Conformation, Length, and Speed Measurements of Electrodynamically Stretched DNA in Nanochannels

By Reccius, Christian H Stavis, Samuel M; Mannion, John T; Walker, Larry P; Craighead, H G

ABSTRACT A method is presented to rapidly and precisely measure the conformation, length, speed, and fluorescence intensity of single DNA molecules constrained by a nanochannel. DNA molecules were driven electrophoretically from a nanoslit into a nanochannel to confine and dynamically elongate them beyond their equilibrium length for repeated detection via laser-induced fluorescence spectroscopy. A single-molecule analysis algorithm was developed to analytically model bursts of fluorescence and determine the folding conformation of each stretched molecule. This technique achieved a molecular length resolution of 114 nm and an analysis time of around 20 ms per molecule, which enabled the sensitive investigation of several aspects of the physical behavior of DNA in a nanochannel. lambda-bacteriophage DNA was used to study the dependence of stretching on the applied device bias, the effect of conformation on speed, and the amount of DNA fragmentation in the device. A mixture of lambda-bacteriophage with the fragments of its own HindIII digest, a standard DNA ladder, was sized by length as well as by fluorescence intensity, which also allowed the characterization of DNA speed in a nanochannel as a function of length over two and a half orders of magnitude.

INTRODUCTION

The demand for increased analytical ability in the biological sciences has spurred the development of submicrometer- and nanometer- scale structures for single-molecule analysis. These structures facilitate the manipulation and analysis of biological molecules with higher speed and precision than is possible with conventional technology. Such capabilities promise to be useful in applications ranging from genomic sequencing to pathogen detection and in fundamental research in Melds such as molecular biology and biophysics.

An assortment of nanoscale structures for enhanced singlemolecule analysis has recently been developed, including solid-state nanopores (1,2) entropie trap arrays (3-5), zero mode waveguides (6,7), metallic nanoslit near field scanners (8), and pillar arrays (9-11). Submicrometer- and nanometerscale fluidic channels used in conjunction with fluorescence spectroscopy have also shown significant potential for the manipulation and analysis of single DNA molecules. Much of this work has focused on the implementation of rapid and sensitive analytical techniques such as fragment sizing (12,13), correlation spectroscopy (14), binding assays (15), identification of nucleic acid engineered labels (16), mobility measurements (17), and polymerase chain reaction analysis (18). The physical behavior and genetic analysis of single DNA molecules in nanochannels are subjects of particular interest as well (10,11,19,20). DNA has been hydrodynamically linearized in submicrometer fluidic devices, which can be used for genomic sequencing when combined with repeated fluorescence detection (21- 25). DNA molecules have also been shown to become elongated to an extended equilibrium length when introduced into a nanochannel (26), which has been utilized for restriction mapping (27). Further work has investigated other aspects of the physics of elongated DNA strands in nanochannels, including entropically driven dynamics and compression against nanoscale constrictions (28-30). There has also been a growing interest in using nanochannels (26) and other methods (8,31,32) to analyze single molecules with spatial resolution beyond the optical diffraction limit while benefiting from the advantages of established fluorescence spectroscopy techniques.

In this study, a method is described to quickly and precisely measure the conformation, length, speed, and fluorescence intensity of single DNA molecules constrained by a nanochannel. DNA molecules were driven electrophoretically from a nanoslit into a nanochannel, as illustrated in Fig. 1 A, which confined and dynamically elongated the molecules beyond their equilibrium length in a nanochannel. The stretched molecules were then transported through two spatially separated focal volumes, defined by lasers focused sequentially on the nanochannel, which enabled speed and cross correlation measurements (8) and increased statistical validity and experimental throughput. The use of a nanochannel also reduced fluorescent background noise, increased excitation uniformity, and allowed single-molecule detection at higher concentrations when compared to measurements made in larger fluidic channels or free solution (14,15).

FIGURE 1 Experimental schematic. (A) Fluorescently labeled DNA molecules are dynamically elongated by driving them electrophoretically from a nanoslit into a nanofluidic channel (DNA 1). The nanochannel is probed by two sequentially focused lasers. DNA molecules driven through the resulting focal volumes generate two similar fluorescent signals, which are shifted in time relative to each other (DNA 2). These signals can be used to determine single- molecule statistics forme sample (such as speed, length, folding conformation, and fluorescence intensity) and are used in this work to illuminate several aspects of the physics of DNA translocation through nanofluidic channels. (B) Two photon count signals p resulting from the two focal volumes and fits versus time t with a 100 [mu]s bin time at a device bias of 50 V. The fits result in an apparent DNA length l^sub A^ = 9.10 +- 0.05 [mu]m, speed v^sub s^ = 1315 +- 3 [mu]/s, and folded length/apparent length ratio l^sub L^/ l^sub A^ = 22.3 +- 0.4%.

For each DNA molecule detected, photon bursts from the two fluorescent signals were matched and subsequently fit to analytical models describing the conformation, length, speed, and intensity of the DNA strands. An example of the signals and fits resulting from the analysis of a DNA molecule interpreted as folded at the front end is shown in Fig. 1 B. This analysis algorithm made possible a direct determination of molecular length and conformation with spatial resolution beyond the optical diffraction limit, established in the work presented here at 114 nm, with an analysis time of 20 ms per molecule. The measurements depicted in Fig. 1 B were also used to infer DNA length from total fluorescence burst intensity, a previously demonstrated analytical method (12,13), and the two methods were compared and combined. The confluence of these factors represents an important step forward toward applications that place a premium on spatial resolution and analysis time, such as single- molecule genomic sequencing.

The introduced methods were then used with the well-known system lambda-bacteriophage DNA and its derivatives to study DNA fragmentation, folding, and dynamic stretching as a function of applied bias, and speed as a function of apparent length, folding, and contour length. The results of these experiments help elucidate several aspects of the electrophoresis and friction of DNA molecules in nanoscale environments. DNA speed was found to increase slightly with folding, and stretching was found to increase with applied device bias and electric field. For mixtures of DNA fragments, speed was found to be almost constant with length, showing a slight decrease only for short fragments.

