Sequence-Dependent Persistence Length of Long DNA

Real-Time Visualization of Single Polymer Conformational Change in the Bulk State during Mechanical Deformation

Although polymers are most often used within bulk materials, investigating their conformations and dynamics has long been a challenging endeavor in this configuration, particularly under external forces. Addressing this, we utilize single-molecule localization microscopy as a powerful imaging tool to visualize bottlebrush poly(n-butyl acrylate) chains in the bulk state under spherical indentation, quantitatively describing changes in behavior of single polymer chains. We compare these experiments to displacement fields determined analytically and confirmed through finite element analysis. This study pioneers visualizing polymer conformational changes in their native environment in situ, offering transformative insights into polymer behavior and dynamics.

Mechanical causes and implications of repetitive DNA motifs

Experimental research suggests that local patterns in DNA sequences can result in stiffer or more curved structures, potentially impacting chromatin formation, transcription regulation, and other processes. However, the effect of sequence variation on DNA geometry and mechanics remains relatively underexplored. Using rigid base pair models to aid rapid computation, we investigated the sample space of 100 bp DNA sequences to identify mechanical extrema based on metrics such as static persistence length, global bend, or angular deviation. Our results show that repetitive DNA motifs are overrepresented in these extrema. We identified specific extremal motifs and demonstrated that their geometric and mechanical properties significantly differ from standard DNA through hierarchical clustering. We provide a mathematical argument supporting the presence of DNA repeats in extremizing sequences. Finally, we find that repetitive DNA motifs with extreme mechanical properties are prevalent in genetic databases and hypothesize that their unique mechanical properties could contribute to this abundance.

The impact of sequence periodicity on DNA mechanics: investigating the origin of A-tract's curvature

Periodic sequences in phase with DNA helical shape are prevalent in genomes due to their capacity to modulate DNA elasticity on a global scale. However, how this occurs is not well understood. We use all-atom molecular dynamics simulations on 40 bp DNA fragments to assess the effect of periodicity on bending, twisting, and stretch elasticity. We observe that DNA static curvature is the mechanical parameter most influenced by periodicity, with A-tract sequences having the greatest effect. A-tracts generate global curvature by bending in distinct directions (minor groove and backbones) that complement the bending of the rest of DNA, which predominantly is towards the major groove. Even if A-tracts are rigid at the local scale, these small bends integrate with the greater bends from the sequences between, producing an amplifying effect. As a result, our findings support a 'delocalized bend' model in which the A-tract operates as an 'adaptable mechanical part'. By understanding how global curvature emerges from local fluctuations, we reconcile previous contradictory theories and open an avenue for manipulating DNA mechanics through sequence design.

Collective Molecular Machines: Multidimensionality and Reconfigurability

Molecular machines are key to cellular activity where they are involved in converting chemical and light energy into efficient mechanical work. During the last 60 years, designing molecular structures capable of generating unidirectional mechanical motion at the nanoscale has been the topic of intense research. Effective progress has been made, attributed to advances in various fields such as supramolecular chemistry, biology and nanotechnology, and informatics. However, individual molecular machines are only capable of producing nanometer work and generally have only a single functionality. In order to address these problems, collective behaviors realized by integrating several or more of these individual mechanical units in space and time have become a new paradigm. In this review, we comprehensively discuss recent developments in the collective behaviors of molecular machines. In particular, collective behavior is divided into two paradigms. One is the appropriate integration of molecular machines to efficiently amplify molecular motions and deformations to construct novel functional materials. The other is the construction of swarming modes at the supramolecular level to perform nanoscale or microscale operations. We discuss design strategies for both modes and focus on the modulation of features and properties. Subsequently, in order to address existing challenges, the idea of transferring experience gained in the field of micro/nano robotics is presented, offering prospects for future developments in the collective behavior of molecular machines.

Intrinsic Flexibility beyond the Highly Ordered DNA Tetrahedron: An Integrative Spectroscopic and Molecular Dynamics Approach

Since the introduction of DNA-based architectures, in the past decade, DNA tetrahedrons have aroused great interest. Applications of such nanostructures require structural control, especially in the perspective of their possible functionalities. In this work, an integrated approach for structural characterization of a tetrahedron structure is proposed with a focus on the fundamental biophysical aspects driving the assembly process. To address such an issue, spin-labeled DNA sequences are chemically synthesized, self-assembled, and then analyzed by Continuous-Wave (CW) and pulsed Electron Paramagnetic Resonance (EPR) spectroscopy. Interspin distance measurements based on PELDOR/DEER techniques combined with molecular dynamics (MD) thus revealed unexpected dynamic heterogeneity and flexibility of the assembled structures. The observation of flexibility in these ordered 3D structures demonstrates the sensitivity of this approach and its effectiveness in accessing the main dynamic and structural features with unprecedented resolution.

