The limited storage capacity at the transmitters of a molecular communication (MC) system can affect the system's performance. One of the reasons for this limitation is the size restriction of the transmitter, which the storage must be replenished so that the transmitter has enough molecules for future transmission. This paper proposes a biologically inspired transmitter model based on neurons for MC whose storage charging and discharging follow differential equations. The proposed transmitter opens its outlet for a specific time in each time frame to exponentially release a portion of stored molecules to code bit-1 and remains silent to code bit-0. We analyze our model based on different transmission parameters. These parameters are the symbol duration, the release time duration, the storage capacity, and the release and replenishment rate of the storage. We find that the storage outlet must be open for a certain period within the time slot duration in order to improve the performance of the proposed system. Additionally, we demonstrate that determining the effect of storage capacity size can be important for practical MC due to the significant differences between the ideal transmitter and the proposed one, which have a limited size. We show that increases in the transmitter storage size can improve the system performance. As a result, taking a closer look at these practical transmitters is essential to solving the problems and challenges of molecular communication systems.