Monte Carlo simulations of locally melted supercoiled DNAs in 20 mM ionic strength

Supercoiling induces denaturation bubbles in circular DNA

We present a theoretical framework for the thermodynamic properties of supercoiling-induced denaturation bubbles in circular double-stranded DNA molecules. We explore how DNA supercoiling, ambient salt concentration, and sequence heterogeneity impact on the bubble occurrence. An analytical derivation of the probability distribution to find multiple bubbles is derived and the relevance for supercoiled DNA discussed. We show that in vivo sustained DNA bubbles are likely to occur due to partial twist release in regions rich in weaker AT base pairs. Single DNA plasmid imaging experiments clearly demonstrate the existence of bubbles in free solution.

Temperature dependence of circular DNA topological states

Circular double-stranded DNA has different topological states which are defined by their linking numbers. Equilibrium distribution of linking numbers can be obtained by closing a linear DNA into a circle by ligase. Using Monte Carlo simulation, we predict the temperature dependence of the linking number distribution of small circular DNAs. Our predictions are based on flexible defect excitations that resulted from local melting or unstacking of DNA base pairs. We found that the reduced bending rigidity alone can lead to measurable changes of the variance of linking number distribution of short circular DNAs. If the defect is accompanied by local unwinding, the effect becomes much more prominent. The predictions can be easily investigated in experiments, providing a new method to study the micromechanics of sharply bent DNAs and the thermal stability of specific DNA sequences. Furthermore, the predictions are directly applicable to the studies of binding of DNA-distorting proteins that can locally reduce DNA rigidity, form DNA kinks, or introduce local unwinding.

A structural transition in duplex DNA induced by ethylene glycol

The twist energy parameter ( E T) that governs the supercoiling free energy, and the linking difference (Delta l) are measured for p30delta DNA in solutions containing 0-40 w/v % ethylene glycol (EG). A plot of E T vs -ln a w, where a w is the water activity, displays the full (reverse) sigmoidal profile of a discrete structural transition. A general theory for the effect of added osmolyte on a cooperative structural transition between two duplex states, 1 right arrow over left arrow 2, is formulated in terms of parameters applicable to individual base-pair subunits. The resulting fraction of base pairs in the 2-state ( f 2 (0)) is incorporated into expressions for the effective torsion and bending elastic constants, the effective twist energy parameter ( E T (eff)), and the change in intrinsic twist (delta l 0). Fitting the expression for E T (eff) to the measured E T values yields reasonably unambiguous estimates of E T 1 and E T 2 , the midpoint value (ln a w) 1/2, and the midpoint slope ( partial differential E T/ partial differential ln a w) 1/2, but does not yield unambiguous estimates of the equilibrium constant ( K 0), the difference in DNA-water preferential interaction coefficient (DeltaGamma), or the inverse cooperativity parameter ( J). Fitting a noncooperative model (assumed J = 1.0) to the data yields K 0 = 0.067 and DeltaGamma = -30.0 per base pair (bp). Essentially equivalent fits are provided by models with a wide range of correlated J, DeltaGamma, and K 0 values. Other results favor DeltaGamma in the range -1.0 to 0, which then requires K 0 > or = 0.914, and a cooperativity parameter, 1/ J > or = 30.0 bp. The measured delta l 0 and circular dichroism (CD) at 272 nm are found to be compatible with curves predicted using the same f 2 (0) values that best-fit the E T data. At least 7-10% of the base pairs are inferred to exist in the 2-state in 0.1 M NaCl in the complete absence of added osmolyte. Compared with the 1-state, the 2-state has a approximately 2.0- to 2.1-fold greater torsion elastic constant, a approximately 0.70-fold smaller bending elastic constant, a approximately 0.91-fold smaller E T value, a approximately 0.2% lower intrinsic twist, a somewhat lower CD near both 272 and 245 nm, and less water and/or more EG in its neighborhood. However, the relative change in preferential interaction coefficient associated with the transition is likely rather slight.

