# Biological Basis of the Model The provided code simulates a simple computational model of neuronal interactions within the brain using the leaky integrate-and-fire (LIF) model. This approach is rooted in the field of computational neuroscience, which aims to understand the functioning of neurons and neural networks using mathematical models and simulations. Here, the model focuses on interactions between two neurons and includes critical biological elements of neuronal dynamics. ## Neuron Dynamics: Leaky Integrate-and-Fire Model - **LIF Neurons:** The model represents neurons using the leaky integrate-and-fire (LIF) framework, a widely accepted approach for simulating the electrical characteristics of neurons. In the LIF model, each neuron is treated as an electrical circuit, comprising a capacitor (representing the cell membrane) and a resistor (leak conductance). - **Membrane Potential:** The membrane potential of the neuron is updated based on a differential equation that captures the leaky integration of incoming signals and an input current. This reflects the biological process whereby ions cross the cell membrane, altering the membrane potential and integrating synaptic inputs over time. - **Action Potentials (AP):** If the membrane potential exceeds a specific threshold (spike threshold), an action potential (spike) is generated. This spike is modeled as a sudden increase to a peak voltage (spike height), followed by a reset of the membrane potential. Such spikes are biologically analogous to the rapid depolarization and repolarization phases seen during neuron firing. ## Synaptic Interactions - **Inhibitory Synapse:** The biological inspiration of synaptic interaction involves neuron 1 inhibiting neuron 2 whenever it fires an action potential. This is implemented by checking if the first neuron spikes and applying negative current to the second neuron, mimicking the inhibitory postsynaptic potentials (IPSPs) seen in actual neuronal networks. - **Refractory Period:** Both neurons have a refractory period following a spike, during which they cannot fire again. This is reflective of the biological refractory period during which a neuron's ionic channels are resetting and the neuron is less excitable. ## Input Current - **Sinusoidal Input Current:** The neurons receive a sinusoidal input current, representing rhythmic or oscillatory input that may be akin to oscillatory external stimuli or network activity in the brain. This type of input is biologically significant for modulating neuron firing in response to rhythmic brain signals. ## Noise and Variability - **Additive White Gaussian Noise:** This process introduces variability to the input currents, simulating the intrinsic variability and randomness found in biological neuronal inputs, which can arise from synaptic noise, ion channel noise, or external unpredictable stimuli. Overall, this code simulates key aspects of biological neuronal function and interaction, including membrane dynamics, action potentials, synaptic inhibition, and the effect of oscillatory and stochastic inputs. The model captures fundamental concepts of how neurons integrate inputs and communicate through electrical signaling in the brain.