Critical time scales for morphogen gradient formation: Concentration or gradient criteria?

Highlights - Investigate time for morphogen gradient to effectively reach steady state. - Analyse both the concentration profile and the gradient of the concentration profile. - For typical problem, the gradient effectively reaches steady state faster. Abstract We extend some recent analysis regarding an approximation of the time scale required for a transient morphogen concentration profile to approach steady state. Motivated by experimental observations, we consider the time scale required for the spatial gradient of morphogen concentration to approach steady state. The analysis shows that the spatial gradient approaches steady state faster than the associated concentration profile approaches steady state. For typical parameter values, this difference in time scales appears to be significant because it is comparable to the time scale of a typical experiment.