Solución de la ecuación de Fokker-Plank para simular ADN confinado fuera del equilibrio considerando condiciones electrostáticas
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Esta tesis explora un método novedoso para el análisis y la comprensión del ADN o polielectrolitos en confinamiento, el método tipo Ewald de geometría general (GgEm). El cual se emplea para evitar la gran separación de escalas de tiempo y longitud, comunmente encontradas en los sistemas biológicos o nano-tecnológicos. Acoplado al uso de simulación de dinámica Browniana a traves de la ecuación de Fokker-Plank y su vínculo con las ecuaciones diferenciales estocásticas. En este trabajo se presenta una estrategia para la validación de la solución a la ecuación de Poisson por medio de GgEm utilizando el método de las imágenes, donde se obtuvieron errores inferiores al 4%. Se estudia el comportamiento de sistemas confinados de macroiones y ADN-Flap. Los macroiones forman estructuras ordenadas determinadas por el confinamiento. En el sistema ADN-Flap, el cual es importante en la nano-secuenciación de ADN, investigamos la dinámica del flap dentro de un nanocanal y encontramos que las solapas generan un efecto estabilizador en el ADN, debido a la interacción del flap con las paredes, lo cual es más evidente a mayores longitudes del flap.
Abstract: This thesis explores a novel method towards the analysis and understanding of DNA or polyelectrolites in confinement, the General Geometry Ewald-like Method (GgEm). Which is employee to avoid the great separation of time and length scales, commonly encountered in biological or nano-technological systems. Coupled to the use of Brownian dynamics simulation through the use of the Fokker-Plank equation and its link with stochastic differential equations. An strategy for validating the solution of the Poisson equation through GGEM using the images method is presented, where errors lower than 4% were obtained. The behavior of confined macroions and DNA-flap systems is studied. The macroions form ordered structures determined by confinement. In the DNA-flap system, important in the nano-sequencing of DNA, We research flap dynamics within a nanoslit and found that the flaps generate DNA stabilizing effect, due to the interaction of the flap with the walls, which is more evident at higher flap lengths
Abstract: This thesis explores a novel method towards the analysis and understanding of DNA or polyelectrolites in confinement, the General Geometry Ewald-like Method (GgEm). Which is employee to avoid the great separation of time and length scales, commonly encountered in biological or nano-technological systems. Coupled to the use of Brownian dynamics simulation through the use of the Fokker-Plank equation and its link with stochastic differential equations. An strategy for validating the solution of the Poisson equation through GGEM using the images method is presented, where errors lower than 4% were obtained. The behavior of confined macroions and DNA-flap systems is studied. The macroions form ordered structures determined by confinement. In the DNA-flap system, important in the nano-sequencing of DNA, We research flap dynamics within a nanoslit and found that the flaps generate DNA stabilizing effect, due to the interaction of the flap with the walls, which is more evident at higher flap lengths