Narrow escape problem in synaptic molecular communications.

The narrow escape problem (NEP) is a well-known problem with many applications in cellular biology. It is especially important to understand synaptic molecular communications. Active regions of synapses, also known as apposition zones, are connected to synaptic cleft through narrow slits, from which neurotransmitters can escape to or return from the cleft into the apposition zones. While neurotransmitters leakage into the cleft might be desired for the reuptake process, escaping neurotransmitters might trigger an undesired, i.e., false-positive or action potential in the post-synaptic terminal. Obtaining analytic solutions to NEPs is very challenging due to its geometry dependency. Slight alterations in either or both shape or the size of the hole and the outer volume may cause drastic changes in the solution. Thus, we need a simulation-based approach to solve NEPs. However, NEP also requires the size of the hole to be much smaller than the dimensions of the volume. Combined with the requirement for Brownian motion, where the step size is much smaller than the dimensions of the volume, simulations can be prohibitively long, even for modern computers. Therefore, in this work, we suggest a simulation algorithm that simultaneously satisfies the NEP and Brownian motion simulation requirements. Our simulation framework can be used to quantify the neurotransmitter leakage within synaptic clefts.