Parametric Resonance in a Mesoscopic Discrete DNA Model
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Parametric Resonance in a Mesoscopic Discrete DNA Model D. Lacitignola · G. Saccomandi · I. Sgura
Received: 29 November 2013 / Accepted: 31 January 2014 © Springer Science+Business Media Dordrecht 2014
Abstract In this paper we investigate from the numerical point of view the discrete DNA model proposed in Lacitignola and Saccomandi (Bull. Math. Biol., 2014) in order to test the robustness of the parametric resonance condition found in the limit of the continuum approximation. To describe more realistically the binding of RNA polymerase to the DNA macromolecule during the first stage of the transcription process, we here consider a localized DNA-RNA polymerase interaction and a relatively high number of base-pairs. Even with these more realistic assumptions, our findings confirm the ones found in the continuum limit and indicate that the parametric resonance phenomenon can be an intrinsic property of the discrete DNA model. Keywords DNA mesoscopic models · Discrete systems · RNA polymerase · Localized binding · Geometric numerical intergrators
1 Introduction It is well known that DNA consists essentially of four nucleotide bases, combined together (A-T and C-G couples) to yield the typical double helical shape. The sequences of nucleotide bases form the genetic code, the blueprint that contains all the information necessary to
D. Lacitignola Dipartimento di Ingegneria Elettrica e dell’Informazione, Università di Cassino e del Lazio Meridionale, Via di Biasio 43, 03043 Cassino, Italy e-mail: [email protected]
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G. Saccomandi ( ) Dipartimento di Ingegneria, Università degli Studi di Perugia, 06125 Perugia, Italy e-mail: [email protected] I. Sgura Dipartimento di Matematica e Fisica “E. De Giorgi”, Università del Salento, Via per Arnesano, 73100 Lecce, Italy e-mail: [email protected]
D. Lacitignola et al. Fig. 1 A schematic picture of the DNA transcription process
build new proteins. To read information stored within DNA the transcription and translation processes are essential: transcription allows a portion of the DNA be copied giving rise to a single-stranded RNA molecule; translation ends with the production of a protein molecule. Three are the main steps involved in DNA transcription, as shown in Fig. 1. (i) Initiation: the process of transcription begins when an enzyme, the RNA Polymerase, binds to a specific area of DNA—the promoter region—and start catalyzing the production of complementary RNA. Specific nucleotide sequences tell RNA polymerase where to begin and where to end. (ii) Elongation: the transcription factors unwind the DNA strands and allow RNA polymerase to transcribe a single strand of DNA into a single stranded RNA polymer called messenger RNA. The strand that serves as the template is called the antisense strand. The strand that is not transcribed is called the sense strand. (iii) Termination: RNA polymerase moves along the DNA until it reaches a terminator sequence. RNA polymerase releases the messenger RNA and separate from DNA. We are here interested in the i
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