What is the dynamics of a negatively autoregulation gene onc

What is the dynamics of a negatively auto-regulation gene once its maximal promoter activity is suddenly reduced from 1 to 2=0? What is the response time, and how does it compare to simple regulation?

Solution

Response time for negative regulatory promoter is inversely proportional to its activity. If promoter activity reached to zero then response time would reach to infinite which means promoter is no longer able to regulate negatively the expression of gene for an uncertain time. Simple regulation on such condition will lead to no expression of gene for an infinite time.