Equilibrium melting probabilities of a DNA molecule with a defect: An exact solution of the Poland-Scheraga model.

In this study we derive analytically the equilibrium melting probabilities for basepairs of a DNA molecule with a defect site. We assume that the defect is characterized by a change in the Watson-Crick basepair energy of the defect basepair, and in the associated two stacking energies for the defect, as compared to the remaining parts of the DNA. The defect site could, for instance, occur due to DNA basepair mismatching, cross-linking, or by the chemical modifications when attaching fluorescent labels, such as fluorescent-quencher pairs, to DNA. Our exact solution of the Poland-Scheraga model for DNA melting provides the probability that the labeled basepair, and its neighbors, are open at different temperatures. Our work is of direct importance, for instance, for studies where fluorophore-quencher pairs are used for studying single basepair fluctuations of designed DNA molecules.

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.

Stochastic unfolding of nanoconfined DNA: Experiments, model and Bayesian analysis.

Nanochannels provide a means for detailed experiments on the effect of confinement on biomacromolecules, such as DNA. Here we introduce a model for the complete unfolding of DNA from the circular to linear configuration. Two main ingredients are the entropic unfolding force and the friction coefficient for the unfolding process, and we describe the associated dynamics by a non-linear Langevin equation. By analyzing experimental data where DNA molecules are photo-cut and unfolded inside a nanochannel, our model allows us to extract values for the unfolding force as well as the friction coefficient for the first time. In order to extract numerical values for these physical quantities, we employ a recently introduced Bayesian inference framework. We find that the determined unfolding force is in agreement with estimates from a simple Flory-type argument. The estimated friction coefficient is in agreement with theoretical estimates for motion of a cylinder in a channel. We further validate the estimated friction constant by extracting this parameter from DNA's center-of-mass motion before and after unfolding, yielding decent agreement. We provide publically available software for performing the required image and Bayesian analysis.

Bacteriophage strain typing by rapid single molecule analysis.

Rapid characterization of unknown biological samples is under the focus of many current studies. Here we report a method for screening of biological samples by optical mapping of their DNA. We use a novel, one-step chemo-enzymatic reaction to covalently bind fluorophores to DNA at the four-base recognition sites of a DNA methyltransferase. Due to the diffraction limit of light, the dense distribution of labels results in a continuous fluorescent signal along the DNA. The amplitude modulations (AM) of the fluorescence intensity along the stretched DNA molecules exhibit a unique molecular fingerprint that can be used for identification. We show that this labelling scheme is highly informative, allowing accurate genotyping. We demonstrate the method by labelling the genomes of λ and T7 bacteriophages, resulting in a consistent, unique AM profile for each genome. These profiles are also successfully used for identification of the phages from a background phage library. Our method may provide a facile route for screening and typing of various organisms and has potential applications in metagenomics studies of various ecosystems.

Competitive binding-based optical DNA mapping for fast identification of bacteria--multi-ligand transfer matrix theory and experimental applications on Escherichia coli.

We demonstrate a single DNA molecule optical mapping assay able to resolve a specific Escherichia coli strain from other strains. The assay is based on competitive binding of the fluorescent dye YOYO-1 and the AT-specific antibiotic netropsin. The optical map is visualized by stretching the DNA molecules in nanofluidic channels. We optimize the experimental conditions to obtain reproducible barcodes containing as much information as possible. We implement a multi-ligand transfer matrix method for calculating theoretical barcodes from known DNA sequences. Our method extends previous theoretical approaches for competitive binding of two types of ligands to many types of ligands and introduces a recursive approach that allows long barcodes to be calculated with standard computer floating point formats. The identification of a specific E. coli strain (CCUG 10979) is based on mapping of 50-160 kilobasepair experimental DNA fragments onto the theoretical genome using the developed theory. Our identification protocol introduces two theoretical constructs: a P-value for a best experiment-theory match and an information score threshold. The developed methods provide a novel optical mapping toolbox for identification of bacterial species and strains. The protocol does not require cultivation of bacteria or DNA amplification, which allows for ultra-fast identification of bacterial pathogens.

