Liquid crystal self-assembly of random-sequence DNA oligomers

Abstract

In biological systems and nanoscale assemblies, the self-association of DNA is typically studied and applied in the context of the evolved or directed design of base sequences that give complementary pairing, duplex formation, and specific structural motifs. Here we consider the collective behavior of DNA solutions in the distinctly different regime where DNA base sequences are chosen at random or with varying degrees of randomness. We show that in solutions of completely random sequences, corresponding to a remarkably large number of different molecules, e.g., approximately 10(12) for random 20-mers, complementary still emerges and, for a narrow range of oligomer lengths, produces a subtle hierarchical sequence of structured self-assembly and organization into liquid crystal (LC) phases. This ordering follows from the kinetic arrest of oligomer association into long-lived partially paired double helices, followed by reversible association of these pairs into linear aggregates that in turn condense into LC domains.

Fig. 1.

Duplex motifs of oligomeric DNA: pairing errors and random sequences. (A) Definite pairing achieved by selected sequences, e.g., LC-forming fully paired blunt-ended duplexes, and duplexes with mutually complementary overhangs (5, 8). Effects of errors introduced by design, such as terminal mismatches, are described in SI Text. (B) ranDNA sequences are synthesized by randomly choosing one of the four basic nucleobases at given positions along the chains and are thus mixtures of 4^R different sequences, where R is the number of randomly chosen bases. Because of the large number of sequences, ranDNA forms duplexes with a variety of distinct pairing motifs, the distribution of which is controlled by their binding energy ΔG, given in units of ΔG_o, the mean binding energy of a quartet of complementary bases, and by their lifetime τ ∼ exp(ΔG/ΔG_o). (C–E) Sketches of the behavior of ranDNA oligomers of different lengths in solution. Blue shading: ΔG < 15ΔG_o; τ short; equilibrium binding. Red shading: ΔG > 15ΔG_o, τ long compared to experimental time; kinetically arrested binding. Thus, short oligomers (C) form an equilibrated ensemble of duplexes; oligomers of intermediate length (D) form kinetically arrested duplex cores with weakly mutually attractive tails enabling linear aggregation and LC ordering; long oligomers (E) form multiple kinetically arrested cross-linking bonds leading to gelation.

Fig. 2.

Phase diagram of ranDNA. (A and B) A variety of ranDNA solutions self-assemble into N^∗ (A) and COL (B) LC phases, recognized by the textures in thin cells observed in DTLM. (B) DTLM image of 0.5-mm-diameter capillary of 20N in solution, showing COL domains before and after centrifuging. (C and D) Maps of the LC phases observed in ranDNA of different total number of bases N_B and of random bases, R, either internally (C) or at the terminals (D). Symbols indicate the presence of the nematic (blue square) and of the columnar (green circle) phases in some range of concentrations and temperatures of the solution. The half green circle indicates that the columnar phase is present in a very narrow range of conditions (low T, large c_DNA). Shaded regions highlight specific phase behavior: light blue—fully random sequences; pink—double helices with a single overhanging random tail per duplex terminal; and orange—two random tails per duplex terminal.

Fig. 3.

Experimental characterization of the self-assembly and LC formation of 20N. (A) Red dots—LC-ISO phase coexistence at T = 25 °C as determined by the cell area fraction filled by the LC phase, ϕ_LC, as a function of the 20N concentration c_DNA. Green line and shading—LC-ISO phase coexistence of a self-complementary 20-mer. Full and empty blue dots—respectively, the concentration of coexisting ISO and COL phases as measured by UV absorption on a capillary as in Fig. 2B, where macroscopic phase separation was forced through centrifugation. Gray shading—LC-ISO phase coexistence range of 20N; black dashed and dotted lines—concentration of the coexisting ISO and COL phases. (B) LC volume fraction ϕ_LC vs. temperature T. Red curves (1–5)—progressive melting of the 20N COL phase in cells of various ϕ_LC in A. Curves 2 and 3 are obtained with the same cell and curve 3 with longer thermalization time at room T. Gray curve (6)—COL-ISO ϕ_LC vs. T for 12SC at approximately 1,200 mg/mL. Green curve (7)—COL-ISO ϕ_LC vs. T for 20SC at approximately 600 mg/mL. (C) Fluorescent emission I_F of EtBr in a 20N solution (c_DNA ≈ 700 mg/mL) vs. T as a probe of duplex unbinding, measured in both the coexisting COL (blue and green lines) and ISO (red line) phases. Because of the polarized fluorescent emission of EtBr, I_F depends on the orientation of the COL ordering, parallel (blue line) and perpendicular (green line) to the cell plane. The mean, orientation-independent, fluorescent emission in the COL phase (, gray line) can be obtained from the weighted average of the parallel and perpendicular I_F. The Inset shows the excess of mean fluorescent emission of the COL phase with respect to the ISO phase. (D) Number of duplexes remaining at T relative to the number at T = 25 °C, extracted from I_F: orange dashed line (1)—12N. Red line (2)—20N. Blue line (3)—10SC. Gray line (4)—12SC. Purple line (5)—16SC. Green line (6)—20SC. For all the sequences, the curves were obtained in the concentration range 600–800 mg/mL.

Fig. 4.

Calculated equilibrium and nonequilibrium distributions for ranDNA. (A) Number n(ΔG) of duplexes differing in sequences or in shift that can be formed within the ensemble of fully random sequences of a given length as a function of the pairing free energy ΔG. Blue squares—20N; gray diamonds—12N; green dots—6N. The n(ΔG) are normalized to n(ΔG) = 1 for the largest energy for each given oligomer length. Black dashed line—ΔG dependence of the Boltzmann factor, on the same scale. Free energy is expressed in units of ΔG₀. (B) Equilibrium distribution P(ΔG) of the intraduplex binding free energy in fully random ranDNA at T = 25 °C. Blue squares—20N. Gray diamonds—12N. Green dots—6N. Dashed and dotted blue lines—P(ΔG) for 20N at T = 45 °C and T = 60 °C, respectively. (C) Free energy distribution P(ΔG) calculated through kinetic evolution on the basis of duplex lifetime and random collisions. Red squares—20N. Gray diamonds—12N. Green dots—6N. Dotted lines repeat, for comparison, the equilibrium distributions in B. Whereas 6N and 12N are at equilibrium or nearly so, the distribution of 20N is kinetically arrested and far from equilibrium. (D) Left axis: Calculated overhang length distributions P(ℓ) for 20N. Blue dots—equilibrium distribution. Red open squares—kinetically arrested distribution, on the same scale. Right axis: black diamonds—mean interduplex interaction free energy, calculated as the average value of the binding free energy resulting from collisions of random overhangs.