# Biological Basis of the Model The code provided is modeling synaptic transmission in a neuron using a double exponential model. This type of model is particularly useful in capturing the dynamics of synaptic currents characterized by an initial rise followed by a decay to baseline. Below are the key aspects of the biological processes the model aims to simulate: ## Synaptic Transmission **Synapses** are the junctions where neurons communicate with each other. At synaptic sites, neurotransmitters are released by the presynaptic neuron, which then bind to receptors on the postsynaptic neuron’s membrane, leading to ion channel opening and subsequent changes in the postsynaptic membrane potential. ## Kinetic Scheme The model implements a **two-state kinetic scheme**, representing the transition of the synapse from an activated state (A) to a conductance state (G), which is responsible for ion flow. The states are defined by two time constants: - **tauRise (tau1)**: Represents the rise time constant, which is the time taken for the synaptic current to rise to its peak after receptor activation. This models the time it takes for the neurotransmitter to bind to the receptor and induce channel opening. - **tauFall (tau2)**: Represents the decay time constant, which is the time taken for the synaptic current to return to baseline after reaching its peak. This models the time course of neurotransmitter unbinding and receptor desensitization or deactivation. ## Dynamics of Synaptic Conductance The code models the **conductance changes** via two coupled exponential processes. The initial rise is attributed to the rapid activation of synaptic receptors leading to opening of ion channels, while the decay reflects the slower process of receptor deactivation and neurotransmitter clearance. - The rise and decay as expressed by exponential functions (A = a*exp(-t/tauRise) and G = a*tauFall/(tauFall-tauRise)*(-exp(-t/tauRise) + exp(-t/tauFall))) are significant in describing the biological interplay between receptor activation and channel kinetics. ## Unit Consistency The adjustment of units to **siemens** is significant. Conductance (g), expressed in siemens, directly relates to a synapse's ability to allow ionic current flow between the neuron interior and its external environment, driven by voltage and concentration gradients, which fundamentally underlies **neuronal signaling.** ## Synaptic Currents - **i (current)**: The model calculates synaptic current (`i = g*(v - e)`) which is driven by the difference between the membrane potential (`v`) and the synaptic reversal potential (`e`). This reflects excitatory or inhibitory postsynaptic currents, fundamental for action potential generation or inhibition. ## Biophysical Relevance - **Normalization and Factor Calculation**: The model includes calculations ensuring that synaptic events of similar neurotransmitter release result in predictable, normalized peak conductance. This reflects homeostatic mechanisms that maintain efficient synaptic transmission. - **State Transition and Discontinuity Events**: Handling of state transitions (`state_discontinuity` calls) mimics the abrupt nature of neurotransmitter release and binding, modeling the stochastic aspect of synaptic interactions. Together, these elements model the time-dependent changes in synaptic conductance following neurotransmitter release, reflecting the sophisticated biophysical processes neurons use to transmit information across the synapses.