA origami solution, incubated at 100% humidity for 1–5 min and flash frozen in liquid ethane. Grids were stored in liquid nitrogen until image collection with a Krios G3i transmission electron microscopy (TEM) device at 300 kV. Images were captured in the energy-filtered transmission electron microscopy (EFTEM) selected-area (SA) mode at ×81k with a 10-eV slit using K3 BioQuantum, with an exposure of 4.4 s per 45 frames at a dose rate of 0.90 e Å^−2^ per frame.

TEM

DNA origami samples (3 µl, 5–10 nM) were applied to glow-discharged formvar/carbon-coated copper grids (FCF400-Cu, EMS) and incubated for 1.5 min. Excess sample was blotted away using filter paper. The grids were then immediately stained with 15 µl of 2% (w/v) uranyl formate for 40 s and blotted dry. To neutralize the acidic pH of the uranyl formate solution, 8 µl of 1-M NaOH was added to 400 µl of 2% uranyl formate, followed by centrifugation at 16,000g for 5 min before use. Negative-stained samples were imaged using a Talos L120C G2 TEM device (Thermo Fisher Scientific) operated at 120 kV. Images were acquired at ×57,000 magnification using a Ceta-D detector.

Blood samples from mice and ethical permit

All animal handling and experimental procedures were conducted in compliance with local ethics guidelines and received approval from the Stockholm Animal Experimentation Ethics Committee (Stockholms djurförsöksetiska nämnd, Dnr 16041-2019). Mice were house in ventilated cages under specific pathogen-free conditions with a 12-h light/dark cycle, at an ambient temperature of 22 ± 2 °C and relative humidity of 45%–65%. Animals had free access to standard chow and water ad libitum. For each BALB/c mouse (Mus musculus, substrain BALB/cAnNCrl, 6–8 weeks old, from Charles River Laboratories), a volume of 100 μl with 50 nM of DNA origami structures was administered either intravenously or intraperitoneally. Subsequently, 2 μl of blood was collected from the tail tip at each designated time point and immediately utilized for proximity ligation reactions. No statistical methods were used to predetermine the sample sizes, but our sample sizes are similar to those reported in previous publications examining the DNA origami pharmacokinetics and in vivo nanostructure stability^23^.

Proximity ligation on DNA origami in blood

To conduct the ligation reaction, 1 μl of blood was added to a reaction mixture consisting of 4 μl of T4 ligase (New England Biolabs, M0202), 4 μl of 10X T4 DNA Ligase Buffer (New England Biolabs, B0202S) and 31 μl of nuclease-free water. The reaction was incubated at room temperature for 10 min, followed by a denaturation step at 95 °C for 10 min. Subsequently, the samples were centrifuged, and the supernatants were retained for downstream analyses, including PCR, qPCR and library preparation for Illumina sequencing.

PCR and gel assays

For the pooled PCR amplification of the ligated LSPs of the rod and the barrel origami structures, one set of forward (CATGTCCGACGTCCTCCAC) and reverse (CTCACTGCTGCACCACACAC) PCR primers was used. For the amplification of the DNA scaffold, two primer pairs (forward 1, ACTCGTTCTGGTGTTTCTCG; reverse 1, TGAAAGAGGACAGATGAACGG; forward 2, CTGGCTCGAAAATGCCTCT; reverse 2, ACCAGTATAAAGCCAACGCT) targeting different regions were used. Each PCR reaction had a total volume of 50 μl consisting of 20 μl of the target sample, 25 μl of 2× Platinum II Hot-Start PCR Master Mix (Invitrogen), 0.15 μM of forward and reverse primers, and nuclease-free water. On a thermocycler, 25 cycles of PCR reactions were then performed according to the product instructions of the Platinum II Hot-Start PCR Master Mix. The amplified samples were analysed by denaturing PAGE gel of 10% 19:1 acrylamide:bisacrylamide (BioRad), 8 M of urea and 1× TBE. The samples were mixed with formamide and run for 30 min at 300 V. The gels were post-stained with SYBR Gold (Invitrogen) and imaged using a GE LAS 4000 imager.

