The provided script is a computational model that simulates the dynamics of a neuron receiving input from both excitatory and inhibitory neuronal populations. This model is particularly focused on studying how changes in the rate of inhibitory input can balance the activity of a target neuron to match the firing rate of the excitatory input. ### Biological Basis of the Model #### Neuronal Populations - **Excitatory Neurons**: These neurons are characterized by synapses that increase the likelihood of the postsynaptic neuron firing an action potential. In the script, the excitatory population is represented by neurons firing Poisson-distributed spike trains at a mean rate (`r_ex`) of 5 Hz. The excitatory postsynaptic currents (EPSCs) have a peak amplitude of 45.0 pA. - **Inhibitory Neurons**: These neurons decrease the likelihood of postsynaptic neuron firing. The script uses an inhibitory population firing at an initial mean rate (`r_in`) and aims to adjust this rate so that the postsynaptic neuron fires at the same rate as the excitatory population. These neurons generate inhibitory postsynaptic currents (IPSCs) with a peak amplitude of -45.0 pA, reflecting the hyperpolarizing influence of the inhibitory inputs on the target neuron. #### Target Neuron - **Leaky Integrate-and-Fire Model (LIF)**: The neuron in the model is described as an "iaf_neuron," which stands for integrate-and-fire (IAF). This is a simple yet widely used model for simulating neuronal activity. It integrates incoming synaptic inputs until a threshold is reached, after which it "fires" an action potential and resets. - **Membrane Potential Monitoring**: The model includes a voltmeter to monitor the membrane potential of the target neuron over time. This allows for observing how the neuron's potential changes in response to the combined excitatory and inhibitory inputs. #### Synaptic Dynamics - **Synaptic Delay (d)**: The model incorporates a synaptic delay of 1 ms. This factor represents the time taken for neurotransmitters to be released and bind to receptors across the synaptic cleft, affecting postsynaptic response. #### Model Objective The primary goal of the simulation is to adjust the rate of the inhibitory inputs so that the target neuron fires at the same rate as the excitatory population. This involves finding an optimal inhibitory firing rate using the bisection method to achieve a balance that reflects a biologically plausible state of excitatory-inhibitory homeostasis—a critical aspect of maintaining stable neural network dynamics. #### Biological Relevance - **Excitatory-Inhibitory Balance**: Maintaining a balance between excitatory and inhibitory inputs is vital for normal brain function. This balance prevents runaway excitation, mitigating issues such as seizures, and enables complex neural computations and network stability. - **Network Dynamics and Oscillations**: Simulations like this can help understand how networks maintain balance and how network dynamics might be perturbed in neurological disorders. In summary, the model captures fundamental principles of neuronal dynamics by simulating the interplay between excitatory and inhibitory signals, contributing to our understanding of neuronal firing regulation and balance within neural circuits.