THEORY, METHODS, AND MATERIALS

Single-molecule burst theory

The two collected photon count signals are generated by projecting the fluorescent images of individual DNA molecules moving in the nanochannel on two different optical fibers, which are connected to separate avalanche photodiodes. To describe the general signal shape, a DNA molecule with N basepairs and contour length L in a nanochannel with a depth and width D is considered. The strand is homogenously stained with Nf fluorescent dye molecules, giving a dye/basepair ratio g = N^sub t^/N, and uniformly stretched to an end- to-end length l^sub R^ = sL, where s is the stretching factor (0

Single-molecule burst analysis

The analysis algorithm for the two photon count signals consisted of the localization of bursts of fluorescence resulting from the detection of DNA molecules, the matching of corresponding bursts in both photon count signals, and the combined fitting of the corresponding bursts. Partner bursts were analyzed simultaneously to enable the most sensitive determination of molecular speed from the time of travel between the two focal volumes, as well as from both individual bursts. Analysis parameters were modified with varying device bias and resulting molecular speed. The following parameter ranges correspond to device biases, V, of 1 – 100 V. The photon count signals were originally recorded at a bin time of 10 [mu]s and then rebinned to 10-500 [mu]s to improve and accelerate analytic burst fitting. Rebinning was limited to preserve the shape of each fluorescent burst.

All bursts in both signals were localized by the use of a thresholding algorithm. Single-molecule detection thresholds were set at least seven standard deviations above the mean background noise values, which were determined by fitting the overall photon count distributions of the two signals to Poisson distributions. This eliminated virtually all noise from inadvertent analysis. Multiple bursts separated by

Gaussian fitting of logarithmic distributions

Optical setup

An Olympus 1X71 inverted microscope (Olympus, Melville, NY) with a Prior Pro-Scan II stage (Prior Scientific, Rockland, MA) was used in conjunction with nanochannel devices for single-molecule detection. The microscope stage was equipped with integrated position sensors and servo motors to control lateral drift, and drift in the focal plane was measured using a stage height probe (Heidenhain, Traunreut, Germany) and controlled with an external focus servo motor (Prior Scientific). An argon-krypton mixed gas tunable laser (Melles Griot Laser Group, Carlsbad, CA) and a solid- state sapphire laser (Coherent, Santa Clara, CA) were used with Z488/ 10X excitation filters (Chroma Technology, Rockingham, VT) for fluorescence excitation at 488 tim. A variety of optical elements including miirors and kinematic mounts (Newport, Irvine, CA) were used to guide the laser beams into the microscope, with their entry angles tuned to yield focal volumes separated along the length of the nanochannel by 11 – 12 [mu]m. Both lasers were tuned to have a power of 250 [mu]W, as measured after the circular polarizer, except in the experiment shown in Fig. 7 in which the laser power was 1.5 mW.

A Z488RDC dichroic mirror (Chroma) reflected the laser beams into the back of a UApo/340 water immersion objective (40 x , 1.15 NA, Olympus). Collected fluorescence emission passed through a 535AF45 emission filter (Omega Optical, Brattleboro, VT). The signal was divided using a beam splitter (Omega) and focused by the internal tube lens of the microscope on two high power step-index fused silica multimode optical fibers (50 [mu]m inner diameter, 125 [mu]m cladding diameter; OZ Optics Limited, Ottawa, ON, Canada). At the end of the fibers light was detected with two avalanche SPCM-AQR-14- FC photodiodes (Perkin Elmer, Fremont, CA). An overview of the optical setup is shown in Fig. 2 A. A Photometries Cascade 512B camera (not shown in Fig. 2 A; Photometries, Tucson, AZ) was used to align the focused lasers to the nanochannel, visualize the experiment, and image several hundred quantum dots (Qdot 525 streptavidin conjugate, Invitrogen, Carlsbad, CA) adsorbed to a fused silica coverslip for characterization of the point spread function of the microscope objective. The point spread function was described by a Gaussian with a standard deviation of sigma = 140 +- 20 nm. Further details of the optical setup can be found elsewhere (17).

Device fabrication

Nanochannels were fabricated in fused silica using a combination of electron beam and optical lithography. A 150-nm-thick film of poly(methyl-methacrylate) resist was spun onto a 500-/im-thick substrate wafer (Mark Optics, Santa Ana, CA) followed by an evaporated 25-nm-thick film of gold. A negative device pattern was exposed using a JBX-9300FS electron beam lithography system (JEOL, Peabody, MA). After removal of gold and development of the resist, the nanochannel pattern was transferred to a chromium mask by evaporation and liftoff. A microchannel etch mask was patterned using standard optical lithography procedures and the same liftoff process. An optical micrograph of the resulting chromium mask can be seen in Fig. 2 B. The micro- and nanochannels were then simultaneously etched into the substrate using a Plasmalab SOPlus RIE (Oxford Instruments, Eynsham, UK) with a CHF^sub 3^/O^sub 2^ mixture. Fig. 2, C and D, presents electron micrographs showing the interface between the microchannel and a nanochannel. Inlet and outlet holes were excised from the substrate by alumina powder blasting through the backside of the wafer. To enclose the channels, a 170-[mu]m-thick fused silica cover wafer (Mark Optics) was bonded and annealed at a temperature of 1050[degrees]C to the substrate wafer. After device fabrication, sample reservoirs were glued to the inlet and outlet holes and sealed with reusable adhesive during use. Platinum wires provided electrical contacts with the sample solutions. Further details of the fabrication process can be found elsewhere (30).

Samples

DNA samples were labeled using the bis-intercalating fluorescent dye YOYO-1 (Invitrogen) with a dye/basepair ratio of 1:5. lambda- bacteriophage DNA (New England Biolabs, Ispwich, MA) at a concentration of 25 [mu]g/mL was heated to a temperature of 65[degrees]C for 5 min and added to a mixture of YOYO-1 dye in 5 x Tris-Borate-EDTA buffer (TBE, pH 8.3, Sigma-Aldrich, St. Louis, MO) with 6% (v/v) beta-mercaptoethanol (Sigma-Aldrich) as an antiphotobleaching reagent. A Hindlll digest of lambda- bacteriophage DNA (New England Biolabs) was prepared in a similar manner with the exception that it was heated to 60[degrees]C. The digest was mixed in equal parts with pure lambda-bacteriophage at a total concentration of 50 [mu]g/mL, with the appropriate heating temperature used for each constituent before mixing. The sample was then labeled with YOYO-1. In this case the buffer also contained 1% (w/w) poly(n-vinylpyrrolidone) (PVP, molecular mass 40 kD; Sigma- Aldrich) to reduce both electroosmotic flow and nonspecific binding of DNA to channel walls (38-40). The contour length of lambda- bacteriophage DNA (48.5 kbp) can be calculated from the basepair spacing of 0.34 run to be L^sub lambda^ = 16.5 [mu]m. Recent studies have shown that the dye TOTO-1, which is similar to YOYO-1, increases the contour length L^sub lambda^ by 30-35% at a dye/ basepair ratio of 1:4 (24,41 ). L^sub lambda^ is therefore expected to rise by 23% to 20 lambdam for a dye ratio of 1:5.

