Biological Basis of the Modified Morris-Lecar Model

The provided code models the electrophysiological behavior of neurons with a focus on ionic currents responsible for action potential generation and propagation. Specifically, it is a modification of the Morris-Lecar model, enhanced with a variable T-type calcium current, drawing on work by Prescott and Rubin. Here are the key biological aspects modeled by this code:

Ionic Currents

Fast Sodium Current (INa)

• Role: This current is essential for the rapid depolarization phase of the action potential in neurons.
• Activation: The sodium current here activates instantaneously with voltage change, which is typical for fast sodium channels. This is represented by the gating variable minf(V) which is dependent on the membrane potential V.
• Conductance and Reversal Potential: The model includes parameters gna (maximum conductance) and vna (reversal potential), reflecting sodium ion dynamics in real neurons.

Delayed Rectifier Potassium Current (IKdr)

• Role: Responsible for repolarization and the regulation of action potential duration.
• Activation: This current activates more slowly than INa, which is captured by the dynamic gating variable y. It mimics the cumulative effect of potassium channel opening, which helps return the membrane potential to its resting state.
• Tau and Inf Variables: The yinf(V) and tauy(V) define the steady-state activation and time constant of the potassium current.

Leak Current (Il)

• Role: This represents the passive flow of ions across the membrane, which helps maintain the resting membrane potential.
• Parameters: The conductance (gl) and reversal potential (vl) are set to simulate the non-voltage dependent, constant background current.

T-type Calcium Current (IT)

• Role: T-type calcium channels contribute to pacemaking and modulation of neuronal firing patterns, especially during bursts.
• Activation and Inactivation: The current relies on both fast activation (mtinf(V)) and slow inactivation (htinf(V)), reflecting the dual gating properties of this current type.
• Equation Specifics: The function itf(v,mt,ht) embodies the T-type current dependent on both the gating variables mt and ht.

Other Biological Aspects

• Noise: The introduction of a normal noise component (dc_noise and nd) aims to replicate the stochastic nature of neuronal firing.
• Membrane Capacitance (c): This is a passive electrical property of the neuron's membrane, affecting how the membrane potential responds to ionic currents.
• External Stimuli: The variable Iext, linked to external stimulations, models experimental conditions or synaptic input affecting neuronal behavior.

Summary

This model combines fast sodium, delayed rectifier potassium, leak, and T-type calcium currents to simulate the complex behavior of neuronal action potentials and firing patterns. By incorporating noise and parameters for external stimuli, it reflects realistic neuronal dynamics within a computational framework, providing insights into the interplay between different ionic currents and their contribution to neuronal excitability and signaling.