Analytical Investigation of Long-Time Diffusion Dynamics in a Synaptic Channel With Glial Cells

Abdullah Enes Oncu, Halil Umut Ozdemir, Halil Ibrahim Orhan, Bayram Cevdet Akdeniz, Asaf Toprakci, Mehmet Anil Aslihak, Huseyin Birkan Yilmaz, Ali Emre Pusane, Tuna Tugcu, Fatih Dinc

Abstract: In this letter, we first derive the analytical channel impulse response for a cylindrical synaptic channel surrounded by glial cells and validate it with particle-based simulations. Afterwards, we provide an accurate analytical approximation for the long-time decay rate of the channel impulse response by employing Taylor expansion to the characteristic equations that determine the decay rates of the system. We validate our approximation by comparing it with the numerical decay rate obtained from the characteristic equation. Overall, we provide a fully analytical description for the long-time behavior of synaptic diffusion, e.g., the clean-up processes inside the channel after communication has long concluded.