Biological Basis of the Code

The provided code models the spiking activity of neurons using concepts and principles from computational neuroscience. Here's an outline of its biological underpinnings:

Neuron Model

• Leaky Integrate-and-Fire (LIF) Neurons: The model employs LIF neurons, which are a simplified representation of neurons. The LIF model describes how the membrane potential (( V )) of a neuron integrates incoming synaptic inputs over time, eventually causing the neuron to spike (generate an action potential) if a threshold is exceeded. The membrane potential resets after spiking. This model disregards the complexity of ion channel kinetics but captures essential features of neuronal firing.

Synaptic Transmission

• Synaptic Inputs: The model integrates incoming spikes from pre-synaptic neurons. This mimics biological synaptic transmission where incoming action potentials from pre-synaptic neurons cause excitatory post-synaptic potentials (EPSPs) in post-synaptic neurons. In the code, synaptic input is represented as a homogeneous Poisson process when not following a specific pattern, simulating stochastic spike arrival in biological systems.

Spike-Timing-Dependent Plasticity (STDP)

• Plasticity Mechanism: Spike-timing-dependent plasticity (STDP) is implemented to model how synapses strengthen or weaken over time based on the precise timing of pre- and post-synaptic spikes. This reflects a biological learning rule observed in many neural systems, which underlies processes like memory and learning.
  • LTP and LTD: The code includes long-term potentiation (LTP; strengthening of synapses) and long-term depression (LTD; weakening of synapses), which depend on the timing of spikes. Exponential decay variables (a_post and a_pre) represent synaptic weight changes dependent on past activity.

Homeostatic Mechanisms

• Synaptic Weight Scaling: To maintain stability in synaptic strengths, the model incorporates a homeostatic mechanism whereby all synaptic weights are decreased following a post-synaptic spike. This reflects biological processes that ensure neural activity remains within a functional range, preventing runaway excitation.

Simplifications and Assumptions

• No Refractory Period: The code simplifies the biological model by ignoring the refractory period, a time during which a neuron is less likely to fire following an action potential. This simplification allows for straightforward computation but deviates from actual neuron behavior.
• Use of Noise: Introducing stochastic elements (homogeneous Poisson processes for random spikes) represents the inherent variability and noise present in biological neural systems, acknowledging that neurons often operate in noisy environments.

Neuronal Network and Input Patterns

• Patterns of Input Spikes: The model is designed to recognize specific spatiotemporal patterns in input spikes, akin to how biological neurons detect and respond to certain stimuli or patterns in input.

Overall, this code provides a simplified yet biologically-inspired framework for understanding neuronal dynamics and learning through synapse modification, capturing key functionalities of neural computation and plasticity mechanisms observed in the brain.