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Updated: May 30, 2026

An Optogenetic Method to Control and Analyze Gene Expression Patterns in Cell-to-cell Interactions
Published on: March 22, 2018
Exact time-dependent solutions for a self-regulating gene
A F Ramos1, G C P Innocentini, J E M Hornos
1Escola de Artes, Ciências e Humanidades, Universidade de São Paulo, São Paulo, SP, Brazil. alex.ramos@usp.br
Abstract:
The exact time-dependent solution for the stochastic equations governing the behavior of a binary self-regulating gene is presented. Using the generating function technique to rephrase the master equations in terms of partial differential equations, we show that the model is totally integrable and the analytical solutions are the celebrated confluent Heun functions. Self-regulation plays a major role in the control of gene expression, and it is remarkable that such a microscopic model is completely integrable in terms of well-known complex functions.
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