Description of ligation strategy

Abiotic ligation experiments are carried out in aqueous solutions containing DNA oligomers and the water-soluble ligating agent 1-ethyl-3-(3-dimethylaminopropyl) carbodiimide (EDC; Fig. 1b and ref. 9). EDC activates the phosphate terminals, so that they can react with hydroxyl terminals to generate a native covalent phosphodiester bond, with isourea as a by-product as sketched in Fig. 1c (details in Supplementary Note 1 and Supplementary Fig. 1). We investigate ligation in solutions of EDC and the self-complementary Dickerson dodecamer 3′ phosphate (5′- CGCGAATTCGCGp -3′, D1p), shown in extensive previous study to organize into isotropic (ISO), nematic (NEM) or columnar (COL) LC phases1, depending on concentration and temperature T. EDC-activated phosphate terminals can also react with water, in this case producing isourea and a phosphate terminal ready to react again with another EDC molecule (Supplementary Note 2).

We observe that the solubility of EDC in the LC phases is limited to molar ratios R=[EDC]/[D1p]<3, a condition that does not allow an EDC supply large enough to generate significant polymerization. This limitation is effectively bypassed by exploiting the self-selection properties of phase separation. We thus dilute DNA by a solution of polyethylene glycol (PEG), a chemically inert water-soluble polymer often used as a depletant to control osmotic pressure Π (refs 10, 11). Previous experiments5 indicated that as the PEG concentration (c PEG ) is providing a large enough Π, the solution phase separates into DNA-rich COL LC domains surrounded by a PEG-rich isotropic fluid (Fig. 1f). Therefore, DNA solutions with a concentration c DNA much smaller than c DNALC , which is necessary to induce LC ordering in a pure water–D1p solution, are homogeneously mixed with PEG at low c PEG (Fig. 1e), but for sufficiently large c PEG , D1p LC COL domains will appear, surrounded by an isotropic phase that contains EDC at values of R that can be orders of magnitude larger than above, typically in the range 10<R<50. The properties of the LC condensate depend only on Π, which in this case is mainly provided by PEG and to a lesser extent by EDC and isourea, but could, in principle, be provided by single-stranded DNA or by ill-terminating duplexes4,5. In these conditions, and by virtue of the intrinsic self-selection properties of phase separation12, LC domains, constituting only a small fraction of the entire sample volume, act as microreactors having a state established by T and Π, effective access to reactants, and a large waste sink.

Samples are prepared by dissolving a small amount of lyophilized D1p in fresh prepared EDC mixture with PEG at various c PEG =100–400 g l−1 to obtain a homogeneous solution with c DNA ~0.05 c DNALC and R=50. Experiments are carried out in parallel in small plastic tubes and in flat cells to enable visual confirmation of LC domains formation through light microscopy. Tests revealed that the ligation reaction was completed in ~24 h, so we set this as the incubation time for all the experiments reported here, terminating the reaction at the end by 20-fold dilution with 50 mM ethanolamine (details in Methods section).

Enhanced ligation in LC domains segregated from PEG

Typical 15% polyacrylamide gel scans of DNA extracted from such solutions are shown in Fig. 1g, where the signal is given by the fluorescent emission provided by ethidium bromide staining (details in Supplementary Methods). Ligation in the low c PEG homogeneous mixtures is limited even at this relatively high c EDC , but the appearance of condensed droplets with LC ordering produces a qualitatively new behaviour, manifested by the growth of a large peak in oligomer population having a mean degree of polymerization, ‹n›>10. To better visualize the length distribution, the same samples are also run in 3.5% agarose gels where the bands associated with longer oligomers are more easily distinguished (Fig. 1h). Profiles of the fluorescent emissions of the gel runs are presented in Fig. 2 and analysed by exploiting the approximate proportionality between electrophoretic mobility and logarithm of chain length13 (details in Supplementary Methods and Supplementary Figs 2–4). Despite the intrinsic uncertainty in the quantitative information carried by the fluorescence profiles of the gels, the product length distribution P(n) extracted from the profiles is well described by a simple Flory model14 (Supplementary Note 3, Supplementary Methods and Supplementary Figs 5–7). This enables quantification of the increment in polymerization yield (Flory parameter, p) owing to the phase separation and LC condensation: from p~0.13 (c PEG =200 g l−1, mixed D1p/PEG ISO phase) to p~0.84 (c PEG =400 g l−1, D1p LC COL domains), as shown in Fig. 2a for the polyacrylamide gel runs. Moreover, integration of the agarose gel profile in Fig. 2b indicates that in the COL domains 20% (10%) of the DNA mass is part of chains with n>30 (n>50) and that ‹n›~19, corresponding to oligomers of N b =12n=208 base pairs.

