Mono- and bilayer smectic liquid crystal ordering in dense solutions of “gapped” DNA duplexes

Significance

Liquid crystalline behavior of DNA has been studied for decades, yet only recently has one of the most fundamental liquid crystal phases—the smectic phase in which rod-like objects assemble into stacks of fluid layers—been demonstrated in this system. Here, we describe distinct bilayer and monolayer smectic phases in solutions of “gapped” DNA (GDNA), consisting of two DNA duplexes connected by a single strand. The smectic order is amphotropic (sensitive to temperature as well as concentration), and the layer structure is stable against significant perturbations of the GDNA construct (e.g., “gap” length variation and asymmetry in duplex lengths). The temperature sensitivity may provide a means to compare end-to-end interaction strengths between DNA duplexes at biologically relevant concentrations.

Abstract

Although its mesomorphic properties have been studied for many years, only recently has the molecule of life begun to reveal the true range of its rich liquid crystalline behavior. End-to-end interactions between concentrated, ultrashort DNA duplexes—driving the self-assembly of aggregates that organize into liquid crystal phases—and the incorporation of flexible single-stranded “gaps” in otherwise fully paired duplexes—producing clear evidence of an elementary lamellar (smectic-A) phase in DNA solutions—are two exciting developments that have opened avenues for discovery. Here, we report on a wider investigation of the nature and temperature dependence of smectic ordering in concentrated solutions of various “gapped” DNA (GDNA) constructs. We examine symmetric GDNA constructs consisting of two 48-base pair duplex segments bridged by a single-stranded sequence of 2 to 20 thymine bases. Two distinct smectic layer structures are observed for DNA concentration in the range $\sim 230\text{to}\sim 280$ mg/mL. One exhibits an interlayer periodicity comparable with two-duplex lengths (“bilayer” structure), and the other has a period similar to a single-duplex length (“monolayer” structure). The bilayer structure is observed for gap length $\gtrsim$10 bases and melts into the cholesteric phase at a temperature between 30 °C and 35 °C. The monolayer structure predominates for gap length $\lesssim$10 bases and persists to $>\mathrm{40}\hspace{0.17em}°$C. We discuss models for the two layer structures and mechanisms for their stability. We also report results for asymmetric gapped constructs and for constructs with terminal overhangs, which further support the model layer structures.

DNA is an iconic lyotropic liquid crystal (LC). When duplexes with lengths above the threshold for nematic ordering of hard rods, but below or comparable with the persistence length of the DNA polymer, are concentrated in an aqueous solvent, one observes a sequence of cholesteric, hexagonal columnar, and higher-ordered crystalline phases (1–5). Remarkably, LC structure also emerges spontaneously when ultrashort duplexes (well below the normal threshold for a nematic phase) are concentrated and through blunt end–end attraction, assemble into longer aggregates (6). LC ordering has also been observed in solutions of short single-stranded oligomers (7, 8), or even mononucleotides (9), that first pair (via base–base complementarity) and then stack to form rod-like aggregates.

However, until its recent discovery (10), elementary layered (smectic) phases—so fundamental to small-molecule LCs with sufficiently long, flexible terminal groups—were conspicuously missing from an otherwise representative range of mesophases exhibited in concentrated DNA solutions. One key to stabilizing smectic layering is the introduction of a “gap,” or sequence of single bases of sufficient number, into the middle of a duplex, thereby producing a “gapped” DNA (GDNA) construct consisting of two rigid segments connected by a flexible spacer (Fig. 1). This architecture enables entropy-driven segregation of the spacer and the enthalpic attraction between blunt duplex ends to operate together to stabilize a smectic layer structure.

Fig. 1.

Schematic motifs of GDNA constructs. (A) “Symmetric” GDNA composed of two 48-bp duplexes connected by a single-strand segment (gap) consisting of n = 2, 4, 7, 10, or 20 T (thymine) bases. (B and C) Asymmetric constructs containing 60/48- and 60/24-bp duplexes connected by a 20 T spacer. (D) Symmetric construct with terminal 2 T overhangs.

Identifying and characterizing minimal, essential entropic and enthalpic factors for the self-assembly of smectic phases in dense solutions of semiflexible, anisotropic particles are important challenges in soft materials science. The present work further explores this problem in the GDNA system by examining the effects of altering basic architectural features of the GDNA construct and varying temperature on the nature and stability of the smectic phase.

In particular, we demonstrate that basic characteristics of smectic ordering of GDNA depend sensitively on the gap length. We establish that two distinct smectic-A–type layer structures occur in concentrated GDNA solutions. One (the “bilayer” structure) is characterized by an interlayer periodicity comparable with the length of two-duplex segments. The other (“monolayer” structure) has a period comparable with the length of a single duplex. The bilayer structure prevails for longer gap lengths ($\gtrsim 10$ bases). The monolayer morphology predominates when the gap length is shortened to $\lesssim 10$ bases and is evident down to at least a 4-base gap. No evidence of smectic layer structure is observed for gaps $\le 2$ bases.

We also establish that the GDNA system is amphotropic, with the smectic phases being sensitive to temperature in addition to DNA concentration. Specifically, we observe a smectic to cholesteric (chiral nematic) phase transition, occurring between 30 °C and 35 °C in solutions of GDNA constructs that exhibit the bilayer smectic phase. We argue that this transition reflects a temperature dependence of the enthalpic end-to-end interactions that stabilize the bilayer structure.

