Abstract
The equilibrium shapes of a closed DNA are investigated by employing a model of a thin, homogeneous, isotropic, linearly elastic rod of circular cross section. An equilibrium configuration of such an initially straight and twisted rod, submitted to external forces and moments at its ends only, obeys equations identical to those governing the rotation of a symmetric gyrostat spinning about a fixed point in a gravitational field (the Kirchhoff analogy). To represent the equilibrium of the looped DNA, the model rod must be smoothly closed into a ring. The corresponding BVP results in a system of four nonlinear equations with respect to four parameters. The perturbation analysis and the parameter continuation approach are used to find nonplanar solutions. The conformation change is discussed for various values of parameters.
Sommario
Si analizzano le configurazioni di equilibrio di una molecola chiusa di DNA per mezzo di un modello di trave sottile, omogenea, isotropa e linearmente elastica, con sezione circolare. La configurazione di equilibrio di una tale trave, inizialmente rettilinea e poi ritorta, soggetta a forze esterne e momenti solo alle sue estremità, è descritta dalla soluzione di equazioni identiche a quelle che governano il moto di un girostato simmetrico in rotazione intorno ad un punto fisso in un campo gravitazionale (l'analogie di Kirchhoff). Per poter rappresentare l'equilibrio del cappio di DNA, il modello di trave deve essere racchiuso in un anello, Il corrispondente problema al contorno consiste in un sistema di quattro equazioni nonlineari rispetto a quattro parametri. Le soluzioni del problema fuori del piano vengono ottenute tramite l'analisi perturbativa ed una procedura di continuazione al variare di un parametro. Si discutono le modifiche di configurazione del sistema per diversi valori dei parametri.
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Starostin, E.L. Three-dimensional shapes of looped DNA. Meccanica 31, 235–271 (1996). https://doi.org/10.1007/BF00426990
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DOI: https://doi.org/10.1007/BF00426990