The provided code is designed to model the intracellular calcium dynamics in neurons, focusing specifically on the mechanisms of calcium concentration decay and removal. It simulates how calcium ions (Ca++) are regulated within the cell, recognizing both their influx and efflux, which is critical for numerous cellular processes. ### Biological Basis of the Model #### Calcium Influx and Buffers - **Calcium Influx**: The model considers calcium entry through calcium channels quantified by the variable `ica`, representing the calcium ion current. These currents may correspond with action potentials or synaptic activity that lead to the influx of calcium into the neuronal interior. The factor `10000` (adjusted to `10000/18` in this model) transforms this current into a change in concentration, accounting for the unit conversions and model specifics. - **Calcium Buffering**: The term `depth` represents the shell thickness, a virtual layer with a defined volume near the cell membrane where calcium changes are computed. This simplification allows the model to accommodate calcium buffering, wherein molecules within the neuron bind to calcium ions, effectively reducing the free calcium concentration. #### Calcium Removal Mechanisms - **Calcium Pumping**: A crucial component is the model's representation of calcium extrusion via ATPase pumps. These pumps actively transport calcium ions out of the neuron, an essential process to maintain cellular calcium homeostasis. The Michaelis-Menten approximation simplifies the pump dynamics into a kinetic model, expressed through parameters `kt` (pump time constant) and `kd` (dissociation constant). - **Decay of Calcium**: The decay process is modeled by `cainf` and `taur`. `cainf` represents the equilibrium or target intracellular calcium concentration, while `taur` is the time constant defining how quickly the calcium level returns to this baseline after a perturbation. In the modified model, `taur` is multiplied by 7 to accelerate the rate of calcium removal, reflecting a modification to account for biological observations from literature on calcium spike repolarization. ### Modifications and Implications - The code modifications, particularly the acceleration of calcium removal (`taur*7`), are grounded in empirical findings (e.g., the research of Golding et al. 1999), which have implications on how quickly neurons can return to resting calcium levels after activity. - The inclusion of both influx and efflux mechanisms, alongside adjustments to the calcium removal kinetics, provides a more biologically accurate depiction of calcium dynamics, crucial for modeling neuronal excitability and signaling. Overall, this code provides a foundational model of intracellular calcium dynamics, integrating both passive buffering and active transport processes to reflect the dynamic nature of calcium signaling in neurons.