Figure 2: Fluorescence intensity profiles of the gel electrophoresis runs. Measurements are performed on DNA/PEG/EDC mixtures, and gels are stained by ethidium bromide. Plots are shown as a function of n, the position along the gel converted in degree of polymerization (Supplementary Methods). i F (n) (continuous lines) is the fluorescence intensity. C F (n) (open dots) is the cumulative weight fraction distribution, obtained integrating i F (n) (Supplementary Methods). Dotted lines in a–c and the dashed line in b have been obtained by fitting the data with the Flory model for simple polymerization from which the polymerization yield p has been determined (see Supplementary Figs 6 and 7). Dotted lines: C(n), Supplementary Equation (3). Dashed line: P(n), Supplementary Equation (2). (a) D1p/PEG/EDC mixtures measured in a 15% polyacrylamide gel for increasing PEG concentration: c PEG =200 g l−1, red lines (upper panel), uniform isotropic DNA/PEG/EDC mixture, ‹n›<2, p≈0.13; c PEG =400 g l−1, blue lines (lower panel), DNA COL domains in a PEG ISO background, ‹n›≈11, p≈0.84. The c PEG =300 g l−1 profile (not shown) can be obtained by a superposition of the c PEG =200 g l−1 and c PEG =400 g l−1 profiles, consistent with the appearance of a few small DNA COL domains. (b) D1p/PEG/EDC mixtures for c PEG =400 g l−1 measured in 3.5% agarose gels for 60 min running time. At this long running time, enabling better detection of longer products, the first detectable peak corresponds to n=5. Analysis indicates ‹n›≈19 and p≈0.90. (c) D1p/PEG/EDC mixtures measured at T=65 °C. Upper panel: c PEG =300 g l−1, D1p-rich ISO phase coexisting with a PEG-rich ISO phase, ‹n›≈3.5, p≈0.49. Lower panel: c PEG =400 g l−1, D1p-rich COL domains coexisting with a PEG-rich ISO phase, ‹n›≈10, p≈0.81. (d) D2pTT/PEG/EDC mixtures at various c PEG , yielding uniform mixtures (c PEG =200) or condensation of COL domains (c PEG ≥300 g l−1; ‹n›<3. Full size image

These results show that the chemical ligation of DNA oligomers into linear chains is greatly enhanced by COL ordering. Mechanisms contributing to this enhancement include the organization of the duplexes into the base pair stacks characteristic of the already ligated bases; the promotion of the ligation reaction by maintenance of continuous stable proximity (high local concentration) of the reacting terminals, according to the law of mass action; the provision by the LC phase of a fluid environment for transport and reaction, and the coexistence of phases that provides an ISO environment surrounding the LC domains in which EDC can freely diffuse. In this way, the limitations of the finite solubility of EDC in the COL phase are overcome by a continuous supply from the ISO phase. Gel data from ligation in the COL phase (Fig. 1d) show a very strong depletion of the monomer band, indicating that such EDC supply mechanism combined with the reaction time (~1 day; Supplementary Note 4 and Supplementary Fig. 8) ensure that the largest part of the duplexes within the COL domains takes part in the reaction.

Comparison of ligation in ISO and LC phases

To discriminate the individual relevance of DNA LC ordering versus the local increase in c DNA provided by phase separation, we exploit the new observation that PEG can phase separate droplets of concentrated duplexed DNA oligomers in either the ISO or the LC COL phase, depending on T, c PEG and oligomer structure. This provides us the opportunity to compare ligation efficiencies between conditions where the only significant difference is the LC ordering, which is pursued in two distinct experiments.

In a first experiment, we compare ligation of D1p in ISO and COL at the same T and different Π. Indeed, we find that at T~65 °C, a T at which the COL phase melts but D1p duplexes are still stable, condensation of D1p into the ISO phase is possible (details in Methods section and Supplementary Figs 9 and 10). This behaviour contrasts the one observed at T=20 °C, where, upon increasing c PEG , D1p condenses directly into the COL phase. Specifically, by maintaining a constant T=65 °C, we select and study in parallel the ligation of D1p at c PEG =300 g l−1, at which the DNA phase separates from PEG into ISO droplets (Fig. 3b), and at c PEG =400 g l−1, where COL domains are found (Fig. 3c). Optical observation and simulated phase diagram versus Π (ref. 6) indicate that c DNA is very similar in these two condensed phases, being no >10% larger in the COL. The data of the resulting gel runs are shown in Fig. 3e, with the intensity profile plotted in Fig. 2c. The difference in the product length distribution directly attributable to the LC ordering is quite marked, analysis of the curves yielding ‹n›≈3.5 in the ISO phase and ‹n›≈10 in the COL phase (details in Supplementary Note 5, 6 and Supplementary Figs 11–13).

