On the dimensionless model of the transcription bubble dynamics

Larisa A. Krasnobaeva; Ludmila V. Yakushevich; Larisa A. Krasnobaeva; Ludmila V. Yakushevich

doi:10.3934/biophy.2023013

AIMS Biophysics

2023, Volume 10, Issue 2: 205-219. doi: 10.3934/biophy.2023013

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On the dimensionless model of the transcription bubble dynamics

Larisa A. Krasnobaeva ^1,2,
Ludmila V. Yakushevich ^{3
,
,}

1.
Siberian State Medical University, 634050 Tomsk, Moscow traсt 2, Russia
2.
Tomsk State University, 634050 Tomsk, Lenin Avenue 36, Russia
3.
Institute of Cell Biophysics, Russian Academy of Sciences, 142290 Pushchino. Institutskaya str. 3, Moscow region, Russia

Received: 18 January 2023 Revised: 18 April 2023 Accepted: 03 May 2023 Published: 19 May 2023

The dynamics of transcription bubbles is modeled using a system of nonlinear differential equations, the one-soliton solutions of which (kinks), are interpreted as a mathematical images of transcription bubbles. These equations contain a lot of DNA dynamic parameters, including the moments of inertia of nitrous bases, distances between base pairs, distances from the centers of mass of bases to sugar-phosphate chains, rigidity of the sugar-phosphate backbone, and interactions between bases within pairs. However, estimates of the parameter values are often difficult, and it is not convenient or simple to operate with such multi-parameter systems. One of the ways to reduce the number of the DNA dynamic parameters is to transform the model equations to a dimensionless form. In this work, we construct a dimensionless DNA model and apply it to study transcription bubbles dynamics. We show that transformation to a dimensionless form really leads to a decrease in the number of the model parameters and really simplifies the analysis of model equations and their solutions.
- transcription bubble,
- nonlinear DNA model,
- kinks,
- McLaughlin-Scott equation,
- kink trajectories
Citation: Larisa A. Krasnobaeva, Ludmila V. Yakushevich. On the dimensionless model of the transcription bubble dynamics[J]. AIMS Biophysics, 2023, 10(2): 205-219. doi: 10.3934/biophy.2023013

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Abstract

The dynamics of transcription bubbles is modeled using a system of nonlinear differential equations, the one-soliton solutions of which (kinks), are interpreted as a mathematical images of transcription bubbles. These equations contain a lot of DNA dynamic parameters, including the moments of inertia of nitrous bases, distances between base pairs, distances from the centers of mass of bases to sugar-phosphate chains, rigidity of the sugar-phosphate backbone, and interactions between bases within pairs. However, estimates of the parameter values are often difficult, and it is not convenient or simple to operate with such multi-parameter systems. One of the ways to reduce the number of the DNA dynamic parameters is to transform the model equations to a dimensionless form. In this work, we construct a dimensionless DNA model and apply it to study transcription bubbles dynamics. We show that transformation to a dimensionless form really leads to a decrease in the number of the model parameters and really simplifies the analysis of model equations and their solutions.

Use of AI tools declaration

The authors declare they have not used Artificial Intelligence (AI) tools in the creation of this article.

Conflict of interest

All authors declare no conflicts of interest in this paper.

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