In this paper we analyse molecular communications (MC) in a proposed artificial synapse (AS), whose main difference from biological synapses (BSs) is that it is closed, i.e., transmitter molecules cannot diffuse out from AS. Such a setup has both advantages and disadvantages. Besides higher structural stability, being closed, AS never runs out of transmitters. Thus, MC in AS is disconnected from outer environment, which is very desirable for possible intra-body applications. On the other hand, clearance of transmitters from AS has to be achieved by transporter molecules on the presynaptic membrane of AS. Except from these differences, rest of AS content is taken to be similar to that of a glutamatergic BS. Furthermore, in place of commonly used Monte Carlo based random walk experiments, we derive a deterministic algorithm that attacks for expected values of desired parameters such as evolution of receptor states. To assess validity of our algorithm we compare its results with average results of an ensemble of Monte Carlo experiments, which shows near exact match. Moreover, our approach requires significantly less amount of computation compared to Monte Carlo approach, making it useful for parameter space exploration necessary for optimisation in design of possible MC devices, including but not limited to AS. Results of our algorithm are presented in case of single quantal release only, and they support that MC in closed AS with elevated uptake has similar properties to that in BS. In particular, similar to glutamatergic BSs, the quantal size and density of receptors are found to be main sources of synaptic plasticity. On the other hand, the proposed model of AS is found to have slower decaying transients of receptor states compared to BSs, especially desensitised ones, which is due prolonged clearance of transmitters from AS.