Nanoconfined circular and linear DNA - equilibrium conformations and unfolding kinetics

Studies of circular DNA confined to nanofluidic channels are relevant both from a fundamental polymer-physics perspective and due to the importance of circular DNA molecules in vivo. We here observe the unfolding of DNA from the circular to linear configuration as a light-induced double strand break occurs, characterize the dynamics, and compare the equilibrium conformational statistics of linear and circular configurations. This is important because it allows us to determine to which extent existing statistical theories describe the extension of confined circular DNA. We find that the ratio of the extensions of confined linear and circular DNA configurations increases as the buffer concentration decreases. The experimental results fall between theoretical predictions for the extended de Gennes regime at weaker confinement and the Odijk regime at stronger confinement. We show that it is possible to directly distinguish between circular and linear DNA molecules by measuring the emission intensity from the DNA. Finally, we determine the rate of unfolding and show that this rate is larger for more confined DNA, possibly reflecting the corresponding larger difference in entropy between the circular and linear configurations. Introduction Nanofluidic channels have, during the last decade, emerged as a powerful tool to study single DNA molecules using fluorescence microscopy. When a DNA molecule is confined to a channel that is narrower than its radius of gyration it must stretch along the channel. The resulting extension of the DNA molecule depends linearly upon the contour length. Furthermore, there is no fundamental upper limit of the size of the DNA that can be investigated. A main advantage of using nanochannels, compared to most other single DNA-molecule techniques, such as optical and magnetic tweezers, is the possibility to stretch DNA without attaching any handles. This allows us to straightforwardly stretch circular DNA and DNA configurations with higher topologies. The polymer physics of confined DNA molecules has been studied intensively during the last decade and the effects of solvent characteristics and molecular crowding have been analyzed in detail. Recently, several groups have used nanofluidic channels to investigate the physical properties of nanoconfined DNA-protein complexes and for optical mapping of single DNA molecules. Circular DNA is of interest for at least two reasons. First, several different biological DNA molecules are circular, such as mitochondrial DNA in eukaryotic cells and chromosomal and plasmid DNA in bacteria. The latter has recently attracted strong interest since plasmids carry genes involved in antibiotic resistance. Second, it is of interest to analyze the equilibrium conformational fluctuations of confined circular DNA because it makes it possible to test statistical theories for the extension of confined polymers in new ways. Segments of strongly confined circular DNA configuration may interact substantially, even when they are located far from each other along the contour length. A peculiar property of DNA stained with fluorescent dyes, such as YOYO-1 (the dye used here), is that the dye in its excited state forms reactive oxygen species that cause single-strand breaks on DNA, so called “nicks”. When two such single-strand nicks occur sufficiently close to each other, but on opposite strands, then the duplex DNA between the two nicks becomes unstable and a double-strand break occurs. Since the folded conformation of the now linear configuration is entropically unfavorable, the broken DNA must unfold. In our experiments we observe how this unfolding proceeds in real time. After sufficiently long time a new equilibrium is reached, making it possible to compare the equilibrium conformational fluctuations of the circular and linear configurations of the same DNA molecule. It is much easier to compare to theoretical predictions for equilibrium conformational fluctuations of circular and linear DNA configurations when their contour lengths are the same. The channel sizes that we use in our experiments are of the same order as the persistence length of DNA. As a consequence, the conformational statistics of the confined DNA molecule cannot be adequately described by any of the established theories for confined polymers. However, we here show that the ratio between the extension of the circular and linear topologies of a 42 kbp DNA falls between theoretical predictions for the Odijk regime, valid at very strong