How nanochannel confinement affects the DNA melting transition within the Poland-Scheraga model.

When double-stranded DNA molecules are heated, or exposed to denaturing agents, the two strands are separated. The statistical physics of this process has a long history and is commonly described in terms of the Poland-Scheraga (PS) model. Crucial to this model is the configurational entropy for a melted region (compared to the entropy of an intact region of the same size), quantified by the loop factor. In this study, we investigate how confinement affects the DNA melting transition, by using the loop factor for an ideal Gaussian chain. By subsequent numerical solutions of the PS model, we demonstrate that the melting temperature depends on the persistence lengths of single-stranded and double-stranded DNA. For realistic values of the persistence lengths, the melting temperature is predicted to decrease with decreasing channel diameter. We also demonstrate that confinement broadens the melting transition. These general findings hold for the three scenarios investigated: 1. homo-DNA, i.e., identical basepairs along the DNA molecule, 2. random sequence DNA, and 3. "real" DNA, here T4 phage DNA. We show that cases 2 and 3 in general give rise to broader transitions than case 1. Case 3 exhibits a similar phase transition as case 2 provided the random sequence DNA has the same ratio of AT to GC basepairs (A - adenine, T - thymine, G - guanine, C - cytosine). A simple analytical estimate for the shift in melting temperature is provided as a function of nanochannel diameter. For homo-DNA, we also present an analytical prediction of the melting probability as a function of temperature.

Non-Markovian effects in the first-passage dynamics of obstructed tracer particle diffusion in one-dimensional systems.

The standard setup for single-file diffusion is diffusing particles in one dimension which cannot overtake each other, where the dynamics of a tracer (tagged) particle is of main interest. In this article, we generalize this system and investigate first-passage properties of a tracer particle when flanked by identical crowder particles which may, besides diffuse, unbind (rebind) from (to) the one-dimensional lattice with rates k(off) (k(on)). The tracer particle is restricted to diffuse with rate k(D) on the lattice and the density of crowders is constant (on average). The unbinding rate k(off) is our key parameter and it allows us to systematically study the non-trivial transition between the completely Markovian case (k(off) ≫ k(D)) to the non-Markovian case (k(off) ≪ k(D)) governed by strong memory effects. This has relevance for several quasi one-dimensional systems. One example is gene regulation where regulatory proteins are searching for specific binding sites on a crowded DNA. We quantify the first-passage time distribution, f(t) (t is time), numerically using the Gillespie algorithm, and estimate f(t) analytically. In terms of k(off) (keeping k(D) fixed), we study the transition between the two known regimes: (i) when k(off) ≫ k(D) the particles may effectively pass each other and we recover the single particle result f(t) ∼ t(-3/2), with a reduced diffusion constant; (ii) when k(off) ≪ k(D) unbinding is rare and we obtain the single-file result f(t) ∼ t(-7/4). The intermediate region displays rich dynamics where both the characteristic f(t) - peak and the long-time power-law slope are sensitive to k(off).

Photophysical image analysis: Unsupervised probabilistic thresholding for images from electron-multiplying charge-coupled devices.

We introduce the concept photophysical image analysis (PIA) and an associated pipeline for unsupervised probabilistic image thresholding for images recorded by electron-multiplying charge-coupled device (EMCCD) cameras. We base our approach on a closed-form analytic expression for the characteristic function (Fourier-transform of the probability mass function) for the image counts recorded in an EMCCD camera, which takes into account both stochasticity in the arrival of photons at the imaging camera and subsequent noise induced by the detection system of the camera. The only assumption in our method is that the background photon arrival to the imaging system is described by a stationary Poisson process (we make no assumption about the photon statistics for the signal). We estimate the background photon statistics parameter, λbg, from an image which contains both background and signal pixels by use of a novel truncated fit procedure with an automatically determined image count threshold. Prior to this, the camera noise model parameters are estimated using a calibration step. Utilizing the estimates for the camera parameters and λbg, we then introduce a probabilistic thresholding method, where, for the first time, the fraction of misclassified pixels can be determined a priori for a general image in an unsupervised way. We use synthetic images to validate our a priori estimates and to benchmark against the Otsu method, which is a popular unsupervised non-probabilistic image thresholding method (no a priori estimates for the error rates are provided). For completeness, we lastly present a simple heuristic general-purpose segmentation method based on the thresholding results, which we apply to segmentation of synthetic images and experimental images of fluorescent beads and lung cell nuclei. Our publicly available software opens up for fully automated, unsupervised, probabilistic photophysical image analysis.

