The pervasive von Neumann architecture uses complex processor cores and sequential computation. In contrast, the brain is massively parallel and highly efficient, owing to the ability of the neurons and synapses to store and process information simultaneously and to adapt according to incoming information. These features have motivated researchers to develop a host of brain-inspired computers, devices, and models, collectively referred to as neuromorphic computing systems. The quest for synaptic materials capable of closely mimicking biological synapses has led to an alamethicin-doped, synthetic biomembrane with volatile memristive properties which can emulate key synaptic functions to facilitate learning and computation. In contrast to its solid-state counterparts, this two-terminal, biomolecular memristor features similar structure, switching mechanisms, and ionic transport modality as biological synapses while consuming considerably lower power. To use the device as a circuit element, it is important to understand its response to different kinds of input signals. Here we develop a simplified closed form analytical solution based on the underlying state equations for pulse and sine wave inputs. A Verilog-A model based on Runge-Kutta method was developed to incorporate the device in a circuit simulator. Finally, the paper demonstrates possible applications for short- A nd long-term learning using its unique volatile memristive properties.