An elastic rod model to evaluate effects of ionic concentration on equilibrium configuration of DNA in salt solution

Abstract

As a coarse-gained model, a super-thin elastic rod subjected to interfacial interactions is used to investigate the condensation of DNA in a multivalent salt solution. The interfacial traction between the rod and the solution environment is determined in terms of the Young-Laplace equation. Kirchhoff's theory of elastic rod is used to analyze the equilibrium configuration of a DNA chain under the action of the interfacial traction. Two models are established to characterize the change of the interfacial traction and elastic modulus of DNA with the ionic concentration of the salt solution, respectively. The influences of the ionic concentration on the equilibrium configuration of DNA are discussed. The results show that the condensation 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 forces that drive DNA condensation. With the change of concentration, the DNA segments will undergo a series of alteration from the original configuration to the condensed configuration, and the spiral-shape appearing in the condensed configuration of DNA is independent of the original configuration.

Analysis of DNA equilibrium configuration under interfacial traction

“…Using the Frenet formulae, the configurations of the rod can be obtained, which are shown in Figure 2. The results show that the reconfiguration of the DNA elastic rod was owing to the interaction between the interfacial traction and the elastic property, which has also been previously reported by Xiao et al (2014). 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).…”

“…In a more recent study, Xiao et al (2014) accurately obtained the interfacial energy factor in terms of the concentration of the salt solution using the following formula:…”

“…where f i refers to the interfacial traction, which characterizes the effects of the intracellular solution on the rod (Xiao et al, 2014;Wang et al, 2014).…”

“…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.…”

“…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. This interaction should, in essence, be characterized by van der Waals forces or electrostatic forces and is a very critical factor in studying DNA reconfiguration.…”