The provided code is part of a computational neuroscience model that is likely simulating the dynamics of a recurrent neural network (RNN), focusing on the structure and connectivity patterns typical of such systems. The script outlines methods for creating connections within this network model using two probabilistic mechanisms: Gaussian and Gamma distributions, which are biologically relevant in modeling neuronal connectivity.

Key Biological Concepts

1. Recurrent Neural Networks (RNNs):

   • Recurrent networks are a class of artificial neural networks where connections between units form a directed cycle. This cycle introduces a form of temporal dynamic behavior which is a foundational structure in several neural processes, such as pattern generation, memory formation, and sequential context processing typically observed in cortical circuits.

2. Neuronal Connectivity:

   • The script focuses on connections among neurons in a grid, modeling a spatial architecture that resembles the organization of cortical columns. The Gaussian and Gamma distribution models for generating these connections represent an attempt to mimic the variability and structured randomness observed in synaptic connections among neurons.

3. Gaussian Connectivity Pattern:

   • The lcrn_gauss_targets function uses a Gaussian distribution to determine which neurons are targeted by a specific neuron’s projections. This type of pattern is often used to model local connectivity where neurons have a higher probability of connecting to nearby neurons, akin to how neurons in regions like the cortex exhibit high local connectivity.

4. Gamma Connectivity Pattern:

   • The lcrn_gamma_targets function employs a Gamma distribution to specify synaptic targets. Gamma distributions are useful for modeling asymmetric and skewed data like synapse strength distribution in biological networks. They account for variability in connection distance and density among neurons.

5. Synaptic Delays:

   • Both connection methods incorporate synaptic delays, which in the neural network, influence the timing of neuronal firing and play a crucial role in network dynamics and computational properties. Real biological synapses have delays due to the time taken for neurotransmitter release and signal propagation.

6. Self-Connectivity:

   • The code includes a parameter (selfconnection) to allow or disallow self-connections (autapses), which are connections a neuron makes to itself. While rare, autapses can occur in biological systems and contribute to the regulation of neuronal activity.

7. Population Dynamics:

   • The plot_targets function is set up to visualize network connectivity for excitatory and inhibitory populations. This aligns with the typical division in neurobiological systems where excitatory and inhibitory neurons have distinct roles in network modulation and control.

Overall, this code captures essential features of biological neural networks, including non-uniform connectivity, spatial structure, and temporal dynamics, all of which contribute to the emergent properties seen in brain function.