AT-specific DNA visualization revisits the directionality of bacteriophage λ DNA ejection

In this study, we specifically visualized DNA molecules at their AT base pairs after in vitro phage ejection. Our AT-specific visualization revealed that either end of the DNA molecule could be ejected first with a nearly 50% probability. This observation challenges the generally accepted theory of Last In First Out (LIFO), which states that the end of the phage λ DNA that enters the capsid last during phage packaging is the first to be ejected, and that both ends of the DNA are unable to move within the extremely condensed phage capsid. To support our observations, we conducted computer simulations that revealed that both ends of the DNA molecule are randomized, resulting in the observed near 50% probability. Additionally, we found that the length of the ejected DNA by LIFO was consistently longer than that by First In First Out (FIFO) during in vitro phage ejection. Our simulations attributed this difference in length to the stiffness difference of the remaining DNA within the phage capsid. In conclusion, this study demonstrates that a DNA molecule within an extremely dense phage capsid exhibits a degree of mobility, allowing it to switch ends during ejection.

Brownian ratchet for directional nanoparticle transport by repetitive stretch-relaxation of DNA

Brownian motion subject to a periodic and asymmetric potential can be biased by external, nonequilibrium fluctuations, leading to directional movement of Brownian particles. Sequence-dependent flexibility variation along double-stranded DNA has been proposed as a tool to develop periodic and asymmetric potentials for DNA binding of cationic nanoparticles with sizes below tens of nanometers. Here, we propose that repetitive stretching and relaxation of a long, double-stranded DNA molecule with periodic flexibility gradient can induce nonequilibrium fluctuations that tune the amplitude of asymmetric potentials for DNA-nanoparticle binding to result in directional transport of nanometer-sized particles along DNA. Realization of the proposed Brownian ratchet was proven by Brownian dynamics simulations of coarse-grained models of a single, long DNA molecule with flexibility variation and a cationic nanoparticle.

Cytosine methylation regulates DNA bendability depending on the curvature

Cytosine methylation plays an essential role in many biological processes, such as nucleosome inactivation and regulation of gene expression. The modulation of DNA mechanics may be one of the regulatory mechanisms influenced by cytosine methylation. However, it remains unclear how methylation influences DNA mechanics. Here, we show that methylation has contrasting effects on the bending property of dsDNA depending on DNA curvature. We directly applied bending force on 30 base pairs of dsDNA using a D-shaped DNA nanostructure and measured the degree of bending using single-molecule fluorescence resonance energy transfer without surface immobilization. When dsDNA is weakly bent, methylation increases the stiffness of dsDNA. The stiffness of dsDNA increased by approximately 8% with a single methylation site for 30 bp dsDNA. When dsDNA is highly bent by a strong force, it forms a kink, i.e., a sharp bending of dsDNA. Under strong bending, methylation destabilizes the non-kink form compared with the kink form, which makes dsDNA near the kink region apparently more bendable. However, if the kink region is methylated, the kink form is destabilized, and dsDNA becomes stiffer. As a result, methylation increases the stiffness of weakly bent dsDNA and concurrently can promote kink formation, which may stabilize the nucleosome structure. Our results provide new insight into the effect of methylation, showing that cytosine methylation has opposite effects on DNA mechanics depending on its curvature and methylation location.

