## Biological Basis of the Synapse Model Code This code is part of a computational model designed to simulate synaptic activity in a neural network. It specifically represents the dynamics of synaptic transmission at two types of synapses, Delta and Exponential, using different mathematical frameworks to capture the biophysical phenomena associated with synaptic activity. ### Synapse Basics In the biological context, a synapse is a junction between two neurons, allowing for the transmission of signals via neurotransmitters. When an action potential reaches the presynaptic terminal, it triggers the release of neurotransmitters into the synaptic cleft, which subsequently bind to receptors on the postsynaptic neuron, leading to potential changes in the postsynaptic neuron. ### Synapse Type: Delta The `SynapseTypeDelta` class simulates a delta function-like synaptic response. Biologically, this could represent synapses where the effect of transmitter release is instantaneous and brief, perhaps akin to fast ionotropic synapses. These synapses typically result in very rapid and transient postsynaptic potentials. - **Biophysical Details**: The model processes spikes, stored as events with associated weights (strengths), which translate into immediate changes in postsynaptic potential. ### Synapse Type: Exponential The `SynapseTypeExponential` class models a synaptic response that decays exponentially over time, which is common in neurotransmitter-induced conductance changes. - **Parameters**: - **Time Constant (`Param[0]`)**: This parameter governs the rate of exponential decay, related to the time it takes for the synaptic conductance to decrease by a significant factor. Biologically, this reflects the dynamics of channel closing or neurotransmitter dissipation. - **Reversal Potential (`Param[1]`)**: This is the equilibrium potential for the ions involved, affecting the direction and magnitude of the current. - **Maximal Conductance (`Param[2]`)**: This parameter defines the peak conductance value that the synapse can achieve, indicative of the synapse's efficacy. - **State Variables**: - **Synaptic Gating Variable (`State[0]`)**: Represents the proportion of open channels or active synaptic state, affected by incoming spikes and decaying over time. - **Exponential Decay**: The synapse changes state based on received spikes and experiences an exponential decay of the synaptic gating variable, capturing the temporal dynamics of realistic synaptic responses. This is akin to AMPA or NMDA receptor-mediated synapses in the brain, where the response is not instantaneous and persists for a short duration due to ionic channel kinetics. ### Synaptic Current Calculation - **Currents through Synapses**: The current (`I_ext`) is calculated based on Ohm’s law, reflecting conductance (`g`) and driving force (`Vm-E`). This represents the flow of ions that lead to excitatory or inhibitory postsynaptic potentials, directly influencing neuronal firing. ### Conclusion Overall, the code provides a simplified computational representation of synaptic transmission, capturing key aspects of synaptic behavior like rapid response and exponential decay. These elements are crucial for modeling neuronal interactions, contributing to the emergent behavior seen in larger neural networks.