Qualitative Patterns.

We begin with what appeared to our eyes (Fig. 2A and Movie S1) when we first saw it to be the drastic conformational change of single-stranded DNA (no definite shape) to double-stranded DNA (rigid and rod-shaped). A tantalizing point was that it involved concerted rotation, which we quantified by considering histograms of the step sizes of rotational angles. The assembly pair rotated first in one direction during hybridization (53–58 s) and then in the opposite (58–67 s), with speed ranging from 2 to 40° per second (Fig. 2B). Various control experiments were performed. Individual molecules in the absence of the complementary strand were imaged as a function of time (Fig. 2C); one observed images consistent with the projection, onto the image plane, of a fluctuating random coil whose 2D radius was ∼5 nm. This was consistent with the expected radius of gyration for this chain length (27), as the persistence length was ∼2 nm (28). The projected area of these images fluctuates around a constant level, consistent with the surface-hugging molecular conformations anticipated from old arguments in the field of polymer physics that dilute polymer chains form “pancake” surface conformations (29). Testing our interpretation that the rod-shaped object in Fig. 2A was a double helix, length and width of fully hybridized molecules were quantified in separate experiments (Fig. 2D). Projected onto the image plane, these fluctuated around the expected width (2 nm) and the expected length (30 nm) of a double helix shorter than the known persistence length of 50 nm (30). These fluctuations to lesser projected length than the average were reasonably interpreted to reflect transient tilts out of the image plane. The instances of apparent width larger than 2 nm were reasonably interpreted to reflect motion blurring. With these control experiments in mind, we interpreted the imaged hybridization process (Fig. 2A and Movie S1) to display two single-stranded coils of random base-pair sequence that started as separated molecules, diffused to intertwine as a fluctuating blob-shaped object, and finished as a rod-shaped double helix. Note that the transient V shape (46 s), loop with hole in the middle (51 s), and rod were fatter than a well-formed double helix (64 s).

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Fig. 2.

DNA self-assembly and mobility in aqueous buffer. (A) Using detection condition 1, complementary single-stranded molecules with random base-pair sequence were imaged while they hybridized (Movie S1). The expanded view of times 46–69 s includes, for better visual contrast, accompanying binarized images obtained from threshold intensity and red circles identifying the imaging-tracking results. Dotted circles in Upper identify single molecules. Red arrows highlight rotations in the indicated directions at the indicated times. (B) Quantification of rotation steps, evaluated over three time steps (one step = 300 ms) during the indicated time intervals, for the data in A. Bin size is 2 angular degrees. (C) A single strand of random sequence DNA measured in the absence of the complementary strand; the snapshots at different times up to 85 s illustrate conformational changes and diffusion. Red circles identify the objects tracked. Detection condition 1 was used. (Scale bar, 10 nm.) (D) A preformed double helix of random base-pair sequence measured as a function of time, accompanied by quantification of the projected apparent length in the image plane (crosses) and width (stars). The former values, less than the known length of 30 nm, are believed to reflect tilting in the z direction. The latter values, larger than the known width of 2 nm, are believed to reflect motion blurring. Detection condition 1 was used. (E) On log–log scales, mean square displacement (MSD) of the double-helix center of mass is plotted against time with reference slope unity; each curve comes from a single experiment, and there is no systematic dependence on base-pair microstructure. Blue, hybridization events; light gray, single strand; dark gray, double strands. Circles, squares, and triangles indicate random, hairpin, and pentablock sequences, respectively. Filled symbols show detection condition 1. Open symbols show detection condition 2. E, Inset shows the projected trajectory in the x–y plane for the experiment in A. Open symbols refer to times when single-stranded DNA was observed; filled symbols refer to times after individual single-stranded DNA started to intertwine; the color code, from red to blue, indicates increasing time elapsed. (F) Probability distributions of step size during translational diffusion under detection condition 1. (F, Top) Diffusion during hybridization (2,653 images) of nine hybridization events from random, pentablock, and hairpin sequences, three of each kind. (F, Middle) Diffusion of single-stranded DNA (1,455 points from five movies). (F, Bottom) Fully formed double helix (1,149 points from four movies). Bin size is 0.25 nm (half of 1 pixel = 0.45 nm). The most probable step size is the same in every case. During hybridization, it is broadened.

