Wellposedness of a DNA replication model based on a nucleation-growth process

J. Nieto; M. O. Vásquez

doi:10.3934/cpaa.2022065

Article Contents

2022, Volume 21, Issue 8: 2643-2660. Doi: 10.3934/cpaa.2022065

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Wellposedness of a DNA replication model based on a nucleation-growth process

J. Nieto^1, , and
M. O. Vásquez^2,

1.
Dpto. Matemática Aplicada and Research Unit "Modeling Nature" (MNat), Universidad de Granada, 18071 Granada, Spain
2.
Universidad de Cartagena, Cartagena, Colombia

^* Corresponding author
^* Corresponding author

Received: June 30, 2021

Revised: September 30, 2021

Early access: April 2022

Published: August 2022

The first author is supported by JJAA (Spain) projects P18-RT-242 & A-FQM-311-UGR18, and MICINN (Spain) project RTI2018-098850-B-I00

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Abstract

In this paper, we analyze a nonlinear equation modeling the mechanical replication of the DNA molecule based on a Kolmogorov-Jhonson-Mehl-Avrami (KJMA) type model inspired on the mathematical analogy between the DNA replication process and the crystal growth. There are two different regions on the DNA molecule deep into a duplication process, the connected regions where the base pairs have been already duplicated, called eyes or islands and the regions not yet duplicated, called holes. The Cauchy problem associated with this model will be analyzed, where some dependences and nonlinearities on the replication velocity and the origins of replication are introduced.

Keywords:

Mathematics Subject Classification: Primary: 35Q92, 35A01; Secondary: 00A71, 45K05.

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Figure 1. Analogy between DNA replication and crystal growth. We identify the growing islands with the growing eyes in the DNA case, a nucleation point (N) or zero size island with an origin of replication and holes with non replicated DNA regions. The arrows indicate the symmetric bidirectional growth of the islands or the DNA synthesis

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Figure 2. Several characteristics curves $ Y(s) = \ln \left( e^{Y(0)} -2vs \right) $

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