Figure 3: Ligation in condensed LC and isotropic DNA droplets. (a) Sketch, bright-field and fluorescent emission microscope picture of condensed D2TTp ISO droplets in a D2TTp/PEG mixture at T=20 °C. Duplexes are selectively marked by EvaGreen dye. (b) Sketch and polarized microscope images (crossed and parallel polarizers) of ISO D1p droplets in a D1p/PEG/EDC mixture at T=65 °C and c PEG =300 g l−1, respectively. (c) Sketch and polarized microscope images (crossed and parallel polarizers) of COL D1p droplets in a D1p/PEG/EDC mixture at T=65 °C and c PEG =400 g l−1, respectively (identical structures are found at 20 °C). (d) Polyacrylamide gel (15%) comparing the ligation products in D1p and D2TTp in identical conditions. The formation of concentrated DNA domains produces in the case of D2TTp (lanes on the left-hand side of the gel) a minor increment in the product length, contrasting with the marked discontinuity in the case of D1p. (e) Polyacrylamide gel (15%) comparing the ligation products obtained in D1p/PEG/EDC at T=65 °C, where, depending on c PEG , the system is either uniformly mixed or it partitions into two coexisting ISO phases (c PEG =300 g l−1, sketch b), or else it phase separates into coexisting COL and ISO phases (c PEG =400 g l−1, sketch c). Numbers along the lanes indicate the oligomer lengths expressed in number of bases (N b ) and the polymerization number (n). In both gels, the ladder contains DNA oligomers 12, 24, 36 and 48 bases long, synthesized by repetition of D1p sequence. The straight lines are a guide for the eyes, helping the identification of bands corresponding to selected N b . Full gel images are shown in Supplementary Fig. 16. Full size image

In a second experiment, we compare ligation at T=20 °C and equal Π in the PEG-induced condensed phases of two different DNA sequences: D1p and 5′- GCCGTATACGGC TTp -3′ (D2TTp). D2TTp is a self-complementary dodecamer sequence (underlined section) with two additional T bases on the 3′ end. Hence, D2TTp forms duplexes terminating in non-pairing TT overhangs that suppress end-to-end duplex adhesion and thus LC ordering. We thus explore PEG/D2TT/EDC mixtures (R=50, variable c PEG ) according to the protocol described above and characterize the products by gel electrophoresis. We find phase separation of ISO droplets (Fig. 3a) for c PEG >300 g l−1. The condensation of DNA-rich ISO droplets of D2TTp brings about a much smaller effect in the ligation efficiency than the condensation of the D1p LC droplets, as visible in the gel runs (Fig. 3d) and in their intensity profiles (Fig. 2d). The appearance of bands in the gel not corresponding to multiple of D2TTp, probably indicating the formation of circular products, makes impossible the semi-quantitative analysis with the Flory model used above. However, the intensity profiles can be directly integrated to extract ‹n›, which yields ‹n›<3 even at the largest c PEG .

These results clearly support the notion that phase separation and LC ordering are both essential factors in the self-assembly-induced enhancement of the abiotic EDC-based ligation used here. LC ordering provides continuous close contact between the reacting terminals, without which no significant elongation is observed. However, phase separation is crucial as well; it selectively confines the DNA LC into domains whose internal fluid structure bounded by an aqueous/aqueous interface that enables easy transport of material, proving to be a convenient and effective arrangement to carry out the ligation reaction.

Selectivity of LCs microreactors

It is clear from these and earlier experiments that in a mixture of oligomers, the selectivity afforded by the cascaded phase separation of sequences provides an effective self-sorting mechanism by rejecting, for example, the entry of single strands into the LC domains1,5, or else admitting duplexes with sufficiently adhesive tails, such as in solutions of complementary duplexes with overhangs3 or of random sequence DNA oligomers4. In systems such as oligomeric DNA, where the modes of self-assembly are strongly interdependent, sequence dependent and hierarchical (for example, end-to-end adhesion of oligomers is more or less irrelevant if they are not duplexed), phase separation also becomes a type of staged or cascaded selection mechanism, manifested in a cascade of thermodynamic instabilities. This is illustrated in Fig. 4 (for a more detailed discussion, see Supplementary Note 7 and Supplementary Table 1), displaying the phase coexistence observed in a three-component mixed solution of D1p, D2TTp and PEG. At low PEG concentration, these solutions are single phase, consisting of random coil PEG and duplexed DNA oligomers. For c PEG >300 g l−1, the DNA duplexes phase separate from PEG, a result of their compact rigid structure, originating in their hybridized portions. As the concentration of duplexed DNA locally increases because of this PEG versus DNA phase separation, a second-phase separation takes place between the isotropic (ISO) and columnar (COL) LC phases, the COL phase principally comprises blunt-end D1p and the ISO phase is mainly composed of D2TTp, which cannot form LCs. Thus, this second-phase separation is carried in a context that is created by the first. These staged partitioning acts as a hierarchical selection mechanism, condensing together the blunt-ended D1p duplexes that enable LC ordering, which are precisely those in which contacting terminals promote enhanced ligation.