The provided code models a **graded synapse** with first-order binding kinetics. This is a synaptic model that simulates how neurotransmitter release influences synaptic conductance in a manner that depends on the presynaptic membrane potential, \( V_{\text{pre}} \). The core biological features represented in this code can be described as follows: ### Synaptic Conductance - **Maximal Conductance (\( g_{\text{max}} \))**: This parameter, set to 0.00256 umho, represents the maximal possible conductance of the synapse when fully activated. It correlates with the density and effectiveness of ionotropic receptor channels present at the synaptic site. ### Synaptic Activation and Modulation - **Presynaptic Voltage Dependency**: The model incorporates a threshold voltage (\( V_{\text{thr}} \)) at which synaptic changes commence, reflecting a presynaptic influence on synaptic activation. This models the dependency of synaptic transition on presynaptic depolarization. - **Steepness of Activation (\( V_{\text{slope}} \))**: This parameter represents the slope or sensitivity of synaptic current to presynaptic voltage changes, mimicking the graded nature of neurotransmitter release in graded synapses. ### Synaptic Dynamics - **State Variable (\( s \))**: This variable represents the fraction of open synaptic receptors or the fraction of maximal conductance. It is influenced by the presynaptic voltage, transitioning between 0 and 1. The initial value set at 0.1 suggests a baseline level of synaptic activity. - **Steady-state Activation (\( s_{\text{inf}} \))**: A function of presynaptic voltage, determining the target level of the state based on the membrane potential. It transitions based on the voltage threshold and smoothly changes with a hyperbolic tangent function representing binding kinetics resembling receptor-ligand interactions. - **Time Constant (\( \tau \))**: Set at 10 ms, it governs the rate of change in the synaptic conductance dynamics and reflects the kinetics of neurotransmitter binding and unbinding from receptors. ### Current Calculation - **Driving Force for Current (\( i \))**: The synaptic current is calculated by the product of conductance and the driving force, \( (v - e) \), where \( e \) is the reversal potential, representing the equilibrium potential for the particular ions mediated by the synaptic channels (here, set to -70 mV, typical for inhibitory synapses like GABAergic receptors). ### Biological Interpretations This model captures concepts central to graded synapses, such as those often found in sensory systems and certain central nervous system synapses, where synaptic output correlates directly with graded electrical input rather than discrete action potentials. The graded response means signal strength is modulated based on presynaptic potential rather than an all-or-nothing action potential response. The incorporation of presynaptic voltage thresholds and graded transition steepness also reflects biological constraints in synaptic transmission fidelity and synaptic plasticity mechanisms.