We obtain an analytic solution for the relationship between the number of copies of protein and time for the differential equation qualitatively investigated in the previous video. We find that the rise time, T1/2, is ln(2) divided by the degradation rate coefficient, α. The fact that the rise time is independent of the translation rate β is sometimes used as a pedagogical example of the importance of quantitative reasoning for gaining insights into biological dynamics that would be difficult to develop through natural-language and vaguely-structured notional reasoning alone.

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