Nonlinear Elasticity of DNA Bending

Abstract

Double stranded (ds) DNA has been used as a “molecular spring” to mechanically control the conformation of proteins, ribozymes and peptides [1]. It is thus interesting to characterize quantitatively the mechanics of DNA springs in the relevant regime of sharp bending (x<<2L<<ld, where x is the end-to-end distance (EED), 2L the contour length of the DNA, ld ∼50 nm the persistence length). This nonlinear elasticity regime is also relevant to several cell biology mechanisms, such as DNA packaging and transcription regulation.We address the problem with the stressed molecules consisting of a bent ds DNA part and a stretched ss part: essentially a system of two coupled nonlinear springs. We measured the elastic energy of these molecules with two different equilibrium methods, based on dimer formation [2, 3] and melting curve analysis [4] respectively. We deduce the bending energy of the ds part as a function of EED x. The finding is that the DNA kinks at a critical bending torque τc ∼30 pN x nm, entering a nonlinear regime where the maximum torque is constant (= τc). We derive an analytic expression for the bending energy valid in the linear and nonlinear regimes [3].The critical torque τc introduces a universal energy scale ∼12 kT in the physics of DNA bending.[1] G. Zocchi, “Controlling proteins through molecular springs”, Ann. Rev. Biophys. 38, 75-88 (2009).[2] H. Qu, C.-Y. Tseng, Y. Wang, A. J. Levine, and G. Zocchi, “The elastic energy of sharply bent nicked DNA”, Europhys. Lett. 90, 18003 (2010).[3] H. Qu and G. Zocchi, “The complete bending energy function for nicked DNA”, Europhys. Lett. 94, 18003 (2011).[4] H. Qu, Y. Wang, C.-Y. Tseng, and G. Zocchi, “Critical torque for kink formation in double stranded DNA”, accepted by Phys. Rev. X (2011).