FIGURE 2 Optical setup and devices. (A) Two lasers are directed into the back of a microscope objective and focused at different positions along the length of a single nanochannel. The two fluorescent signals are collected, split, and focused on optical fibers coupled to avalanche photodiodes (APDs). (B) An optical micrograph of the chromium etch mask shows the structure of the nanochannel device. The white arrows mark the entrances to one of the eight nanochannels in the array. The mask consists of a coarse layer for the nanoslit made with optical lithography and a fine layer for the nanochannels made with electron beam lithography. The electron beam layer was designed to reduce write times and proximity exposure effects. (C) An electron micrograph shows the interface between the nanoslit and a nanochannel. The etch depth is 100run, and the nanochannels are 90nm wide. (D) An electron micrograph shows the entrance to a nanochannel. The device floor roughness of 10 – 20 nm is attributed to the etching process. RESULTS AND DISCUSSION

This work has two purposes. The first is to demonstrate a new method to dynamically elongate, rapidly detect, and carefully analyze single DNA molecules in a nanofluidic channel. The second is to use this method to investigate some of the physical phenomena occurring when DNA strands are manipulated in this manner, including speed as a function of folding, stretching and speed as a function of electric field, and speed as a function of length. Several experiments were conducted using variations of the well-known system lambda-bacteriophage DNA, including random fragments thereof and controlled fragments from a mixture of lambda-bacteriophage DNA with its own HindIII digest.

Length analysis of single A-bacterlophage DNA molecules

Each experimental run yielded two photon count signal traces as well as their cross correlation function. Bursts of fluorescence in the two photon count signals were identified by a thresholding algorithm. Corresponding partner bursts were matched by estimating the time window of their occurrence based on preceding fits of the cross correlation function, yielding estimates for the speed v^sub c^ and average apparent length l^sub c^ of the molecules. The majority of bursts exhibited multiple levels of fluorescence intensity, which were interpreted as the result of folded DNA molecules. The observed burst shapes are similar to the electrical current changes observed during DNA translocation through artificial nanopores (2,42). An example of this phenomenon is shown in Fig. 1 B. Almost all molecules exhibited some degree of front end folding, which was also observed in previous experiments involving single DNA molecules in nanochannels (29,30). but to a lesser degree.

The increased difference in the electric field strength between the nanoslit and the nanochannel in the device used here is a likely cause for this increased front end folding. It is hypothesized that the large electric field gradient leads to the random entrance of whatever part of the DNA molecule first comes close enough to the nanochannel, despite the higher entropie forces hindering the entrance of looped structures into the channels. The metaphor of “sucking spaghetti” (43) helps explain why folding is rarely observed in the middle or at the end of the molecules, which are stretched out at these locations. There are several other possible explanations for the observed front end folding. For the high speeds used in these experiments, molecules may become folded inside the channel due to hydrodynamic effects or interactions with the channel surface. Elongation and folding caused by interactions with the nanoslit surfaces before entrance into the nanochannel is possible, and interactions with the nanochannel surfaces may also lead to a compression of the leading strand end. None of these alternative explanations were observed at lower speeds (30); and the long persistence length of DNA as well as the existence of quantized burst shapes including 3, 6, and 7 in Fig. 3 makes compression unlikely, which is why the folding interpretation was preferred in this work. A mixture of the mentioned effects is also possible, and in this case molecules with a short initial peak could be modeled by a modified version of Eq. 10 using a variable initial step height. This would lead to fitting functions with shapes that differ from those used here only by different slopes in the leading signal edge. As analysis of the slopes is currently limited by fluctuations in fluorescence, the results for the real length would be very close to the results here. Moving to smaller nanochannel dimensions in future work will help to further clarify this topic.

FIGURE 3 Single-molecule analysis. (A) Seven theoretical molecular conformations with up to three folds were used to describe electrodynamically stretched DNA molecules in a nanochannel. Six analytical models, denominated alpha – xi, were developed from these conformations to fit bursts of fluorescence, with model E covering two shapes. (B) Observed bursts of fluorescence and fits from the first focal volume (signal 1) are shown. Fluorescence bursts are interpreted with the folding model and conformation drawn underneath (fits shown in red). Burst 8 shows a rare fold, knot, or overlapping fragment in the middle of the molecule and is fitted using model beta. The most frequently observed burst shapes were shapes 2, 4, and 5; the others were rare.

Based on these observations, seven theoretical molecular conformations were used to describe up to three levels of front end folding, as shown in Fig. 3 A. For two and three folds, respectively, two and three conformations exist which differ in the length of the folded section of a molecule relative to neighboring nonfolded ends, when considering the molecule from right to left. Using these seven molecular conformations, six analytical models denominated alpha – xi were developed to fit measured fluorescence bursts. Differentiation of the fluorescence burst models comes from the mathematical description of the resulting fluorophore concentration profiles along the channel axis. For two folds, the apparent length of the molecules can be dominated either by the single strand end or by the loop, leading to different basic fluorophore concentration levels. The length of the next concentration level is then described as a fraction of the apparent length. For three folds, the apparent length of the molecules can again be dominated either by a single strand end or by the loop, leading to two different models.

The lengths of the two left shapes are both dominated by the single strand end, enabling them to be described by the same model epsilon. Almost all single-molecule detection events in the work here could be described by these various models. Several examples of fluorescent bursts, corresponding molecular conformations, and analytical fits are shown in Fig. 3 B. Although the fluorescence intensity was quite constant in the unfolded regions, as seen in burst shape 1, super-Poissonian signal fluctuations were still evident. This indicates that although the molecules were uniformly stretched, they were not fully elongated to their contour lengm, resulting in strand density fluctuations. For each DNA molecule investigated, a fitting model was selected based on burst height, and the two partner bursts were fitted together. An unfolded molecule, for example, was fitted with the function p(v^sub s^(t – t^sub 0^)) +p^sub Off1^ for signal 1 and p(v^sub s^ (t – t^sub 0^) – sd) + p^sub Off1^ for signal 2, both based on the function p(x^sub 0^) of Eq. 7. For a molecule with a single front end loop, P^sub fold^(v^sub s^(t – t^sub 0^)) +P^sub Off1^ was used to fit signal 1 and P^sub fold^(vs(t – t^sub 0^) – sd) + p^sub Off^ was used to fit signal 2, both based on Eq. 11.