Library preparation, quantification and sequencing

The PCR product was purified using AMPure XP beads (Beckman Coulter, A63881) at 2× excess. The resulting product was prepared into a library using the xGen DNA Lib Prep MC UNI 96rxn kit (Integrated DNA Technologies, 10009820) in combination with xGen-UDI-UMI adaptors (Integrated DNA Technologies, 10005903). The library was subjected to eight cycles of PCR following the manufacturer’s protocol, and purified using AMPure XP beads at 0.8× excess, resuspended in low-EDTA TE buffer supplied with the kit. The library size and amount were estimated using the Invitrogen Quant-iT Qubit dsDNA HS Assay Kit (Thermo Fisher, Q32851) and High Sensitivity Bioanalyzer chips (Agilent, 5067-4626). The library was diluted to 4 nM, pooled and loaded onto a NextSeq 550 High Output Kit v. 2.5 (75 cycles; Illumina, 20024906) according to the manufacturer’s protocol. Sequencing reads were assigned to specific pairs by aligning them to the sequences of the ligation pairs using bowtie2 with default settings and keeping the best alignment per pair. The alignment was further analysed with in-house scripts.

qPCR

Following the manufacturer’s instructions, each 20 μl of the qPCR reaction mix contained 7.4 μl of the sample, 10 μl of Luna Universal qPCR Master Mix (New England Biolabs), 0.25 μM of the forward primer, 0.25 μM of the reverse primer and 1.6 μl of nuclease-free water. The reaction consisted of an initial denaturation step of 1 min at 95 °C followed by 40 cycles of 95 °C for 15 s and 60 °C for 30 s. The analyte sample was either from the blood of in vivo experiments or DNA origami ligated in vitro. To generate the standard curves of each ligated LSP, the DNA origami structure was ligated in vitro and diluted in 1× PBS to a final amount of 10–1 million molecules per concentration point, and run in parallel with the corresponding in vivo sample. The primers used for the qPCR analysis are listed in Supplementary Data 1. The recorded CT values were used for plotting the standard curves and to calculate the copy number of the corresponding analytes run on the same 96-well plate.

Data statement

Mice were randomly assigned to different experimental groups to minimize potential bias. No specific randomization algorithm was used, but group allocation was performed in an unbiased manner based on animal availability at the time of treatment. No animals or data points were excluded from the analyses. All data collected were included in the reported results. Data collection and analysis were not performed blind to the conditions of the experiments. Data distribution was assumed to be normal, but this was not formally tested.

Pharmacokinetics model of dynamic in vivo origami distribution

The dynamic distribution of DNA origami in vivo, injected either intravenously or into the peritoneal cavity, was modelled using a system of ordinary different equations that were solved to obtain concentration values as a function of time. The model was designed to capture the aspects of absorption from the peritoneal cavity into the bloodstream and subsequent elimination from the bloodstream as a function of time from the initial injection. The model was then fitted to the experimental data, independently for each individual LSP trajectory, to obtain parameter values and goodness-of-fit tests.

Experimental data were preprocessed before fitting, including a cleaning step to remove NaN values, and by subtracting a baseline value from each trajectory. The baseline was determined, in each case, by taking the mean of the last time points under the assumption that the signal had stabilized by that point. Negative values resulting from baseline subtraction were clipped to zero.

The i.v. conditions in which DNA origami was directly injected into the blood takes the form of a single-compartment model consisting of equation (4), repeated here:

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{{\rm{d}}{C}_{\mathrm{blood}}}{{\rm{d}}t}=-{k}_{{\rm{e}}}{C}_{\mathrm{blood}},$$\end{document}

where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${C}_{\mathrm{blood}}$$\end{document} is in pM and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${k}_{{\rm{e}}}$$\end{document} is in min^−1^, representing the process by which DNA origami is degraded or removed from the bloodstream.

For the i.p. conditions, a two-compartment model was used consisting of the following differential equations, repeated here:

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{{\rm{d}}{C}_{{peri}}}{{\rm{d}}t}=-{k}_{{\rm{a}}}{C}_{\mathrm{peri}}$$\end{document}

and

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{{\rm{d}}{C}_{\mathrm{blood}}}{{\rm{d}}t}={k}_{{\rm{a}}}\left(\frac{{V}_{\mathrm{peri}}}{{V}_{\mathrm{blood}}}\right){C}_{\mathrm{peri}}-{k}_{{\rm{e}}}{C}_{\mathrm{blood}}.$$\end{document}

Here \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${V}_{\mathrm{peri}}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${V}_{\mathrm{blood}}$$\end{document} are assumed to be \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.5\times {10}^{-3}l$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.5\times {10}^{-3}l$$\end{document} , respectively.