Additionally, we report results on GDNA constructs containing either duplexes of unequal length (“asymmetric” GDNA) or duplexes with noncomplementary, single-strand “overhangs” positioned at the ends opposite the gap. These results further buttress the evidence for two distinct smectic layer structures and for the significance of blunt end-to-end attraction in stabilizing the bilayer smectic.

The GDNA constructs investigated are summarized schematically in Fig. 1. Symmetric constructs consisted of two 48-base pair (bp) duplexes connected by a single-strand gap of $n=2$, 4, 7, 10, or 20 unpaired thymine (T) bases; we abbreviate these constructs as 48-$n$T-48 (Fig. 1A). We also assembled asymmetric constructs, designated 48-20T-60 and 24-20T-60, composed of 24- or 48- and 60-bp duplexes linked by a 20 T single strand (Fig. 1 B and C), and synthesized symmetric constructs, designated 2T-48-20T-48-2T, with two unpaired T bases “overhanging” the free ends of the duplexes (Fig. 1D).

Results: Polarizing Optical Microscopy

We conducted polarizing optical microscopy (POM) on thin films of concentrated 48-20T-48 GDNA sandwiched between clean, untreated microscope slides with a spacing of several micrometers. Samples were prepared by the edge-evaporation technique described in Materials and Methods, which enables one to observe the evolution of liquid crystalline phases continuously within gradients of the DNA concentration near the boundary of the film. The cholesteric phase is first identified by the development of a classic “fingerprint” texture (SI Appendix, Fig. S4) that, with sufficient time, evolves into a darker state in which the helical axis is predominantly oriented perpendicular to the glass slides [“Grandjean” texture (5)], and the helical pitch is in the micrometer range (SI Appendix, Fig. S5). Coexistence of these darker domains with bright smectic domains is shown in Fig. 2E, which is overexposed for contrast. As shown at higher magnification and normal exposure in Fig. 2A, the smectic domains are characterized by a focal conic (FC) “fan” texture (11).

Fig. 2.

POM results on a thin film of a 48-20T-48 GDNA solution sandwiched between microscope slides. Liquid crystalline structure emerged as water evaporated from the open edge of the film. The edge was sealed after the nucleation of large smectic domains, with the average DNA concentration estimated to be $\approx 240$ mg/mL. (A) FC fan texture of the smectic domains at $25\hspace{0.17em}°$C with orientations of polarizer (P) and analyzer (A) axes shown at Upper Left. (B and C) Blown-up views of the region within the dashed white square near the center of the image in A, highlighting two FC brushes, before (B) and after (C) insertion of a quartz wedge compensator into the optical path. A yellow arrow in C (Upper Left) indicates the orientation of the compensator’s extraordinary axis ${\mathbf{e}}_c$. (D) Schematic showing two alternative orientations of GDNA duplexes in the FC brushes in B and C. The extraordinary axis of the compensator ${\mathbf{e}}_c$ is aligned along the average azimuthal direction in the upper brush and along the average radial direction in the lower brush. The sketch in D, Right shows a splay in the orientation of duplexes (blue rods) corresponding to a smectic phase; the average extraordinary axis of the duplexes ${\mathbf{e}}_{dna}$ is nearly parallel (perpendicular) to ${\mathbf{e}}_c$ in the upper (lower) brush, which increases (decreases) the optical phase shift $\mathrm{\Delta }\phi$, as indicated by upward (downward) arrows in C and D. The shifts in $\mathrm{\Delta }\phi$ are just the opposite for a columnar phase, depicted in D, Left. The orange to purple color variation from the lower to upper brushes in C represents a positive gradient in $\mathrm{\Delta }\phi$ (further discussion is in SI Appendix), which is consistent with the duplex orientation for a smectic rather than columnar phase. Similar color variation and gradient in $\mathrm{\Delta }\phi$ is observed for other FCs, such as those indicated by arrows, in A (see SI Appendix, Fig. S2). (E–K) Temperature dependence of smectic domains observed over an approximately millimeter-sized region of the sample. (E) A 2-s exposure taken at $25\hspace{0.17em}°$C showing coexisting bright smectic and darker domains, which are indicated by red and green rectangles, respectively, (F) Same region as E with exposure time reduced to 0.2 s at the start of a heating scan. (G–I) Melting of the smectic domains on heating. The longer (2-s) exposure time in I (vs. 0.2 s in G and H) reveals that the smectic domains have transformed to the darker texture that resembles the cholesteric Grandjean texture in SI Appendix, Fig. S5. (J and K) Subsequent cooling from $33\hspace{0.17em}°$C to $10\hspace{0.17em}°$C. At $25\hspace{0.17em}°$C, smectic domains have partially reformed (compare J and F). At $10\hspace{0.17em}°$C in K, the smectic phase fills a larger area than in the initial image (F).

