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

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    * Corresponding author 

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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  • 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.

    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

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

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