Modulating DNA configuration by interfacial traction: an elastic rod model to characterize DNA folding and unfolding

Abstract

As a continuum model of DNA, a thin elastic rod subjected to interfacial interactions is used to investigate the equilibrium configuration of DNA in intracellular solution. The interfacial traction between the rod and the solution environment is derived in detail. Kirchhoff's theory of elastic rods is used to analyze the equilibrium configuration of a DNA segment under the action of the interfacial traction. The influences of the interfacial energy factor and bending stiffness on the toroidal spool formation of the DNA segment are discussed. The results show that the equilibrium configuration of DNA is mainly determined by competition between the interfacial energy and elastic strain energy of the DNA itself, and the interfacial traction is one of the forces that drives DNA folding and unfolding.

Analysis of DNA equilibrium configuration under interfacial traction

“…A kink is characterized by a piece of a filament with a high curvature κ (or small radius of curvature, R = 1/κ) (Alexandre et al, 2006). The Kirchhoff approach is not appropriate for modeling kinks in rods because, in the derivation of Kirchhoff equations, it is assumed that the centerline radius of curvature of the rod is much larger than the cross-sectional radius (Huang, 2011). However, Zhao et al (1998) used the Kirchhoff rod model to find that the spontaneous curvature has a great influence on the stability of kinked DNA.…”

“…where σ > 0 is the interfacial energy factor, which is generally a constant in a given salt solution and describes a result of the comprehensive hydrophilic and hydrophobic effect distributed along the surface of the DNA segments and relates to the solution environment (Huang, 2011). It is known that dw 3 /ds = 0, that is to say that w 3 = constant.…”

“…The interaction between the DNA elastic rod and the molecules of the solution plays a significant role in the reconfiguration of the DNA segments (Benham and Mielke, 2005). Several studies (Huang, 2011;Xiao et al, 2014;Wang et al, 2014) have shown that microequilibrium configurations of DNA chains are affected by the interaction of the DNA molecule with positive ions in a salt solution. Huang (2011) modeled the interaction using distributed traction, which is caused due to interfacial energy, in a Kirchhoff model, and characterized the folding and unfolding of DNA chains using a numerical simulation of the elastic model.…”

“…Several studies (Huang, 2011;Xiao et al, 2014;Wang et al, 2014) have shown that microequilibrium configurations of DNA chains are affected by the interaction of the DNA molecule with positive ions in a salt solution. Huang (2011) modeled the interaction using distributed traction, which is caused due to interfacial energy, in a Kirchhoff model, and characterized the folding and unfolding of DNA chains using a numerical simulation of the elastic model. However, Huang had incorrectly determined the interfacial traction on the central axis of the DNA elastic rod, which was later corrected by two different groups of researchers (Xiao et al, 2014;Wang et al, 2014) in 2014.…”

Helical configurations of elastic rods in the presence of interfacial traction

“…In salt solution, the geometrical configuration of a DNA chain is determined by the interaction between DNA chain and solution molecules. Huang [9] modeled the interaction by the interfacial traction in an elastic rod model, which characterized DNA folding and unfolding, and Wang et al [10] corrected the incorrect tractions induced by the interfacial energy. Xiao et al [11] used the elastic rod model to evaluate the effects of ionic concentration on the equilibrium configuration.…”