Microscopic origin of the logarithmic time evolution of aging processes in complex systems.

There exists compelling experimental evidence in numerous systems for logarithmically slow time evolution, yet its full theoretical understanding remains elusive. We here introduce and study a generic transition process in complex systems, based on nonrenewal, aging waiting times. Each state n of the system follows a local clock initiated at t = 0. The random time τ between clock ticks follows the waiting time density ψ(τ). Transitions between states occur only at local clock ticks and are hence triggered by the local forward waiting time, rather than by ψ(τ). For power-law forms ψ(τ) ≃ τ(-1-α) (0 < α < 1) we obtain a logarithmic time evolution of the state number ⟨n(t)⟩ ≃ log(t/t(0)), while for α > 2 the process becomes normal in the sense that ⟨n(t)⟩ ≃ t. In the intermediate range 1 < α < 2 we find the power-law growth ⟨n(t)⟩ ≃ t(α-1). Our model provides a universal description for transition dynamics between aging and nonaging states.

Strain-level bacterial typing directly from patient samples using optical DNA mapping.

BACKGROUND: Identification of pathogens is crucial to efficiently treat and prevent bacterial infections. However, existing diagnostic techniques are slow or have a too low resolution for well-informed clinical decisions. METHODS: In this study, we have developed an optical DNA mapping-based method for strain-level bacterial typing and simultaneous plasmid characterisation. For the typing, different taxonomical resolutions were examined and cultivated pure Escherichia coli and Klebsiella pneumoniae samples were used for parameter optimization. Finally, the method was applied to mixed bacterial samples and uncultured urine samples from patients with urinary tract infections. RESULTS: We demonstrate that optical DNA mapping of single DNA molecules can identify Escherichia coli and Klebsiella pneumoniae at the strain level directly from patient samples. At a taxonomic resolution corresponding to E. coli sequence type 131 and K. pneumoniae clonal complex 258 forming distinct groups, the average true positive prediction rates are 94% and 89%, respectively. The single-molecule aspect of the method enables us to identify multiple E. coli strains in polymicrobial samples. Furthermore, by targeting plasmid-borne antibiotic resistance genes with Cas9 restriction, we simultaneously identify the strain or subtype and characterize the corresponding plasmids. CONCLUSION: The optical DNA mapping method is accurate and directly applicable to polymicrobial and clinical samples without cultivation. Hence, it has the potential to rapidly provide comprehensive diagnostics information, thereby optimizing early antibiotic treatment and opening up for future precision medicine management.

For bacterial infections, it is important to rapidly and accurately identify and characterize the type of bacteria involved so that optimal antibiotic treatment can be given quickly to the patient. However, current diagnostic methods are sometimes slow and cannot be used for mixtures of bacteria. We have, therefore, developed a method to identify bacteria directly from patient samples. The method was tested on two common species of disease-causing bacteria ­ Escherichia coli and Klebsiella pneumoniae ­ and it could correctly identify the bacterial strain or subtype in both urine samples and mixtures. Hence, the method has the potential to provide fast diagnostic information for choosing the most suited antibiotic, thereby reducing the risk of death and suffering.

First passage times for a tracer particle in single file diffusion and fractional Brownian motion.

