Gene interactions in the spin-boson model

Author(s)

Willian Andrighetto Trevizan

• Document type: Master's Dissertation
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Física de São Carlos (IFSC/BT)
• Defense date: 2011-02-24

Examining board members

Jose Eduardo Martinho Hornos; Luiz Agostinho Ferreira; Alexandre Souto Martinez

• Advisor: Jose Eduardo Martinho Hornos

Abstract

Several functional modules in cells or bacteria are controlled by genes that regulate each other by coding repressive or inducer proteins. The understanding of these genetic networks is still an open problem in biology. In this work we apply the stochastic spin-boson model to the simplest interacting network, made of two genes, the first repressing the second. We present the exact solution for the stationary probability distribution over their both protein numbers, and the temporal evolution of the second genes state (on or off). We also discuss ways of generalizing these results to larger networks. (AU)