Potential of Mean Force for DNA Wrapping Around a Cationic Nanoparticle

Sharp bending and wrapping of DNA around proteins and nanoparticles (NPs) has been of extensive research interest. Here, we present the potential of mean force (PMF) for wrapping a DNA double helix around a cationic NP using coarse-grained models of a double-stranded DNA and a cationic NP. Starting from a NP wrapped around by DNA, the PMF was calculated along the distance between the center of the NP and one end of the DNA molecule. A relationship between the distance and the extent of DNA wrapping is used to calculate the PMF as a function of DNA wrapping around a NP. In particular, the PMF was compared for two DNA sequences of (AT)₂₅/(AT)₂₅ and (AC)₂₅/(GT)₂₅, for which the persistence lengths are different by ∼10 nm. The simulation results provide solid evidence of the thermodynamic preference for complex formation of a cationic NP with more flexible DNA over the less flexible DNA. Furthermore, we estimated the elastic energy of DNA bending, which was in good order-of-magnitude agreement with the theoretical prediction of elastic rods. This work suggests that the variation of sequence-dependent DNA flexibility can be utilized in DNA nanotechnologies, in which the position and dynamics of NPs are regulated on large-scale DNA structures, or the structural transformation of DNA is triggered by the sequence-dependent binding of NPs.

Effect of DNA Flexibility on Complex Formation of a Cationic Nanoparticle with Double-Stranded DNA

We present extensive molecular dynamics simulations of a cationic nanoparticle and a double-stranded DNA molecule to discuss the effect of DNA flexibility on the complex formation of a cationic nanoparticle with double-stranded DNA. Martini coarse-grained models were employed to describe double-stranded DNA molecules with two different flexibilities and cationic nanoparticles with three different electric charges. As the electric charge of a cationic nanoparticle increases, the degree of DNA bending increases, eventually leading to the wrapping of DNA around the nanoparticle at high electric charges. However, a small increase in the persistence length of DNA by 10 nm requires a cationic nanoparticle with a markedly increased electric charge to bend and wrap DNA around. Thus, a more flexible DNA molecule bends and wraps around a cationic nanoparticle with an intermediate electric charge, whereas a less flexible DNA molecule binds to a nanoparticle with the same electric charge without notable bending. This work provides solid evidence that a small difference in DNA flexibility (as small as 10 nm in persistence length) has a substantial influence on the complex formation of DNA with proteins from a biological perspective and suggests that the variation of sequence-dependent DNA flexibility can be utilized in DNA nanotechnology as a new tool to manipulate the structure of DNA molecules mediated by nanoparticle binding.

Entropic Unmixing in Nematic Blends of Semiflexible Polymers

Binary mixtures of semiflexible polymers with the same chain length, but different persistence lengths, separate into two coexisting different nematic phases when the osmotic pressure of the lyotropic solution is varied. Molecular Dynamics simulations and Density Functional Theory predict phase diagrams either with a triple point, where the isotropic phase coexists with two nematic phases or a critical point of unmixing within the nematic mixture. The difference in locally preferred bond angles between the constituents drives this unmixing without any attractive interactions between monomers.

Mechanical Flexibility of DNA: A Quintessential Tool for DNA Nanotechnology

The mechanical properties of DNA have enabled it to be a structural and sensory element in many nanotechnology applications. While specific base-pairing interactions and secondary structure formation have been the most widely utilized mechanism in designing DNA nanodevices and biosensors, the intrinsic mechanical rigidity and flexibility are often overlooked. In this article, we will discuss the biochemical and biophysical origin of double-stranded DNA rigidity and how environmental and intrinsic factors such as salt, temperature, sequence, and small molecules influence it. We will then take a critical look at three areas of applications of DNA bending rigidity. First, we will discuss how DNA's bending rigidity has been utilized to create molecular springs that regulate the activities of biomolecules and cellular processes. Second, we will discuss how the nanomechanical response induced by DNA rigidity has been used to create conformational changes as sensors for molecular force, pH, metal ions, small molecules, and protein interactions. Lastly, we will discuss how DNA's rigidity enabled its application in creating DNA-based nanostructures from DNA origami to nanomachines.

Phosphorylated CtIP bridges DNA to promote annealing of broken ends

The DNA of our cells is constantly exposed to various types of damaging agents. One of the most critical types of damage is when both strands of the DNA break, and thus such breaks need to be efficiently repaired. It is known that CtIP promotes nucleases in DNA break repair. Here we show that CtIP can also hold the two DNA strands together in solution when DNA is free to move, using novel methodology that allows the monitoring of thousands of single DNA molecules in nanofabricated devices. DNA bridging likely facilitates the enzymatic repair steps and identifies novel CtIP functions that are crucial for repairing broken DNA.