confinement, and the extended de Gennes regime, valid at weaker confinement. As would be expected from a simple interpolation, the more confinement increases and buffer concentration decreases, the closer are the experimental results to the prediction for the Odijk regime. We also demonstrate that the rate of unfolding is higher for circular DNA at lower buffer concentrations where it is more extended, in agreement with the theoretical prediction that the difference in free energy between the two states is larger. In our experiments we find that circular DNA molecules are more likely to break very close to the ends of the extended circle and potential reasons for this bias are discussed. Finally, we show that measuring the local emission intensity of the confined DNA molecule allows us to automatically separate circular and linear DNA molecules in a nanofluidic device. Materials and Methods DNA samples were mixed in TBE buffer (Tris-Borate EDTA) prepared by dissolving and diluting a standard 10x TBE tablet (Medicago) in milli-Q water to the desired concentration. The reducing agent β-mercaptoethanol (Sigma-Aldrich) was added to the sample (3% v/v) to reduce photo-induced breaking of the DNA. The experiments were performed with circular charomid DNA (9-42, 42.2 kbp) purchased from Wako (Nippon Gene). The dimeric cyanine dye YOYO-1 from Invitrogen was used to stain DNA in dye:bp ratios of 1:10 , 1:20 and 1:40. The samples were not equilibrated, in order to allow different binding ratios to be investigated. The nanofluidic chips were fabricated in fused silica as described in Ref. [1]. Electron-beam lithography and reactive-ion etching were used to define the nanochannels with the following approximate dimensions: channel width 100 nm, channel depth 100 nm or 150 nm, channel length 500 μm. Microchannels with a width of approximately 50 μm and a depth of circa 1 μm connect the nanochannels to four reservoirs of the device. The DNA sample was loaded into the one of the reservoirs and brought into the nanochannels by a pressure-driven flow. For DNA imaging, an epi-fluorescence microscope (Zeiss AxioObserver.Z1) equipped with a high quantum yield EMCCD camera (Photometrics Evolve) and a 100x oil immersion objective with high numerical aperture (NA 1.46) from Zeiss was used. A stack of 200 images was recorded for each DNA molecule with an exposure time of 100 ms per frame at a rate of 7 frames per second. Data analysis was performed with the program ImageJ (http://rsbweb.nih.gov/ij/) and algorithms written in Matlab. In short, DNA molecules were marked in the image stack by a region of interest and the algorithm computed an intensity trace of each individual molecule by averaging over the region of interest in each frame. A kymograph (time trace) was then constructed by stacking these intensity traces on top of each other. Examples are shown in Fig. 1. Each line in the kymograph corresponds to one frame in the image stack. For each frame the intensity trace was fitted to an error-function profile. This procedure gives the average fluorescence intensity and the extension of the DNA molecule in each frame. Note that the above refers to the profile along the channel direction, averaged over the transverse direction. The form of the transverse density profile was discussed by Werner et al. in [26]. From the kymograph (Fig. 1A) it is possible to determine the time when the circular DNA broke, and to find the position of the corresponding breaking point in the channel. To determine the break time and position we first smoothed the kymograph aligned by the intensity weighted center (Fig. 1B) using two-dimensional averaging. Using Otsu’s method we distinguished three different regions in the kymograph (Fig. 1B), corresponding to circular and linear DNA configurations, and a background region. These three regions differ in their fluorescence-emission intensities and are identified using a Matlab script. In Fig. 1B the light regions with the highest fluorescent intensities pertain to times and positions in the kymograph corresponding to unbroken circular DNA configurations. The somewhat darker regions correspond to broken linear DNA configurations. The background is black. In a second step we located the triangular kymograph area that corresponds to broken DNA in the process of unfolding (visible in panel B of Fig. 1). The coordinates of the highest corner of this triangle give the breaking position and the breaking time. All results were verified by manual inspection. More details on the procedure can be found in the Supporting Information. A Matlab