The code provided is a computational model that simulates the decay of internal calcium concentration in neurons. This model is primarily based on the biological processes that govern calcium ion (Ca\(^2+\)) dynamics within a neuronal cell following synaptic or action potential-induced calcium entry. Here is a breakdown of the biological basis of this model: ### Biological Basis 1. **Calcium as a Second Messenger:** - Calcium ions play a crucial role as second messengers in neuronal signaling. They are involved in various cellular processes, such as neurotransmitter release, gene expression, and synaptic plasticity. 2. **Calcium Entry and Buffering:** - When a neuron is activated, calcium enters the cytosol through voltage-gated calcium channels or through receptor-operated channels. This influx is reflected in the code by the calcium current (`ica`), which represents the entry of calcium ions into the cell. - The model includes endogenous (naturally occurring) and exogenous (experimentally introduced) calcium buffering systems. Buffers are molecules that bind calcium and modulate its concentration and availability in the cell. 3. **Calcium Decay:** - The decay of calcium concentration in neurons is critical for returning the cell to its resting state after an influx event. The provided model addresses this decay using a differential equation that considers both the calcium entry and the effect of buffering. - The decay process in the model is influenced by two parameters: the buffer ratio (`kb`) and decay rate (`taur`). The buffer ratio combines effects from endogenous and exogenous buffers, while the decay rate incorporates cellular extrusion mechanisms, modeled here using parameters from Sabatini (2002). 4. **Calcium Extrusion:** - Cells have active transport systems, such as calcium pumps, to extrude calcium back out to maintain proper intracellular calcium levels. The modeled calcium decay rate (`taur = kb/gamma`) accounts for these extrusion mechanisms, as introduced by Helmchen (1996). 5. **Resting Calcium Concentration:** - The resting concentration of calcium (`cainf`), set during the model's initialization, represents the baseline level once all dynamic processes have settled. This ensures that the neuronal cell can effectively reset after each activation event. 6. **Geometry and Calculation of Calcium Concentration:** - The neuronal geometry is considered by calculating the calcium concentration relative to the neuron's diameter (`depth = diam/4`). This reflects real-world neuron morphologies where the cell's shape influences calcium dynamics. In summary, this model is used to simulate the tightly regulated process of calcium handling in neurons, focusing on how calcium concentration changes following an influx, how it is buffered and extruded, and ultimately how it returns to resting levels. These processes are essential for maintaining the proper function and signaling capabilities of neurons.