Albany 2015:Book of Abstracts

Albany 2015
Conversation 19
June 9-13 2015
©Adenine Press (2012)

Modeling the DNA bubbles dynamics

One of the most challenging subjects in biophysics is the relation between biomolecular motions and functioning. On the one hand the DNA molecule can be considered as a dynamic system with many degrees of freedom. On the other hand the molecule is involved to the processes of transcription and replication which are the crucial biological functions. The explicit connection between these two DNA considerations has not been found yet.

In our work we model the moving of DNA bubbles which play important role in processes of transcription and replication as a movement of nonlinear waves switching the DNA base pairs from closed to open states. For the wave dynamics investigation, the new model equation was derived that takes into account heterogeneous DNA sequence structure and has the form of a modified nonlinear sine-Gordon equation. The model equation also includes the dissipation term. The equation has been solved numerically. Nonlinear wave solutions which have the form of kinks are interpreted as bubble moving along DNA.

The movement in two inhomogeneous sequences is investigated. The first sequence is artificial. It contains three homogeneous regions (poly(A), poly(T), poly(G)) of equal length (300 bp). The second one is the sequence of pTTQ18 plasmid. It contains four functional regions: promoter, terminator and two genes, and has 4500 bp length. Using the concentration method for averaging model coefficients in the functional and intermediate regions of the plasmid sequence, it made possible to reduce the problem of bubble movement in the sequence of pTTQ18 plasmid to the problem of its movement in the sequnce containing eight homogeneous regions separated with borders. Energetic profiles were obtained for both sequences. The trajectories of bubbles were built for different values of initial velocities and dissipation coefficients. Three types of bubble behavior were found: reflection from the border between regions, overcoming the border with velocity increase and with velocity decrease (pictured below). The behavior type depends on initial bubble postion, its initial velocity and dissipation coefficient.


Three type of bubble behavior in the artificial sequence. Initial velocity - 400 m/s.

Andrey A. Grinevich
Artem A. Ryasik
Ludmila V. Yakushevich

Institute of Cell Biophysics
Moscow region, Russia, 142290

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