The early steps of DNA double-strand break (DSB) repair in human cells involve the MRE11-RAD50-NBS1 (MRN) complex and its cofactor, phosphorylated CtIP. The roles of these proteins in nucleolytic DSB resection are well characterized, but their role in bridging the DNA ends for efficient and correct repair is much less explored. Here we study the binding of phosphorylated CtIP, which promotes the endonuclease activity of MRN, to single long (∼50 kb) DNA molecules using nanofluidic channels and compare it to the yeast homolog Sae2. CtIP bridges DNA in a manner that depends on the oligomeric state of the protein, and truncated mutants demonstrate that the bridging depends on CtIP regions distinct from those that stimulate the nuclease activity of MRN. Sae2 is a much smaller protein than CtIP, and its bridging is significantly less efficient. Our results demonstrate that the nuclease cofactor and structural functions of CtIP may depend on the same protein population, which may be crucial for CtIP functions in both homologous recombination and microhomology-mediated end-joining.

Structure-mechanics statistical learning unravels the linkage between local rigidity and global flexibility in nucleic acids

The mechanical properties of nucleic acids underlie biological processes ranging from genome packaging to gene expression, but tracing their molecular origin has been difficult due to the structural and chemical complexity. We posit that concepts from machine learning can help to tackle this long-standing challenge. Here, we demonstrate the feasibility and advantage of this strategy through developing a structure-mechanics statistical learning scheme to elucidate how local rigidity in double-stranded (ds)DNA and dsRNA may lead to their global flexibility in bend, stretch, and twist. Specifically, the mechanical parameters in a heavy-atom elastic network model are computed from the trajectory data of all-atom molecular dynamics simulation. The results show that the inter-atomic springs for backbone and ribose puckering in dsRNA are stronger than those in dsDNA, but are similar in strengths for base-stacking and base-pairing. Our analysis shows that the experimental observation of dsDNA being easier to bend but harder to stretch than dsRNA comes mostly from the respective B- and A-form topologies. The computationally resolved composition of local rigidity indicates that the flexibility of both nucleic acids is mostly due to base-stacking. But for properties like twist-stretch coupling, backbone springs are shown to play a major role instead. The quantitative connection between local rigidity and global flexibility sets foundation for understanding how local binding and chemical modification of genetic materials effectuate longer-ranged regulatory signals.

The mechanical properties of nucleic acids underlie biological processes ranging from genome packaging to gene expression. We devise structural mechanics statistical learning method to reveal their molecular origin in terms of chemical interactions.

Limitations of the equivalent neutral polymer assumption for theories describing nanochannel-confined DNA

The prevailing theories describing DNA confinement in a nanochannel are predicated on the assumption that wall-DNA electrostatic interactions are sufficiently short-ranged such that the problem can be mapped to an equivalent neutral polymer confined by hard walls with an appropriately reduced effective channel size. To determine when this hypothesis is valid, we leveraged a recently reported experimental data set for the fractional extension of DNA molecules in a 250-nm-wide poly(dimethyl siloxane) (PDMS) nanochannel with buffer ionic strengths between 0.075 and 48 mM. Evaluating these data in the context of the weakly correlated telegraph model of DNA confinement reveals that, at ionic strengths greater than 0.3 mM, the average fractional extension of the DNA molecules agree with theoretical predictions with a mean absolute error of 0.04. In contrast, experiments at ionic strengths below 0.3 mM produce average fractional extensions that are systematically smaller than the theoretical predictions with a larger mean absolute error of 0.15. The deviations between experiment and theory display a correlation coefficient of 0.82 with the decay length for the DNA-wall electrostatics, linking the deviations with a breakdown in approximating the DNA with an equivalent neutral polymer.

Polymer models for the mechanisms of chromatin 3D folding: review and perspective

In this perspective paper, classical physical models for mammalian interphase chromatin folding are reviewed.

Stretching Wormlike Chains in Narrow Tubes of Arbitrary Cross-Sections

We considered the stretching of semiflexible polymer chains confined in narrow tubes with arbitrary cross-sections. Based on the wormlike chain model and technique of normal mode decomposition in statistical physics, we derived a compact analytical expression on the force-confinement-extension relation of the chains. This single formula was generalized to be valid for tube confinements with arbitrary cross-sections. In addition, we extended the generalized bead-rod model for Brownian dynamics simulations of confined polymer chains subjected to force stretching, so that the confinement effects to the chains applied by the tubes with arbitrary cross-sections can be quantitatively taken into account through numerical simulations. Extensive simulation examples on the wormlike chains confined in tubes of various shapes quantitatively justified the theoretically derived generalized formula on the force-confinement-extension relation of the chains.

