The provided code is part of a computational model simulating homeostatic plasticity in neurons using feedback control mechanisms to deal with noise. This model is centered around the adaptive regulation of ion channel conductances to maintain desired neuronal output characteristics, such as firing rate and energy efficiency. ### Biological Context - **Ion Channels and Conductances**: The model modulates specific ion channel conductances, including sodium (\(g_{\text{Na}}\)), potassium (\(g_{\text{K}}\)), leak (\(g_{\text{L}}\)), M-type potassium conductance (\(g_{\text{M}}\)), and after-hyperpolarization conductance (\(g_{\text{AHP}}\)). These conductances are critical elements for neuronal excitability and are integral to the generation of action potentials. - **Neuronal Homeostasis**: Neurons must maintain stability in their electrical activity despite changes in synaptic input and intrinsic noise. This model represents homeostatic mechanisms where conductances adapt to keep neuronal firing rates and energy expenditure within target ranges. Such mechanisms help ensure functional stability in neural circuits by adjusting the intrinsic excitability of neurons. - **Firing Rate and Energy Efficiency**: The model aims to regulate the firing rate (frequency of action potentials) and energy efficiency (a measure of the metabolic cost related to information processing by neurons). The feedback control system iteratively tunes the maximal conductances to meet these biological targets. Energy efficiency is particularly relevant because it reflects how neurons optimize their resource use, a crucial factor in brain function given the high energy demands of neural activity. - **Ornstein-Uhlenbeck Process**: The model incorporates noisy stimulus currents generated as an Ornstein-Uhlenbeck process, which is a mathematical way to simulate realistic correlated noise in input current over time. This reflects the stochastic nature of synaptic input that neurons experience in a real biological setting. - **Tunable Inputs and Outputs**: The model specifies configurations of inputs and outputs (`N_inputs`, `N_outputs`) that determine which conductances and output variables are actively regulated. This mirrors the biological reality where not all channels are equally regulated or equally important under different conditions. Overall, this computational model simulates the regulation of neuronal properties like excitability and efficiency through intrinsic cellular mechanisms, reflecting the adaptability of neurons to maintain stable function in dynamic environments. The focus on conductance changes and their impact on firing and energy efficiency encapsulates key aspects of neuronal homeostasis and adaptation.