Mean-Square Translational Displacement.

After reaching double-helix form, these DNA microstructures displayed Fickian mobility, mean-square displacement proportional to elapsed time (Fig. 2E), suggesting not only that diffusion proceeded in a homogeneous environment, but also minimal sample damage, though experiments elapsed during continuous electron irradiation. The trajectory in Fig. 2 E, Inset concerns the same experiment as in Fig. 2A, motion of this molecule in the x–y plane while hybridization transpired. From inspecting histograms of step-size distribution accumulated from multiple experiments (Fig. 2F), the most probable step size in the time frame of 300 ms was the same in every case. Tendency (with limited statistics) toward broader distribution during hybridization is confirmed when below we evaluate the mean step during hybridization events.

Hybridization Pathways.

Exploring generality, expected (2⇓–4) hybridization pathways were observed in many cases, but not all. Among these were the zipper-up (3, 4) mechanism initiated by contact of bases located near the middle of strands (Fig. 3A and Movie S2) and defect annealing (2, 3) (Fig. 3B and Movie S2). The zipper-up mechanism was observed regardless of DNA microstructure—for random (Fig. 3A), pentablock (SI Appendix, Fig. S1), and hairpin (SI Appendix, Fig. S2) base-pair sequences. For example, single strands bound at the middle to form a branched structure (7 and 10 s), followed by its disappearance (11 s), as revealed by lesser width and increasing length. Quantifying these intermediate steps on a coarser scale, we plotted the time-dependent projected length, width, and angle in the laboratory frame of reference in Fig. 3C. Histograms of molecular rotations during this process are shown in Fig. 3D. Note that rotation was persistently in one direction (10–14 s), then switched to the opposite direction (14–18 s), and finished as random fluctuation (18–29 s). But defect annealing of blocky base-pair sequences—the pentablock and hairpin sequences—was slower than for the zipper-up mechanism, and we observed transient hairpins during defect annealing of palindromic hairpin defects (Fig. 3B). For example, first, two strands met (17 s) and adapted individual “hairpin” conformations (27 and 34 s), then the correct ends aligned (117 s), and an apparent rod of constant width protruded clockwise. Quantifying these intermediate steps, the projected length, width, and angle in the laboratory frame of reference are plotted against time in Fig. 3E. Histograms of molecular rotations during this process are shown in Fig. 3F. Note that rotation was persistently in one direction (117–131 s), then stalled (131–141 s), then resumed (141–163 s).

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Fig. 3.

Confirmation and quantification of intermediate shapes predicted from earlier literature. Detection condition 1 was used (Movie S2). (A and B) Shown are schematic diagrams of time-dependent conformations (top row), base-pair alignment (3) (second row), actual images (third row), and binarized images for better visual contrast (bottom row). (A) Middle-contact zipper-up for random sequence. Neighboring complementary single strands of random sequence meet and hybridize. Arrows in frames at 11 and 14 s indicate rotations in the indicated opposite directions. (Scale bar, 30 nm.) (B) Defect annealing for hairpin sequence. Neighboring complementary single strands of hairpin sequence meet and hybridize. The red circles at 0 and 17 s highlight individual molecules. Arrows in frames at 117, 144, and 158 s indicate persistent clockwise rotations as hybridization proceeds. Yellow double arrows at 34 s highlight formation of transient intrahairpin states. Arrows in frame 27 s indicate rotations when a hairpin forms. (Scale bar, 30 nm.) (C) Quantification of the zipper-up pathway. Projected length (l; defined in image 29 s in A) of double-stranded DNA (squares) grows quickly from 12 to 14 s, then more slowly until reaching l = 25 nm, accompanied by progressively smaller width, w (circles), while the relative angle θ to the horizontal (triangles) first decreases then increases in synchrony with fast growth in the initial stage, but constant after 15 s. (D) Quantification of rotation steps of zipper-up pathway. Histograms of net rotations, evaluated over three time steps (1 step = 300 ms), during the designated time regimes, are shown. Bin size, 2 angular degrees. (E) Quantification of the defect annealing pathway. Projected length (l; defined in image at 163 s in B) of double-stranded DNA (squares) grows gradually to l = 30 nm after one end of both strands aligns, accompanied by monotonic increase of the relative angle θ to the horizontal (triangles), while the width w (circles) remains constant. Lines are guides to the eye. (F) Quantification of rotation steps, evaluated over 10 time steps (1 step = 300 ms), of the defect annealing pathway. Bin size is 5 angular degrees.

