The code provided models synaptic interactions between cone photoreceptor cells and horizontal cells in the retina. This synapse can exhibit either excitatory or inhibitory behavior, which is determined by the sign of the maximum conductance (g_max).

Biological Basis

Synapse between Cones and Horizontal Cells

• Cones are photoreceptor cells in the retina responsible for color vision. They are sensitive to different wavelengths of light and are crucial for high-acuity vision. When light hits the cones, it alters their membrane potential, releasing neurotransmitters to downstream cells.

• Horizontal Cells are interneurons located in the retina that integrate and regulate input from multiple photoreceptor cells. Their major role is in lateral inhibition, which helps enhance contrast and sharpens visual responses.

Synaptic Mechanism

• Conductance-Based Synapse: The synapse operates based on changes in conductance, typical of many neuronal synapses. The conductance (g) is calculated using a hyperbolic tangent function (tanh), which approximates the sigmoidal activation-inactivation response seen in biological systems. This represents the opening probability of synaptic channels as a function of the presynaptic membrane voltage (V_pre).

• Threshold and Slope:

  • v_th (threshold voltage) and v_slope (slope factor) dictate the sensitivity of the synapse to presynaptic voltage changes.
  • The threshold voltage suggests the level at which the synaptic response becomes significant, while the slope affects how steeply the conductance changes with voltage.

• Inhibitory/Excitatory Nature: By altering the sign of g_max, the synapse can simulate either an excitatory or inhibitory synapse:

  • Excitatory Synapses: Increase the likelihood that the postsynaptic neuron will fire an action potential by depolarizing the postsynaptic membrane.
  • Inhibitory Synapses: Make it less likely for the postsynaptic neuron to fire by hyperpolarizing it.

• Current (i) Calculation: The synaptic current is calculated as the product of the maximum conductance and the synaptic conductance, where a negative current denotes the usual inward flow for inhibitory synapses.

Functional Implications

This synaptic model is significant for understanding how cones process visual signals and transmit these signals to horizontal cells. The dynamic range manipulation and sign inversion aspects are crucial for retinal circuits, which must finely tune the visual information before it's conveyed to the brain. Adjusting synaptic strength or nature based on these parameters allows for studying how retinal information processing reacts to different lighting conditions and contrasts.