Analogous functions were created and used for higher degrees of folding. In all cases, the fitting parameters included the speed v^sub s^, the apparent lengths l^sub A1^ and l^sub A2^ resulting from the two signals, and the initial burst time t^sub 0^. Previously determined parameters such as the laser spot distance sd, fiber diameter d, objective magnification m, background noise levels p^sub Off1^ and p^sub Off2^ for the two signals, and the Gaussian radius of the point spread function sigma were kept constant for all fits. The signal amplitude prefactors p^sub 0,1^ and p^sub 0,2^ for the two signals were generally kept constant. For analysis times longer than 2 min, the prefaciers were fitted to account for dye loss and photobleaching effects in the nanoslit. Depending on the degree of folding, additional folding factors were also fitted, such as f^sub a^ = l^sub L1^/l^sub A1^ = l^sub L2^/l^sub A2^ for a molecule with a single fold. It was assumed that the folding factors for both signals were constant for this experiment, whereas changes in apparent length (l^sub A1^ , l^sub A2^ and folded over (looped) length (l^sub L1^, /^sub L2^) were possible. Due to slightly different optical fiber alignments, the two signals gave molecule lengths differing up to 10%, and the higher average length was selected, as the smaller value was assumed to arise from a slight misalignment of that optical fiber. An actual variation of the strand length between the two detection volumes was unlikely as length changes were expected to happen on a timescale of 9 s (30).

A total of 752 intact lambda-bacteriophage molecules were detected in three similar experiments with a device bias of 50 V. Bursts of fluorescence described by the beta-, gamma-, and epsilon- folding models were observed most often (33%, 46%, and 20%, respectively), whereas only 1 % of observed bursts were described by the other models. The automated fitting algorithm selected the 0- fitting model for short fragments only, although the gamma-fitting model would have also worked, and never for intact lambda- bacteriophage molecules. The eighth burst shape in Fig. 3 B is shown as an example of a rare detection event which was not described fully by one of the six basic models shown in Fig. 3 A. Model beta came closest to describing the shape of the burst in this case, which could have been caused by overlapping molecules, a fold, or a knot. A similar phenomenon was observed previously (30); in this earlier study, a knot was detected in a DNA molecule undergoing entropie recoil from a nanochannel, which did not dispel over time as a simple fold would have. Although this detection event shows a limitation of the models used to fit the bursts of fluorescence, it is also an illustration of the ability in a single-molecule measurement to detect rare species or transient events.

Fig. 4 shows the results of a l min experiment in which 416 molecules from a lambda-bacteriophage DNA sample were detected. The definitions of the different lengths used to describe a folded DNA strand with a single loop are shown in Fig. 4 C. The apparent length /A neglects any folding of the strand and is determined by analyzing only the start to end length of the DNA strand. The apparent length is of interest, as it enables a more direct comparison of the results presented here with other methods of DNA analysis, including translocation of DNA through nanopores and hydrodynamic stretching. The looped length l^sub L^ is the length of the folded over segment of DNA, and the real length l^sub R^ is the sum of the apparent and looped lengths. The free length l^sub F^ describes the section of DNA that is not folded over. Although the apparent length could also be determined by a simple thresholding algorithm, the other length values result only from fitting the burst shapes. A comparison of these different length values is shown in Fig. 4, A and B. The distribution of real lengths in Fig. 4 B shows a much sharper peak, corresponding to intact lambda-bacteriophage DNA molecules, than the apparent length distribution in Fig. 4 A. FIGURE 4 Photon count, length, and folding. In a 1 min run, 416 molecules from a lambda- bacteriophage DNA sample are analyzed. The average molecule speed is V^sub S^ = 1.33+- 0.07 mm/s at a device bias of U = 50 V. (A) Distribution of the apparent length l^sub A^. (B) Distribution of the real length l^sub R^. (C) Schematic defining apparent length l^sub A^, real length l^sub R^, free length l^sub F^, and folded (looped) length l^sub L^ for a molecule with a single loop. (D) Photon counts (cnts) per molecule versus apparent length l^sub A^. (E) Photon counts per molecule versus real length l^sub R^. The linear fit passing through the origin has a slope of 4,430 +- 20 cnts/[mu]m. (F) Distribution of the photon count per molecule. A comparison of D and Pounds shows that folding explains the distribution of molecules with the same photon count over different apparent lengths. Fitting the photon count (F) and real length distributions (C) with Gaussian distributions leads to a mean photon count of 48,000 +- 2,000 photons and a real length of 10.7 +- 0.3 [mu]m for intact lambda-DNA molecules. All molecules within two standard deviations of the mean photon count and the mean real length are considered to be intact (horizontal and vertical arrows indicate region). This accounts for 52% of the molecules analyzed, whereas the rest of the molecules are interpreted as fragments or concatemers. (E, inset) Distribution of the free length/real length ratio l^sub F^/l^sub R^ for all intact molecules; 79% of the intact molecules have l^sub F^/l^sub R^ > 0.5.

Based on analysis accounting only for apparent length, many molecules in this distribution appear to be fragments. When the real length is calculated, however, the molecules are found instead to be intact and folded, correcting the distribution. This is readily observed when the number of photons collected from each molecule is plotted against the apparent length (Fig. 4 D) and the real length (Fig. 4 E) of the molecules. Although the apparent length distribution of molecules in Fig. 4 D is widely scattered, the real length distribution in Fig. 4 Pounds is focused and fit to a single Une. The sample also contained a small fraction of A-DNA multimers, which were observed at higher photon counts and with longer length than visualized in Fig. 4. The distributions of the photon count per molecule and of the real length can be fitted with Gaussians yielding a mean photon count of 48,000 +- 2,000 photons and a real length of 10.7 +- 0.3[mu]m for intact lambda-bacteriophage DNA molecules. This is longer than the equilibrium length of 7 – 8 [mu]m measured for lambda-bacteriophage molecules in 100 nm x 200 nm channels (26,29), which is expected, as the measured value is not the equilibrium length but rather the dynamically stretched length.