Enzyme-free optical DNA mapping of the human genome using competitive binding

Optical DNA mapping (ODM) allows visualization of long-range sequence information along single DNA molecules. The data can for example be used for detecting long range structural variations, for aiding DNA sequence assembly of complex genomes and for mapping epigenetic marks and DNA damage across the genome. ODM traditionally utilizes sequence specific marks based on nicking enzymes, combined with a DNA stain, YOYO-1, for detection of the DNA contour. Here we use a competitive binding approach, based on YOYO-1 and netropsin, which highlights the contour of the DNA molecules, while simultaneously creating a continuous sequence specific pattern, based on the AT/GC variation along the detected molecule. We demonstrate and validate competitive-binding-based ODM using bacterial artificial chromosomes (BACs) derived from the human genome and then turn to DNA extracted from white blood cells. We generalize our findings with in-silico simulations that show that we can map a vast majority of the human genome. Finally, we demonstrate the possibility of combining competitive binding with enzymatic labeling by mapping DNA damage sites induced by the cytotoxic drug etoposide to the human genome. Overall, we demonstrate that competitive-binding-based ODM has the potential to be used both as a standalone assay for studies of the human genome, as well as in combination with enzymatic approaches, some of which are already commercialized.

Building machines with DNA molecules

In nature, DNA molecules carry the hereditary information. But DNA has physical and chemical properties that make it attractive for uses beyond heredity. In this Review, we discuss the potential of DNA for creating machines that are both encoded by and built from DNA molecules. We review the main methods of DNA nanostructure assembly, describe recent advances in building increasingly complex molecular structures and discuss strategies for creating machine-like nanostructures that can be actuated and move. We highlight opportunities for applications of custom DNA nanostructures as scientific tools to address challenges across biology, chemistry and engineering.

Extension distribution for DNA confined in a nanochannel near the Odijk regime

DNA confinement in a nanochannel typically is understood via mapping to the confinement of an equivalent neutral polymer by hard walls. This model has proven to be effective for confinement in relatively large channels where hairpin formation is frequent. An analysis of existing experimental data for Escherichia coli DNA extension in channels smaller than the persistence length, combined with an additional dataset for λ-DNA confined in a 34 nm wide channel, reveals a breakdown in this approach as the channel size approaches the Odijk regime of strong confinement. In particular, the predicted extension distribution obtained from the asymptotic solution to the weakly correlated telegraph model for a confined wormlike chain deviates significantly from the experimental distribution obtained for DNA confinement in the 34 nm channel, and the discrepancy cannot be resolved by treating the alignment fluctuations or the effective channel size as fitting parameters. We posit that the DNA-wall electrostatic interactions, which are sensible throughout a significant fraction of the channel cross section in the Odijk regime, are the source of the disagreement between theory and experiment. Dimensional analysis of the wormlike chain propagator in channel confinement reveals the importance of a dimensionless parameter, reflecting the magnitude of the DNA-wall electrostatic interactions relative to thermal energy, which has not been considered explicitly in the prevailing theories for DNA confinement in a nanochannel.

DNA sequence-dependent chromatin architecture and nuclear hubs formation

In this study, by exploring chromatin conformation capture data, we show that the nuclear segregation of Topologically Associated Domains (TADs) is contributed by DNA sequence composition. GC-peaks and valleys of TADs strongly influence interchromosomal interactions and chromatin 3D structure. To gain insight on the compositional and functional constraints associated with chromatin interactions and TADs formation, we analysed intra-TAD and intra-loop GC variations. This led to the identification of clear GC-gradients, along which, the density of genes, super-enhancers, transcriptional activity, and CTCF binding sites occupancy co-vary non-randomly. Further, the analysis of DNA base composition of nucleolar aggregates and nuclear speckles showed strong sequence-dependant effects. We conjecture that dynamic DNA binding affinity and flexibility underlay the emergence of chromatin condensates, their growth is likely promoted in mechanically soft regions (GC-rich) of the lowest chromatin and nucleosome densities. As a practical perspective, the strong linear association between sequence composition and interchromosomal contacts can help define consensus chromatin interactions, which in turn may be used to study alternative states of chromatin architecture.