Planar FC textures are also observed in the columnar phase of fully paired (FP) DNA duplexes. To demonstrate that the FCs observed in Fig. 2A are associated with smectic layering of the GDNA duplex segments, we used the same variable optical compensation method employed in the identification of columnar ordering in concentrated solutions of FP duplexes (2, 5, 9). Fig. 2 B and C shows a magnified view of two neighboring brushes of an FC, highlighted by the dashed box in Fig. 2A, before and after insertion of the compensator. The schematic sketches in Fig. 2D depict arrangements of DNA duplexes that would correspond to a columnar (Fig. 2 D, Left) or smectic (Fig. 2 D, Right) phase. The orientations of the extraordinary axes of the compensator (${\mathbf{e}}_c$) and of the GDNA duplexes (${\mathbf{e}}_{dna}$) are indicated for the two cases; the orientation of ${\mathbf{e}}_{dna}$ reflects the negative optical anisotropy of the duplexes (12–14). The lowest energy deformation of a smectic preserves the layer spacing (at least to lowest order in the layer displacement); thus, the layers bend and the molecules splay around the core of the FC, and the duplexes are radially oriented (Fig. 2D). On the other hand, in a columnar phase, splay changes the spacing between the hexagonally packed columns and therefore, comes at a high energy cost. The columns are, however, relatively free to slide along one another, and a bend in their orientation tends to maintain the column–column separation; consequently, the duplexes in this case point along the azimuthal direction surrounding the center of the FC.

Since the duplex orientations are $90\hspace{0.17em}°$ apart in the two scenarios, the optical phase shift ($\mathrm{\Delta }\phi$, indicated in Fig. 2D) is higher in the brushes of an FC domain where ${\mathbf{e}}_c\parallel {\mathbf{e}}_{dna}$ and lower in those where ${\mathbf{e}}_c\perp {\mathbf{e}}_{dna}$. These differences result in a variation in the color of transmitted light (Fig. 2C). The observed color gradient may be correlated with the gradient in $\mathrm{\Delta }\phi$ using a Michel–Levy interference color chart (15), and thus, the average duplex orientation in the brushes may be deduced (SI Appendix has further discussion). The resulting correlation indicates smectic layering of the duplexes rather than a columnar phase.

We also explored the temperature dependence of the smectic domains in Fig. 2E. Since concentration gradients within the sample are very slow to relax due to the high viscosity of the GDNA solutions, we can only estimate an average DNA concentration of $\sim 240$ mg/mL over the total volume (brighter and darker domains) where liquid crystalline texture is evident. As revealed in Fig. 2 E–I, the smectic (bright) domains melt as the temperature is raised from $25\hspace{0.17em}°$C to $33\hspace{0.17em}°$C, at which point only the darker (cholesteric) texture is observed. However, the smectic domains evidently do not all melt at precisely the same temperature, which likely reflects some variation in DNA concentration among them. On subsequent cooling back to $25\hspace{0.17em}°$C, they begin to reform at the original sites (compare Fig. 2 J and F) but with significant thermal hysteresis. After further cooling to $10\hspace{0.17em}°$C, the smectic phase populates most of the region imaged (Fig. 2K).

Small-Angle X-ray Scattering

We obtained small-angle X-ray scattering (SAXS) data on concentrated solutions of symmetric or asymmetric GDNA constructs, symmetric constructs with variable gap length, and constructs with terminal overhangs. Key results are presented in Fig. 3 and discussed in the subsections below.

Fig. 3.

Results from SAXS. (A–D) Temperature dependence of the azimuthally averaged natural log of the SAXS intensity vs. scattering wave number $q$ on heating (red traces) and subsequent cooling (blue traces) for symmetric and asymmetric GDNA samples with gap lengths $n=7$, 10, or 20. The samples were initially prepared by slow evaporation of water to reach GDNA concentrations in the smectic range. The nominal concentrations and the smectic layer spacings (calculated from the $q$ values of the fundamental peaks indicated by vertical arrows) are 250 mg/mL and 34.5 nm for the 48-20T-48 sample, 260 mg/mL and 38.8 nm for 60-20T-48, 260 mg/mL and 16.1 nm for 48-10T-48, and 280 mg/mL and 16.0 nm for 48-7T-48. For the samples with $n=20$, the layer spacing is comparable with the sum of lengths of the duplex segments (bilayer smectic), while for $n\le 10$, the spacing is comparable with a single duplex (monolayer smectic). (E) Comparison at ambient temperature of SAXS peak positions in symmetric GDNA samples with variable $n$. The horizontal scale is split and magnified in order to highlight the systematic shift of the fundamental peak to slightly higher $q$ (slightly smaller layer spacing) with decreasing gap length. Weak first harmonic peaks are also observable at higher $q$. (F) Comparison at $10\hspace{0.17em}°$C of SAXS intensity vs. $q$ from the smectic phase of symmetric blunt-ended 48-20T-48 GDNA and of the same construct with 2 T overhangs on the ends. Note the transition from a bilayer smectic (fundamental peak at $q=0.363/2=0.182$ ${\mathrm{n}\mathrm{m}}^{-1}$ corresponding to approximately two-duplex periodicity) to a monolayer smectic (fundamental peak at $q=0.332$ ${\mathrm{n}\mathrm{m}}^{-1}$ corresponding to slightly larger than single-duplex periodicity).

Symmetric 48-20T-48 GDNA Solutions.

A typical SAXS pattern from smectic 48-20T-48 GDNA samples features multiple, sharp, small-angle peaks, representing several orders of diffraction from the stacking of duplexes in smectic layers, combined with a diffuse peak at wider angle, arising from the liquid-like in-layer packing of the duplexes. Certain samples aligned in a high magnetic field produced diffraction patterns from well-oriented smectic domains (SI Appendix, Fig. S7), where the arrangement of small and wider angle peaks along orthogonal axes indicates a smectic-A–type layer structure with average duplex orientation parallel to the layer normal. The absence of any sharp features at wider angle rules out a columnar or higher-order smectic phase.

