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...

The opening of the Y-fork -the first step of DNA replication -is shown to be a critical phenomenon under an external force at one of its ends. From the results of an equivalent delocalization in a nonhermitian quantum-mechanics problem we show the different scaling behavior of unzipping and melting. The resultant long-range critical features within the unzipped part of Y might play a role in the highly correlated biochemical functions during replication.