Bending DNA increases its helical repeat

Abstract

In all biological systems, DNA is under high mechanical stress from bending and twisting. For example, DNA is tightly bent in nucleosome complexes, virus capsids, bacterial chromosomes, or complexes with transcription factors that regulate gene expression. A structurally and mechanically accurate model of DNA is therefore necessary to understand some of the most fundamental molecular mechanisms in biology including DNA packaging, replication, transcription and gene regulation. An iconic feature of DNA is its double helical nature with an average repeat $h_0$ of ~10.45 base pairs per turn, which is commonly believed to be independent of curvature. We developed a ligation assay on nicked DNA circles of variable curvature that reveals a strong unwinding of DNA to over 11 bp/turn for radii around 3-4 nm. Our work constitutes a major modification of the standard mechanical model of DNA and requires reassessing the molecular mechanisms and energetics of all processes involving tightly bent DNA.

Fig. 1.. Conformational states in nicked minicircles.

(A) Representative snapshots from oxDNA simulations of nicked minicircles in a (1) kinked + twisted, (2) kinked, or (3) stacked conformation (rendered with oxView ^,). See Fig. S3 for analysis of kink angles $\theta$. In a ligation experiment (Fig. 2), only the ends of stacked configurations (3) can be joined into a fully ligated circle (4). Complex with T4 DNA ligase (PDBID: 6DT1) is for size comparison and illustration only. (B) Plot of the fraction of stacked configurations from 21 different oxDNA simulations of nicked circles between 80–100 bp. Dotted line: Gaussian fits. (C-E) Analysis of dynamics between kinked (blue) and stacked (red) conformations as well as ℎ in oxDNA simulations of nicked circles with 82 (C), 84 (D) and 86 bp (E). $h$ (scale on left) was calculated from the average twist angle $\varphi$ between adjacent base pairs (scale on right; $h=360°⁄\varphi$). Note that kinked conformations fluctuate around the equilibrium $h_0$ of oxDNA (10.55 bp/turn), while stacked conformations can be overwound (C) or underwound (E).

Fig. 2.. Experimental ligation of nicked circles of different lengths.

(A) Splint ligation of oligonucleotides (67–105 nt) produces ss minicircles (B). oxDNA simulation snapshot illustrates flexibility of ss region. (C) Respective complementary strands are annealed to yield nicked circles (D), which can then be enzymatically ligated into double-stranded circles (E). (F) Denaturing PAGE gel. (1) Five oligonucleotides (same as pool 7 in (G) and (H)) before and (2) after splint ligation. The splints run out of the gel; (3) Hybridization to the blue complementary strand before and (4) after ligation. M = size marker (linear ds DNA). (G) Denaturing PAGE analysis of the ligation experiment at 37 °C of all nicked circles $N_{bp}=67-105bp$, that are distributed between eight pools as annotated. Note that some circles split into two bands (73, 83, 93, and 103 bp) indicating different topoisomers. We hypothesize that the ligase does not change $h_0$ of DNA and that splitting occurs at half-integer multiples of $h_0$, or $N_{bp}\approx \left(n+\frac{1}{2}\right)h_0$. Ligase concentration in the final ligation step (D to E) was 100-fold lower in experiment H (4 U/μl). Uncropped gel images, an independent repeat of experiment G and of a 0.1X [ligase] experiment are shown in Fig. S4. (I) Helical repeat $h=N_{bp}/Lk$ for theoretically possible (grey) and experimentally observed (blue) ligated circles. Vertical lines indicate $N_{bp}$ where nicked circles form two topoisomers after ligation. Red datapoints: circles that should have been observed for a constant $h_0=10.5bp/turn$. Circles with $h=h_0$ are torsionally relaxed ($\Delta Tw=0),h>h_0$ are underwound ($\Delta Tw<0$), and $h<h_0$ are overwound ($\Delta Tw>0$). (J) The total mechanical energy of DNA in stacked or ligated circles is the sum of twisting energy $E_{Tw}$ and bending energy $E_{bend}$. At the local minima, circles are torsionally relaxed; to the left they are overwound, and to the right underwound. Red: Expected energy landscape if $h_0=10.5bp/turn$ was constant and independent of curvature.

Fig. 3.. Extent of change of h0.

(A) A 39 bp DNA fragment is displayed with decreasing radii of curvature ($r=50,12,6.4or4.2nm$). All DNA with a smaller radius of curvature than $r=50nm~l_p$ is considered tightly bent. The fragment with $r=4.2nm$ has $h_0=11.14bp/turn$ and is unwound by ~82° compared to the canonical 10.45 bp/turn (transparent overlay); a full circle is unwound by almost ½ turn. (B) Relaxed helical repeat of a duplex bent with a constant radius of curvature $r$ (top axis) matching that of a minicircle of $N_{bp}$ base pairs (bottom axis). Green: $h_0$ from gel data (topoisomer splitting); black: data from circularization experiments ^–; blue: fit using the Marko/Siggia model with fit parameters $h_{(k=0)}=10.42bp/turn$ (=linear DNA) and G/C = 2.7, where G is the twist-bend coupling parameter and C is the torsional stiffness; red: TBC prediction with parameters from ref. ^,. (C) A Nucleosome (PDBID: 3LZ0) has a helical repeat of ~10.1 bp/turn , but a circle with this curvature is torsionally relaxed at ~11.1 bp/turn according to our measurements (D). It follows that $\Delta Tw\approx 1.2turns$.