Extension, torque, and supercoiling in single, stretched, and twisted DNA molecules.

We reinvestigate the model originally studied by Neukirch and Marko that describes the extension, torque, and supercoiling in single, stretched, and twisted DNA molecules, which consists of a mixture of extended state and supercoiled state, using now a more accurate form of the free energy for the untwisted but stretched DNA. The original model uses an approximate form of this free energy and the agreement with experiment is only qualitative. We find that this more accurate free energy significantly improves the results, which bring them into quantitative agreement with experiment, throughout the entire force regime. This is rather surprising, considering that the theory is completely parameter-free.

Role of chain entropy in an analytic model of protein binding in single-DNA stretching experiments.

We show that the simple analytical model proposed by Zhang and Marko [Phys. Rev. E 77, 031916 (2008)] to illustrate Maxwell relations for single-DNA experiments can be improved by including the zero-force entropy of a Gaussian chain. The resulting model is in excellent agreement with the discrete persistent-chain model and is in a form convenient for analyzing experimental data.

Discrete persistent-chain model for protein binding on DNA.

We describe and solve a discrete persistent-chain model of protein binding on DNA, involving an extra σ(i) at a site i of the DNA. This variable takes the value 1 or 0, depending on whether or not the site is occupied by a protein. In addition, if the site is occupied by a protein, there is an extra energy cost ɛ. For a small force, we obtain analytic expressions for the force-extension curve and the fraction of bound protein on the DNA. For higher forces, the model can be solved numerically to obtain force-extension curves and the average fraction of bound proteins as a function of applied force. Our model can be used to analyze experimental force-extension curves of protein binding on DNA, and hence deduce the number of bound proteins in the case of nonspecific binding.

Adsorption of externally stretched two-dimensional flexible and semiflexible polymers near an attractive wall.

We study analytically a model of a two-dimensional partially directed flexible or semiflexible polymer, attached to an attractive wall which is perpendicular to the preferred direction. In addition, the polymer is stretched by an externally applied force. We find that the wall has a dramatic effect on the polymer. For wall attraction epsilon1 smaller than the nonsequential nearest-neighbor attraction epsilon, the fraction of monomers at the wall is zero and the model is the same as that of a polymer without a wall. However, for epsilon1 greater than epsilon, the fraction of monomers at the wall undergoes a first-order transition from unity at low temperature and small force, to zero at higher temperatures and forces. We present phase diagram for this transition. Our results are confirmed by Monte Carlo simulations.

Driven translocation of a polynucleotide chain through a nanopore: a continuous time Monte Carlo study.

Using the continuous time Monte Carlo method, we simulated the translocation of a polynucleotide chain driven through a nanopore by an electric field. We have used two models of driven diffusion due to the electric field. The chain may have strong interaction with the pore, and depends on which end of the chain first enters the pore. Depending on this interaction, in both cases, the distribution of times for the chain to pass through the pore in our model is found to have three peaks, as observed in the experiment of Kasianowicz Brandin, Branton, and Deamer [Proc. Natl. Acad. Sci. USA 93, 13770 (1996)].

Unzipping DNA from the condensed globule state-effects of unraveling.

We have studied theoretically the unzipping of a double-stranded DNA from a condensed globule state by an external force. At constant force, we found that the double-stranded DNA unzips an at critical force Fc and the number of unzipped monomers M goes as M approximately (Fc - F)-3, for both the homogeneous and heterogeneous double-stranded DNA sequence. This is different from the case of unzipping from an extended coil state in which the number of unzipped monomers M goes as M approximately (Fc - F)-chi, where the exponent chi is either 1 or 2 depending on whether the double-stranded DNA sequence is homogeneous or heterogeneous, respectively. In the case of unzipping at constant extension, we found that for a double-stranded DNA with a very large number N of base pairs, the force remains almost constant as a function of the extension, before the unraveling transition, at which the force drops abruptly to zero. Right at the unraveling transition, the number of base pairs remaining in the condensed globule state is still very large and goes as N(3/4), in agreement with theoretical predictions of the unraveling transition of polymers stretched by an external force.

Comment on "theory of high-force DNA stretching and overstretching".

Recently, Phys. Rev. E 67, 051906 (2003)]] introduced the discrete persistent chain model which contains features both of the freely jointed chain (FJO) and the wormlike chain (WLC) models. Equation (20) of their paper is correct only in a special case of large l, the ratio of the persistence length to the monomer length. This special case is unnecessary because the general case can be studied just as easily. Working out the general case, we obtain the force extension relation correct for all values of the parameter l. This force extension relation reduces to the FJC result at small l and to the WLC at large l. At small force, it reduces to the result of Rosa et al. (e-print cond-mat/0307015).

Excluded volume effect in unzipping DNA with a force.

A double stranded DNA molecule when pulled with a force acting on one end of the molecule can become either partially or completely unzipped depending on the magnitude of the force F. For a random DNA sequence, the number M of unzipped base pairs goes as M approximately (F - Fc)(-2) and diverges at the critical force Fc with an exponent chi = 2. We find that when excluded volume effect is taken into account for the unzipped part of the DNA, the exponent chi = 2 is not changed but the critical force Fc is changed. The force versus temperature phase diagram depends on only two parameters in the model, the persistence length and the denaturation temperature. Furthermore a scaling form of the phase diagram can be found. This scaling form is parameter independent and depends only on the spatial dimension. It applies to all DNA molecules and should provide a useful framework for comparison with experiments.

Excluded volume effects in gene stretching.

We investigate the effects excluded volume on the stretching of a single DNA in solution. We find that for small force F, the extension h is not linear in F but proportion to F(gamma), with gamma = (1 - nu)/nu, where nu is the well-known universal correlation length exponent. A freely joint chain model with the segment length chosen to reproduce the small extension behavior gives excellent fit to the experimental data of lambda-phage DNA over the whole experimental range. We show that excluded volume effects are stronger in two dimensions and derive results in two dimensions that are different from the three-dimensional results. This suggests experiments to be performed in these lower dimensions.