This stretching effect was previously found for T4-bacteriophage DNA molecules entering nanochannels. The ensuing relaxation showed a time constant of 9.3 s (30). The relative standard deviation of the Gaussian fits was found to be smaller for the real length distribution than for the photon count distribution (3.1% vs. 4.7%). All molecules within two standard deviations of the mean photon count and the mean real length were assumed to be intact lambda- bacteriophage DNA molecules (black arrows mark region in Fig. 4 D), which accounts for 52% of all molecules detected. Assuming that the rest of the smaller molecules were fragments of lambda- bacteriophage DNA molecules, and neglecting the few lambda- bacteriophage concatemers detected, the sum of the length of these fragments divided by the mean real length of lambda-bacteriophage DNA gives 60 as the original number of intact molecules.

The percentage of intact strands was then calculated to be 78%, which is somewhat lower than the 86% of intact lambda-bacteriophage DNA molecules as determined by agarose gel electrophoresis. This measurement was performed by the manufacturer using samples from the same lot, and the resulting fluorescence image was analyzed with a rolling ball background correction using ImageJ (National Institute of Mental Health, Bethesda, MA), a Gaussian distribution to model the spatially averaged intensity of the DNA band, and a range of two standard deviations around the mean to differentiate intact molecules from fragments. Contributing factors to this increased fragmentation include hydrodynamic shear forces from manual sample loading, electrical forces in the nanochannel device, and photodamage from scattered laser light. The amount of fragmentation reported here compares favorably, however, to that observed using other methods of elongation and analysis (23).

To estimate the resolution of the method, the mean standard error of the fitted apparent length and the real length of the intact lambda-bacteriophage molecules were calculated to be 84 nm and 114 nm, respectively, from 97 molecules analyzed using model beta. For higher orders of folding, the mean standard error for the real length increases: 143 nm for model y and 278 nm for model e. These values can be indirectly compared with a resolution of 150 nm obtained in l min by Tegenfeldt et al. for a single lambda- bacteriophage DNA molecule in a nanochannel at its equilibrium length of 8/im (26). The values cannot be directly related, however, as the former is the average standard error of fits to single bursts and the latter results from a Gaussian fit to a distribution of length measurements taken over a longer period of time to average out thermal fluctuations for a single molecule.

The free length of the folded molecules is of particular interest, as this is the section of the strand where the position of a site-specific fluorescent label could be determined in future experiments without ambiguity. The inset in Fig. 4 E shows the distribution of the free length/real length ratio l^sub F^/l^sub R^ for all intact molecules. Of the intact molecules, 79% show a l^sub F^/l^sub R^ > 0.5, meaning that in half of these cases (39.5%) any position up to the middle of the strand can be determined. This is based, however, on the assumption that half of the molecules enter the channel in the right direction (5′-end first, for example). This reduces the number of lambda-bacteriophage molecules that could yield information about the site-specific position of a fluorescent tag to 26% (0.67 x 0.39). The inset in Fig. 4 E also justifies the interpretation of the peak value of the photon count distribution of all bursts as the result of an unfolded DNA strand occupying the focal volume and the use of this value as a signal prefactor.

A limiting factor of the method presented in Fig. 4 is the length of the focal volume l – d/m = 1.25 [mu]m. When the length of a DNA molecule in the nanochannel was shorter than this value, the resulting fluorescent bursts did not exhibit quantized intensity levels, and the signal amplitude was determined only by the number of dye molecules which are intercalated in the strand. Eq. 7 predicts that although molecular folding would not affect the amplitude of these signals, it would be visible in a sudden variation in the slopes at the beginning and the end of the fluorescent burst. These slope changes were not detectable, however, as signal fluctuations were too high. The alpha-fitting model was used in this case to describe signal intensities lower than the average burst height, resulting in an apparent length value determined by peak amplitude and as a result photon count. The burst- fitting and photon-counting methods therefore converged for molecules shorter than 1.25 [mu]m, which can be seen in Fig. 4 D. The same limitation affected folded molecules with a folded over length of <1.25 [mu]m.

Additional information, such as molecular conformation, was theoretically present as variations in the signal slopes, but its analysis was again obscured by signal fluctuations as well as any deviations from assumptions made about the optical system, such as laser illumination and fiber collection efficiency profiles. In the case of conformation, different conformations of the folded strands were described by the same fitting model, and it was not possible to determine if a burst of fluorescence with a short initial peak was the result of a strand folded over at the end or a molecule showing a random coil configuration at the end. Although the latter configuration has been found in microchannel structures for DNA stretching (8), it was not described in DNA translocation experiments using 10-20 nm pores (2) nor was it found in optical investigations of longer DNA molecules in 1OO nm nanochannels (30). Further insight into the conformation of smaller molecules could be gained by reducing the length of the focal volume. This could be achieved by using smaller fiber diameters, by using an objective with higher magnification (with the resulting reduction in spot distance for the optical setup used here), or by combining nanochannels with optical nanoslits for near field microscopy (8). Velocity information was also present in the signal slopes, and its analysis was similarly limited. This limit was overcome, however, by fitting partner bursts simultaneously, in which case the time of travel between the focal volumes dominated the determination of velocity due to its large effect on the combined fit. Previous work involving DNA stretching and analysis has made use of hydrodynamic forces to elongate DNA and subsequently determine the position of fluorescent peptide nucleic acid tags bound to specific motif sites, yielding sequence information about the strand (21,22). Although this method is able to fully stretch DNA strands, the fluidic channels used were inhomogeneously illuminated. As shown here, dynamic electrophoretic stretching in nanochannels is not yet optimized to yield fully stretched strands but achieves uniform illumination across the nanochannel. This increases excitation uniformity and enables the determination of the DNA conformation by analytic fitting, theoretically permitting even the use of folded strands for the determination of site-specific information. Uniform illumination also yields more accurate fragment sizing based on photon counting, which leads to a higher percentage of molecules that can be confirmed as intact. This is achieved without the velocity correction of the photon count as often used in hydrodynamic stretching (22,23).

