Dynamical Scaling of the DNA Unzipping Transition

Abstract

We report studies of the equilibrium and the dynamics of a general set of lattice models which capture the essence of the force-induced or mechanical DNA unzipping transition. Besides yielding the whole equilibrium phase diagram in the force vs temperature plane, which reveals the presence of an interesting re-entrant unzipping transition for low T , these models enable us to characterize the dynamics of the process starting from a non-equilibrium initial condition. The thermal melting of the DNA strands displays a model dependent time evolution. On the contrary, our results suggest that the dynamical mechanism for the unzipping by force is very robust and the scaling behaviour does not depend on the details of the description we adopt.The replication of DNA is a correlated process involving many proteins and other molecules [1] working at different points in space and time. An understanding of the nature and origin of this correlation is expected to shed light on this complex mechanism. It has recently been shown [2][3][4][5][6] that the force induced unzipping of DNA is a genuine phase transition different from the thermal melting transition of DNA. It was then hypothesized [2] that the initiation of replication at the origins along the DNA, e.g, by dnaA for E.Coli [1,7] or by the "origin recognition complex" (ORC) in eukaryotes [8] is like this unzipping near the critical threshold (with dnaA or ORC acting as the force-inducing agent) and the resulting correlation during unzipping leads the co-operativity required for replication.In contrast to real biological situations, techniques like laser tweezers [9], atomic force microscopes (AFM) [10][11][12] etc have been used to study DNA by pulling at one end. This has led to strand separation by force. In particular, AFM experiments reported hysteresis in the unzipping process, indicating the presence of a first order transition. These mechanical unzipping experiments have opened up new ways of thinking about DNA, just as similar stretching experiments of DNA showed the possibility of several structures other than the most prevalent B-DNA [13]. The activities of polymerases, topoisomerase etc on single stranded DNA have now been analyzed in terms of the force they exert or the force applied against them [14][15][16]. What needs to be investigated, to mimic the biological situation, is the coupling between the opening of the strands and the subsequent events during replication. Such a study involves the dynamics of the unzipping process [3].The purpose of this paper is to define a set of simpler models, in the spirit of Poland and Sheraga [17], for which the unzipping transition can be studied exactly. On the basis of this, the dynamics can be understood. The proposed lattice models (bubble models: b-models) incorporate the mutual-avoidance (hard-core repulsion) of the strands (and also self-avoidance). A further simplification is obtained by suppressing the bubbles along the chains, thereby defining a "fork model" or "Y-model". The phase diagram of the equilibrium...

Scaling of hysteresis loop of interacting polymers under a periodic force

“…It is evident from these plots (Fig. 3) that the melting temperature decreases with the applied force in accordance with the earlier studies [52,53]. We find that the peak height increases with the chain length, though, the transition temperature (melting temperature) remains almost the same for different lengths.…”

Three-dimensional dynamic Monte Carlo simulations of elastic actin-like ratchets

“…The Monte Carlo local dynamics we use, also known as the "kink-jump" algorithm, has recently been successfully applied to many polymer problems, both on and off lattice [10,[13][14][15][16][17][18][19][20], and naturally fits the stochastic nature of the growth rules typically used in the ratchet literature.…”

An exact solution of three interacting friendly walks in the bulk

“…The study of two polymers with interpolymer interactions and interacting with a surface has received much recent attention because of connections to modelling the unzipping of DNA. Typically these have been modelled via either selfavoiding or directed walk systems on lattices in two and three dimensions with various types of contact interactions [2][3][4][5][6][7][8][9][10]. The exact solution of directed friendly walkers on the square lattice with such interactions [9,10] has led to the extension of a key combinatorial technique for lattice paths, the obstinate kernel method [11].…”