# Biological Basis of the Code The code provided is a computational model of a network of integrate-and-fire neurons with synaptic plasticity. It simulates the dynamics of membrane potentials and synaptic weights in a recurrent neuronal network, with the inclusion of mechanisms for synaptic plasticity. The focus of this model is to capture the emergence of functional specificity and the balanced state of excitatory and inhibitory activity within the neural network. ## Key Biological Concepts ### **Integrate-and-Fire Neurons** - **Membrane Potential Dynamics**: The neurons in this model are represented as integrate-and-fire units, which are driven by a subthreshold dynamics matrix, `A`. This captures the passive integration of inputs until a threshold voltage, `vth`, is reached. - **Spike Generation**: Once the membrane potential surpasses the threshold, a spike is generated, and the membrane potential is reset. This reflects the basic excitation and spike emission process in biological neurons. ### **Synaptic Plasticity** - **Plastic vs. Static Synapses**: The model allows for two types of synapses: static and plastic. Static synapses do not change over time, while plastic synapses adjust their strength based on activity, a representation of learning and memory processes in the brain. - **Depression and Potentiation**: The code simulates two types of synaptic changes—depression (`dw_m`) and potentiation (`dw_p`). These correspond to activity-dependent reductions and increases in synaptic strength, respectively. - **Depression**: Modeled via a reduction in synaptic weight when postsynaptic neuronal activity exceeds certain conditions. - **Potentiation**: Described by an increase in synaptic strength based on presynaptic activity and postsynaptic membrane states, reflecting forms of Hebbian learning. - **Filtered Membrane Potential**: Low-pass filtered membrane potentials (`ym_plst` and `yp_plst`) are used to implement voltage-dependency in plasticity rules. This aspect captures the time-averaged activity influencing synaptic changes, analogous to biological mechanisms where calcium concentration or other signaling cascades are filtered over time to modulate synaptic efficacy. ### **Balanced Network Dynamics** - **Excitatory and Inhibitory Balance**: The code models different synapse types (e.g., excitatory `W[0:ne,0:n]`, and inhibitory `W[ne:, 0:ne]`). This captures the biological concept of balanced excitation and inhibition in neural circuits, crucial for maintaining stable network activity and preventing runaway excitation or dampened network responses. - **Bounds and Constraints**: The weights are constrained (`w_max`, `w_max_inh`) to maintain physiologically realistic conditions and prevent unbounded growth that could lead to network instability, reflecting natural limitations on synaptic strength. ### **Mean Depolarization and Homeostasis** - **Running Average of Membrane Potential**: The average depolarization `y_avg` is used in the code as a homeostatic measure. Biological neurons often rely on homeostatic mechanisms to maintain activity within a functional range, ensuring network stability and robustness to changes. This code segment models critical aspects of neural computation and plasticity, geared towards understanding learning mechanisms, network stability, and self-organization in neuronal assemblies as inferred from the referenced study by Sadeh et al. (2015).