Simulations corroborate telegraph model predictions for the extension distributions of nanochannel confined DNA

Hairpins in the conformation of DNA confined in nanochannels close to their persistence length cause the distribution of their fractional extensions to be heavily left skewed. A recent theory rationalizes these skewed distributions using a correlated telegraph process, which can be solved exactly in the asymptotic limit of small but frequent hairpin formation. Pruned-enriched Rosenbluth method simulations of the fractional extension distribution for a channel-confined wormlike chain confirm the predictions of the telegraph model. Remarkably, the asymptotic result of the telegraph model remains robust well outside the asymptotic limit. As a result, the approximations in the theory required to map it to the polymer model and solve it in the asymptotic limit are not the source of discrepancies between the predictions of the telegraph model and experimental distributions of the extensions of DNA during genome mapping. The agreement between theory and simulations motivates future work to determine the source of the remaining discrepancies between the predictions of the telegraph model and experimental distributions of the extensions of DNA in nanochannels used for genome mapping.

Submicrometer elasticity of double-stranded DNA revealed by precision force-extension measurements with magnetic tweezers

Submicrometer elasticity of double-stranded DNA (dsDNA) governs nanoscale bending of DNA segments and their interactions with proteins. Single-molecule force spectroscopy, including magnetic tweezers (MTs), is an important tool for studying DNA mechanics. However, its application to short DNAs under 1 μm is limited. We developed an MT-based method for precise force-extension measurements in the 100-nm regime that enables in situ correction of the error in DNA extension measurement, and normalizes the force variability across beads by exploiting DNA hairpins. The method reduces the lower limit of tractable dsDNA length down to 198 base pairs (bp) (67 nm), an order-of-magnitude improvement compared to conventional tweezing experiments. Applying this method and the finite worm-like chain model we observed an essentially constant persistence length across the chain lengths studied (198 bp to 10 kbp), which steeply depended on GC content and methylation. This finding suggests a potential sequence-dependent mechanism for short-DNA elasticity.

In silico construction of a flexibility-based DNA Brownian ratchet for directional nanoparticle delivery

Brownian particles confined in a system with periodic and asymmetric potential can be transported in a specific direction along the potential by repetitively switching the potential on and off. Here, we propose a DNA-based Brownian ratchet for directional transport of positively charged nanoparticles in which nanoparticle delivery follows the path dictated by a single, long, double-stranded DNA. We performed Brownian dynamics simulations to prove its realization using coarse-grained models. A periodic and asymmetric potential for nanoparticle binding is constructed along a single, long, double-stranded DNA molecule by a novel strategy that uses variation in sequence-dependent DNA flexibility. Directional and processive motion of nanoparticles is achieved by changing salt concentration repetitively over several cycles to switch the asymmetric potential on and off. This work suggests that double-stranded DNA molecules with elaborately designed flexibility variation can be used as a molecule-scale guide for spatial and dynamic control of nanoparticles for future applications.

Measuring the wall depletion length of nanoconfined DNA

Efforts to study the polymer physics of DNA confined in nanochannels have been stymied by a lack of consensus regarding its wall depletion length. We have measured this quantity in 38 nm wide, square silicon dioxide nanochannels for five different ionic strengths between 15 mM and 75 mM. Experiments used the Bionano Genomics Irys platform for massively parallel data acquisition, attenuating the effect of the sequence-dependent persistence length and finite-length effects by using nick-labeled E. coli genomic DNA with contour length separations of at least 30 µm (88 325 base pairs) between nick pairs. Over 5 × 106 measurements of the fractional extension were obtained from 39 291 labeled DNA molecules. Analyzing the stretching via Odijk's theory for a strongly confined wormlike chain yielded a linear relationship between the depletion length and the Debye length. This simple linear fit to the experimental data exhibits the same qualitative trend as previously defined analytical models for the depletion length but now quantitatively captures the experimental data.

Distribution of label spacings for genome mapping in nanochannels

In genome mapping experiments, long DNA molecules are stretched by confining them to very narrow channels, so that the locations of sequence-specific fluorescent labels along the channel axis provide large-scale genomic information. It is difficult, however, to make the channels narrow enough so that the DNA molecule is fully stretched. In practice, its conformations may form hairpins that change the spacings between internal segments of the DNA molecule, and thus the label locations along the channel axis. Here, we describe a theory for the distribution of label spacings that explains the heavy tails observed in distributions of label spacings in genome mapping experiments.