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Europhysics Letters (EPL)

Entropy-driven denaturation and bubble nucleation in DNA melting

Subhamoy Singha Roy, Pratul Bandyopadhyay

Published Feb 1, 2015• 12 citations
Publisher

Abstract

The conformational properties of a DNA molecule when mapped onto a Heisenberg spin system denaturation transition can be formulated in terms of quantum phase transition induced by a quench where the temperature effect is incorporated in the quench time. Here torsion takes on the role of the external field. The denaturation transition occurs when the entanglement entropy of the spin system vanishes. As the critical region corresponds to a two-limit behaviour the entanglement entropy gradually decreases with the gradual increase in the fraction of open base pairs and when the entropy vanishes the two strands are separated. The sequence heterogeneity interplays with the entropy effects and we have the onset of denaturation bubbles. We have studied the melting profiles for different sequence-specific DNA molecules and the results are found to be in excellent agreement with experiment.

DOI
10.1209/0295-5075/109/48002

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The conformational properties of a DNA molecule when mapped onto a Heisenberg spin system denaturation transition can be formulated in terms of quantum phase transition induced by a quench where the temperature effect is incorporated in the quench time. Here torsion takes on the role of the external field. The denaturation transition occurs when the entanglement entropy of the spin system vanishes. As the critical region corresponds to a two-limit behaviour the entanglement entropy gradually decreases with the gradual increase in the fraction of open base pairs and when the entropy vanishes the two strands are separated. The sequence heterogeneity interplays with the entropy effects and we have the onset of denaturation bubbles. We have studied the melting profiles for different sequence-specific DNA molecules and the results are found to be in excellent agreement with experiment.
When a DNA molecules conformational characteristics are charted adjacent to a Heisenberg-spin-system, the denaturation shift be able to be expressed in stipulations of a QFT (quantum-phase-transition) brought on through a quench, in which the external field is torsion and the temperature effect is integrated into the quench time. When the spin system's entanglement entropy disappears, the denaturation transition takes place. The energy of torsion includes temperature, stress, and torque, the latter of which is correlated with the twist angle. A DNA molecule put on the Heisenberg spin chain experiences torsion as the outer field. When the EE (entanglement entropy) disappears, the transition to denaturation takes place. The entanglement entropy steadily drops as the proportion of unlock stand pairs gradually increases, the two strands split until the entropy disappears, since the dangerous area corresponding to a 2-boundary actions. The melting profiles of specific DNA molecules have been examined, and the findings show great agreement with biotechnology.
One approach to imagine spins on the axis generating an antiferomagnatic chain is described as simulating a DNA molecule as a Heisenberg spin system. In a DNA molecule, the entanglement entropy of the spin system is shown to be in good agreement with the thermodynamic entropy. At times when the impact of temperature is included during the time of quench, It is shown that denaturation corresponds to a quantum phase change triggered by a quench. The critical point is attained and When the entanglement entropy is eliminated, it equates to a critical torsonal energy. DNA loops now appear as solitonic (skyrmionic) excitations upon base pair opening.
Two significant consequences of quantum fluctuations are entanglement and criticality. Entangled states may not be critical but a critical state shows signatures of universality in entanglement. A surprising result found here is that the entanglement entropy may become arbitrarily large and negative near the dissociation of a bound pair of quantum particles. Although apparently counterintuitive, it is shown to be consistent and essential for the phase transition, by mapping to a classical problem of DNA melting. We associate the entanglement entropy to a sub-extensive part of the entropy of DNA bubbles, which is responsible for melting. The absence of any extensivity requirement in time makes this negative entropy an inevitable consequence of quantum mechanics in continuum. Our results encompass quantum critical points and first-order transitions in general dimensions.
We have considered here that the conformational properties of a DNA molecule can be mapped onto a Heisenberg spin system when spins are located on the axis forming an antiferromagnatic chain.This helps us to study the topological and elastic properties of a DNA molecule in terms of SU(2) gauge fields.The entanglement entropy of the spin system in a supercoil has been determined and it is pointed out that this effectively corresponds to the thermodynamic entropy.The model reproduces salient features of the Rod-Like-Chain model avoiding the "RLC model crisis".
Abstract Here we have study the conceptual properties of DNA molecules that can be mapped in the Heisenberg spin system, and the reduction in the formation of the effect of temperature through the quantum phase transition (QPT) when the refining time occurs. Delayed free rotation of molecules, reverse replication is a complement that uses RNA molecules to produce single-stranded DNA molecules and aids in the diffusion of DNA molecules. This explains the large ternary stress observed near the reverse copy point. We have projected the curve extent which is created to be in good agreement.
It is known that at the critical point of a zero-temperature quantum phase transition in a one-dimensional spin system the entanglement entropy of a block of LLL spins with the rest of the system scales logarithmically with LLL with a prefactor determined by the central charge of the relevant conformal field theory. When we introduce critical slowing down incorporating the Kibble-Zurek mechanism of defect formation induced by a quench, the implicit nonadiabatic transition disturbs the scaling behavior. We have shown that in this case the entanglement entropy also obeys a scaling law such that it increases logarithmically with LLL but the prefactor depends on the quench time. This puts a constraint on the block size LLL so that we cannot arbitrarily choose it. Thus, the entanglement entropy obeys the scaling law only in a restrictive sense due to the formation of defects.