Azimuthally averaged SAXS intensity profiles vs. $q$ are plotted as a function of temperature in Fig. 3A for an $\approx 250$-mg/mL 48-20T-48 smectic GDNA sample. At the lowest temperature, four orders of small-angle diffraction are detected (the third and fourth being barely above the background level). The wave number $q$ of the fundamental order, $q_0=2\pi /d$, corresponds to a smectic layer spacing of $d\approx 34.5$ nm, about 8% larger than the $\approx 32$-nm length of two 48-bp duplexes. A broad peak centered at larger $q$ ($q\approx 1.9$ ${\mathrm{n}\mathrm{m}}^{-1}$) (SI Appendix, Fig. S10) indicates liquid-like correlations between duplexes within the layers and implies an average lateral center–center spacing of 3.3 nm (about 60% larger than the $\approx 2.0$-nm diameter of a single duplex).

The intensity of the small-angle peaks drops monotonically, across all orders, as the sample is heated; at $35\hspace{0.17em}°$C, the small-angle scattering has disappeared. This is consistent with melting of smectic domains into the cholesteric state in the concentrated 48-20T-48 GDNA sample studied optically (Fig. 2 E–I), although the comparison is not precise because as noted earlier, the DNA concentration in the optical cells is not uniform and the melting temperature is apparently sensitive to concentration.

As seen in Fig. 3A, the small-angle peaks reappear—and the layer structure is recovered—when the sample is cooled back to $20\hspace{0.17em}°$C, although there is significant thermal hysteresis in the reformation of smectic domains (as observed optically). It is also possible that the domains reform with a distribution of layer orientations that does not scatter as efficiently in the fixed incident beam and detector geometry.

Asymmetric 60-20T-48 and 60-20T-24 GDNA Solutions.

If the duplexes in the GDNA constructs have unequal lengths (but the single-strand gap is kept at 20 T), we find that the temperature range over which the smectic phase exists is reduced and with sufficiently large asymmetry, disappears altogether within the DNA concentration range (up to 300 mg/mL) studied.

Fig. 3B shows the azimuthally averaged SAXS intensity vs. $q$ for an $\approx 260$-mg/mL solution of 60-20T-48 GDNA at various temperatures between $6\hspace{0.17em}°$C and $26\hspace{0.17em}°$C. Several points are notable. First, three orders of diffraction from the smectic layer structure are visible at small angles, and the peaks are somewhat broader than observed for 48-20T-48 symmetric GDNA samples with similar DNA concentration, indicating a smaller characteristic domain size. The lowest-order peak at $q_0=0.162$ ${\mathrm{n}\mathrm{m}}^{-1}$ implies a layer spacing of 38.8 nm, corresponding to slightly more than the sum of the asymmetric duplex lengths (60 + 48 bp $\approx 36$ nm). Second, the small-angle peaks disappear—and thus, the smectic phase fully melts—at a temperature $\sim 25\hspace{0.17em}°$C, about $10\hspace{0.17em}°$C lower than for the symmetric 48-20T-48 GDNA sample. Third, after cooling from the melted state back to $20\hspace{0.17em}°$C, there is no indication of the smectic phase reforming (no recovery of the small-angle diffraction) over the $\sim 10$-min period that the sample continued to be monitored on the synchrotron beamline. Although we subsequently confirmed reformation of the low-temperature phase optically, highly concentrated smectic samples containing asymmetric constructs evidently show a substantially greater thermal hysteresis when cycled through the melting temperature than samples of symmetric constructs.

When the asymmetry ratio is doubled from 60/48 to 60/24 (again keeping the same 20 T gap), we found no evidence of a smectic phase. During slow evaporation of water, starting from an isotropic solution, we observed SAXS patterns consistent with the cholesteric and columnar phases only, as the DNA concentration increased up to $\approx 300$ mg/mL. The columnar phase is characterized by a sharp ring at wider angle ($q\approx 2.1$ ${\mathrm{n}\mathrm{m}}^{-1}$), indicating positional ordering of the duplexes in the lateral directions, and by the absence of any small-angle peaks (no layer structure along the duplex axis).

Symmetric 48-nT-48 GDNA Solutions for Variable Gap Lengths $\mathit{n}=\mathbf{2},\mathbf{4},\mathbf{7},\mathbf{10}$.

When the gap length of symmetric GDNA constructs is reduced from 20 to 10 T, the contributions to the total SAXS intensity shift from scattering attributable to the two-duplex layer structure (peaks at $m\hspace{0.17em}{q}_0=2\pi m/d$, $m=1-4$, $d$ comparable with two duplexes) to scattering associated with single-duplex layer structure (peaks at $\simeq 2q_0$ and $4q_0$). Fig. 3C shows azimuthally averaged SAXS intensity vs. $q$ profiles from an $\approx 260$-mg/mL solution of 48-10T-48 GDNA as a function of temperature. The position of the fundamental peak at 0.39 ${\mathrm{n}\mathrm{m}}^{-1}$ yields a layer spacing of 16.1 nm, comparable with the length of a single duplex. A much weaker harmonic is observed at 0.78 ${\mathrm{n}\mathrm{m}}^{-1}$. The sample also exhibits a diffuse wider-angle peak, which is consistent with liquid-like correlations in the directions lateral to the duplexes and a lateral duplex–duplex spacing of $\approx 3.1$ nm. As the sample is heated above $\sim 35\hspace{0.17em}°$C, the small-angle peaks diminish significantly in intensity, and above $\sim 40\hspace{0.17em}°$C, the $2q_0$ peak exhibits pronounced wings. The peak heights only partially recover upon cooling, suggesting either the reformation of smectic domains in a different average orientation (that produces weaker diffraction) or a significant thermal hysteresis.

