Fig 1.
(a) The atomic structure of the B-form DNA double helix, (b-c) helical continuum models consisting of the soft core (blue) and two stiff ribbons (red) without and with major-minor grooves. The cross-section of the helix is parameterized using either the width (W) and the height (H) or the diagonal length (D) and the aspect ratio (AR = W/H) with the groove angle (Ф).
Fig 2.
Stress distributions on the cross-section of the rectangular prism (left) and of the bare helix model without backbone stiffness (right).
(a) Three-dimensional structures, (b) the axial stresses under tension, (c) the axial stresses under bending, and (d) the in-plane shear stresses under torsion. Results are calculated using Ec = 668 MPa, D = 2.4 nm, and 1/AR = 0.6 with the default helical parameters for the helical continuum model. Stresses are given in MPa.
Fig 3.
Mechanical properties of the bare helix model without backbone stiffness.
(a) S/B depends on both D and AR while (b) C/B is insensitive to D. Shaded regions represent the range of experimental S/B and C/B values. (c) The bare helix model is not able to reproduce the positive, experimental ΔLc values corresponding to the shaded region for the entire range of D and AR tested. Results are calculated using Ec = 668 MPa with the default helical parameters.
Fig 4.
Mechanical properties of the helical model with backbone stiffness.
(a) S/B is insensitive to Sr while (b) C/B depends on both Sr and AR. Shaded regions represent the range of experimental S/B and C/B values. (c) The helical model can reproduce the positive, experimental ΔLc values corresponding to the shaded region for a wide range of Sr and AR values. Results are calculated using Ec = 668 MPa and D = 2.6 nm with the default helical parameters.
Table 1.
The mechanical properties and the diameter of the B-form DNA.
For the isotropic cylinder model, we report C and g in consequence of choosing Young’s modulus and the diameter to satisfy S = 1100 pN and B = 230 pNnm2. For the helical model without major-minor grooves, the mechanical properties are calculated using D = 2.8 nm, 1/AR = 0.6, Ec = 411 MPa and Sr = 880 pN with the default helical parameters. For the helical model with major-minor grooves, the mechanical properties are obtained using D = 2.4 nm, 1/AR = 0.6, Ec = 668 MPa and Sr = 1100 pN with the default helical parameters.
Fig 5.
Effect of major-minor grooves.
(a) The major-minor grooves increase ΔLc for the entire range of AR. Shaded region represents the range of experimental values. Inset shows the ribbon configuration of the helical model without major-minor grooves (blue) and with major-minor grooves (red). Results are calculated using Ec = 668 MPa, D = 2.4 nm, and Sr = 1100 pN with the default helical parameters. (b) Feasible parameter values of D and AR necessary to reproduce the experimental mechanical properties of the B-form DNA when we use the helical model with major-minor grooves (red) and without them (blue).
Fig 6.
Effect of the groove angle on the mechanical properties of the bare helix model.
(a-c) The groove angle has negligible effects on S, B, and C. (d) However, ΔLc is sensitive to the groove angle particularly when the aspect ratio is high. Results are calculated using Ec = 668 MPa and D = 2.4 nm with the default helical parameters.
Fig 7.
Effect of the helical parameters.
Results are calculated using Ec = 668 MPa, D = 2.4 nm, 1/AR = 0.6, Sr = 1100 pN and Ф = 130°. Colors show (a) (S − Sref)/Sref, (b) (B − Bref)/Bref, (c) (C − Cref)/Cref, and (d) (ΔLc − ΔLc,ref)/ΔLc,ref where Sref, Bref, Cref, and ΔLc,ref are the reference stretching, bending and torsional rigidities and the axial displacement coupled to twist, respectively, computed using the default helical parameters, Δθ = 34.29°/bp and ΔZ = 0.34 nm/bp. While the rigidities increase, ΔLc decreases with the helix angle, α = tan-1(2ΔZ/DΔθ).