DNA Bubble Dynamics as a Quantum Coulomb Problem

Fogedby, Hans C.; Metzler, Ralf

doi:10.1103/physrevlett.98.070601

Cited by 82 publications

(123 citation statements)

References 18 publications

(60 reference statements)

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“…The model fit thus leads to parameter values in accord with experiment. Our model predictions for experimentally accessible A-T pair quantities are also in agreement with accepted values [3,39]…”

Section: Application To Synthetic Dna Thermal Denaturationsupporting

confidence: 86%

“…Very recent work [39,50,51] studied the growth of already nucleated bubbles using the Fokker-Planck equation applied to the Poland-Scheraga model (i.e., an effective Ising model including loop entropy). The agreement with experimental results obtained by fluorescence correlation spectroscopy is remarkably good [39]. The issue of bubble nucleation is, however, not solved and will be continued to be explored in the near future.…”

Section: Discussionmentioning

confidence: 99%

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Thermal denaturation of fluctuating finite DNA chains: The role of bending rigidity in bubble nucleation

2008

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Statistical DNA models available in the literature are often effective models where the base-pair state only (unbroken or broken) is considered. Because of a decrease by a factor of 30 of the effective bending rigidity of a sequence of broken bonds, or bubble, compared to the double stranded state, the inclusion of the molecular conformational degrees of freedom in a more general mesoscopic model is needed. In this paper we do so by presenting a 1D Ising model, which describes the internal base pair states, coupled to a discrete worm like chain model describing the chain configurations [J. Palmeri, M. Manghi, and N. Destainville, Phys. Rev. Lett. 99, 088103 (2007)]. This coupled model is exactly solved using a transfer matrix technique that presents an analogy with the path integral treatment of a quantum two-state diatomic molecule. When the chain fluctuations are integrated out, the denaturation transition temperature and width emerge naturally as an explicit function of the model parameters of a well defined Hamiltonian, revealing that the transition is driven by the difference in bending (entropy dominated) free energy between bubble and double-stranded segments. The calculated melting curve (fraction of open base pairs) is in good agreement with the experimental melting profile of polydA-polydT and, by inserting the experimentally known bending rigidities, leads to physically reasonable values for the bare Ising model parameters. Among the thermodynamical quantities explicitly calculated within this model are the internal, structural, and mechanical features of the DNA molecule, such as bubble correlation length and two distinct chain persistence lengths. The predicted variation of the mean-square-radius as a function of temperature leads to a coherent novel explanation for the experimentally observed thermal viscosity transition. Finally, the influence of the DNA strand length is studied in detail, underlining the importance of finite size effects, even for DNA made of several thousand base pairs. Simple limiting formulae, useful for analyzing experiments, are given for the fraction of broken base pairs, Ising and chain correlation functions, effective persistence lengths, and chain mean-square-radius, all as a function of temperature and DNA length.

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Section: Application To Synthetic Dna Thermal Denaturationsupporting

confidence: 86%

Section: Discussionmentioning

confidence: 99%

Thermal denaturation of fluctuating finite DNA chains: The role of bending rigidity in bubble nucleation

2008

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“…Base pair openings are thus highly localized at biological temperatures and remain such also in homopolymers. Theoretical modeling for DNA has then to incorporate nonlinear dynamics and large fluctuational effects which lead to base pair disruption and formation of bubbles whose size varies with temperature and environment pH values [30,31]. While fully atomistic descriptions become computationally very heavy even for short fragments, mesoscopic models have proven capable to capture the essentials of the interactions in DNA molecules.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamics of twisted DNA with solvent interaction

Zoli

2011

The Journal of Chemical Physics

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The imaginary time path integral formalism is applied to a nonlinear Hamiltonian for a short fragment of heterogeneous DNA with a stabilizing solvent interaction term. Torsional effects are modeled by a twist angle between neighboring base pairs stacked along the molecule backbone. The base pair displacements are described by an ensemble of temperature dependent paths thus incorporating those fluctuational effects which shape the multisteps thermal denaturation. By summing over ∼ 10 7 − 10 8 base pair paths, a large number of double helix configurations is taken into account consistently with the physical requirements of the model potential. The partition function is computed as a function of the twist. It is found that the equilibrium twist angle, peculiar of B-DNA at room temperature, yields the stablest helicoidal geometry against thermal disruption of the base pair hydrogen bonds. This result is corroborated by the computation of thermodynamical properties such as fractions of open base pairs and specific heat.