Symmetric GDNA samples with a 7 T gap also show a smectic-A layer structure with small-angle peaks at the $2q_0$ and $4q_0$ positions only (Fig. 3D), which are again consistent with a single-duplex layer structure. In heating, these peaks weaken at $\sim 35\hspace{0.17em}°$C, disappear above $40\hspace{0.17em}°$C, and recover with evident hysteresis on subsequent cooling. Small-angle peaks at $2q_0$ continue to be observed with further reduction of the gap length to 4 T. As in the case of the 10 and 7 T samples, the scattering at $q$ corresponding to the lateral spacing between duplexes is diffuse, consistent with an elementary smectic phase.

Fig. 3E displays a comparison of the $2q_0$ peak positions in symmetric GDNA samples with 10, 7, and 4 T gaps. These peaks index to layer spacings of 16.1, 16.0, and 15.9 nm, respectively, which decrease with decreasing length of the gap and consequently, of the overall construct, as expected.

Solutions of constructs with 2 T gap showed no evidence of smectic layering. In the SAXS patterns (SI Appendix, Fig. S9), we observed no small-angle peaks and only a diffuse or sharp ring at wider angle corresponding to lateral correlations characteristic of cholesteric and columnar phases, respectively.

Solutions of 48-20T-48 GDNA with Terminal Overhangs.

Our results presented above provide compelling evidence that two distinct layer structures characterize smectic ordering in GDNA solutions—one with periodicity approximately two duplexes, observed for gap lengths $n\gtrsim 10$, and the other with approximately one duplex period that predominates for $n\lesssim 10$. One mechanism that would promote the stability of the two-duplex layer structure is the hydrophobic attraction between the blunt ends of different duplexes (6, 16–18), which could promote pairing of folded duplexes and their organization into a regular bilayer structure with end–end paired duplexes separated by thin layers containing the flexible single-strand segments of the GDNA constructs (Fig. 4D).

Fig. 4.

(A) End–end pairing of symmetric “folded” (Top), “unfolded” (Middle), and mixed (Bottom) GDNA constructs that could serve as building blocks for a bilayer smectic-A phase. (B and C) Examples of how a regular bilayer structure may be frustrated when unfolded constructs are incorporated into larger aggregates with all blunt ends paired. In B, a “void” in the layer structure of a symmetric 48-20T-48 GDNA aggregate is filled by a pair of folded constructs, resulting in a mix of folded and unfolded single strands between the duplex layers. A difference in the equilibrium spacing between duplexes, imposed by the two different single-strand morphologies, would tend to frustrate a regular layer structure. For a system of asymmetric 60-20T-48 constructs, C indicates how a mixture of long–long, short–long, and short–short pairings in an aggregate containing unfolded constructs disrupts a regular layer structure. (D) Portions of a uniform bilayer smectic-A phase produced by end-to-end pairing and packing of folded symmetric 48-20T-48 or asymmetric 60-20T-48 constructs. The layer spacing in each case is comparable with the sum of the duplex segments. In the asymmetric case, the uniform layer structure requires that each end of a shorter duplex pair with the end of a longer one, which gives a layer spacing consistent with the X-ray results from Fig. 3. (E) Portion of proposed monolayer smectic-A phase of GDNA. The duplex segments of unfolded, symmetric constructs interdigitate, yielding a uniform layer structure with spacing similar to the length of a single duplex in accordance with our X-ray data on constructs having gap lengths between 4 and 10 T.

To further test this scenario, we synthesized 48-20T-48 duplexes with terminal 2 T overhangs (Fig. 1D), which we abbreviate as 2T-48-20T-48-2T. As demonstrated in Fig. 3, blunt-ended GDNA constructs with 20 T gaps exhibit the two-duplex layer structure, even in samples with some degree of duplex asymmetry. If this layer structure is stabilized by attraction between base pairs at the blunt ends of duplexes, we would expect it to be disrupted by the addition of nonsticky single-strand overhangs to these ends. Fig. 3F compares the azimuthally averaged intensity profile for a smectic 2T-48-20T-48-2T solution at $25\hspace{0.17em}°$C with a blunt-ended 48-20T-48 homolog at similar DNA concentration. The small-angle peak positions of the former (lowest-order $q=0.332$ ${\mathrm{n}\mathrm{m}}^{-1}$) yield a layer spacing of $d=18.9$ nm, which is consistent with a single-duplex layer structure that is “swollen” by the overhangs but clearly differs from the two-duplex layer structure exhibited by the blunt-ended homolog.

