The code provided is a computational model that simulates neural dynamics in networks of excitatory (E) and inhibitory (I) neurons. This simulation is inspired by fundamental principles in neuroscience and aims to explore the interactions between these types of neurons, as well as mechanisms of synaptic plasticity like spike-timing dependent plasticity (STDP). Here's an overview of the biological basis for each component modeled in the code: ### Neuronal Dynamics The neuronal dynamics are primarily modeled using the Leaky Integrate-and-Fire (LIF) model. This is a computationally efficient way to approximate neuron behavior based on the following biological principles: - **Membrane Potential:** The differential equation `dV/dt` simulates the evolution of the membrane potential `V` over time, incorporating leakiness (due to the resting membrane potential `E`) and various inputs. - **Spiking Mechanisms:** Neurons generate action potentials (spikes) when the membrane potential reaches a certain threshold (`thresh`). This is modeled with the reset mechanism post-spike. - **Refractory Periods:** The code includes an absolute refractory period (`tabs`), during which the neuron cannot fire another spike, modeling real biological constraints on neuronal firing. ### Synaptic Interactions - **Excitatory and Inhibitory Connections:** The code implements synaptic interactions using mechanisms such as `iampa`, `AMPAstdp`, and `AMPAee`, emulating AMPA receptor-mediated synaptic transmission which is typically excitatory. These models capture the generation and integration of synaptic currents, reflecting real neurotransmitter dynamics. - **Axonal Delays:** The use of explicit delays in synaptic transmission (`delay`) reflects the biological time it takes for signals to travel through axons and be transmitted across synapses. ### Synaptic Plasticity - **Spike-Timing Dependent Plasticity (STDP):** The code includes STDP, a biological process where the timing of spikes from pre- and post-synaptic neurons determines synaptic strength changes. This is crucial for learning and memory and is reflected in the differential equations modifying synaptic weights (`w`), based on spike timings. ### Network Connectivity - **Connectivity Patterns:** Gaussian connectivity matrices represent how connections are distributed across populations of neurons, mimicking biological neural networks where spatial proximity often determines connectivity strengths. ### Population Dynamics - **Populations of Neurons:** The model simulates interactions between populations of neurons, each represented as excitatory or inhibitory neurons. This can be used to study dynamical patterns like oscillations and synchronization, typical in biological systems such as cortical circuits. By capturing these principles, the code simulates the essential properties of neural networks, serving as a bridge between abstract neuronal descriptions and the complexity of brain circuits. Such models help in understanding how specific parameters influence behavior in biological systems, guiding experiments and the development of neuro-computational theories.