Threshold activation for stochastic chemical reactions in microdomains

The mean time to reach a threshold (MTT) is the mean first passage time for the number of bound molecules to reach a given value. In the theory of chemical reactions involving a small number of ligands and molecules, the MTT represents the first time a given number of binding sites is formed. In that context, the MTT can be used to characterize the stability of chemical processes, especially when they underlie a biological function. Using a Markov-chain description, we compute here the MTT, in terms of fundamental parameters, such as the number of molecules, the ligands and the forward and backward binding rates. We find that the MTT depends non-linearly on the threshold T , and this result may have several applications, ranging from cellular biology to synaptic plasticity. We confirm our analytical computations with Brownian simulations.