Diffusion of Nanoparticles in a Potential Energy Well

The diffusion motion of particles in a potential energy well is important to study the time dependence of the density of synaptic receptors in the neighborhood of a presynaptic bouton, and hence crucial to our understanding of short-term plasticity of neurons. Here, we focus on the case in which the potential energy below the presynaptic bouton is lower than the extrasynaptic membrane and the diffusion constant is identical in the whole system. By executing Gillespie Algorithm, we can simulate the diffusion motion of a nanoparticle which is initially inside a potential well. We found that there are two peaks in the lifetime distribution using log binning, which account for the time the nanoparticle takes to escape the well, and the two peaks show a significant change in their magnitude and position when the shape of the potential well changes. Our simulation results can be compared with experimental results based on microscope images of diffusing nanoparticles in the presence of fabricated wells. Our results provide a new insight in understanding the dynamics of synaptic receptors in synaptic transmission.