We investigate the full functional form of the first passage time density (FPTD) of a tracer particle in a single-file diffusion (SFD) system whose population is: (i) homogeneous, i.e., all particles having the same diffusion constant and (ii) heterogeneous, with diffusion constants drawn from a heavy-tailed power-law distribution. In parallel, the full FPTD for fractional Brownian motion [fBm-defined by the Hurst parameter, H ∈ (0, 1)] is studied, of interest here as fBm and SFD systems belong to the same universality class. Extensive stochastic (non-Markovian) SFD and fBm simulations are performed and compared to two analytical Markovian techniques: the method of images approximation (MIA) and the Willemski-Fixman approximation (WFA). We find that the MIA cannot approximate well any temporal scale of the SFD FPTD. Our exact inversion of the Willemski-Fixman integral equation captures the long-time power-law exponent, when H ≥ 1/3, as predicted by Molchan [Commun. Math. Phys. 205, 97 (1999)] for fBm. When H < 1/3, which includes homogeneous SFD (H = 1/4), and heterogeneous SFD (H < 1/4), the WFA fails to agree with any temporal scale of the simulations and Molchan's long-time result. SFD systems are compared to their fBm counter parts; and in the homogeneous system both scaled FPTDs agree on all temporal scales including also, the result by Molchan, thus affirming that SFD and fBm dynamics belong to the same universality class. In the heterogeneous case SFD and fBm results for heterogeneity-averaged FPTDs agree in the asymptotic time limit. The non-averaged heterogeneous SFD systems display a lack of self-averaging. An exponential with a power-law argument, multiplied by a power-law pre-factor is shown to describe well the FPTD for all times for homogeneous SFD and sub-diffusive fBm systems.

A simple cut and stretch assay to detect antimicrobial resistance genes on bacterial plasmids by single-molecule fluorescence microscopy.

Antimicrobial resistance (AMR) is a fast-growing threat to global health. The genes conferring AMR to bacteria are often located on plasmids, circular extrachromosomal DNA molecules that can be transferred between bacterial strains and species. Therefore, effective methods to characterize bacterial plasmids and detect the presence of resistance genes can assist in managing AMR, for example, during outbreaks in hospitals. However, existing methods for plasmid analysis either provide limited information or are expensive and challenging to implement in low-resource settings. Herein, we present a simple assay based on CRISPR/Cas9 excision and DNA combing to detect antimicrobial resistance genes on bacterial plasmids. Cas9 recognizes the gene of interest and makes a double-stranded DNA cut, causing the circular plasmid to linearize. The change in plasmid configuration from circular to linear, and hence the presence of the AMR gene, is detected by stretching the plasmids on a glass surface and visualizing by fluorescence microscopy. This single-molecule imaging based assay is inexpensive, fast, and in addition to detecting the presence of AMR genes, it provides detailed information on the number and size of plasmids in the sample. We demonstrate the detection of several ß-lactamase-encoding genes on plasmids isolated from clinical samples. Furthermore, we demonstrate that the assay can be performed using standard microbiology and clinical laboratory equipment, making it suitable for low-resource settings.

Dissimilar bouncy walkers.

We consider the dynamics of a one-dimensional system consisting of dissimilar hardcore interacting (bouncy) random walkers. The walkers' (diffusing particles') friction constants ξ(n), where n labels different bouncy walkers, are drawn from a distribution ϱ(ξ(n)). We provide an approximate analytic solution to this recent single-file problem by combining harmonization and effective medium techniques. Two classes of systems are identified: when ϱ(ξ(n)) is heavy-tailed, ϱ(ξ(n))≃ξ(n) (-1-α) (0<α<1) for large ξ(n), we identify a new universality class in which density relaxations, characterized by the dynamic structure factor S(Q, t), follows a Mittag-Leffler relaxation, and the mean square displacement (MSD) of a tracer particle grows as t(δ) with time t, where δ = α∕(1 + α). If instead ϱ is light-tailed such that the mean friction constant exist, S(Q, t) decays exponentially and the MSD scales as t(1/2). We also derive tracer particle force response relations. All results are corroborated by simulations and explained in a simplified model.

Observing plasmonic-molecular resonance coupling on single gold nanorods.