Discussion

The occurrence of mono- and bilayer smectic phases in concentrated GDNA solutions recalls earlier observations of lamellar self-assembly in solutions and melts of copolymers morphologically similar to the GDNA construct (19). Transmission electron microscopy studies on dried films cast from dense solutions of rod–coil polyisocyanate–polystyrene diblocks revealed both single- and double-layer smectic structure (20, 21). Although films cast from solutions of the homologous rod–coil–rod triblock exhibited weak, discontinuous layering (22), well-ordered smectic layer structure has been reported on different rod–coil–rod copolymers (23). Theoretical models (24, 25) have accounted for both mono- and bilayer smectic phases in rod–coil melts. In the monolayer smectic, the rod segments interdigitate, whereas in the bilayer phase, they are arranged end to end. In both cases, the coils are segregated and occupy space between single or double layers of rods. The bilayer structure is favored only for large rod to coil length ratio, which reduces the entropy penalty due to the rods being constrained to slide along each other in pairs. Recent simulations (26) also support the possibility of various lamellar self-assembly by rod–coil–rod triblocks. Very recently, lamellar and various bicontinuous phases have been characterized in coil–rod–coil DNA–polymer hybrids (27).

Although one might model microphase separation of the flexible single-strand and rigid duplex components of GDNA constructs with a Flory–Huggins-type interaction, as in the copolymer melts, two additional features of the GDNA system tend to promote a lamellar structure: Attractive, hydrophobic interaction between blunt duplex ends enthalpically favors their end-to-end pairing, and the presence of an aqueous solvent mitigates the entropy penalty on sliding motions of the duplexes associated with this pairing.

Bilayer Smectic-A Phase of GDNA Constructs with $\mathit{n}=\mathbf{20}$ T.

A smectic-A phase with approximately two-duplex periodicity can be constructed by pairing blunt ends of the duplex segments of two GDNA constructs and then packing these aggregates into a layer structure where the flexible gaps are segregated from the duplexes and the duplexes are oriented normal to the layers. As sketched in Fig. 4A, this can be done with constructs in either “unfolded” (i.e., extended) or “folded” (U-shaped) conformations. The entropy penalty associated with pairing the duplex ends (noted above) is offset by a reduction in free energy due to the attractive interaction between blunt ends, as well as by the presence of the aqueous solvent. The reduction in free energy from end–end stacking of DNA fragments, concentrated in a 120-mM NaCl buffer, has been estimated to be $\mathrm{\Delta }G\simeq 5$ kcal/mol (16) per pair at the optimum end-to-end separation.

In order for a bilayer structure composed of “folded” GDNA constructs to be feasible, the contour length ($L_{C,ss}$) of the flexible 20 T gap segment must be sufficiently long to make folded conformations statistically likely. The probabilities of folded and unfolded constructs will be comparable when $L_{C,ss}$ is substantially larger than the Kuhn length $L_{K,ss}=2L_{P,ss}$ (twice the persistence length of a single strand of thymines) and/or when $L_{C,ss}\gtrsim 2D+s\approx 5$ nm (where $D$ is the duplex diameter and $s$ is the lateral duplex–duplex separation). If the former holds, the single strand can be treated as a freely jointed chain with $\approx L_{C,ss}/L_{K,ss}$ links. Using monomer spacing $a=0.5$ nm and $L_{P,ss}=1.5$ nm for a single strand of thymines in 150-mM NaCl buffer (28), we estimate $L_{C,ss}/L_{K,ss}=\left(20\times 0.5\hspace{0.17em}\mathrm{n}\mathrm{m}\right)/\left(2\times 1.5\hspace{0.17em}\mathrm{n}\mathrm{m}\right)\approx 3$ for a 20 T single strand. Also, for this strand length, $L_{C,ss}\approx 10$ nm is twice $2D+s$. Thus, GDNA constructs with 20 T gap should have a significant probability of folding.

As Fig. 4 B and C illustrates, there are two significant problems associated with assembling a uniform bilayer smectic-A that contains unfolded constructs. End-to-end pairing of mixtures of folded and unfolded constructs can produce layered aggregates having “voids” (Fig. 4B) that must be filled by pairings of constructs with various sizes, shapes, and/or different folded/unfolded composition. As suggested in Fig. 4B, filling such voids could result in a mix of single strands with distinct morphologies (corresponding to a folded vs. unfolded GDNA construct) being packed between duplex layers, which would tend to disrupt a regular smectic layer structure.

A more severe issue arises in constructing a bilayer smectic-A using unfolded, asymmetric GDNA constructs. Stacking such constructs would result in either 1) a mixture of smectic domains with period comparable with one short plus one long duplex (“short–long” pairing) and domains with twice this periodicity (“short–short” alternating with “long–long” pairings), with comparable SAXS intensities at the corresponding $q$ values, or 2) no uniform layer structure due to incommensurability of these pairings in a side to side arrangement of duplexes within the layers, as illustrated in Fig. 4C. Neither is consistent with our experimental data in Fig. 3B, where the peak intensities diminish monotonically with increasing $q$ and where the peak positions correspond strictly to harmonics of short–long duplex pairing.

For these reasons, we propose the bilayer structures indicated in Fig. 4D, which are formed purely from pairing folded symmetric or asymmetric constructs. Not only does this scenario produce a uniform smectic layer spacing and account for the exclusive short–long periodicity observed experimentally in the asymmetric case, but it also explains the absence of a bilayer smectic-A when the single-strand gap is significantly shortened and the probability of folding is consequently reduced. Our SAXS data indicate that the bilayer spacing is approximately 8% greater than the length of two duplexes, which accounts for the additional space occupied by the single-stranded segments between layers of duplexes.

In asymmetric GDNA constructs, when the aspect ratio of the short duplex drops below the threshold [$\simeq 4.7$ (29)] predicted for ordering of hard spherocylinders, one might expect that the entropy cost of pairing and constraining the short duplexes within the bilayer structure in Fig. 4D would preclude smectic ordering. This may explain the observed absence of a smectic phase in the highly asymmetric 60-20T-24 system, where the aspect ratio of the short duplex is $\simeq 4$.

