Base-pair opening and bubble transport in a DNA double helix induced by a protein molecule in a viscous medium

Abstract

The protein-DNA interaction dynamics is studied by modeling the DNA bases as classical spins in a coupled spin system, which are bosonized and coupled to thermal phonons and longitudinal motion of the protein molecule in the nonviscous limit. The nonlinear dynamics of this protein-DNA complex molecular system is governed by the completely integrable nonlinear Schrödinger (NLS) equation which admits N -soliton solutions. The soliton excitations of the DNA bases in the two strands make localized base-pair opening and travel along the DNA chain in the form of a bubble. This may characterize the bubble generated during the transcription process, when an RNA polymerase binds to a promoter site in the DNA double helical chain. When the protein-DNA molecular system interacts with the surrounding viscous solvating water medium, the dynamics is governed by a perturbed NLS equation. This equation is solved using a multiple scale perturbation analysis, by treating the viscous effect as a weak perturbation, and the results show that the viscosity of the solvent medium damps out the soliton as time progresses.

Protein-DNA Interaction: Effect of Helicity on Bubble Size

“…However, Sataric and Tuszinsky 9 used the Peyrard-Bishop model 10 and found that the interaction between the DNA and the proteins generates breather solitons spontaneously. Recently, Vasumathi and Daniel 11 proposed a theoretical model based on the spinlike model, and confirmed that bubbles that are experimentally observed within the process of base-pair opening are simply due to the presence of proteins around the DNA molecule. The purpose of the present work is to update this model by taking into account the helicoidal coupling, as introduced by Tabi et al, 7 in order to model the DNAprotein interaction in a more realistic way.…”

“…2 + 2 −Jf a n a + n+1 + a + n a n+1 − a + n a n − a + n+1 a n +b n b + n+1 + b + n b n+1 − b + n b n − b + n+1 b n −Jg a n b + n+h + a + n b n+h + b n a + n+h + b + n a n+h −a + n+h a n+h − b + n+h b n+h − a + n a n − b + n b n − − 1 X n+1 − X n−1 a n b + n + a + n b n − a + n a n −b + n b n − 2 y n+1 − y n−1 a + n a n + b + n b n (11) Delivered by Ingenta to: Chinese University of Hong From the above semi-classical Hamiltonian it is easier to construct the equations of motion as i a n t = a n H = F 1 a n a + n a n+1 a + n+1 a n+h a + n+h (12a)…”

Helicoidal Peyrard–Bishop Model of DNA Dynamics*

“…4(b) and 6. It may be interesting to point out that this approach can be used to study modulation instability in DNA double helix [30] as well as DNA-protein interaction [31].…”

Траектории Кинков ДНК В Последовательностях, Содержащих Кодирующие Области Генов

“…Surprisingly, the passage of the DNA kinks through the CDS region was not modeled by investigators, though the necessary mathematical formalism has been already developed. We can point out the model of Peyrard and Bishop [10] that takes into account the transverse motions of nucleotides, the Y-model [11][12][13] that takes into account the angular displacements of nitrous bases, the combined model [14] that takes into account both the angular and the transverse displacements, and numerous modifications of these models [15][16][17][18][19][20]. Any of them could be used for the purpose.…”