A spatiotemporal master equation model of morphogen transport: Local accumulation times, noise measurement and diffusion force

•A spatiotemporal master equation model for morphogen transport has been built.•We have derived analytical expressions of a local accumulation time of the first-order and second-order moments and variances.•The analytical expression of the variances for this model has been obtained.•Potential energy, diffusion force and work acting on morphogen molecules are further measured.