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

Nieto Muñoz, Juan José; Vásquez Ávila, María Ofelia

doi:https://doi.org/10.3934/cpaa.2022065

Artículo completo (407.0Kb)

Identificadores

URI: https://hdl.handle.net/10481/100741

DOI: https://doi.org/10.3934/cpaa.2022065

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Editorial

AIMS - American Institute of Mathematical Sciences

Materia

DNA replication model

Nucleation-and-growth model

Partial differential equations - Cauchy problem

Crystal growth

KJMA

Date

2022-08

Referencia bibliográfica

J. Nieto, O. Vásquez, Wellposedness of a DNA replication model based on a nucleation-growth process, Comm. Pure Appl. Anal. 21(8), (2022), 2643-2660.

Sponsorship

Junta de Andalucía, project P18-RT-242; Junta de Andalucía, project A-FQM-311-UGR18; MICINN (Spain) project RTI2018-098850-B-I00

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.

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