Electrodynamic stretching was also observed to be uniform along the length of the nanochannel, although the molecules were not completely elongated. This means that even at speeds an order of magnitude smaller than in hydrodynamic stretching, tag positions could be determined using the stronger fluorescent signals resulting from longer illumination times. Further electrodynamic stretching of the strands could most likely be achieved by the creation of stronger electric field gradients at the entrance of the nanochannel. Gradients of at least an order of magnitude stronger can be achieved by the use of smaller nanochannels, the connection of fewer parallel nanochannels to the nanoslit, or increasing the depth of the nanoslit. The fabrication of 10 nm nanochannels (44) and the repetitive translation of DNA molecules from nanoslits to microchannels (3,4) have already been shown.

Dependence of molecular speed on degree of folding

To investigate the effects of DNA folding on speed, the results of three subsequent l min runs of lambda-bacteriophage DNA (including the experiment shown in Fig. 4) at a device bias of U = 50 V were combined. Fig. 5 A shows the distribution of the speed vs versus the apparent length/real length ratio l^sub A^/l^sub R^ for 752 intact e-bacteriophage DNA molecules. Molecules with increased folding and therefore smaller l^sub A^/l^sub R^ had a slightly higher speed v^sub S^. The speed distribution VS is also plotted as a function of the number of folds in the strands in Fig. 5 B. The number of folds for each molecule was determined by the analytical model chosen to describe its resulting fluorescent burst. The overall influence of folding was found to be weak. Unfolded molecules were rare, resulting in just two data points, and molecules with three folds were observed to have a slightly higher speed v^sub s^ than molecules with one or two folds. This could be the result of increased hydrodynamic interactions between the parallel strands of the folded molecules. As electrophoretically driven DNA molecules are supposed to be free draining, these hydrodynamic interactions might take place only when the strand segments are very close, explaining the weakness of the effect. But molecular dynamics simulations may be necessary to fully explain this result.

FIGURE 5 Speed and folding. (A) Distribution of speed v^sub s^ versus apparent length to real length ratio l^sub A^/l^sub R^ for 752 lambda-bacteriophage DNA molecules. Intact lambda-bacteriophage molecules from three subsequent 1 min runs (including the experiment in Fig. 4) at a device bias of U = 50 V are presented. DNA molecules with increased folding and smaller l^sub A^/l^sub R^ have a slightly higher speed v^sub s^. (B) Normalized distribution of speed VS versus number of folds for the same molecules shown above. The number of folds is determined by the analytical model (Fig. 3 A) chosen to analyze each molecule and is a measure of the number of parallel strands in the channel. DNA molecules with three folds in the molecule confirmation have slightly higher speed v^sub s^.

Dependence of molecular speed, mobility, and friction on device bias

To investigate the effects of device bias on molecule speed and length, moiecules from a lambda-bacteriophage DNA sample were driven through a nanochannel at several different device biases U. Five continuous runs were performed for each device bias, and the cross correlation curves as well as the single bursts of fluorescence were analyzed by use of the respective models. The average single- molecule speed v^sub s^ is plotted as a function of device bias U in Fig. 6 E. A linear fit of v^sub s^(U) yields a slope of m^sub s^ = 60.9 +- 1.4 [mu]m/(Vs), confirming that speed increases linearly with device bias and electric field, as expected. For comparison, a plot of the speed v^sub C^(U) resulting from the cross correlation functions is added to the figure and shows a very similar slope of m^sub c^ = 61.0 +- 0.7 [mu]m/(Vs).

The ratio of the electric field E inside one of the nanochannels to the device bias U was calculated from device dimensions to be 31 cm^sup -1^. Dividing the slope of the linear fit of v^sub s^ (U) by this ratio gives the mobility of a DNA molecule as [mu]^sub s^ = v^sub s^/E = 2.0 x 10^sup -4^ cm^sup 2^/(Vs). Assuming a charge per unit length of lambda = 1.1 e^sub 0^/nm for the labeled DNA molecules (30) and considering that folding seems to have only a slight effect on speed, the friction coefficient per unit contour length was estimated to be xi^sub s^ = lambda/[mu]^sub s^ = 9.3 fNs/ [mu]^sup 2^. This is close to the 10.0 fNs/[mu]^sup 2^ found in similar nanochannel devices (30). This calculation can be viewed only as an approximation, however, as some parallel channels to the investigated channel showed unintended constrictions with unknown influence on the real electric field in this particular device.

FIGURE 6 Speed, length, and device bias. The dependence of DNA speed and length on device bias for a lambda-bacteriophage sample is shown. Five continuous runs were performed for each bias, and the cross correlation functions as well as the single-molecule photon bursts are analyzed. (A) Average single-molecule speed v^sub s^ and average cross correlation speed v^sub c^ versus device bias U. Linear fitting of v^sub s^(U) yields a slope of m^sub s^ = 60.9 +- 1.4 [mu]m/(Vs), and a linear fit of v^sub c^(U) gives a slope of m^sub c^ = 61.0 +- 0.7 [mu]m/(Vs). The plots overlap with each other. (B) Normalized distribution of real length l^sub R^ versus device bias U. The maximum of the length distribution shows up in black and corresponds to the majority of intact DNA molecules, which increase in real length l^sub R^ as the device bias increases. This behavior is not as evident for the average length l^sub c^ (black dots) resulting from cross correlation curves, probably because this analysis neglects folding and fragmentation. The number of molecules n for the different device biases U was 263 at 1 V, 381 at 2 V, 226 at 5 V, 144 at 10 V, 270 at 20 V, 417 at 50 V, 1217 at 75 V, and 868 at 100 V.

Dependence of stretching on device bias

Fig. 6 B illustrates the variation of real length of the DNA strands with increasing device bias. Because of the fragmentation of the lambda-bacteriophage DNA molecules, the results for the single- molecule length are plotted as grayscale intensity distributions instead of the mean values. As the number of molecules per distribution varied between ~140 and ~1200 molecules, the real length distributions are shown normalized for each device bias. In rough terms, the maximum of the real length distributions, corresponding to the majority of intact lambda-bacteriophage DNA strands, remains constant until ~10 V. An increase in real length is then observed until -75 V, followed by a plateau at higher device biases. A complete explanation for this trend is beyond the scope of this study and must account for DNA stretching as a result of entrance effects and entropie confinement in the nanochannel, as well as hydrodynamic and channel surface friction. The average length l^sub c^ resulting from cross correlation analysis is plotted as an overlay to the single-molecule distributions. The increasing trend from the single-molecule distributions is not as evident, as the single-molecule analysis routine accounts for folding and fragmentation of the molecules neglected by the correlation analysis.

