The code provided models certain aspects of neuronal dynamics and synaptic plasticity observed in the brain. Here's a breakdown of the biological basis of the code:

Neuron Model Parameters

The neuronal dynamics are modeled using an "integrate-and-fire" approach:

• Tau_m (Time Constant): Represents the membrane time constant, which dictates how quickly the neuron's membrane potential can change in response to input.
• Resistance (R): The electrical resistance across the neuronal membrane. In this model, it is set to 1 Ohm, simplifying calculations.
• Resting Potential (El): Corresponds to the membrane potential when the neuron is at rest, typically around -70 mV in biological neurons (0 mV is used here for simplicity).
• Threshold and Reset Potentials (Vth and Vres): Determine the voltage at which a neuron will "fire" an action potential and the potential to which it resets after spiking.
• Refractory Period (Tref): The time after a spike during which the neuron cannot fire again, reflecting the biological refractory period of real neurons.

Synaptic Parameters

The model includes dynamics for synaptic conductance changes:

• Excitatory Synapses: The reversal potential (EsynE) is represented as 30 mV, which reflects the excitatory effect of neurotransmitter release.
• Synaptic Conductance Parameters (tauSynEx, tauSynIn, gBarEx): Reflect the temporal dynamics of synaptic potentials. Tau constants govern the decay of excitatory and inhibitory post-synaptic potentials, while gBarEx denotes peak excitatory synaptic conductance.

Plasticity Mechanisms

This code models synaptic plasticity, specifically spike-timing-dependent plasticity (STDP):

• Time Constants (tp_plast, tm_plast): Govern the decay of pre-synaptic and post-synaptic activity, underlying STDP dynamics.

• Plasticity Parameters (a_pre, a_post, a_plus, a_minus): Define changes in synaptic strength based on the timing of neuronal activity. The sign and magnitude of these parameters depict whether potentiation or depression occurs during different neuronal states (e.g., "up" and "down" states). Notably:

  • "Up" states incorporate a depression mechanism where pre-synaptic activity alone leads to a reduction in synaptic strength.
  • "Down" states involve standard STDP where precise timing between pre- and post-synaptic spikes leads to synaptic strengthening or weakening, as indicated by a_plus and a_minus.

Biological Relevance

These models capture essential features of neuronal and synaptic behavior that are central to understanding brain dynamics:

• Action Potential Firing: The integrate-and-fire model approximates how neurons generate spikes in response to input, a fundamental aspect of neuronal communication.
• Synaptic Integration: The temporal dynamics of synaptic conductance determine how synaptic inputs are integrated over time.
• Synaptic Plasticity: STDP is a critical biological phenomenon believed to underlie learning and memory, where the timing of spikes controls synaptic strengthening or weakening.

Collectively, this code models the interplay between neuronal excitability, synaptic currents, and plasticity, reflecting fundamental processes observed in the nervous system.