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Master's Dissertation
DOI
10.11606/D.76.2011.tde-04052011-091752
Document
Author
Full name
Willian Andrighetto Trevizan
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2011
Supervisor
Committee
Hornos, Jose Eduardo Martinho (President)
Ferreira, Luiz Agostinho
Martinez, Alexandre Souto
Title in Portuguese
Interação entre genes no modelo de spins e bósons
Keywords in Portuguese
Analiticidade
Expressão gênica
Método variacional
Modelos estocásticos
Soluções exatas
Abstract in Portuguese
Vários módulos funcionais de células ou bactérias são controlados por meio de genes que se regulam através da codificação de proteínas repressoras ou indutoras. A compreensão destas redes gênicas é um problema em aberto da biologia. Nesta dissertação procuramos aplicar o modelo estocástico de spins e bósons para o caso da rede mais simples, contiduída de dois genes, o primeiro reprimindo o segundo. Apresentamos a solução exata para a distribuição de probabilidades sobre o número das proteínas dos dois genes no estado estacionário, e a probabilidade dependente do tempo sobre o estado do segundo gene (ativado ou desativado). Discutimos também maneiras de generalizar os resultados para redes maiores.
Title in English
Gene interactions in the spin-boson model
Keywords in English
Analyticity
Exact solutions
Gene expression
Stochastic models
Variational method
Abstract in English
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.
 
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Publishing Date
2011-05-06
 
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