arXiv subjects

Pui-Man Lam

Publications and source records attributed to Pui-Man Lam.

16 recordsLinked to original sources

arXiv2017

Stretching, Twisting and Supercoiling in Short, Single DNA Molecules

We had combined the Neukirch-Marko model that describes the extension, torque and supercoiling in single, stretched and twisted DNA of infinite contour length, with a form of the free energy suggested by Sinha and Samuels to describe short DNA, with contour length only a few times the persistence length. We find that the free energy of the stretched but untwisted DNA, is significantly modified from its infinitely length value and this in turn modifies significantly the torque and supercoiling. We show that this is consistent with short DNA being more flexible than infinitely long DNA. We hope our results will stimulate experimental investigation of torque and supercoiling in short DNA.

cond-mat.soft↗

arXiv2017

Cyclization of Short DNA Fragments

From the per unit length free energy for DNA under tension, we have calculated an effective contour length dependent persistence length for short DNA. This effective persistence length results from the enhanced fluctuations in short DNA. It decreases for shorter DNA, making shorter DNA more flexible. The results of the J-factor calculated using this effective persistence length are in good agreement with experimental data.

cond-mat.soft↗

arXiv2015

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 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, bring them into quantitative agreement with experiment, throughout the entire force regime. This is rather surprising, considering that the theory is completely parameter-free.

cond-mat.soft↗

arXiv2015

Dynamic scaling theory of the forced translocation of a semi-flexible polymer through a nanopore

We present a theoretical description of the dynamics of a semi-flexible polymer being pulled through a nanopore by an external force acting at the pore. Our theory is based on the tensile blob picture of Pincus in which the front of the tensile force propagates through the backbone of the polymer, as suggested by Sakaue and recently applied to study a completely flexible polymer with self-avoidance, by Dubbledam et al. For a semi-flexible polymer with a persistence length P , its statistics is self-avoiding for a very long chain. As the local force increases, the blob size starts to decrease. At the blob size P/a^2 , where a is the size of a monomer, the statistics becomes that of an ideal chain. As the blob size further decreases to below the persistence length P, the statistics is that of a rigid rod. We argue that semi-flexible polymer in translocation should include the three regions: a self-avoiding region, an ideal chain region and a rigid rod region, under uneven tension propagation, instead of a uniform scaling picture as in the case of a completely flexible polymer. In various regimes under the effect of weak, intermediate and strong driving forces we derive equations from which we can calculate the translocation time of the polymer. The translocation exponent is given by α=1+μ, where μis an effective exponent for the end-to-end distance of the semi-flexible polymer, having a value between 1/2 and 3/5, depending on the total contour length of the polymer. Our results are of relevance for forced translocation of biological polymers such as DNA through a nanopore.

cond-mat.stat-mech↗

arXiv2014

Worm-Like-Chain Model of Forced Desorption of a Polymer Adsorbed on an Attractive Wall

Forced desorption of a semiflexible polymer chain on a solid substrate is theoretically investigated. The pulling force versus displacement is studied for different adsorption energy and persistence length P. It is found that the relationships between pulling force and cantilever displacement show a series of characteristic force spikes at different persistence length P. These force spikes becomes more pronounced but the average magnitude of this force decrease as P grows. Our results are of relevance to forced desorption of DNA on an attractive wall in single-molecule pulling experiments.

cond-mat.stat-mech↗

arXiv2011

The 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.

cond-mat.soft↗

arXiv2011

Forest-Fire Model with Resistant Trees

The role of forest heterogeneity in the long-term, large-scale dynamics of forest fires is investigated by means of a cellular automata model and mean field approximation. Heterogeneity was conceived as trees (or acres of forest) with distinct strengths of resistance to burn. The scaling analysis of fire-size and fire-lifetime frequency distributions in the non-interacting fire steady-state limit indicates the breakdown of the power-law behavior whenever the resistance strength parameter R exceeds a certain value. For higher resistant strength, exponential behavior characterizes the frequency distributions, while power-law like behavior was observed for the lower resistant case in the same manner as reported in the literature for a homogeneous counterpart model. For the intermediate resistance strength, however, it may be described either by a stretched exponential or by a power-law plot whenever the fraction of recovering empty cells by susceptible trees not-exceeds or exceeds a certain threshold respectively, also suggesting a dynamical percolation transition with respect to the stationary forest density.

cond-mat.stat-mech↗

arXiv2011

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 sigma_i s at a site i of the DNA. This variable takes the value 1 or 0 depending on whether the site is occupied by a protein or not. In addition, if the site is occupied by a protein, there is an extra energy cost epsilon. For 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 non-specific binding.

cond-mat.stat-mech↗

arXiv2010

Stretching self-interacting, partially directed, flexible and semi-flexible polymers by an external force

We study the model of a partially directed flexible or semi-flexible homopolymer on a square lattice, subject to an externally applied force, in a direction either parallel to, or perpendicular to the preferred direction. The polymer is self-interacting and can therefore undergo a collapse transition. We show that this model can be solved and we obtain the force-temperature phase diagrams which, for the case of flexible polymers, agree with that of Brak et al obtained using a different method. At sufficiently low temperatures, the polymer conformation changes from compact to coil state as the force is increased beyond a critical value. This transition is second or first order for the completely flexible or semi-flexible polymer, respectively.

cond-mat.stat-mech↗

arXiv2009

Adsorption of Externally Stretched Two-Dimensional Flexible and Semi-flexible 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 smaller than the non-sequential nearest neighbor attraction, 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 greater than, 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.

cond-mat.stat-mech↗

arXiv2006

Driven translocation of a polynucleotide chain through a nanopore--A continuous time Monte-Carlo study

Using 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 (KBBD).

cond-mat.soft↗

arXiv2006

Unzipping DNA from the condensed globule state--Effects of unraveling

We study theoretically the unzipping of a double stranded DNA from a condensed globule state by an external force. At constant force, we find that the double stranded DNA unzips an at critical force Fc and the number of unzipped monomers M goes as M~(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~(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 find 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.

cond-mat.soft↗

arXiv2004

Comment on "Theory of high-force DNA stretching and overstretching"

Recently Storm and Nelson [1] (Phys.Rev. E67, 51906 (2003)) introduced the discrete persistent chain model which contains both features of the freely jointed chain (FJC) 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 (cond-mat/0307015).

cond-mat.soft↗

arXiv2004

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~(F-Fc)^(-2) and diverges at the critical force Fc with an exponent χ=2. We find that when excluded volume effect is taken into account for the unzipped part of the DNA, the exponent χ=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.

cond-mat.soft↗

arXiv2002

Monte-Carlo Simulation of Pulsed Laser Deposition

Using the Monte Carlo method, we have studied the pulsed laser deposition process at the sub-monolayer regime. In our simulations, dissociation of an atom from a cluster is incorporated. Our results indicate that the pulsed laser deposition resembles molecular beam epitaxy at very low intensity, and that it is characteristically different from molecular beam epitaxy at higher intensity. We have also obtained the island size distributions. The scaling function for the island size distribution for pulsed laser deposition is different from that of molecular beam epitaxy.

cond-mat.mtrl-sci↗

arXiv2002

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^χ, with χ=(1-ν)/ν, where νis 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 λ-Phage DNA over the whole experimental range. We show that excluded volume effects are stronger in two dimensions and also derive results in two dimensions which are different from the three dimensional results. This suggests experiments to be performed in these lower dimensions.

cond-mat.stat-mech↗