Thermodynamics of twisted DNA with solvent interaction

2019

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I present a Hamiltonian model and a computational method suitable to evaluate structural and thermodynamic properties of helical molecules embedded in crowded environments which may confine the space available to the base pair fluctuations. It is shown that, for the specific case of a short DNA fragment in a nanochannel, the molecule is markedly over-twisted and stretched by narrowing the width of the channel.

Section: Modelmentioning

confidence: 99%

Mesoscopic model for nano-channel confined DNA

2019

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“…For each loop, we simulate a broad set of values for the twist T w and, for any T w (i.e., h), Z N is calculated by summing over an ensemble of fluctuational paths representing a large number of molecule configurations, about 10 7 paths for each base pair in Eq. (4).…”

Section: Free Energy Of Minicirclesmentioning

confidence: 99%

“…My previous path integral analysis of DNA [2,3,4,5,6,7,8,9,10] were based on the ansatz that the bps displacements could be treated as one dimensional paths x(τ i ), |r i | → x(τ i ), with the imaginary time τ i ∈ [0, β] and β being the inverse the temperature.…”

Section: Space-time Mappingmentioning

confidence: 99%

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Helical Disruptions in Small Loops of DNA

2015

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Abstract. The thermodynamical stability of DNA minicircles is investigated by means of path integral techniques. Hydrogen bonds between base pairs on complementary strands can be broken by thermal fluctuations and temporary fluctuational openings along the double helix are essential to biological functions such as transcription and replication of the genetic information. Helix unwinding and bubble formation patterns are computed in circular sequences with variable radius in order to analyze the interplay between molecule size and appearance of helical disruptions. The latter are found in minicircles with < 100 base pairs and appear as a strategy to soften the stress due to the bending and torsion of the helix.It is known that the helicoidal conformation of DNA is essentially determined by the hydrophobicity of purine and pyrimidine bases and by the bond angles in the flexible sugarphosphate backbone while sequence of the bases and environmental conditions due to the solvent also contribute to the molecule shape [1]. As each strand bears a negative charge (e) for each phosphate group and the rise distance between adjacent nucleotides is ∼ 3.4Å, the bare double helix has a high linear charge density of ∼ 0.6 eÅ −1 . Although the effective charge density is reduced by the counterions in the solvent, the electrostatic strands repulsion is key to the stability of the helix and also affects the inter-helical chiral interactions in those condensed phases of DNA assemblies (such as liquid crystals) which underlie the impressive growth of DNA-based structures recently witnessed in materials science.Base pairing and base stacking are the fundamental interactions which control the synthesis of DNA and determine the thermodynamic stability both of single helices and of helix aggregates. However even stable duplexes at room temperature show local openings, temporary bubbles, which are intrinsic to the biological functioning as they permit the transcription and replication of the genetic code. Such bubbles are due to the strong fluctuational effects on the hydrogen bonds between complementary strands and cause the local unwinding of the double helix which ultimately leads to a state of negative supercoiled DNA for almost all living beings. While these processes are qualitatively understood, quantitative predictions of (energetically) optimal helical configurations for specific systems are scarce. We contribute to fill this gap by introducing a new path integral computational method which readily applies to loops of DNA as those found in bacterial plasmids, viral genomes and also mammalian cells.

“…Recently, I have proposed to apply the path integral method [3] to a modified DPB Hamiltonian which includes a twist angle θ between adjacent bases, n and n − 1, along the DNA backbone [4] as shown in Fig. 1.…”

Section: Hamiltonian Model For Dnamentioning

confidence: 99%

Modeling DNA Dynamics by Path Integrals

2013

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Complementary strands in DNA double helix show temporary fluctuational openings which are essential to biological functions such as transcription and replication of the genetic information. Such large amplitude fluctuations, known as the breathing of DNA, are generally localized and, microscopically, are due to the breaking of the hydrogen bonds linking the base pairs (bps). I apply imaginary time path integral techniques to a mesoscopic Hamiltonian which accounts for the helicoidal geometry of a short circular DNA molecule. The bps displacements with respect to the ground state are interpreted as time dependent paths whose amplitudes are consistent with the model potential for the hydrogen bonds. The portion of the paths configuration space contributing to the partition function is determined by selecting the ensemble of paths which fulfill the second law of thermodynamics. Computations of the thermodynamics in the denaturation range show the energetic advantage for the equilibrium helicoidal geometry peculiar of B-DNA. I discuss the interplay between twisting of the double helix and anharmonic stacking along the molecule backbone suggesting an interesting relation between intrinsic nonlinear character of the microscopic interactions and molecular topology.