DNA Crookedness Regulates DNA Mechanical Properties at Short Length Scales

Alberto Marin-Gonzalez, J. G. Vilhena, Fernando Moreno-Herrero, and Ruben Perez

Phys. Rev. Lett. 122, 048102 – Published 1 February 2019

Abstract

Sequence-dependent DNA conformation and flexibility play a fundamental role in the specificity of DNA-protein interactions. Here we quantify the DNA crookedness: a sequence-dependent deformation of DNA that consists of periodic bends of the base pair centers chain. Using extensive $100 μ s$ -long, all-atom molecular dynamics simulations, we found that DNA crookedness and its associated flexibility are bijective, which unveils a one-to-one relation between DNA structure and dynamics. This allowed us to build a predictive model to compute the stretch moduli of different DNA sequences from solely their structure. Sequences with very little crookedness show extremely high stretching stiffness and have been previously shown to form unstable nucleosomes and promote gene expression. Interestingly, the crookedness can be tailored by epigenetic modifications, known to affect gene expression. Our results rationalize the idea that the DNA sequence is not only a chemical code, but also a physical one that allows finely regulating its mechanical properties and, possibly, its 3D arrangement inside the cell.

Received 28 May 2018

DOI:https://doi.org/10.1103/PhysRevLett.122.048102

Physics Subject Headings (PhySH)

Biomolecular dynamics Biomolecular structure

Nucleic acids

Molecular dynamics

Physics of Living Systems

Authors & Affiliations

Alberto Marin-Gonzalez^1,*, J. G. Vilhena^2,3,*, Fernando Moreno-Herrero^1,†, and Ruben Perez^2,4,‡

¹Department of Macromolecular Structures, Centro Nacional de Biotecnología, Consejo Superior de Investigaciones Científicas, 28049 Cantoblanco, Madrid, Spain
²Departamento de Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid, E-28049 Madrid, Spain
³Department of Physics, University of Basel, Klingelbergstrasse 82, CH 4056 Basel, Switzerland
⁴Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, E-28049 Madrid, Spain

^*A. M-G. and J. G. V. contributed equally to this work.
^†Corresponding author. fernando.moreno@cnb.csic.es
^‡Corresponding author. ruben.perez@uam.es

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Vol. 122, Iss. 4 — 1 February 2019

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Images

Figure 1
Representation of DNA crookedness. (a) Average structures and computed $β$ values (in rads) over $1 μ s$ -long MD simulation at 1 pN force of the sequences $CGCG (NN)_{5} CGCG$ with $NN = AA$ , AC, AT, and GG. The beads represent the centers of the base pairs. The terminal base pairs have been omitted. (b) Top: average structure over 250 ns MD of a 30 bps poly-G DNA molecule. The solid black line represents the crookedness curvature and the dashed blue line an estimation of the curvature predicted by the WLC. Bottom: examples of highly curved DNA when bound to proteins. (left) Histone octamer crystallized in Ref. [39] (PDB ID: 1AOI), where the histone tails have been removed for clarity. A grey circle of radius 41.8 Å represents the trajectory of nucleosomal DNA. (right) Crystal structure of the homing endonuclease I-PpoI DNA complex taken from Ref. [40] (PDB ID: 1A73), with an estimation of the DNA curvature represented by the solid red line.
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Figure 2
A model to link DNA crookedness with DNA stretch modulus, $S$ . (a) DNA molecule with the base pair centers represented by purple beads. An external force, $F$ , induces a change in DNA extension, $x (F)$ . (b) DNA can elongate by separating consecutive base pairs (top; $Δ x_{l, i}$ ) or by aligning the base pair centers with the helical axis (bottom; $Δ x_{β}$ ). (c) DNA is modelled as a set of $N$ springs in series. The first $N − 1$ springs account for the stiffness of elongating individual base pair steps, $k_{l, i}$ , and the $N$ th spring is the crookedness stiffness, $k_{β}$ .
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Figure 3
Implications of DNA crookedness on DNA stretching flexibility. (a) $k_{β}$ values as a function of the crookedness, $β$ . $k_{β}$ was computed from the MD simulations data using Eq. (1) and taking the $F = 1 pN$ simulation as reference. $β$ was computed from the $F = 1 pN$ simulation as $β = \cos^{- 1} (x / \sum l_{i})$ . The blue squares correspond to the benchmark sequences and are the points used for the fit $k_{β} (β) = A e^{- k β} + B$ (fitting parameters in main text). The red circles represent the sequences simulated to test the model. The void green triangles are the A tracts containing sequences and the filled green triangles are the sequences used to test the effect of the A tracts. See Table S3 [15] for a list of the simulated sequences. The dashed line represents an estimation of nucleosome curvature according to [44]. (b) The computed value of $S$ is plotted as a function of the value directly measured from the force-extension curve as done in Ref. [14]. The stretch modulus was computed from our model for the simulated sequences described above using Eq. (1), the value of the fit of $k_{β} (β)$ , Table S1 [15], and the values of $β$ and $\sum l_{i}$ obtained from the $F = 1 pN$ simulation. The experimental value of the stretch modulus for random DNA and dsRNA sequences are the average value of the measurements from Refs. [42, 45, 46, 47, 48] and [42, 45], respectively; and the error bars are the standard deviation of these values. The experimental value of the CpG island is the one from Ref. [49] with the error reported there.
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Figure 4
Implications of DNA crookedness on DNA-protein interactions. (a) The base pair center chains of a DNA molecule are represented by color beads. We propose that net directional bending could be achieved by alternating high and low crookedness motifs, such as G-rich and A-rich sequences. (b) Additionally, crookedness flexibility could be exploited to induce a conformational change in DNA towards an A-like structure. On the left is the crystal structure of the I-PpoI DNA complex [40] (PDB ID: 1A73), the same as in Fig. 1. When bound to this protein a high distortion is found on the DNA, which would be more favorable for highly crooked and flexible sequences (left) than for sequences for which this flexibility is hindered (right).
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