Strong plasmonic-molecular resonance coupling occurs between noble metal nanocrystals and organic adsorbates when the plasmonic resonance is degenerate with the molecular one. This interaction forms the basis for many fundamental studies and practical applications. We describe here the first direct measurement of the resonance coupling on single gold nanorods. The dark-field scattering technique is employed. The nanorods are embedded in hydrogel to facilitate uniform dye adsorption. The adsorbed dye molecules exhibit both monomer and H-aggregate absorption bands. The same gold nanorods are measured before and after the dye adsorption. Both strong and weak coupling are investigated by selecting nanorods with different longitudinal plasmon bands. Excellent agreement between the experiments and an analytic theory is obtained. The resonance coupling reveals a unique three-band structure. The tunability of the coupling on individual nanorods is further demonstrated by photodecomposing the adsorbed dye molecules.

Combining dense and sparse labeling in optical DNA mapping.

Optical DNA mapping (ODM) is based on fluorescent labeling, stretching and imaging of single DNA molecules to obtain sequence-specific fluorescence profiles, DNA barcodes. These barcodes can be mapped to theoretical counterparts obtained from DNA reference sequences, which in turn allow for DNA identification in complex samples and for detecting structural changes in individual DNA molecules. There are several types of DNA labeling schemes for ODM and for each labeling type one or several types of match scoring methods are used. By combining the information from multiple labeling schemes one can potentially improve mapping confidence; however, combining match scores from different labeling assays has not been implemented yet. In this study, we introduce two theoretical methods for dealing with analysis of DNA molecules with multiple label types. In our first method, we convert the alignment scores, given as output from the different assays, into p-values using carefully crafted null models. We then combine the p-values for different label types using standard methods to obtain a combined match score and an associated combined p-value. In the second method, we use a block bootstrap approach to check for the uniqueness of a match to a database for all barcodes matching with a combined p-value below a predefined threshold. For obtaining experimental dual-labeled DNA barcodes, we introduce a novel assay where we cut plasmid DNA molecules from bacteria with restriction enzymes and the cut sites serve as sequence-specific markers, which together with barcodes obtained using the established competitive binding labeling method, form a dual-labeled barcode. All experimental data in this study originates from this assay, but we point out that our theoretical framework can be used to combine data from all kinds of available optical DNA mapping assays. We test our multiple labeling frameworks on barcodes from two different plasmids and synthetically generated barcodes (combined competitive-binding- and nick-labeling). It is demonstrated that by simultaneously using the information from all label types, we can substantially increase the significance when we match experimental barcodes to a database consisting of theoretical barcodes for all sequenced plasmids.

A Predictive Model of Antibody Binding in the Presence of IgG-Interacting Bacterial Surface Proteins.

Many bacteria can interfere with how antibodies bind to their surfaces. This bacterial antibody targeting makes it challenging to predict the immunological function of bacteria-associated antibodies. The M and M-like proteins of group A streptococci (GAS) exhibit IgGFc-binding regions, which they use to reverse IgG binding orientation depending on the host environment. Unraveling the mechanism behind these binding characteristics may identify conditions under which bound IgG can drive an efficient immune response. Here, we have developed a biophysical model for describing these complex protein-antibody interactions. We show how the model can be used as a tool for studying the binding behavior of various IgG samples to M protein by performing in silico simulations and correlating this data with experimental measurements. Besides its use for mechanistic understanding, this model could potentially be used as a tool to aid in the development of antibody treatments. We illustrate this by simulating how IgG binding to GAS in serum is altered as specified amounts of monoclonal or pooled IgG is added. Phagocytosis experiments link this altered antibody binding to a physiological function and demonstrate that it is possible to predict the effect of an IgG treatment with our model. Our study gives a mechanistic understanding of bacterial antibody targeting and provides a tool for predicting the effect of antibody treatments in the presence of bacteria with IgG-modulating surface proteins.

Detection of structural variations in densely-labelled optical DNA barcodes: A hidden Markov model approach.

