A positive feedback loop, where the gene product directly activates its own production, is the simplest form of a gene regulatory network that exhibits a bistable behavior. An analytic solution for the steady state can be obtained only under various simplifying assumptions, such as simultaneous binding of the activator molecules to the gene or complete inactivation of the gene in the absence of protein binding. Here, I consider a feedback loop without such unrealistic simplification and analyze the fixed point structure of the resulting rate equation. The current model is the most general deterministic model that has been solved analytically. I find that the bifurcation diagram is qualitatively different from that obtained in the absence of transcription leakage.

中文翻译：

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具有部分结合和转录泄漏的自调控基因网络的稳态

基因产物直接激活其自身产生的正反馈回路是表现出双稳态行为的基因调控网络的最简单形式。只有在各种简化假设下才能获得稳态的解析解，例如激活剂分子与基因的同时结合或在没有蛋白质结合的情况下基因的完全失活。在这里，我考虑了一个没有这种不切实际的简化的反馈回路，并分析了所得速率方程的不动点结构。当前模型是最通用的确定性模型，已通过分析求解。我发现分叉图与在没有转录泄漏的情况下获得的分叉图有质的不同。