Mesoscopic models for DNA stretching under force: New results and comparison with experiments

Abstract

Single molecule experiments on double stranded B-DNA stretching have revealed one or two structural transitions, when increasing the external force. They are characterized by a sudden increase of DNA contour length and a decrease of the bending rigidity. The nature and the critical forces of these transitions depend on DNA base sequence, loading rate, salt conditions and temperature. It has been proposed that the first transition, at forces of 60-80 pN, is a transition from B to S-DNA, viewed as a stretched duplex DNA, while the second one, at stronger forces, is a strand peeling resulting in single stranded DNAs (ssDNA), similar to thermal denaturation. But due to experimental conditions these two transitions can overlap, for instance for poly(dA-dT). In an attempt to propose a coherent picture compatible with this variety of experimental observations, we derive analytical formula using a coupled discrete worm like chain-Ising model. Our model takes into account bending rigidity, discreteness of the chain, linear and non-linear (for ssDNA) bond stretching. In the limit of zero force, this model simplifies into a coupled model already developed by us for studying thermal DNA melting, establishing a connexion with previous fitting parameter values for denaturation profiles. Our results are summarized as follows: (i) ssDNA is fitted, using an analytical formula, over a nanoNewton range with only three free parameters, the contour length, the bending modulus and the monomer size; (ii) a surprisingly good fit on this force range is possible only by choosing a monomer size of 0.2 nm, almost 4 times smaller than the ssDNA nucleobase length; (iii) mesoscopic models are not able to fit B to ssDNA (or S to ss) transitions; (iv) an analytical formula for fitting B to S transitions is derived in the strong force approximation and for long DNAs, which is in excellent agreement with exact transfer matrix calculations; (v) this formula fits perfectly well poly(dG-dC) and λ-DNA force-extension curves with consistent parameter values; (vi) a coherent picture, where S to ssDNA transitions are much more sensitive to base-pair sequence than the B to S one, emerges. This relatively simple model might allow one to further study quantitatively the influence of salt concentration and base-pairing interactions on DNA force-induced transitions.

Statistical physics and mesoscopic modeling to interpret tethered particle motion experiments

“…However this type of approach remains valid for very high stretching of ssDNA [75] provided that both the discrete nature of the chain is taken into account [98] and non-linear stretching terms are included [74]. Fits of force-extension curves of ssDNA up to 1200 pN, as shown in Figure 3a, have been nicely fitted using the modified formula that includes both terms [27]: [74]. The fit leads to the bending modulus value κ(ssDNA) = 1.5 k B T and an effective monomer length a = 0.20 nm (see Figure 3a).…”

“…The last decade has witnessed their rapid development, and the reader can for example refer to Refs. [26][27][28][29][30][31][32][33] for further detail. When the connection with TPM experiments is meaningful, we shall discuss some works dealing with force and torque experiments in the present Review.…”

A Hybrid Atomistic Approach for the Mechanics of Deoxyribonucleic Acid Molecules

“…Er -k\(r -ro)2, Eg = £2 (Co + C\ cosO + C2cos20), Ci = 1 2 , Ci = -4 C 2cos0o, Co = C2(2cos20o + 1), 4 su r 0 (13) Here, ku k2, k3 , and k4 are force constants, 0o is the natural bond angle, D is the van der Waals well depth, r* is the van der Waals length, <? ; is the net charge of an atom, g is the dielectric constant, and r,y is the distance between two atoms.…”

“…However, to develop computing devices using DNA, it is necessary to know structural deformation and stability properties [7] under a wide range of mechanical and thermal conditions. Computational methods have been therefore developed for the mechanical analy sis of DNA [11][12][13] and other biological molecules. Over the past two decades, it has been possible to conduct single molecule experiments and observe de formation patterns under various loading conditions [3,[8][9][10].…”

Determining the elastic properties of aptamer-ricin single molecule multiple pathway interactions

“…13,[17][18][19] Great efforts have been made to study the behaviors of single DNA molecule under stretching. [20][21][22][23] However, little is known about elastic behaviors of DNA during their unbinding processes because of the complexity of the DNA binding structures and biophysical properties. 24 In this study, we revealed the single molecule elastic properties from the experimentally measured AFM data, and developed a relatively simple and practical elasticity model to quantitatively explain the elastic behaviors of ssDNA during the single molecule binding/unbinding reaction.…”