Channel Clearance by Perfectly Absorbing Boundaries in Synaptic Molecular Communications

Molecular reuptake is a nature-inspired channel clearance strategy to mitigate intersymbol interference (ISI) in molecular communications. Reuptake is especially important if the communication medium is not cleared of the information-carrying molecules by other means, and if it is not done properly, it decreases the maximum signal rate. In a more practical sense, in nature, reuptake failure may be detrimental to the organisms. Many neurological disorders, including schizophrenia, are related to problems with the reuptake mechanisms in synaptic molecular communications (SMC). To understand the evolutionary solution to the ISI, we start with the glutamate reuptake process as part of SMC. We develop a stochastic approach to the reuptake problem and derive analytic expressions for the probability of absorption for rectangular volumes. To test the validity of perfectly absorbing boundary approximation for real systems, we derive the rate of first incidence and average glutamate transport time for EAAT2, the most prevalent transport molecule. When applied to SMC, our results indicate that perfectly absorbing boundaries assumption is not possible according to the available physiological data, due to the limited number of transporters and the finite amount of time a transporter requires to reuptake a glutamate molecule.