The Bend Stiffness of S-DNA

– We formulate and solve a two-state model for the elasticity of nicked, doublestranded DNA that borrows features from both the Worm Like Chain and the Bragg-Zimm model. Our model is computationally simple, and gives an excellent fit to recent experimental data through the entire overstretching transition. The fit gives the first value for the bending stiffness of the overstretched state as about 12 nm · kBT , a value quite different from either B-form or single-stranded DNA. Introduction and summary. – When double-stranded DNA is subjected to longitudinal forces greater than about 65 pN it undergoes a radical conformational change, marked by a sudden, almost twofold increase in contour length [1, 2]. The structural characterization of the resulting overstretched or (“S-state”) DNA is complicated by the fact that techniques such as X-ray crystallography are not applicable to single molecules. In this letter, we instead characterize overstretched DNA by examining its elastic constants, and to this end formulate and solve a model that synthesizes features of both the Worm Like Chain (WLC) and the Bragg-Zimm model of the helix-coil transition in peptides. Thus, we model DNA as consisting of two different, coexisting conformations, each with its own elastic constants. We solve this model and show that it gives a good fit to recent data on the overstretching transition in nicked, double-stranded DNA. From these fits, we conclude that the bend stiffness of S-DNA is intermediate between the known values for single-stranded and double-stranded DNA. Our result supports the work of Léger et al. [3, 4], who argued that S-DNA has a definite helical pitch and hence is a new duplex conformation of DNA. Our model and solution method differ from those offered by Marko [5], who assumes the bend stiffnesses of the two conformational states to be identical; our analysis will show that, on the contrary, the stiffnesses are markedly different. The analysis of Viovy and Cizeau [6] is essentially a mean-field approximation to the model we study here; in addition, the authors did not quote any value for the S-DNA bend stiffness, presumably because the experimental data available at that time did not permit such a determination. (∗) E-mail: [email protected] c ⃝ EDP Sciences C. Storm et al.: The bend stiffness of S-DNA 761 The model studied here is a continuum limit of a more general “Discrete Persistent Chain” (DPC) model, which also gives a better fit to the stretching curve of single-stranded DNA at very high stretching forces than either the continuum WLC or the freely jointed chain models. Details will appear elsewhere [7]. Our model and method are also of some general interest beyond DNA. For example, both can be adapted to the study of the stretching of polypeptides with a helix-coil transition. Model. – We begin by formulating the Discrete Persistent Chain, a discretized form of the WLC. Later we will introduce an Ising-like variable on each chain link describing a cooperative transition from Bto S-form. The DPC models the polymer as a chain of N segments of length b, whose conformation is fully described by the collection of orientation vectors {t̂i} for each segment. Thus, the relaxed total contour length is Ltot ≡ Nb. Bend resistance is taken into account by including an energy penalty at each link proportional to the square of the angle Θi,i+1 = arccos(t̂i · t̂i+1) between two adjacent links. The energy functional describing this model is thus given by E [ {t̂i} ]