Monolayer Smectic-A Phase of GDNA Constructs with $\mathit{n}\le \mathbf{10}$ T.

In the case of GDNA samples with $n\le 10$, which exhibit a monolayer smectic phase, the ratio $L_{C,ss}/L_{K,ss}$ is $\le 1.5$, and $L_{C,ss}\lesssim 2D+s$, making it considerably less likely that the GDNA constructs constituting the smectic layers are folded and more likely that their conformation is linear. We therefore propose the monolayer smectic structure shown in Fig. 4E, based on unfolded constructs arranged into an interdigitated layer structure with layer spacing of approximately one duplex. (In this figure, imagine the single strands as curling into or out of the page, making a more gradual turn than the two-dimensional schematic might suggest.)

In a layer structure assembled with unfolded GDNA constructs, interdigitation of duplexes provides more lateral space, and therefore more configurational freedom, for the flexible single-strand elements while also enabling their end-to-end extension to be kept to a minimum. Our X-ray results indicate that the layer spacing in the monolayer structure is quite close to the length of a single duplex ($\sim 16$ nm), suggesting that individual duplexes have some freedom to tilt in order to accommodate the single strands in the interlayer regions and therefore, that their ends are not strictly paired in the monolayer phase. We also found that the addition of terminal 2 T overhangs to the ends of symmetric constructs, which frustrates end-to-end pairing, does not preclude a smectic with approximately single-duplex periodicity. Even in certain symmetric, blunt-ended 48-20T-48 samples, we occasionally observed evidence of coexistence of smectic domains with approximately two- and approximately one-duplex layer spacing (SI Appendix, Fig. S8). Taking all these observations together, we can propose that the monolayer structure is stabilized more by the segregation of flexible single-strand components than by end-to-end attraction between duplexes.

Temperature-Dependent Smectic to Nematic Phase Transitions.

The results in Figs. 2 and 3 reveal that the bilayer structure in the $n=20$ GDNA samples melts at significantly lower temperatures than the monolayer structure observed for constructs with $n\le 10$. Considering the model for the bilayer smectic in Fig. 4D, we can suggest that the blunt-end attractive interaction weakens with increasing temperature. In concert with reduced damping of the local motions of the duplexes by the solvent (the viscosity of water decreases nearly threefold from 5 °C to 50 °C), this weakening may destabilize the bilayer structure and drive a transition to a cholesteric/nematic state.

In the model bilayers (Fig. 4D), note that paired ends of the duplexes lie in two separate planes if the GDNA constructs are asymmetric, while in a similar arrangement of symmetric constructs, they occupy a common plane. The pairings are therefore farther apart on average in the asymmetric case, and the overall bilayer may therefore be less stable against temperature (or thermal fluctuations). This would explain the lower melting temperature of bilayers composed of 60-20T-48 vs. 48-20T-48 constructs (Fig. 3).

The monolayer smectic remains stable to at least $10\hspace{0.17em}°$C higher temperatures than the bilayer phase, which is consistent with a different type of layer structure, such as proposed in Fig. 4E, where end-to-end pairing of duplexes is not the main driving factor.

Conclusions

We have presented experimental results on liquid crystalline solutions of various GDNA constructs. These results reveal two distinct types of elementary smectic ordering: one characterized by an approximately two-duplex layer spacing (bilayer structure), and the other characterized by an approximately single-duplex periodicity (monolayer structure). We established that the stability of the smectic layering in both types depends not only on DNA concentration but also, on temperature and the morphology of the individual GDNA construct—namely, the length of the single-strand gap, the degree of asymmetry in the lengths of the duplex segments, and the presence of short, single-strand overhangs that decorate the blunt free ends of the duplexes.

Our results set the stage for investigating the possibility of higher-order smectic phases in GDNA solutions and the mesophase behavior of more complicated GDNA constructs, such as constructs containing duplexes with a conformational bend. Additionally, the close lateral packing of duplexes in the GDNA layer structure may provide an alternative test bed to study the impact of macromolecular crowders on certain biological processes (30, 31). Typical crowding agents, such as polyethylene glycol (PEG), are known to influence the conformation and stability of nucleic acid secondary structures such as G quadruplexes, which develop in nucleic acid sequences rich in guanine. GDNA smectics offer a system that mimics the high cellular DNA concentrations under which these structures form while avoiding the need for external crowding agents.

Materials and Methods

GDNA Synthesis.

Starting oligomers purified by polyacrylamide gel electrophoresis (PAGE) were obtained from commercial sources: Biomers or ExonanoRNA; these include long single strands (98 to 128 nucleotides), which contain a 2, 4, 7, or 20 T central sequence, and shorter strands (24, 48, or 60 bases) that are complementary to segments of the long strand, starting from its opposing ends. The specific nucleotide sequences of the three individual strands used to assemble the GDNA constructs studied are given in SI Appendix, Table S1. The three strands were annealed at equimolar concentrations ($10\hspace{0.17em}\mathrm{\mu }$M) at $90\hspace{0.17em}°$C for 10 min in a 150-mM NaCl, 10-mM trisaminomethane-HCl (pH 7.5), and 0.1-mM ethylenediaminetetraacetic-acid aqueous buffer. The mixture was then slowly cooled overnight to room temperature.

