Replication and transcription are two important processes in living systems. To execute such processes, various proteins work far away from equilibrium in a staggered way. Motivated by this, aspects of hysteresis during unzipping of DNA under a periodic drive are studied. A steady-state phase diagram of a driven DNA is proposed which is experimentally verifiable. As a two-state system, we also compare the results of DNA with that of an Ising magnet under an asymmetrical variation of the magnetic field.

We show that there exists an Efimov-like three strand DNA bound state at the duplex melting point and it is described by a renormalization group limit cycle. A nonperturbative RG is used to obtain this result in a model involving short range pairing only. Our results suggest that Efimov physics can be tested in polymeric systems.PACS numbers: 87.14.gk, 64.60.ae, 87.15.Zg Consider a three-particle quantum system with pairwise short-range potential. Apart from the occurrence of the usual three-body bound state, a very special phenomenon occurs at the critical two-body zero-energy state. An infinite number of three-body bound states appear though the corresponding potential is not appropriate to bind any two of them; the removal of any one of them destroys the bound state. This phenomenon, valid for any short-range interaction, is known as the Efimov effect. The size of the three-body bound states, or Efimov trimers, is large compared to the potential range, and so it is a purely quantum effect [1]. Although it was predicted in the context of nuclear physics [2,3], it has now been detected in cold atoms [4].An ideal DNA consisting of two Gaussian polymers interacting with native base pairing undergoes a critical melting transition where the two strands get detached. Maji et.al. recently showed that if, to a double stranded DNA at its melting point, a third strand is added, the three together would form a bound state instead of remaining critical [5]. The existence of a triplex has further been verified by real space renormalization group (RG) and transfer matrix calculations [5,6]. That this is an Efimov-like effect can be seen by the imaginary time transformation of the quantum problem in the path integral formulation. The paths in quantum mechanics are identified as Gaussian polymers and the equal time interaction maps onto the native base pairing. Such a bound state of a triple-stranded DNA is called an Efimov DNA.In both cases, the special effect is due to a long-range attraction generated by critical fluctuations at the transition point. For the DNA case, the large fluctuations in the bubble sizes at the melting point allow a third strand to form bound segments with the other two. The power law behavior of the size of a polymer is essential to induce a 1/R 2 interaction between any two chains [5].Universal aspects of polymers are well understood in the RG approach [7]. A single chain and many chain solutions are described by length scale dependent running parameters, which, with increasing length scales, are expected to reach certain fixed points. The purpose of this paper is to show that the triple chain bound state at the duplex melting point is of a different type. This "fewchain problem" is actually described by a renormalization group "limit cycle" [2,8]. The appearance of a limit cycle invokes log periodicity in the corresponding three-body coupling in the polymer problem. So they break the continuous scale invariance around the two-body fixed point imposing a discrete scaling symmetry, the hallmark of t...

Thermodynamics is a well developed tool to study systems in equilibrium but no such general framework is available for nonequilibrium processes. Only hope for a quantitative description is to fall back upon the equilibrium language as often done in biology. This gap is bridged by the work theorem. By using this theorem we show that the Barkhausen-type nonequilibrium noise in a process, repeated many times, can be combined to construct a special matrix S whose principal eigenvector provides the equilibrium distribution. For an interacting system S, and hence the equilibrium distribution, can be obtained from the free case without any requirement of equilibrium.

The force induced unzipping transition of a double stranded DNA is considered from a purely thermodynamic point of view. This analysis provides us with a set of relations that can be used to test microscopic theories and experiments. The thermodynamic approach is based on the hypothesis of impenetrability of the force in the zipped state. The melting and the unzipping transitions are considered in the same framework and compared with the existing statistical model results. The analysis is then extended to a possible continuous unzipping transition.

An important step in transcription of a DNA base sequence to a protein is the initiation from the exact starting point, called promoter region. We propose a physical mechanism for identification of the promoter region, which relies on a new classification of DNAs into two types, Type-I and Type-II, like superconductors, depending on the sign of the energy of the interface separating the zipped and the unzipped phases. This is determined by the energies of helical ordering and stretching over two independent length scales. The negative interfacial energy in Type II DNA leads to domains of helically ordered state separated by defect regions, or blobs, enclosed by the interfaces. The defect blobs, pinned by non-coding promoter regions, would be physically distinct from all other types of bubbles. We also show that the order of the melting transition under a force is different for Type I and Type II.