Dynamical versus statistical mesoscopic models for DNA denaturation

Joyeux, Marc; Florescu, Ana-Maria

doi:10.1088/0953-8984/21/3/034101

Cited by 22 publications

(34 citation statements)

References 71 publications

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“…4 of Ref. [37]), because it is not affected by the slow fluctuations that take place in this temperature range [38].…”

Section: Introductionmentioning

confidence: 86%

“…Note that, since the validity of the expansion of Eq. (2.5) depends on the definition of bounds for the k y , one must investigate the case where these bounds become infinite and check that the obtained results do not depend on the precise values of the bounds, provided they are chosen to be sufficiently large [34,37].…”

Section: The Ti Operator Methodsmentioning

confidence: 99%

“…This method is expected to work for all temperatures and coupling strengths (see however the restrictions mentioned in Refs. [34] and [37]). Yet, there exists another method, which consists in replacing, at least approximately, the TI equation by a Pseudo-Schrödinger Equation.…”

Section: Introductionmentioning

confidence: 98%

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On the Pseudo-Schrödinger Equation Approximation of the Transfer-Integral Operator for 1-Dimensional DNA Models

Joyeux¹

2021

JNMP

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The Transfer-Integral (TI) operator is a powerful method to investigate the statistical physics of 1-dimensional models, like those used to describe DNA denaturation. At the cost of a certain number of approximations, the TI equation can be reduced to a Pseudo-Schrödinger Equation (PSE), according to which the DNA sequence is equivalent to a point particle moving in a potential well. In this paper, I check the validity of the standard PSE approximation for two different 1-dimensional DNA models, and show that it fails to provide correct results for both of them. I then propose a generalized PSE, which works well for one of the two models. Finally, I discuss the particle description of DNA denaturation that is derived from this generalized PSE.

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“…4 of Ref. [37]), because it is not affected by the slow fluctuations that take place in this temperature range [38].…”

Section: Introductionmentioning

confidence: 86%

Section: The Ti Operator Methodsmentioning

confidence: 99%

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On the Pseudo-Schrödinger Equation Approximation of the Transfer-Integral Operator for 1-Dimensional DNA Models

Joyeux¹

2021

JNMP

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“…Our conclusion is in qualitative agreement with Refs. [22,45] although the investigated sequences differ. Instead, in Ref.…”

Section: Fractions Of Open Base Pairsmentioning

confidence: 97%

“…As a key refinement of the PB Hamiltonian, anharmonic stiffness has been introduced in the intra-strand stacking potential [18] thus accounting for an entropy driven sharp denaturation [19]. While the PB model has proved successful to predict multistep melting in heterogeneous DNA [20,21], several methodologies such as molecular dynamics, transfer integral calculations [22] and renormalization group techniques [23] have been employed to investigate the nature of the transition but the question is still unsettled.…”

Section: Introductionmentioning

confidence: 99%

Stacking interactions in denaturation of DNA fragments

Zoli

2011

Eur. Phys. J. E

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A mesoscopic model for heterogeneous DNA denaturation is developed in the framework of the path integral formalism. The base pair stretchings are treated as one-dimensional, time dependent paths contributing to the partition function. The size of the paths ensemble, which measures the degree of cooperativity of the system, is computed versus temperature consistently with the model potential physical requirements. It is shown that the ensemble size strongly varies with the molecule backbone stiffness providing a quantitative relation between stacking and features of the melting transition. The latter is an overall smooth crossover which begins from the adenine-thymine rich portions of the fragment. The harmonic stacking coupling shifts, along the T -axis, the occurrence of the multistep denaturation but it does not change the character of the crossover. The methods to compute the fractions of open base pairs versus temperature are discussed: by averaging the base pair displacements over the path ensemble we find that such fractions signal the multisteps of the transition in good agreement with the indications provided by the specific heat plots.

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Mapping between the order of thermal denaturation and the shape of the critical line of mechanical unzipping in one-dimensional DNA models

Buyukdagli

Joyeux

2010

Chemical Physics Letters

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In this Letter, we investigate the link between thermal denaturation and mechanical unzipping for two models of DNA, namely the Dauxois-Peyrard-Bishop model and a variant thereof we proposed recently. We show that the critical line that separates zipped from unzipped DNA sequences in mechanical unzipping experiments is a power-law in the temperature-force plane. We also prove that for the investigated models the corresponding critical exponent is proportional to the critical exponent α, which characterizes the behaviour of the specific heat in the neighbourhood of the critical temperature for thermal denaturation.(#) email : Marc.Joyeux@ujf-grenoble.fr -INTRODUCTIONSeveral fundamental biological processes, like transcription and replication, involve the separation and recombination of the two strands that compose double-stranded (zipped) DNA molecules. Since transcription and replication are quite complex mechanisms, many early studies focused on thermal denaturation, that is the separation of the two strands upon heating [1][2][3][4][5][6][7]. In cells, unzipping is however not mediated by thermal activation but rather by proteins, which apply forces to separate and stretch complementary DNA strands. Compared to thermal denaturation studies, the recent mechanical unzipping experiments, where forces are applied to adjacent 5' and 3' strands of individual DNA molecules [8][9][10][11][12][13][14][15][16], therefore represent a great step towards the understanding of real biological processes. These experiments triggered in turn much theoretical effort (see [17][18][19][20][21][22][23][24][25][26][27] and references therein).The purpose of the present paper is to point out that there actually exists a tight link between thermal denaturation and mechanical unzipping. Indeed, we will show that for the two 1-dimensional mesoscopic DNA models we investigated it is possible to establish a mapping between the order of the thermal denaturation phase transition and the shape of the critical line of mechanical unzipping in the temperature-force plane. More precisely, we will show that the critical line that separates zipped from unzipped sequences in mechanical unzipping experiments is a power-law, whose exponent is proportional to the critical exponent α that characterizes the behaviour of the specific heat in the neighbourhood of the critical temperature for thermal denaturation. This work therefore complements that of Singh and Singh, who showed that the critical force varies as the square root of the temperature gap to denaturation for the Dauxois-Peyrard-Bishop model with a large anharmonic stacking parameter ρ [26]. The coupling constant of this interaction drops from ) 1 ( ρ + K to K as the paired bases separate, which decreases the rigidity of DNA sequences close to dissociation and results in a sharp first-order transition. Numerical values of the parameters used in this work are those of Ref. [26], that is D=0.063 eV, a=4.2 Å -1 , K=0.025 eV Å -2 , α=0.35 Å -1 , except that we

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Dynamical versus statistical mesoscopic models for DNA denaturation

Cited by 22 publications

References 71 publications

On the Pseudo-Schrödinger Equation Approximation of the Transfer-Integral Operator for 1-Dimensional DNA Models

On the Pseudo-Schrödinger Equation Approximation of the Transfer-Integral Operator for 1-Dimensional DNA Models

Stacking interactions in denaturation of DNA fragments

Mapping between the order of thermal denaturation and the shape of the critical line of mechanical unzipping in one-dimensional DNA models

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