The provided code represents a computational model of a synaptic conductance known as an "exp2syn" or double-exponential synapse. This model is used to simulate the dynamics of synaptic transmission, particularly focusing on how the conductance of a synapse changes over time in response to neurotransmitter release. ### Biological Basis #### Synaptic Conductance - **Synapses**: The code models a synapse, which is a junction between two neurons where chemical communication occurs. When an action potential reaches the synaptic terminal, neurotransmitters are released into the synaptic cleft and bind to receptors on the post-synaptic neuron, leading to changes in ion conductance. - **Conductance Dynamics**: The conductance (g) changes in a manner described by two time constants: `tauRise` and `tauFall`. These correspond to the rise and decay phases of the post-synaptic conductance change, mimicking the real biological process of synaptic currents peaking and then decaying back to rest. #### Double-Exponential Kinetics - **Rise and Decay**: The synaptic conductance follows a double-exponential time course characterized by a rapid rise (described by `tauRise`) and a slower decay (described by `tauFall`). This reflects the typical biological pattern where conductance rapidly increases and then decreases over time after neurotransmitter release. - **Exponential Decay**: The rise time constant (`tauRise`) is always shorter than the decay time constant (`tauFall`), ensuring the rapid activation and slower deactivation typical of synaptic responses. #### Electrical Properties - **Nonspecific Current**: The model declares a nonspecific current (`i`), which is the electrical current through the synaptic conductance. This current is influenced by the difference between the membrane potential (`v`) and the reversal potential for the synapse (`e`), the latter often being set to zero for excitatory synapses. #### Model Characteristics - **Synaptic Weight**: In the `NET_RECEIVE` block, a synaptic event characterized by its weight determines the magnitude of the synaptic conductance change. This weight represents the amount of neurotransmitter released or the strength of the synaptic connection. - **Normalization**: The model ensures that when a synaptic event of weight 1 occurs, the peak conductance reaches a normalized value of 1. This allows for relative scaling of synaptic strength in simulations involving multiple synapses with different weights. ### Conclusion In summary, this code models a postsynaptic conductance using kinetic equations that simulate the characteristic rise and fall of conductance observed in biological neurons during synaptic transmission. It captures the essential temporal dynamics of synaptic inputs, which are fundamental to understanding neuronal computation and network dynamics in the brain.