Solving equation (4), a first-order linear differential equation yields the formula for blood DNA origami concentration for the case of i.v. injections:

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${C}_{\mathrm{blood}}\left(t\right)={C}_{\mathrm{blood}}\left(0\right){{\rm{e}}}^{-{k}_{{\rm{e}}}t},$$\end{document}

where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${C}_{\mathrm{blood}}\left(0\right)$$\end{document} is the initial concentration of DNA origami in the blood. Similarly, equation (5) yields the solution:

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${C}_{\mathrm{peri}}\left(t\right)={C}_{\mathrm{peri}}\left(0\right){{\rm{e}}}^{-{k}_{{\rm{e}}}t},$$\end{document}

where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${C}_{\mathrm{peri}}\left(0\right)$$\end{document} is the initial concentration of DNA origami in the peritoneal cavity.

Substituting equation (8) for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${C}_{{\rm{peri}}}$$\end{document} in equation (6) yields the non-homogeneous first-order linear differential equation:

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{{\rm{d}}{C}_{{\rm{blood}}}}{{\rm{d}}{t}}={k}_{{\rm{a}}}\left(\frac{{V}_{{\rm{peri}}}}{{V}_{{\rm{blood}}}}\right){C}_{{\rm{peri}}}\left(0\right){{\rm{e}}}^{-{k}_{{\rm{e}}}t}-{k}_{{\rm{e}}}{C}_{{\rm{blood}}},$$\end{document}

which, assuming zero initial concentration in the blood, has the solution

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${C}_{{\rm{blood}}}\left(t\right)={k}_{{\rm{a}}}\left(\frac{{V}_{{\rm{peri}}}}{{V}_{{\rm{blood}}}}\right)\frac{{C}_{{\rm{peri}}}\left(0\right)}{{k}_{{\rm{e}}}-{k}_{{\rm{a}}}}\left({{\rm{e}}}^{-{k}_{{\rm{a}}}t}-{{\rm{e}}}^{-{k}_{{\rm{e}}}t}\right).$$\end{document}

Equations (7), (8) and (10) enable the dynamic profiling of DNA origami concentrations in their respective compartments. The blood concentrations represented by equations (7) and (10) reflect values represented by experimental data, and were fitted to each LSP trajectory by minimizing the residual sum of squares between the original data and model predictions:

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{Loss}=\mathop{\sum }\limits_{i=1}^{n}\left(\,{\,y}_{i}-\dot{{y}_{i}}\right),$$\end{document}

where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot{{y}_{i}}$$\end{document} are the model predictions, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${y}_{i}$$\end{document} are the individual data points and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n$$\end{document} is the number of points in an LSP trajectory. Goodness of fit was assessed using the coefficient of determination:

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${R}^{2}=1-\frac{{\sum }_{i=1}^{n}{\left({y}_{i}-\dot{{y}_{i}}\right)}^{2}}{{\sum }_{i=1}^{n}{\left({y}_{i}-\bar{{y}_{i}}\right)}^{2}},$$\end{document}

where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar{{y}_{i}}$$\end{document} is the mean of the observed data, and the root mean square error (r.m.s.e.) is

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rm{r}}.{\rm{m}}.{\rm{s}}.{\rm{e}}.=\sqrt{\frac{1}{n}{\sum }_{i=1}^{n}{\left({y}_{i}-\dot{{y}_{i}}\right)}^{2}}.$$\end{document}

Reporting summary

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

Online content

Any methods, additional references, Nature Portfolio reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at 10.1038/s41565-025-02091-z.

Supplementary information

Supplementary InformationSupplementary Figs. 1–14 and Table 1. Reporting Summary Supplementary Data 1Supplementary DNA sequences.

Source data

Source Data Figs. 3–6, Extended Data Figs. 2 and 3Statistical source data. Source Data Figs. 2, 3 and 5, Extended Data Fig. 1. Uncropped gels.