Grooves of the double helix were resolved when the molecule was adventitiously transiently nearly stationary on the time scale of image acquisition (163 s in Fig. 3B). To infer pitch length would require tomography-type 3D imaging, which is too slow for the dynamical process here (18), or 3D reconstruction from 2D images, recently demonstrated as possible in liquid-cell TEM in one favorable system (31), but as DNA helical structure was not in doubt, this direction of investigation was not pursued.

Also unanticipated was that transient loops appeared to facilitate the hybridization process. This contrasts with the standard view that loops are only errors to anneal out. For example, two pentablock coils (Fig. 4A and Movie S3) met and appeared to assemble from near one end (42 s), then opened near the middle to form a loop (44 and 45 s), accompanied by clockwise rotation. The loop size then shrank, suggesting error correction of base pairing primarily near the ends. This propagated toward the chain middle as the loop disappeared and the duplex became better defined (72 s). Anticlockwise rotation accompanied final formation of the intact helix (80 s). Image analysis (Fig. 4B) showed that the projected length l quickly saturated, but the average width w diminished monotonically throughout, echoing the progressive formation and annealing of the loop. Rotation in the laboratory frame of reference was at first random (40–45 s), then monotonic in one direction (45–71 s), but followed by a reverse (71–83 s); the histogram of rotation steps is shown in Fig. 4C. Rather than a single loop, we also observed processes that involved formation of more than a single loop, as illustrated (77 s) in Fig. 4D for a hairpin sequence. Typical images of these processes in Fig. 4E, together with the relative abundance of loops observed during hybridization and failed encounters, are summarized in Fig. 4F. Taken together, we observed loop intermediates in 12 of 36 total interaction events and 6 of 18 hybridization events.

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Fig. 4.

Loop intermediate states. (A) Single-stranded molecules with pentablock base-pair sequence hybridize (Movie S3). The frame at 68 s identifies the angle, length, and width that are plotted in B. Note loops in frames at 44 and 45 s. Detection condition 2 was used. (Scale bar, 30 nm.) (B) In plots against elapsed time, shapes of the duplex are quantified as concern its projected length, l, and width, w (squares and circles, respectively), and the relative angle θ to the horizontal (triangles). Dashed lines are guides to the eye. (C) Quantification of rotation steps of loop annealing pathway, evaluated over 1 s, during the indicated time intervals. Bin size is 1 angular degree. (D) Images of loops observed during hybridization of a hairpin sequence; they appear at 40 and 77 s. Detection condition 1 was used. (Scale bar, 30 nm.) (E) Six additional examples of loop intermediate states: random, random, hairpin, hairpin, pentablock, and pentablock. (Scale bar, 30 nm.) (F) Histogram, normalized to unity, showing relative loop appearance for the three base-pair sequences investigated, with specification of times observed (first number) and the number of movies inspected for each case (second number).