Dependence of length and speed on DNA size

An experiment was performed to test the sensitivity of the method, compare it to previously demonstrated techniques based on intensity measurements, and determine the dependence of DNA speed on the number of basepairs in a nanochannel. This dependence is of interest for the development of theory regarding the electrophoresis of DNA confined to nanoscale environments and for applications that exploit DNA size dependence to achieve biomolecular separation. A sample with a broad size range of DNA molecules was prepared by mixing lambda-bacteriophage DNA in equal parts with its own HindIII digest. The resulting mixture contained nine primary types of DNA molecules (in basepairs: 125, 564, 2,027, 2,322, 4,361, 6,557, 9,416, 23,130, and 48,502). More than 16,000 molecules were detected in a 2 min experiment and automatically analyzed, the results of which are presented in Fig. 7. Almost all the scattered data points were the result of overlapping molecules following Poisson focal volume occupation statistics (12). FIGURE 7 Photon count, length, speed, and size. Analysis of a sample containing a mixture of e- bacteriophage DNA and its HindIII digest In 2 min, 16,315 molecules were detected with an average speed v^sub s^ = 3.6 +- 0.6 mm/s. (A) Distribution of the real length l^sub R^ . The peaks are shown fitted to nine modified Gaussians (red). (B) Real length l^sub R^ versus number of basepairs. (C) Photon count (cnts) per molecule versus the number of basepairs. A linear fit yields a slope of m^sub c^ = 0.63 +- 0.02 cnts/bp. (D) Distribution of photon counts cnts per molecule versus real length /R. (E) Distribution of the photon counts per molecule. The peaks are fitted to eight modified Gaussians (red). The peaks in A and E are interpreted as the following DNA strand sizes, in number of basepaire: 125, 564, (2027 + 2322)/2, 4361, 6557, 9416, 23,130, 23,130 + 4361, 48,502. Whereas peaks 7 and 8 are resolved separately in A, they are combined in E, The values plotted in B and C are the mean values resulting from the Gaussian fits from A and E, respectively. (F) Distribution of molecule speed VS versus real length l^sub R^. DNA speed is essentially constant with length, showing only a slight decrease for the shortest fragment.

Two other phenomena were observed in this experiment which required modifications to the analysis algorithm, as described previously. The second photon burst consistently exhibited increased folding, which was addressed by allowing different folding factors for the partner bursts. This was most likely the result of increased nanochannel surface roughness between the two focal volumes (29). The longest DNA molecules also had a lower than expected photon count and burst height, which was accounted for by choosing a smaller fit amplitude for molecules with counts over 20,000 photons. This was attributed to the lower mobility of longer DNA strands in the nanoslit, with a resulting increase in the observed loss of dye molecules to the nanoslit surfaces and photobleaching by scattered laser light. Although this mobility effect was observed previously only in shallower nanoslits (45), a similar outcome may have occurred here because of the rougher nanoslit channel surfaces.

The sample also contained a small fraction of lambda- bacteriophage DNA multimers which were observed at higher photon counts and with longer length than visualized in Fig. 7. Fig. 7 D shows a color-coded intensity histogram of photon counts per molecule versus real length l^sub R^. The distributions of real length and photon count per molecule are plotted in Fig. 7, A and E, respectively. The distributions in Fig. 7, A and E, were fitted with superpositions of 9 and 8 logarithmically modified Gaussians, respectively, as described in Eq. 14. In both plots, peak 3 was interpreted as a combined peak of the 2,027-bp and 2,322-bp fragments, per the analysis of Foquet et al. (12). Peak 8 in Fig. 7 A results from a fraction of the 4,361-bp and 23,130-bp fragments annealing at the complementary ends and creating an additional 27,491-bp fragment (12), although the sample was heated to avoid this effect. This peak is not observed in Fig. 7 E due to the lower resolution of inferring DNA size through photon count at longer DNA lengths.

The fit results for these peak positions and relative standard deviations are shown in Table 1. The relative standard deviations decrease with increasing strand size for both fits, with the exception of peak 7 in Fig. 7 E, as it contains unresolved 27,491- bp DNA strands, which are fitted as a separate peak in Fig. 7 A. The resolution for both measures increases for longer molecules, as opposed to gel electrophoresis. This was also observed in previous photon count measurements and is related to the fact that fluctuations in dye fluorescence, detection efficiency, and the number of dye molecules attached to strands of equal size obey Poisson statistics (12,13). These fluctuations influence the quality of the burst fits in a similar fashion and therefore lead to a similar resolution increase for longer strands. Additionally, dye binding is sequence dependent, and the number of dye molecules bound to a strand did not reach equilibrium because of the low off-rate of YOYO-I from DNA. Both phenomena negatively affected the resolution. The measured real length of 13.1 [mu]m for lambda-bacteriophage DNA was found to be longer than in the experiments shown in Figs. 4 and 6. These experiments were performed in different devices which may have different channel widths, particularly at the critical channel entrance. In Fig. 7, B and C, the mean length and the mean photon counts per molecule for the fitted peaks were plotted against the assumed number of basepairs for the fragments. The resulting dependence was well described by a linear fit, underscoring the fact that each peak corresponded to the expected fragment. This also indicates that the stretching factor s = l^sub R^/L is independent of strand length. The slopes of the fits were m^sub IR^ = 0.24 +- 0.01 nm/bp and m^sub c^ = 0.63 +- 0.02 cnts/bp. The latter is a factor of four smaller than the 2.5 cnts/bp that was achieved by Foquet et al. (12), which is due to the use of different optical components including smaller optical fibers and increased adsorption of the dye molecules to the nanoslit surfaces. Despite this lower detection efficiency, the smallest fragment of the lambda-HindIII digest was resolved due to decreased noise from a smaller nanochannel and the use of two focal volumes. The second photon count signal had a filtering effect, as fluorescent bursts without partners in the time range predicted by cross correlation analysis were discarded. This allowed time range was about an order of magnitude larger than the observed time difference variation and did not influence the distributions. The photon count for the longest DNA molecules in Fig. 7 C lies significantly below the linear fit, as a result of increased dye loss and photobleaching for this molecule in the device used here.