Large-scale genomic alterations play an important role in disease, gene expression, and chromosome evolution. Optical DNA mapping (ODM), commonly categorized into sparsely-labelled ODM and densely-labelled ODM, provides sequence-specific continuous intensity profiles (DNA barcodes) along single DNA molecules and is a technique well-suited for detecting such alterations. For sparsely-labelled barcodes, the possibility to detect large genomic alterations has been investigated extensively, while densely-labelled barcodes have not received as much attention. In this work, we introduce HMMSV, a hidden Markov model (HMM) based algorithm for detecting structural variations (SVs) directly in densely-labelled barcodes without access to sequence information. We evaluate our approach using simulated data-sets with 5 different types of SVs, and combinations thereof, and demonstrate that the method reaches a true positive rate greater than 80% for randomly generated barcodes with single variations of size 25 kilobases (kb). Increasing the length of the SV further leads to larger true positive rates. For a real data-set with experimental barcodes on bacterial plasmids, we successfully detect matching barcode pairs and SVs without any particular assumption of the types of SVs present. Instead, our method effectively goes through all possible combinations of SVs. Since ODM works on length scales typically not reachable with other techniques, our methodology is a promising tool for identifying arbitrary combinations of genomic alterations.

Cultivation-Free Typing of Bacteria Using Optical DNA Mapping.

A variety of pathogenic bacteria can infect humans, and rapid species identification is crucial for the correct treatment. However, the identification process can often be time-consuming and depend on the cultivation of the bacterial pathogen(s). Here, we present a stand-alone, enzyme-free, optical DNA mapping assay capable of species identification by matching the intensity profiles of large DNA molecules to a database of fully assembled bacterial genomes (>10 000). The assay includes a new data analysis strategy as well as a general DNA extraction protocol for both Gram-negative and Gram-positive bacteria. We demonstrate that the assay is capable of identifying bacteria directly from uncultured clinical urine samples, as well as in mixtures, with the potential to be discriminative even at the subspecies level. We foresee that the assay has applications both within research laboratories and in clinical settings, where the time-consuming step of cultivation can be minimized or even completely avoided.

Bubble merging in breathing DNA as a vicious walker problem in opposite potentials.

We investigate the coalescence of two DNA bubbles initially located at weak domains and separated by a more stable barrier region in a designed construct of double-stranded DNA. In a continuum Fokker-Planck approach, the characteristic time for bubble coalescence and the corresponding distribution are derived, as well as the distribution of coalescence positions along the barrier. Below the melting temperature, we find a Kramers-type barrier crossing behavior, while at high temperatures, the bubble corners perform drift diffusion toward coalescence. In the calculations, we map the bubble dynamics on the problem of two vicious walkers in opposite potentials. We also present a discrete master equation approach to the bubble coalescence problem. Numerical evaluation and stochastic simulation of the master equation show excellent agreement with the results from the continuum approach. Given that the coalesced state is thermodynamically stabilized against a state where only one or a few of the base pairs of the barrier region are re-established, it appears likely that this type of setup could be useful for the quantitative investigation of thermodynamic DNA stability data as well as the rate constants involved in the unzipping and zipping dynamics of DNA in single molecule fluorescence experiments.

Single DNA denaturation and bubble dynamics.

While the Watson-Crick double-strand is the thermodynamically stable state of DNA in a wide range of temperature and salt conditions, even at physiological conditions local denaturation bubbles may open up spontaneously due to thermal activation. By raising the ambient temperature, titration, or by external forces in single molecule setups bubbles proliferate until full denaturation of the DNA occurs. Based on the Poland-Scheraga model we investigate both the equilibrium transition of DNA denaturation and the dynamics of the denaturation bubbles with respect to recent single DNA chain experiments for situations below, at, and above the denaturation transition. We also propose a new single molecule setup based on DNA constructs with two bubble zones to measure the bubble coalescence and extract the physical parameters relevant to DNA breathing. Finally we consider the interplay between denaturation bubbles and selectively single-stranded DNA binding proteins.