Estimation of the persistence length of DNA from the torsion elastic constant and supercoiling free energy: effect of ethylene glycol

Two different methods are proposed to estimate the persistence length ( P) of DNA from the measured torsion elastic constant (alpha) and the twist energy parameter ( E T ) that governs the supercoiling free energy. The first method involves Monte Carlo simulations and reversible-work calculations of E T for model DNAs that possess the measured alpha and selected trial values of P. Comparison of the computed E T values with the experimental value allows estimation of P (or equivalently the bending elastic constant (kappa beta)) by interpolation. A far simpler, though less accurate, alternative is to solve a previously conjectured analytical relation connecting E T , alpha, kappa beta (or P), and an unknown "constant" ( B). The present simulations are used to ascertain the optimum value of B and to assess the validity and accuracy of that relation. Within the simulation errors, P values obtained from the measured alpha and E T via this analytical expression agree with those determined from the simulations and E T values reckoned from the input alpha and kappa beta by this analytical expression agree with the corresponding simulated values. Although B is found to be insensitive to variation in alpha, it appears to decline slightly with increasing kappa beta. The original analytical expression is modified to take this apparent variation of B with kappa beta into account. By using this modified analytical relation to estimate P (from the measured alpha and E T ) or E T (from the input alpha and kappa beta), much closer agreement is obtained respectively with the values of P or E T obtained from the simulations. As specific examples, these methods are applied to determine P in 0 and 20 w/v % ethylene glycol, which has been shown to induce a structural transition in duplex DNA.

Torsional rigidities of weakly strained DNAs

Measurements on unstrained linear and weakly strained large (> or =340 bp) circular DNAs yield torsional rigidities in the range C = 170-230 fJ fm. However, larger values, in the range C = 270-420 fJ fm, are typically obtained from measurements on sufficiently small (< or =247 bp) circular DNAs, and values in the range C = 300-450 fJ fm are obtained from experiments on linear DNAs under tension. A new method is proposed to estimate torsional rigidities of weakly supercoiled circular DNAs. Monte Carlo simulations of the supercoiling free energies of solution DNAs, and also of the structures of surface-confined supercoiled plasmids, were performed using different trial values of C. The results are compared with experimental measurements of the twist energy parameter, E(T), that governs the supercoiling free energy, and also with atomic force microscopy images of surface-confined plasmids. The results clearly demonstrate that C-values in the range 170-230 fJ fm are compatible with experimental observations, whereas values in the range C > or = 269 fJ fm, are incompatible with those same measurements. These results strongly suggest that the secondary structure of DNA is altered by either sufficient coherent bending strain or sufficient tension so as to enhance its torsional rigidity.

Generalized theory of semiflexible polymers

DNA bending on length scales shorter than a persistence length plays an integral role in the translation of genetic information from DNA to cellular function. Quantitative experimental studies of these biological systems have led to a renewed interest in the polymer mechanics relevant for describing the conformational free energy of DNA bending induced by protein-DNA complexes. Recent experimental results from DNA cyclization studies have cast doubt on the applicability of the canonical semiflexible polymer theory, the wormlike chain (WLC) model, to DNA bending on biologically relevant length scales. This paper develops a theory of the chain statistics of a class of generalized semiflexible polymer models. Our focus is on the theoretical development of these models and the calculation of experimental observables. To illustrate our methods, we focus on a specific, illustrative model of DNA bending. We show that the WLC model generically describes the long-length-scale chain statistics of semiflexible polymers, as predicted by renormalization group arguments. In particular, we show that either the WLC or our present model adequately describes force-extension, solution scattering, and long-contour-length cyclization experiments, regardless of the details of DNA bend elasticity. In contrast, experiments sensitive to short-length-scale chain behavior can in principle reveal dramatic departures from the linear elastic behavior assumed in the WLC model. We demonstrate this explicitly by showing that our toy model can reproduce the anomalously large short-contour-length cyclization factors recently measured by Cloutier and Widom. Finally, we discuss the applicability of these models to DNA chain statistics in the context of future experiments.

Exact theory of kinkable elastic polymers

The importance of nonlinearities in material constitutive relations has long been appreciated in the continuum mechanics of macroscopic rods. Although the moment (torque) response to bending is almost universally linear for small deflection angles, many rod systems exhibit a high-curvature softening. The signature behavior of these rod systems is a kinking transition in which the bending is localized. Recent DNA cyclization experiments by Cloutier and Widom have offered evidence that the linear-elastic bending theory fails to describe the high-curvature mechanics of DNA. Motivated by this recent experimental work, we develop a simple and exact theory of the statistical mechanics of linear-elastic polymer chains that can undergo a kinking transition. We characterize the kinking behavior with a single parameter and show that the resulting theory reproduces both the low-curvature linear-elastic behavior which is already well described by the worm-like chain model, as well as the high-curvature softening observed in recent cyclization experiments.