The provided code forms part of a computational neuroscience model aimed at simulating network dynamics within a simplified neuronal sheet. Below, key biological concepts embodied within the code are discussed: ### Network Structure 1. **Neuronal Populations**: - The model consists of excitatory (pyramidal) and inhibitory neurons. The parameters `Inh2Py`, `PyInput`, and `InhInput` define interactions among these two populations within a two-dimensional `n x n` grid (`parameters.n=n`), simulating a neuronal sheet which maps to a simplified cortical microcircuit. 2. **Pyramidal Neurons (Excitatory)**: - The pyramidal neurons are represented by `Py2Py`, depicting connections between excitatory neurons. This aspect reflects the strongest interactions in cortical circuits facilitated by glutamatergic synapses. 3. **Inhibitory Neurons**: - `Py2Inh` models connections from excitatory to inhibitory neurons, reflecting the network's feedback inhibition typical of GABAergic processes in cortical networks. ### Synaptic Dynamics - **Delay Integration**: - The `getDelayMatrix` function computes delays in synaptic transmissions, a crucial aspect representing axonal conduction delays and synaptic transmission times. These delays can cause temporal dispersion in signaling, critical for wave propagation and temporal coding in biological systems. - **Connection Weights**: - Synaptic weights, such as in `parameters.Py2Py` and `parameters.Py2Inh`, underline connection strengths, thereby representing the stochastic release probability of neurotransmitters and the resulting postsynaptic response. ### Temporal Dynamics 1. **Time Scales**: - `parameters.tauPy` and `parameters.tauInh` denote distinct time constants for excitatory and inhibitory neuron populations. These constants reflect neuronal membrane time constants, influencing how rapidly populations respond to synaptic inputs. 2. **Sigmoid Activation**: - The terms `SigThresh` and `SigSteepness` define sigmoid activation functions, commonly used in models to imitate the neuron's response to input currents, reflecting the nonlinear thresholds seen in action potential generation. ### Propagation Speed - **Spatial Delay via Propagation Speed**: - The `propspeed` parameter affects the calculation of delays (`hdtime`), emulating the finite conduction velocity of axons in neural tissue. This is critical to understanding wave forms and signal propagation dynamics. By integrating these elements, the code is modeling the propagation of signals in a simplified cortical network, imitating how excitatory and inhibitory interactions contribute to various spatiotemporal patterns, including wave propagation and oscillatory activity, consistent with observations in biological neural tissue.