# Biological Basis of the Code The provided code is part of a computational model tailored to simulate the dynamic behavior of neuronal populations within the brain. This is typically part of models that aim to capture the essential characteristics of neuronal circuits at an intermediate level of abstraction, focusing on synaptic conductances and membrane potential fluctuations. Here's how the code connects to biological principles: ## Synaptic Input and Conductance 1. **Excitatory and Inhibitory Inputs**: - Parameters such as `Qe`, `Te`, `Ee` for excitatory synapses and `Qi`, `Ti`, `Ei` for inhibitory synapses represent the synaptic weights, time constants, and reversal potentials, respectively. This reflects the biological reality that neurons integrate excitatory and inhibitory inputs to determine their firing activity. 2. **Conductance Variables**: - The functions in the code compute variables such as `muGe`, `muGi` (mean excitatory and inhibitory conductances), which are derived from the properties of excitatory and inhibitory synapses and the frequency of synaptic input. This captures the synaptic integration process in which the conductance change at synapses contributes to the overall input a neuron receives. 3. **Membrane Potential**: - `muV` represents the mean membrane potential, calculated as a weighted sum of the reversal potentials of excitatory, inhibitory, and leak conductances, reflecting the neuron's resting and active states under the influence of synaptic inputs. `sV` is the standard deviation of the membrane potential due to fluctuating synaptic inputs, indicative of membrane potential variability seen in vivo. ## Neuronal Dynamics 1. **Temporal Dynamics**: - The equivalent parameters `Gl`, `Cm`, and `El` correspond to the leak conductance, membrane capacitance, and leak reversal potential, integral components of the Hodgkin-Huxley type models of neuronal dynamics. `Tm` reflects the membrane time constant, a key determinant of how quickly a neuron can respond to inputs. 2. **Threshold Function**: - Neurons exhibit a threshold behavior for firing, and `Vthre` computed in the code is the effective threshold potential. The code uses a polynomial expansion to capture how the threshold varies with membrane potential fluctuations and other neuronal state variables. This mimics real neurons' behavior, where the firing threshold can be dynamic and context-dependent. ## Firing Rate Model 1. **Transfer Function**: - The code includes a transfer function model (`TF_my_template`), which computes the neuronal firing rate (`Fout_th`) based on the mean and variance of the synaptic conductance and membrane potential. This reflects the neuron’s input-output relationship, often used in studies of neural coding and population dynamics. 2. **Recurrent Activity**: - The function `make_loop` suggests that the code simulates network activity over time, allowing for the study of feedback loops essential for understanding network-level dynamics such as oscillations and stability. ## Parameter Fitting 1. **Fitting to Data**: - The latter parts of the code are dedicated to fitting the model parameters to empirical data (`fitting_Vthre_then_Fout`). This involves adjusting the parameters to align the model’s output with observed data, a crucial process for validating that the model accurately captures biological phenomena. Overall, the code is structured around a conductance-based neuronal model framework, focusing on capturing the core dynamics of neurons receiving and processing excitatory and inhibitory inputs, computing membrane potential fluctuations, and generating output firing rates. These factors are fundamental to understanding how signals are propagated and processed in biological neural circuits.