The code provided is designed to simulate neuronal activity using a computational model based on biophysical principles. Specifically, it represents two types of neuron models: the Hodgkin-Huxley (HH) model and a Poisson neuron model. Here's a detailed explanation of the biological basis captured by the code:

Hodgkin-Huxley Model

The Hodgkin-Huxley model is a fundamental framework in computational neuroscience and serves to simulate the electrical characteristics of excitable cells such as neurons. The model reflects the following biological principles:

• Membrane Potential (Vm): Represents the electric potential difference across the neuron's membrane, crucial for signaling and communication in neural systems. The change in membrane potential over time ((dVm/dt)) is determined by ionic currents.

• Ionic Currents: Ionic currents through voltage-gated ion channels are modeled to influence the membrane potential. These include:

  • Sodium (Na(^+)) Current (Ina): Involves fast sodium channels, crucial for the generation of action potentials.
  • Potassium (K(^+)) Current (Ik): Involves delayed rectifier potassium channels, important for repolarizing the membrane after an action potential.
  • Leak Currents (Icl): Account for passive ion flow through the membrane.

• Gating Variables (n, h, m_inf): These variables describe the fraction of ion channels that are open. They are governed by dynamics ('dn/dt', 'dh/dt') which depend on voltage-dependent transition rates ((\alpha) and (\beta)).

• Synaptic Currents: The model also incorporates contributions from synaptic inputs, represented by synaptic currents (Isyn_ext, Isyn_e, Isyn_i). These terms simulate excitatory and inhibitory inputs the neuron might receive from other neurons.

• Parameters: Biophysical parameters like capacitance (Cm), conductances (g_na, g_k, etc.), and reversal potentials (E_na, E_k, E_cl) are included to dictate the neuron's behavior based on intrinsic properties.

Poisson Neuron Model

In addition to the HH model, the code includes a simple Poisson-based model for generating spike trains:

• Poisson Process: Models the neuron's spiking as a stochastic process, where the neuron's firing rate can change over time, reflecting the neuron's response to varying input stimuli or firing patterns.

Biological Relevance

Overall, this code mimics the fundamental electrical activities of neurons in the nervous system. The HH model specifically captures the dynamics of action potential generation, inspired by the pioneering work of Hodgkin and Huxley on the squid giant axon. This model forms the basis for exploring how neurons process and transmit information through bioelectrical signals and how they are affected by synaptic interactions. The inclusion of synaptic currents allows for examination of network-level interactions and neurotransmission. The Poisson model offers a simplified view of spike generation, often used for representing neuronal firing under certain conditions, such as when dealing with background activity or network simulations requiring high-computational efficiency.