The annealed sample was then passed through a 50-kDa membrane filter (Amicon Ultra from Millipore) by centrifuging at 5,000 rpm for 15 min. The supernatant, with a volume of $\sim 100$ $\mathrm{\mu }$L and salt concentration of 150 mM NaCl, was then collected. Next, we added deionized water to the supernatant solution, increasing the total volume by approximately five times and reducing the NaCl concentration to $\sim 30$ mM NaCl. This solution was then concentrated by passing it through a 10-kDa filter (Amicon Ultra from Millipore) and centrifuging it for 12 min at 12,000 rpm, which maintains the NaCl concentration at $\sim 30$ mM NaCl. Using a NanodropOne instrument (Thermo Scientific), we measured the GDNA concentration of the concentrated supernatant in the range $80-100$ mg/mL.

To confirm that the annealing and purification protocols yielded completely formed GDNA constructs of high purity, we performed gel electrophoresis (10% native PAGE) on constructs assembled using a radioactively labeled single-strand component; further details are provided in SI Appendix.

POM.

Samples for POM were prepared by first increasing the GDNA concentration of supernatant solution to $\sim 180$ mg/mL by evaporation of water in a Speedvac. A droplet of the concentrated solution was then placed on a clean microscope slide and covered with second slide. No spacer was used; the resulting film thickness in the sandwich was a few micrometers. The optical texture of the sample was monitored through a Nikon polarizing microscope as water was allowed to evaporate freely from the open edges of the film at $25\hspace{0.17em}°$C in a dry laboratory atmosphere. As the DNA concentration at the edges increased, the sample passed from the isotropic (featureless dark texture) to the cholesteric (typically characterized by a darkened texture with weak intensity variations shown in Fig. 2I and discussed further in SI Appendix) to the smectic phase (bright FC fan texture). After the development of a thick rim of smectic, the sample was sealed around its edge with mineral oil. Areas where the mineral oil infuses into the sample appear as featureless islands separated from the aqueous GDNA solution by a well-defined boundary. After sealed, the DNA concentration between the edges and center of the film gradually became more uniform, although usually a coexistence of cholesteric and smectic domains remained, and the average DNA concentration in the latter could only be estimated with a precision of $\approx 10$ mg/mL. For temperature-dependent studies, the samples were placed in an Instec model TS62 hot/cold stage, which was mounted on the microscope.

To determine the GDNA duplex orientation in FC domains, we utilized a wedge-shaped quartz compensator plate that could be translated in the optical path between crossed polarizer and analyzer, with its slow axis making a $45\hspace{0.17em}°$ angle to the polarizer axis. When the plate is inserted, optical dispersion combined with the azimuthal variation in duplex orientation around the FC core produces a variation in color of the light transmitted through adjacent brushes of the FC optical texture. As described in SI Appendix, this variation can be correlated to a gradient in optical phase shift, which enables a determination of the duplex orientation in the brushes.

Sample Preparation for SAXS Measurements.

Before loading $80-100$ mg/mL GDNA supernatant into laser-cut quartz X-ray capillaries (2-mm inner diameter, 10-$\mathrm{\mu }$m wall thickness) for SAXS, we made minor adjustments to salt and GDNA concentrations of the supernatant, so that $\sim 150$ mM NaCl would be reached at a target DNA concentration between 230 and 280 mg/mL after evaporation of water from the open end of the capillary. Prior to loading, we also calibrated the capillaries by adding known volumes of deionized water and measuring their height in the capillary. The calibrated capillaries were dried, and the supernatant was gradually and carefully pipetted in. Loaded capillaries were placed in a custom-made aluminum holder that was partially immersed in a water bath at 40 °C to 45 °C; both the GDNA and NaCl concentrations increase as the water evaporates, and the solution height decreases. When the desired height, and hence, desired GDNA concentration, was reached, the capillary was removed from the bath, and the open end was sealed with an inert epoxy. The sealed capillaries were kept at $4\hspace{0.17em}°$C for several weeks prior to the X-ray measurements, and the sample height was checked periodically to confirm integrity of the sealing.

SAXS.

SAXS measurements were carried out on beamline 11-BM at the National Synchrotron Light Source II. The incident X-ray energy was 17 keV, and the incident beam size at the sample was $0.2\times 0.2$ mm. The typical acquisition time for SAXS patterns was 5 s. No evidence of X-ray damage to samples was observed. Commercial hot/cold stages with Kapton film windows were used to regulate the sample temperature between $5\hspace{0.17em}°$C and $45\hspace{0.17em}°$C. (This range is well below the $77\hspace{0.17em}°$C denaturation point of the 48-bp GDNA duplexes we used.) We also recorded background scattering from a capillary containing pure buffer solution, which was subtracted from the data taken on the GDNA samples during processing of the SAXS patterns for the results presented in Fig. 3. A capillary filled with silver behenate powder was used to calibrate the scattering wave number ($q$) in the plane of the detector.

We attempted to align certain GDNA samples for SAXS studies in the bore of an NMR magnet at field strengths of $8\text{to}12$ Tesla and with the field direction parallel to the capillary long axis. Details are provided in SI Appendix, together with an example (SI Appendix, Fig. S7) of a favorable outcome. However, the procedure was generally time consuming and not always effective, and it could not be done on the SAXS beamline due to unavailability of a high field magnet. The data presented in Fig. 3 were collected on unaligned samples with a broad distribution of the smectic layer normal.

Data Availability

Some study data are available.