The code provided represents a computational model of Purkinje cells (PCs) in the cerebellum. Purkinje cells are critical to the function of the cerebellum, influencing motor control by integrating synaptic inputs and firing action potentials.

Biological Basis

1. Cell Structure and Passive Properties:

   • The modeled Purkinje cells are simplified with a single compartment geometry using parameters such as length (L = 20 um) and diameter (diam = 20 um). The membrane capacitance (cm = 1 uF/cm2) mimics the membrane's ability to store and discharge ions.

2. Ion Channels and Conductances:

   • Sodium (Na) Channels: Fast sodium channels (pcNarsg, pcNa) are responsible for the rapid depolarization phase of the action potential. Their reversal potential (ena) is set to 60 mV.
   • Potassium (K) Channels: The code includes various potassium channels (pcKv1, pcKv4, pcKbin) which mediate repolarization and after-hyperpolarization. The reversal potential for potassium (ek) is -88 mV.
   • Calcium (Ca) Channels and Currents: Calcium dynamics are included with pcCaP (high-threshold calcium channels) and calcium-activated potassium channels (pcCaBK), crucial for shaping action potentials and facilitating synaptic activity. The external calcium concentration (cao) is set to 2 mM.
   • Leak Channel: A constant background leakage (pcleak) helps maintain the resting membrane potential.
   • Hyperpolarization-activated Cyclic Nucleotide-gated (HCN) Channels: Modeled by pcIhcn, these channels contribute to the pacemaker activity by allowing inward cation flow at hyperpolarized membrane potentials.

3. Input Current (IClamp):

   • The cells receive electrical stimuli through IClamp mechanisms, which apply current (ocPC_amp[i]) based on data read from an external file. This simulates varied baseline levels of synaptic activity or intrinsic excitability reflecting biological diversity among neurons.

4. Noisy Current:

   • Biological noise is modeled using NoisyCurrent added to the membrane potential to account for stochastic fluctuations present in neuronal micro-environments, such as thermal noise and synaptic variability.

5. Temperature:

   • The code sets the simulation temperature (celsius = 36 degC) close to mammalian body temperature, affecting channel kinetics and neuronal behavior.

Overall Purpose

The model simulates the diverse electrophysiological behaviors of a population of Purkinje cells, each with distinct synaptic inputs and membrane properties due to random variations in input current and noise. This allows for the study of how intrinsic properties and noise influence the output and functionality of these critical neurons within the cerebellar microcircuitry.