Statistical Mechanical Model of the B- to Z-DNAStructural Transition

DNA can transition into a multitude of distinct structures. Perhaps the most dramatic of these structural changes is the transition from the canonical right-handed B-form DNA to the left-handed Z-form DNA. To establish how this phenomenon impacts biological processes, we establish a mechanistic model of this transition that incorporates both DNA's elastic response and the energetics of base pairs flipping from B to Z. In this work, we introduce a mesoscopic statistical mechanical theory based on the twistable wormlike chain model (TWLC) and a 1D model of DNA structural transitions that captures the physics of the B- to Z-DNA transition. Our model predicts the extension response of a DNA molecule subjected to a fixed tension as it undergoes progressive unwinding and over winding. Our theory confirms the physically intuitive understanding of the B-Z transition as a mechanism for counteracting negative torsional stress that builds when the molecule is constrained by moderate tensile forces (f >1 pN). Our model's extension response closely matches data from single-molecule magnetic tweezer experiments and provides predictions for key energetic parameters of Z-DNA. By tuning these parameters, we explore their effect on the molecule's conformation and its transition from B- to Z-DNA. Our model predicts bending persistence lengths for Z-DNA of 42 nm and 94 nm, respectively, and the per base pair energetic cost of forming a segment of Z-DNA and a B-Z junction to be 10.44 𝑘𝐵𝑇 and 0.34 𝑘𝐵𝑇, respectively.