script was used to automate the analysis of the unfolding process. Fig. 2 shows the trace of molecule extension as a function of time, overlaid with a fitted empirical formula given by R(t) = 1/2 (Rlin + Rcirc) + 1/2 (Rlin – Rcirc)erf((t-t0)/τ) (1) From the fit the start and end points of the unfolding process were determined as the first points where the difference between adjacent time points in the fitted function differs by more than a user-set threshold, here chosen to be 0.2 pixels (32 nm). The rate of unfolding is taken to be the slope of the line connecting the start and end points (black line in Fig. 2). In addition, the equilibrium extension and its standard deviation for the circular and linear configuration of the DNA were calculated by averaging over all values of R(t) before the start point and after the end point, respectively. Results We start by describing equilibrium extensions of circular and linear DNA configurations. First we show that it is possible to experimentally detect when and how circular DNA breaks and unfolds to the linear configuration, using the fact that there are apparent differences in extension and emission intensity of the circular and the linear configurations (Materials and Methods). Figure 1A shows two examples of extracted kymographs for initially circular DNA configurations that break at the center (left) and the end (right), respectively, and subsequently unfold. Figure 1B shows the same data but aligned as described in the Methods section. Figure 1C compares snap-shots of a YOYO-1-stained circular DNA before and after unfolding in the nanochannel. As expected, the DNA is more extended when it has reached its linear equilibrium configuration. The data in 0.05X TBE buffer is collected in 100x100 nm channels and all other data is collected in 100x150 nm channels. The sample in 0.05X TBE is included in order to push the extension as close to the Odijk regime as possible (see below). Furthermore, when labeling the DNA with YOYO-1 we do not equilibrate our samples. This makes it possible to investigate a wide range of dye loads. We now compare the experimental observations with theoretical predictions. A DNA molecule is commonly modeled as a worm-like chain with contour length L, persistence length lp ≈ 50 nm, and effective width weff ≈ 5–20 nm (depending on buffer concentration). Since the channel dimensions D ≈ 100–150 nm are of the same order as the persistence length of the DNA, there are no exact theories for the extension ratio. However, we show below that the experimental results are consistent with a simple interpolation between the expected results for the Odijk regime and the extended de Gennes regime (valid for smaller and larger channels, respectively). Theory for the extended de Gennes regime For a semi-flexible polymer, such as DNA, there exists a parameter regime at intermediate channel sizes lp < D < lp/weff , known as the extended de Gennes regime. In this regime, an asymptotically exact theory for the equilibrium statistics of a linear polymer predicts that the mean and variance of the extension are given by [31] R!"# = 1.18L l!w!"" D! ! ! 2 σ!"# = 0.51 Ll! ! 3 Unfortunately it is not obvious how to generalize this model to circular polymers. We expect that the method described in Ref. [30] may be applied to circular DNA, but this has not yet been shown. An alternative way to derive the scalings (though not the prefactors) of Eqs. 2-3 is to estimate the Rdependence of the free energy by a Flory-type mean-field argument, yielding 32] F!"# R!"# kT = A R!"# ! Ll! + B Lw!"" R!"#D 4 R!"# = L Bl!w!"" 2AD! ! ! 5 σ!"# ! = Ll! 12A 6 Here, A and B are prefactors of order unity. This calculation for the free energy is easily generalized to a circular polymer, by treating it as two linear chains of length L/2 that are forced to overlap: F!"#! R!"#! kT = 2A R!"#! ! L 2 l! + B Lw!"" R!"#!D 7 R!"#! = L Bl!w!"" 8AD! ! ! 8 σ!"#! ! = Ll! 48A = σ!"# ! 4 9 Here A and B are the prefactors mentioned above. Comparing Eqs. 5-6 and Eqs. 8-9, one finds R!"# R!"#! = 1.59 10 σ!"# σ!"#! = 2 11 It should be noted that whereas the circular DNA molecule is presumably in an unknotted state, the theory averages over all possible knotting states. To which extent this matters remains to be tested. Theory for the Odijk regime The Odijk regime applies to polymers confined to channels with a diameter smaller than the persistence length. In this regime, the mean and variance of the extension of a linear DNA molecule confined to a rectangular channel with cross section Dx × Dy are given by R!"# = L 1− α D! ! ! + D! ! !