Detailed comparisons suggest, but with a small dataset, that hybridization mediated by loop annealing was slower than hybridization by the zipper-up process. This was observed consistently. For random-sequence DNA, one sees it illustrated upon comparing Fig. 2A (82 s) to Fig. 3A (29 s). For the pentablock DNA, one sees it illustrated upon comparing Fig. 4A (80 s) to SI Appendix, Fig. S1 (47 s). For the hairpin DNA, one sees it upon comparing Fig. 4D (145 s) to SI Appendix, Fig. S2 (37 s). Interestingly, the defect-annealing process was slower when we observed it for pentablock DNA (90 s; the ninth graph in Fig. 5F) and the hairpin sequence (163 s in Fig. 3B).

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Fig. 5.

Hybrid and failed mechanisms illustrated and quantified. (A) An example of a failed encounter, the partial assembly followed by disassembly of complementary pentablock base pair sequences (Movie S4). Detection condition 2 was used. (Scale bar, 30 nm.) (B) An example in which different hybridization mechanisms combine. Molecules interact via a middle-contact path (0 and 5 s) but fail to zip up (11 s), recombine (29 s), and, ultimately, a well-formed duplex results (92 s). (B, Top) Schematic diagrams of time-dependent conformations. (B, Middle) Actual images. (B, Bottom) Binarized images for better visual contrast. Arrows in frames at 21, 73, and 89 s indicate rotations. Detection condition 1 was used. (Scale bar, 30 nm.) (C) Quantification of rotation steps of data in A. Histograms of net rotations, evaluated over three time steps (1 step = 300 ms), toward positive, negative, and zero during the indicated time regimes. Bin size is 2 angular degrees. (D) Histogram comparing successful and failed encounter times for the three base-pair sequences studied. Successful events are defined from first superposition of two molecules to time at which a rod shape of constant length is observed. Failed events are defined from when two molecules first present themselves as a single feature to the time of their permanent separation. Hatched and gray bars show the mean time of hybridization and failed encounter, also specified numerically in parentheses and without parentheses, respectively. (E) Histogram of step distribution, over the time intervals indicated, for the hybridization event analyzed in Fig. 2A. Bin size is 0.25 nm. (F) Mean step sizes of translational diffusion, accompanied by the projected area of the molecule, are plotted against time normalized by the total hybridization time, t_hyb, for the hybridization events. The time interval of each step is 300 ms; the mean step size was averaged over 50 frames. Circles, triangles, and squares refer to random, pentablock, and hairpin sequences, respectively. Color codes are navy for loop annealing, olive for middle-contact zipper-up, blue for defect annealing, and pink for combined. These data summarize all data presented in the text from detection condition 1. (G) Mean step sizes of translational diffusion, accompanied by the projected area of the molecule, are plotted against time for no hybridization cases: single strand (brown), double strand (dark gray), and failed encounters (purple). The time interval of each step is 300 ms; the mean step size was averaged over 50 frames. Circles, triangles, and squares refer to random, pentablock, and hairpin sequences, respectively. These data summarize all data presented in the text from detection condition 1.

It was common to observe failed encounters, by which we mean that hybridization initiated but did not proceed to completion. Most often observed for microstructure sequences that offer metastable intermediate states, we illustrate this for pentablock DNA sequences (Fig. 5A and Movie S4). Here, two strands formed rod-shaped segments (47 and 124 s), but accompanied by continual transient merger and separation, so that the assembly lacked definite overall shape. Notice that as the molecules remained within separations of 5–10 nm throughout, intermediate states of this kind would not be resolved, even by using superresolution fluorescence microscopy, even if satisfactory labeling of the molecule backbone could be achieved.

Other hybridization involved mixed mechanisms: sometimes multiple independent initiation events and sometimes combinations of the mechanisms identified above. In a process that was only partially zipper-up (Fig. 5B; rotation quantified in Fig. 5C), rotation direction changed three times (21, 70, and 89 s), growth with elapsed time of rod projection was not monotonic (longer at 70 s than at 89 s), and a tiny loop intermediate was resolved (29 s). Quantifying failed encounters, we constructed histograms of successful hybridization relative to average interaction time with failed encounters included (Fig. 5D). Taken together, among the total of 18 hybridizations of 36 interaction events that we imaged, 8 were for random sequences, 5 for pentablocks, and 5 for hairpins.

