Efimov-DNA phase diagram: Three stranded DNA on a cubic lattice.
TL;DR: In this article, a generalized model for three-stranded DNA consisting of two chains of one type and a third chain of a different type was defined, and the DNA strands were modeled by random walks on the three-dimensional cubic lattice with different interactions between two chains.
Abstract: We define a generalized model for three-stranded DNA consisting of two chains of one type and a third chain of a different type. The DNA strands are modeled by random walks on the three-dimensional cubic lattice with different interactions between two chains of the same type and two chains of different types. This model may be thought of as a classical analog of the quantum three-body problem. In the quantum situation, it is known that three identical quantum particles will form a triplet with an infinite tower of bound states at the point where any pair of particles would have zero binding energy. The phase diagram is mapped out, and the different phase transitions are examined using finite-size scaling. We look particularly at the scaling of the DNA model at the equivalent Efimov point for chains up to 10 000 steps in length. We find clear evidence of several bound states in the finite-size scaling. We compare these states with the expected Efimov behavior.
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TL;DR: In this article , a simple coarse-grained model of DNA which includes both Watson-Crick and Hoogsteen base pairing has been used to study the melting and unzipping of triplex DNA.
Abstract: A simple coarse-grained model of DNA which includes both Watson-Crick and Hoogsteen base pairing has been used to study the melting and unzipping of triplex DNA. Using Langevin dynamics simulations, we reproduce the qualitative features of one-step and two-step thermal melting of triplex as seen in experiments. The thermal melting phase diagram shows the existence of a stable interchain three-strand complex (bubble-bound state). Our studies based on the mechanical unzipping of a triplex revealed that it is mechanically more stable compared to an isolated duplex-DNA.
2 citations
TL;DR: In this paper , the authors summarized the progress of research on the stability and dynamics of dsDNA in cell-like environments and discuss current challenges and future directions, and provided valuable guidelines for predicting DNA thermodynamic quantities and for designing DNA/RNA nanostructures.
Abstract: Deoxyribonucleic acid (DNA) is a fundamental biomolecule for correct cellular functioning and regulation of biological processes. DNA’s structure is dynamic and has the ability to adopt a variety of structural conformations in addition to its most widely known double-stranded DNA (dsDNA) helix structure. Stability and structural dynamics of dsDNA play an important role in molecular biology. In vivo, DNA molecules are folded in a tightly confined space, such as a cell chamber or a channel, and are highly dense in solution; their conformational properties are restricted, which affects their thermodynamics and mechanical properties. There are also many technical medical purposes for which DNA is placed in a confined space, such as gene therapy, DNA encapsulation, DNA mapping, etc. Physiological conditions and the nature of confined spaces have a significant influence on the opening or denaturation of DNA base pairs. In this review, we summarize the progress of research on the stability and dynamics of dsDNA in cell-like environments and discuss current challenges and future directions. We include studies on various thermal and mechanical properties of dsDNA in ionic solutions, molecular crowded environments, and confined spaces. By providing a better understanding of melting and unzipping of dsDNA in different environments, this review provides valuable guidelines for predicting DNA thermodynamic quantities and for designing DNA/RNA nanostructures.
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TL;DR: The reunion and survival probabilities of p random walkers in d dimensions with a mutual repulsive interaction are formulated via appropriate partition functions of directed polymers via renormalization-group theory to O, and an interesting consequence is a logarithmic correction for one-dimensional walkers with a three-body repulsion interaction.
Abstract: The reunion and survival probabilities of p random walkers in d dimensions with a mutual repulsive interaction are formulated via appropriate partition functions of directed polymers. The exponents that describe the decay of these probabilities with length are obtained through renormalization-group theory to O(${\mathrm{\ensuremath{\epsilon}}}^{2}$), where \ensuremath{\epsilon}=2-d. The distribution function and the probability of n out of p walkers meeting are also discussed. To first order, the distribution function is a Gaussian one modified by an anomalous exponent of the length of the polymer, N. The procedure is generalized to multicritical many-body interactions. For these multicritical cases, the exponents are obtained to second order in the relevant \ensuremath{\epsilon}s. At the upper critical dimension of the interaction, there is a logarithmic correction other than the Gaussian exponent. An interesting consequence is a logarithmic correction for one-dimensional walkers with a three-body repulsive interaction.
35 citations
TL;DR: In this article, it is predicted that a three-strand DNA exhibits the unusual behaviour of the existence of a threechain bound state in the absence of any two being bound.
Abstract: The base sequences of DNA contain the genetic code, and, to decode it, a double helical DNA has to be unzipped to reveal the bases. Recent studies have shown that a third strand can be used to identify the base sequences, not by opening the double helix but rather by forming a triple helix. It is predicted here that a three-strand DNA exhibits the unusual behaviour of the existence of a three-chain bound state in the absence of any two being bound. Such a state can occur at or above the duplex melting point. This phenomenon is analogous to the Efimov state in three-particle quantum mechanics. A scaling theory is used to justify the Efimov connection. Real space renormalization group (RG) and exact numerical calculations are used to validate the prediction of a biological Efimov effect.
22 citations
TL;DR: It is shown 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.
Abstract: 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 renormalization group 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.
21 citations
TL;DR: In this paper, it was predicted that such a three chain system exhibits the unusual behaviour of the existence of a three-chain bound state in the absence of any two being bound, analogous to the Efimov state in three particle quantum mechanics.
Abstract: The base sequences of DNA contain the genetic code and to decode it a double helical DNA has to open its base pairs. Recent studies have shown that one can use a third strand to identify the base sequences without opening the double helix but by forming a triple helix. It is predicted here that such a three chain system exhibits the unusual behaviour of the existence of a three chain bound state in the absence of any two being bound. This phenomenon is analogous to the Efimov state in three particle quantum mechanics. A scaling theory is used to justify the Efimov connection. Real space renormalization group (RG), and exact numerical calculations are used to validate the prediction of a biological Efimov effect.
17 citations
TL;DR: It is shown that the Efimov DNA can occur even if the three-chain (i.e., three-monomer) interaction is repulsive in nature, and a striking result that emerged in this repulsive zone is a continuous transition from the critical state to the EFimov DNA.
Abstract: We study the melting of three-stranded DNA by using the real-space renormalization group and exact recursion relations. The prediction of an unusual Efimov-analog three-chain bound state, that appears at the critical melting of two-chain DNA, is corroborated by the zeros of the partition function. The distribution of the zeros has been studied in detail for various situations. We show that the Efimov DNA can occur even if the three-chain (i.e., three-monomer) interaction is repulsive in nature. In higher dimensions, a striking result that emerged in this repulsive zone is a continuous transition from the critical state to the Efimov DNA.
10 citations