TABLE 1 Fitting results for Fig. 7, A and E

The percentage of the total molecules detected in each peak is also reported in Table 1. Considering annealing effects ( 12), peaks 1 -8 comprise the expected percentages of the total count. Peak 9 is reduced due to the retardation of long molecules in the nanoslit. Neglecting lambda-bacteriophage molecules, the total percentage of intact digest fragments in these peaks was calculated to be 82%, based on the results shown in Fig. 7 A. The same value was determined to be 81% using agarose gel electrophoresis. This higher percentage of intact molecules as compared to lambda-bacteriophage DNA results from random fragments coinciding with digested fragment peaks.

Fig. 7 F is a color-coded intensity histogram of the number of molecules against the molecule speed vs and the real length l^sub R^ . This measurement was repeated for device biases of 25 V and 100 V (results not shown) and the same trend was observed, which was also similar to that observed for DNA molecules of comparable lengths in free solution (46). This indicates that the deformation from the random coil shape of unconfined DNA into the elongated and stretched conformation has a negligible influence on the speed of strands with length longer than the channel width. The smallest fragment (125 bp) was observed to have a slightly lower speed; a similar trend was observed around 100 bp in free solution (47) and attributed to electrolyte friction. It could also be related here to DNA lengths which are smaller than the width and depth of the nanochannel, permitting molecular orientations more transverse to the channel length which result in increased hydrodynamic friction. These orientations are denied to longer molecules, as the known stiffness of doublestranded DNA characterized by its persistence length results in an orientation more aligned to the channel axis. Further investigation is needed to clarify this effect.

This measurement shows the current limits of this method. To correctly interpret shorter DNA fragments with apparent length smaller than the focal volume length d/m = 50 [mu]m/40 = 1.25 [mu]m, the prefactors p^sub 0,1^ and p^sub 0,2^ of the fitting formulas must be accurately predetermined. This was possible only if the burst height for single unfolded DNA strands remained constant throughout the experiment. The time limit for this was found to be ~ 2 min as a result of stage or laser drift, which limited the number of molecules detected at lower voltages. Another limit was related to the device loading time. The fluorescence intensity of the molecules was found to decrease with the time the DNA molecules spent in the nanoslit region of the device, even before being directly exposed to the focused lasers. Explanations for this effect include photobleaching by scattered or reflected laser light or loss of positively charged YOYO-1 dye molecules attracted to the negatively charged channel walls. Increasing channel background fluorescence was indeed observed after the nanochannel outlets, although the solution contained PVP to dynamically coat the channel surfaces and reduce interactions. This phenomenon was particularly evident with the device used in the experiment shown in Fig. 7.

CONCLUSION

A method is presented to rapidly analyze fluorescently labeled DNA molecules, and several experiments investigating the physics of DNA in nanochannels were performed. DNA molecules were driven electrophoretically from a nanoslit into a nanochannel to confine and dynamically elongate the strands beyond their equilibrium conformation. Two lasers were focused sequentially along the length of the nanochannel to induce bursts of fluorescence from the molecules. These bursts showed multiple intensity levels indicative of folding, and the collected photon count signals were analyzed with various analytical fitting models which yielded molecular conformation, length, and speed of single DNA strands. Molecular length was determined both by fitting each fluorescent burst shape to analytical models and by photon counting. Although counting photons was simpler, modeling and fitting the bursts yielded better resolution for longer strands for the optical setup used here and has several other advantages for analyzing unknown samples: no calibration sample is needed for burst shape fitting, and it is less affected by excitation intensity and variations in fluorescent labeling. The resolution for lambda-bacteriophage DNA with one fold at the front end was 114 nm for individual molecules with a mean real length of 11 [mu]m, and the analysis time was -20 ms per molecule. The speed of the molecules was found to increase only slightly with folding. A possible cause of this trend is increased hydrodynamic interactions between strand segments in proximity. Deeper insight into the influence of hydrodynamic friction and surface interactions on the molecule speed could be achieved by molecular dynamics simulations. DNA stretching was found to increase with applied device bias and electric field, which was estimated from device dimensions to be 56 times higher in the nanochannels than in the nanoslit.

The analysis of a mixture of lambda-bacteriophage with its own HindIII digest demonstrated that our method can identify, by length, 9 of 10 fragments ranging over 2.5 orders of magnitude in size. When compared to standard agarose gel electrophoresis, longer strands (>20 kbp) can be analyzed, the measurement time is at least 30 times faster, and much less sample is consumed. Although resolution decreases with size for agarose gels, the opposite is found for this method. DNA speed was found to be almost constant for all fragments investigated, showing only a slight decrease for short fragments. Confinement, elongation, and interaction with channel surfaces did not lead to a significant size-dependent influence on speed.

Future work will focus on extracting information pertaining to the length and conformation of molecules shorter than the focal volume length that is present in the signal start and end slopes but is currently obscured by signal fluctuations. This may be achieved by further elongating the DNA molecules by using smaller nanochannels, which would lead to a higher uniformity of basepair density along the channel. This will yield fluorescence signals with smaller fluctuations, leading to improved length determination using the method here. The accuracy of other physical information such as molecular conformation and speed will also increase, leading to more insight into the behavior of DNA molecules in highly constrained environments. As burst fitting can provide spatial information beyond the diffraction limit, the method here has potential for extremely rapid and ultrahigh spatial resolution measurements. Other pertinent applications of interest are the position of a site- specific label and biophysical effects such as knot formation. As this label or knot may fall in a folded over segment of DNA, with a resulting ambiguous position, models must be developed to extract positional information. The analysis of samples containing longer DNA strands will have to use photon burst fitting models that account for the increased probability of more complicated folding conformations and knot formation.

The authors gratefully acknowledge New England Biolabs for assistance with gel electrophoresis. Device fabrication was performed in part at the Cornell NanoScale Science and Technology Facility (CNF) with the assistance of Rob Ilic as well as in the Cornell Center for Materials Research.

This work was supported by the National Human Genome Research Institute as well as the Nanobiotechnology Center, which is funded by the STC Program of the National Science Foundation under agreement No. ECS-9876771 and the New York State Office of Science, Technology, and Academic Research (NYSTAR). CNF is a member of the National Nanotechnology Infrastructure Network, which is supported by the National Science Foundation.

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