Transiently Enhanced Mobility during Hybridization.

For example, regarding the data shown in Fig. 2A, Fig. 5E shows step-size distribution at different times, and one observes transient shift toward larger step sizes and a broader distribution (30–45 s). The mean step size, plotted against time in Fig. 5F, rose transiently and returned to the initial value when hybridization was complete. This pattern held consistently, as one sees when the mean step size of other examples is plotted against time normalized to the hybridization time, but it was not observed for failed encounters and cases of incomplete hybridization (Fig. 5G). Taken together, we observed that for 17 events of 18 hybridization events, the mean step size was enhanced by a factor of at least 2. This is consistent with the tendency toward longer step sizes in the probability plot in Fig. 2F. It was accompanied by rotation in the laboratory frame of reference, discussed above in connection with Figs. 3 and 4. Additional examples are presented in SI Appendix, Figs. S1 and S2.

Three-Strand Coexistence.

There is need for error correction when three strands coexist during intermediate stages of self-assembly (A + A + B); it is interesting to notice that three-strand helices can carry biological function (32). When three such strands meet in competitive binding (Fig. 6A and Movie S5), one sees transient pairing of two strands (4 s), a triplex (6 s), and ejection of one strand (9 s), followed by repetitions of this cycle and subsequent annealing of a duplex accompanied by rotation (24 s) and final state at 39 s. It can also happen that a late-arriving third strand inserts itself into a partially hybridized duplex of two other strands. This is observed sometimes near the center of the original duplex (Fig. 6A, 13 and 16 s). In other experiments, insertion of the third strand was observed close to the geometrical end of the original duplex (Fig. 6B, 71 s; and Movie S5). This caused a loop to form near the center (80 and 84 s), while the invading strand slowly integrated into the duplex, as indicated by shortening of the visible dangling tail, to facilitate annealing with a rotation (92 s) prior to completion (93 s). Occasionally, invasion by a third strand caused the original duplex to melt. In Fig. 6C, taken from Movie S5, an invading strand approaches a rod-shaped duplex (0 s), attaches (11 s), and hops off, accompanied by rotation (17 s) probably caused by initial melting. It reattaches (37 s), then further melts (77 and 102 s). Quantitative image analysis showed that the total intensity was constant within experimental uncertainty, reflecting the same amount of electron scattering, while it originated in different events (Fig. 6D). Physically, this means that rod microstructure associated with the double helix smoothly shortened to zero, offset by growth of size and intensity of the coil-shaped object that we identify with the melted state, the kinetically stable intermediate state in which three strands coexist.

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Fig. 6.

Transient three-molecule helices (A + A + B). (A–C) The images (Middle) are accompanied by schematic diagrams of time-dependent conformations (Top) and binarized images for better visual contrast (Bottom). Dotted circles highlight individual molecules. Red arrows highlight sudden rotation (Movie S5). (A) Random base-pair sequence, detection condition 1. An invading blue strand attaches to the loop near the center of the original duplex (red + purple). (Scale bar, 30 nm.) (B) Pentablock strands, detection condition 2. An invading blue strand attaches to the duplex at one end, facilitating loop formation (71, 80, and 84 s). (Scale bar, 30 nm.) (C) Pentablock base-pair sequence, detection condition 2. An invading blue strand attaches to a rod-shaped pentablock duplex and melts it. (Scale bar, 30 nm.) (D) Intensity on the electron detector plotted against time. The original rod-shaped double helix (circles) and the invading molecule (triangles) are quantified as mean pixel intensity times their projected area. Note that the total intensity (rod + coil) is close to constant during melting. The shaded times highlight times when three strands interact. a.u., arbitrary units.