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“…Experiments show, for example, that there exist a bubble initiation barrier of ∼ 10k B T and free energy cost of ∼ 0.1k B T for breaking an additional base pair in an existing A-T bubble [4]. A detailed understanding of equilibrium [1] and dynamical [5] properties of DNA in solution is still being sought and a consensus concerning the physical mechanism behind the denaturation transition has not yet been reached.A variety of mesoscopic models have been proposed to account for the thermodynamical properties of denaturation bubbles in DNA. They range from i) simple effective Ising-like two-state models [1] to more detailed ones such as ii) loop entropy models (with or without chain selfavoidance) [1,2,6,7], and iii) non-linear phonon models, where the shape of the interaction potential between base pairs is more precisely taken into account [8,9].…”

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confidence: 99%

Thermal Denaturation of Fluctuating DNA Driven by Bending Entropy

2007

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A statistical model of homopolymer DNA, coupling internal base pair states (unbroken or broken) and external thermal chain fluctuations, is exactly solved using transfer kernel techniques. The dependence on temperature and DNA length of the fraction of denaturation bubbles and their correlation length is deduced. The thermal denaturation transition emerges naturally when the chain fluctuations are integrated out and is driven by the difference in bending (entropy dominated) free energy between broken and unbroken segments. Conformational properties of DNA, such as persistence length and mean-square-radius, are also explicitly calculated, leading, e.g., to a coherent explanation for the experimentally observed thermal viscosity transition.PACS numbers: 87.10.+e, 87.15.Ya, 82.39.Pj Double-stranded DNA (dsDNA) is made up of two intertwined interacting semi-flexible single-strand DNA (ssDNA) chains. Over fifty years ago it was recognized that the intracellular unwinding of DNA at physiological temperature has as counterpart the thermally induced denaturation above physiological temperature of purified DNA solutions where dsDNA completely separates into two ssDNA. Despite the differences between the two mechanisms, this observation has led to an intensive study of thermal denaturation [1,2]. The stability of dsDNA at physiological temperature is due to the selfassembly of neighboring base pairs within a same strand via base-stacking interactions and of both strands via hydrogen bonds between complementary bases. The bonding energy is, however, on the order of k B T (thermal energy) [3] and thermal fluctuations can lead, even at physiological temperature, to local and transitory unzipping of dsDNA [1]. The cooperative opening of consecutive base pairs leads to denaturation bubbles and the melting temperature, T m , above which bubbles proliferate, depends on sequence, chain length, and ionic strength. Experiments show, for example, that there exist a bubble initiation barrier of ∼ 10k B T and free energy cost of ∼ 0.1k B T for breaking an additional base pair in an existing A-T bubble [4]. A detailed understanding of equilibrium [1] and dynamical [5] properties of DNA in solution is still being sought and a consensus concerning the physical mechanism behind the denaturation transition has not yet been reached.A variety of mesoscopic models have been proposed to account for the thermodynamical properties of denaturation bubbles in DNA. They range from i) simple effective Ising-like two-state models [1] to more detailed ones such as ii) loop entropy models (with or without chain selfavoidance) [1,2,6,7], and iii) non-linear phonon models, where the shape of the interaction potential between base pairs is more precisely taken into account [8,9]. To get a transition in models i) and ii), an effective temperature dependent base-pair chemical potential must be inserted by hand. For finite chains, type (ii) models simply refine the sharpness of the transition [1], but do not attempt to provide a deeper explanation of the ...

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DNA Bubble Dynamics as a Quantum Coulomb Problem

Cited by 82 publications

References 18 publications

Thermal denaturation of fluctuating finite DNA chains: The role of bending rigidity in bubble nucleation

Thermal denaturation of fluctuating finite DNA chains: The role of bending rigidity in bubble nucleation

Thermodynamics of twisted DNA with solvent interaction

Thermal Denaturation of Fluctuating DNA Driven by Bending Entropy

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