The provided code simulates a computational model of synaptic transmission with a focus on short-term plasticity (STP). STP is a prominent feature of synaptic transmission in the brain that allows synapses to dynamically adjust their strength in response to different patterns of neuronal activity. The two primary forms of STP are facilitation and depression, which can coexist and often influence neuron behavior in a frequency-dependent manner. ### Biological Basis #### Synaptic Transmission Synaptic transmission is the process by which neurons communicate with each other. It involves the release of neurotransmitters from a presynaptic neuron, crossing the synaptic cleft, and binding to receptors on a postsynaptic neuron. This initiates a postsynaptic potential, which can be excitatory or inhibitory. #### Short-Term Plasticity (STP) STP refers to the rapid, reversible changes in synaptic strength that occur over milliseconds to minutes in response to recent activity. In the code: - **Facilitation** (`tau_f`): A mechanism by which the likelihood of neurotransmitter release is temporarily increased following an action potential. It is modeled as an increase in the utilization of synaptic resources (`u`), driven by residual calcium ions in the presynaptic terminal. - **Depression** (`tau_d`): A temporary reduction in synaptic strength due to the depletion of readily releasable neurotransmitter vesicles. It is represented by the variable `r`, which indicates the fraction of available synaptic efficacy before an incoming spike. The model combines these two processes using the parameters `U`, `tau_f`, and `tau_d`. `U` represents the baseline utilization of available synaptic efficacy, while `tau_f` and `tau_d` are the time constants for facilitation and depression, respectively. #### Synaptic Current and Membrane Dynamics - **Synaptic Efficacy (`A`)**: The maximal strength of synaptic connection, representing the amplitude of postsynaptic potentials. - **Synaptic Time Constant (`tau_s`)**: This determines the time course over which post-synaptic currents decay, reflecting the kinetics of synaptic receptor channels. #### Neuronal Dynamics - **Membrane Potential (`V`)**: Represents the voltage across the neuronal membrane, which integrates incoming synaptic currents and defines whether a neuron will fire an action potential. - **Membrane Resistance (`Res`)** and **Membrane Time Constant (`tau_m`)**: These are biophysical parameters of the neuron that influence how it responds to synaptic inputs. ### Inputs and Outputs The code simulates how a sequence of synaptic spikes affects the membrane potential of a postsynaptic neuron over time. It integrates these dynamics using Euler's method, a numerical technique to approximate solutions to differential equations. The output includes the time-varying membrane potential (`V`) and a plot of spike-related synaptic events (`V_pre`), providing visual insights into how synaptic inputs and STP impact postsynaptic response. In summary, the model captures essential features of synaptic transmission and short-term plasticity, enabling detailed exploration of how neurons process information through synaptic interactions in varying activity patterns.